To find the length of the entire perimeter of the region inside r = 7 sin Ф but outside r = 2, we first need to determine the boundaries of the region.
The equation r = 7 sin Ф represents a curve that forms a flower-like shape, while the equation r = 2 represents a circle with radius 2.
To find the region inside r = 7 sin Ф but outside r = 2, we need to find the points where these two curves intersect.
Setting the two equations equal to each other, we get:
7 sin Ф = 2
Solving for sin Ф, we get:
sin Ф = 2/7
Using a calculator, we can find the two values of Ф that satisfy this equation to be approximately 0.304 and 2.837 radians.
Thus, the region inside r = 7 sin Ф but outside r = 2 is bounded by the angles 0.304 and 2.837 radians.
To find the length of the entire perimeter of this region, we need to integrate the length element around this curve:
L = ∫(from 0.304 to 2.837) √[r² + (dr/dФ)²] dФ
Using the equation r = 7 sin Ф, we can substitute and simplify the expression under the square root:
L = ∫(from 0.304 to 2.837) √[49sin²(Ф) + 49cos²(Ф)] dФ
L = ∫(from 0.304 to 2.837) 7 dФ
L = 7(2.837 - 0.304)
L = 16.1
Therefore, the length of the entire perimeter of the region inside r = 7 sin Ф but outside r = 2 is approximately 16.1 units.
To find the length of the entire perimeter of the region inside r = 7 sin Ф but outside r = 2, we must first identify the points of intersection between the two curves.
1. Set the equations equal to each other:
7 sin Ф = 2
2. Solve for Ф:
sin Ф = 2/7
Ф = arcsin(2/7)
Now, we must determine the length of the perimeter of each curve in the region of interest:
3. Length of the perimeter of r = 7 sin Ф (half of the curve, since it's within the specified region):
For a polar curve r = f(Ф), the arc length L is calculated using the formula L = ∫√(r² + (dr/dФ)²) dФ.
In this case, f(Ф) = 7 sin Ф, so dr/dФ = 7 cos Ф. Integrating over the range [0, arcsin(2/7)], we can find the half-length of this curve.
4. Length of the perimeter of r = 2 (portion of the circle outside the region):
Since we know the points of intersection from step 2, we can find the central angle of the circular segment using Ф. The central angle is 2 * arcsin(2/7), and the circumference of the circle is 2π * 2. The portion of the perimeter is given by the ratio of the central angle to 2π, multiplied by the circumference.
Finally, add the lengths obtained in steps 3 and 4 to get the total length of the entire perimeter of the region.
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PLEASE HELP ME WITH THIS MATH PROBLEM!!! WILL GIVE BRAINLIEST!!! 20 POINTS!!!
The average price of milk in 2018 was $6.45 per gallon.
The average price of milk in 2021 was $189.15 per gallon.
How to calculate the priceWhen x = 0 (which represents the year 2018), the function becomes:
3.55 + 2.90(1 + 0)³
= 3.55 + 2.90(1)³
= 3.55 + 2.90
= 6.45
The average price of milk in 2018 was $6.45 per gallon.
When x = 3 (which represents the year 2021), the function becomes:
3.55 + 2.90(1 + 3)³
= 3.55 + 2.90(4)³
= 3.55 + 2.90(64)
= 3.55 + 185.6
= 189.15
The average price of milk in 2021 was $189.15 per gallon.
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Question 1 2 pts A researcher is interested in determining whether sugar consumption increases memory. She recruits 100 participants and randomly assigns them to one of two groups, sugar vs. No sugar. She then measures their word recall: Sugar group: M = 4. 5, SD = 1. 8, n = 55 • No sugar group: M = 2. 6, SD =. 68, n = 45 1. Is this an example of a quasi-experimental design? (yes or no) 2. What is the dependent variable? 3. What is the independent variable?
1. This is not an example of a quasi-experimental design because the researcher randomly assigned participants to the two groups. In a quasi-experimental design, the researcher does not have full control over the assignment of participants to groups.
2. The dependent variable in this study is the word recall. It is the variable that the researcher is interested in measuring and is expected to be affected by the independent variable.
3. The independent variable in this study is sugar consumption. It is the variable that the researcher manipulated by assigning participants to one of two groups, sugar vs. no sugar.
The purpose of manipulating the independent variable is to examine its effect on the dependent variable, word recall.
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A supermarket has three options for purchasing a brand of cereal:
Standard $2. 49 for 220g
Economy $5. 00 for 725g
Supersize $11. 50 for 2kg
Compare the cost of each for 100g, and order the brands from cheapest to most expensive
A comparison of the cost of each for 100 g indicates that the standard which costs about $1.13 per 100 grams is more expensive than the supersize which costs about $0.69 per 100 g and the supersize is more expensive than the economy which costs $0.575 per 100 g.
The cost per 100 g the standard is more than the cost per 100 g of the supersizeThe cost per 100 g of the supersize is more than the cost of the economy brand per 100 grams.The order of the cost of the brands from cheapest to most expensive can be presented as follows;
Supersize > Economy > StandardWhat is a cost per unit?The cost per unit is the cost of a number of items, divided by the number of units of the item.
The unit cost of the brands of cereal sold at the supermarket are therefore;
Unit cost per 100 gram for Standard = $2.49/220 g × 100 ≈ $1.13/g
Unit cost per gram for Economy = $5.00/725 g × 100 = $100/145/ g ≈ $0.69/g
Unit cost per gram for Supersize = $11.50/2kg × 100 = $1150/2,000 g ≈ $0.575/g
Based on the above unit cost, we get;
1.13 > 0.69 > 0.575
Therefore, the cheapest brand is the supersize with a cost per 100 gram of $0.575/g, followed by the economy, with a cost per 100 grams which is about $0.69/g then the most costly is the standard, with a cost per 100 gram of $1.13/g
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CAN SOMEONE SHOW ME STEP BY STEP ON HOW TO DO THIS SOMEONE GAVE ME THE WRONG STEPS
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
A polygon with a horizontal top side labeled 45 yards. The left vertical side is 20 yards. There is a dashed vertical line segment drawn from the right vertex of the top to the bottom right vertex. There is a dashed horizontal line from the bottom left vertex to the dashed vertical, leaving the length from that intersection to the bottom right vertex as 10 yards. There is another dashed horizontal line that comes from the vertex on the right that intersects the vertical dashed line, and it is labeled 12 yards.
What is the area of the playground?
900 square yards
855 square yards
1,710 square yards
1,305 square yards
Unlocked badge showing an astronaut’s boot touching down on the moon
The area of the playground include the following: 900 square yards.
How to calculate the area of a regular polygon?In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:
Area = (n × s × a)/2
Where:
n is the number of sides.s is the side length.a is the apothem.In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:
Area of a parallelogram, A = base area × height
Area of playground, A = 45 × 20
Area of a playground, A = 900 square yards.
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Students measured the length of several pencils and recorded their data in a table.
Pencil Lengths (Inches)
3
7
8
,
5
1
4
,
4
,
6
1
8
,
4
1
2
,
5
1
4
,
3
1
2
,
5
3
8
,
4
3
4
,
5
The students will make a line plot of the data. They will use only one fraction in their scale. They must be able to plot all of the data above a label. Which should this fraction be?
Step-by-step explanation:
To determine the appropriate fraction for the line plot, we need to find the greatest common factor (GCF) of all the pencil lengths, and then express each length as an equivalent fraction with the GCF as the denominator.
The GCF of the pencil lengths is 1. Therefore, we can simply express each pencil length as an equivalent fraction with 1 as the denominator:
3/1, 7/1, 8/1, 5/1, 1/1, 4/1, 6/1, 8/1, 4/1, 2/1, 5/1
Now, we can see that the smallest unit increment we can use on the line plot is 1/8. This is because 1/8 is the smallest fraction that can represent all of the pencil lengths above the label (5/8, which is equivalent to 10/16).
Therefore, the students should use 1/8 as the fraction for the line plot.
If Kawan paints the visible outside
surfaces of his shed, what is the
total surface area that he paints?
3 ft
5
8 ft
8ft
8ft
A. 256 ft²
B. 286 ft²
C. 360 ft²
D. 444 ft²
If kawan paints the visible outside faces of her shed, she paints two rectangle faces and two triangle faces then the total surface area that she paints is 88ft².
The area of a triangle of altitude h and base b is given by;
A = 0.5bh
Therefore the area of one triangle face ;
At = 0.5 × 8 × 5
At = 20ft²
Area of a rectangle of length l and breadth b is;
A = lb
Therefore the area of a rectangle face;
Ar = 8 × 3
Ar = 24ft²
We have 2 triangle faces and 2 rectangle face, therefore total surface area as;
A = 2At + 2Ar
A = 2×20 + 2×24
A = 40 + 48
A = 88ft²
Therefore the answer is; 88ft².
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Question Help
Kimo's Material Company hauls gravel to a construction site, using a small truck and a large truck. The
carrying capacity and operating cost per load are given in the accompanying table. Kimo must deliver a
minimum of 350 cubic yards per day to satisfy her
contract with the builder. The union contract with her drivers
requires that the total number of loads per day is a minimum of 9. How many loads should be made in each
truck per day to minimize the total cost?
Small Truck Large Truck
50
Capacity (yd)
70
Cost per Load
$87
$73
In order to minimize the total cost, the number of loads in a small truck that should be made is
number of loads in a large truck that should be made is
and the
Kimo should make 5 loads in the small truck and 4 loads in the large truck per day to minimize the total cost while meeting the delivery and union requirements.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
the total cost will be minimized when the loads are distributed in the following way:
5 loads in the small truck (total capacity of 5 * 50 = 250 cubic yards)
4 loads in the large truck (total capacity of 4 * 70 = 280 cubic yards)
This will result in a total of 9 loads and a total capacity of 530 cubic yards, which meets both the daily minimum delivery requirement of 350 cubic yards and the union contract requirement of 9 loads per day.
The total cost can be calculated as follows:
Cost of 5 loads in small truck = 5 * $87 = $435
Cost of 4 loads in large truck = 4 * $73 = $292
Total cost per day = $435 + $292 = $727
Therefore, Kimo should make 5 loads in the small truck and 4 loads in the large truck per day to minimize the total cost while meeting the delivery and union requirements.
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identify B on the following diagram: a: y-axis b origin c quadrant I d x-axis
Answer:
b
Step-by-step explanation:
point B has coordinates (0, 0 ) which is the origin
Regular quadrilateral prism has a height h = 11 cm and base edges b= 8cm. Find the sum of al edges
The sum of all edges of the regular quadrilateral prism is 108 cm.
To find the sum of all edges of a regular quadrilateral prism with height h = 11 cm and base edges b = 8 cm, follow these steps:
1. Determine the number of base edges: A quadrilateral has 4 edges, so there are 4 base edges for the top and 4 for the bottom, totaling 8 base edges.
2. Determine the number of height edges: There are 4 vertical edges connecting the top and bottom bases.
3. Add the number of base and height edges: 8 base edges + 4 height edges = 12 edges in total.
4. Calculate the sum of all edge lengths: (8 base edges (8 cm)) + (4 height edges (11 cm)) = 64 cm + 44 cm = 108 cm.
So, the sum of all edges of the regular quadrilateral prism is 108 cm.
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Let f(x) =x^2 + x + 9 and g(x)x = -4x - 3.
Find (fg) (x) and (f/g) (x)
Answer: First, we need to find the composite function (fg)(x):
(fg)(x) = f(g(x))
= f(-4x-3)
= (-4x-3)^2 + (-4x-3) + 9 (substituting g(x) into f(x))
= 16x^2 + 24x + 18
Therefore, (fg)(x) = 16x^2 + 24x + 18.
Next, we need to find the quotient function (f/g)(x):
(f/g)(x) = f(x) / g(x)
= (x^2 + x + 9) / (-4x - 3) (substituting f(x) and g(x))
To simplify this expression, we can use polynomial long division or synthetic division. Using synthetic division, we get:
-4 | 1 1 9
|_____-4__ 12
| 1 -3 21
Therefore, (f/g)(x) = -4x + 3 - 21 / (-4x - 3)
Simplifying further, we get:
(f/g)(x) = -4x + 3 + (21/4)(1/(x + 3/4))
Therefore, (f/g)(x) = -4x + 3 + (21/4)(1/(x + 3/4)).
Step-by-step explanation:
It is typical for the person who is most difficult to convince in an argument to say that everyone else is stubborn. group of answer choices displacement sublimation projection rationalization regression
"It is typical for the person who is most difficult to convince in an argument to say that everyone else is stubborn." refers projection (option c).
To understand projection in mathematical terms, we can think of it as a function f(x), where x represents the individual's own thoughts or emotions. The output of the function, f(x), represents the projection of these thoughts or emotions onto someone else.
In the case of arguments, the person who is most difficult to convince may have a high value of x, indicating that they are feeling stubborn. However, instead of accepting this feeling, they project it onto others, resulting in a high value of f(x) for those around them.
Projection is just one example of the many defense mechanisms that humans use to protect themselves from unpleasant thoughts or emotions. Understanding these mechanisms can help us to better navigate difficult situations, including arguments, and improve our communication skills.
Hence the correct option is (c).
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Qn in attachment . ..
The variance of first n even natural numbers is n²-1/12. So, the correct option is (a) .
The first n even natural numbers can be represented as 2, 4, 6, ..., 2n. The mean or expected value of this sequence is given by:
mean = (2 + 4 + 6 + ... + 2n) / n
= 2(1 + 2 + 3 + ... + n) / n
= 2n(n+1)/2n
= n+1
The variance of a sequence is the average of the squared differences from the mean, so we need to calculate:
Var = [(2- (n+1))² + (4- (n+1))² + (6- (n+1))² + ... + (2n- (n+1))²] / n
Simplifying the expression inside the brackets and using the formula for the sum of the first n integers, we get:
Var = [4(1² + 2² + 3² + ... + n²) - 4(n+1)(1 + 2 + 3 + ... + n) + n(n+1)²] / n
Substituting the formula for the sum of the first n squares and the sum of the first n integers, we get:
Var = [4n(n+1)(2n+1)/6 - 4(n+1)n(n+1)/2 + n(n+1)²] / n
Simplifying and factoring out (n+1), we get:
Var = (n+1)(n² - 1) / 3
Thus, the correct option is (a) n²-1/12.
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A bookmark has an area of 150 square centimeters and a perimeter of 62 centimeters. what are the dimensions of the bookmark
The dimensions of the bookmark are length = 15 centimeters and width = 10 centimeters.
Let's denote the length of the bookmark as L and the width as W.
The area of a rectangle is given by the formula A = L * W, and the perimeter is given by P = 2L + 2W.
From the given information, we have two equations:
Equation 1: A = 150 square centimeters
Equation 2: P = 62 centimeters
Substituting the formulas for area and perimeter, we get:
Equation 1: L * W = 150
Equation 2: 2L + 2W = 62
To solve these equations, we can use substitution or elimination. Let's solve by substitution:
From Equation 1, we can express one variable in terms of the other:
L = 150 / W
Substituting this into Equation 2:
2(150 / W) + 2W = 62
300 / W + 2W = 62
300 + 2W^2 = 62W
2W^2 - 62W + 300 = 0
Now we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:
[tex]2W^2 - 62W + 300 = 0[/tex]
(W - 10)(2W - 30) = 0
This gives us two possible solutions:
W - 10 = 0 -> W = 10
2W - 30 = 0 -> W = 15
Since the width cannot be longer than the length, we discard the solution W = 15.
So, the width of the bookmark is W = 10 centimeters.
Now, we can substitute this value into Equation 1 to find the length:
L * 10 = 150
L = 150 / 10
L = 15
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14
Find the limit of the rational function a. as x and b. as X-→ - 00 X + 6 f(x) = +3 + 20 X+6 a. lim x x² + 20 (Simplify your answer.) X + 6 b. lim x--00x2 + 20 = (Simplify your answer.) (
Both the limits are equal to 0: a. lim (x→∞) f(x) = 0 b. lim (x→-∞) f(x) = 0
Know more about rational function,
First, let's rewrite the rational function f(x) more clearly and identify the two limits we need to find: f(x) =[tex](x + 6) / (x^2 + 20)[/tex]
a. lim (x→∞) f(x) b. lim (x→-∞) f(x)
To find these limits, we can use the following steps:
Step 1: Divide both the numerator and the denominator by the highest power of x in the denominator.
In this case, it is x^2. f(x) = [tex][(x + 6) / x^2] / [(x^2 + 20) / x^2][/tex]
Step 2: Simplify the function. f(x) =[tex][(1/x) + (6/x^2)] / [1 + (20/x^2)][/tex]
Step 3: Evaluate the limits.
a. lim (x→∞) f(x)
= [(0) + (0)] / [1 + (0)]
= 0 / 1 = 0
b. lim (x→-∞) f(x)
= [(0) + (0)] / [1 + (0)]
= 0 / 1 = 0
So, both the limits are equal to 0: a. lim (x→∞) f(x) = 0 b. lim (x→-∞) f(x) = 0
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√4x^2 BRAINLIEST IF CORRECT!!!!!!!!!
Answer:
Step-by-step explanation:
√4x^2=2x
Im actually going to explode I hate geometry with a passion
Answer: B 28√15
Step-by-step explanation:
They want you to find the Area of the quadrilateral. But if you can find the area of 1 trangle then you can double it because the 2 triangles are congruent.
We know the 2 triangles are congruent from the theorem (see diagram
We also know that QR=TR=SR They are all radius
Let's solve for triangle PRS
PR = hypotenuse = 10+7 =17
SR=7 radius
Use pythagorean to find PS
c²=a²+b²
17²=7²+b²
289 = 49 + b²
b²=289 -49
b² = 240
b=√240
b=[tex]\sqrt{16*15}[/tex]
b= 4√15 This is PS
Area of triangle = 1/2 bh b=PS h=7
Area of triangle = 1/2 (4√15)(7)
Area of triangle = (2√15)(7)
Area of triangle = 14√15
Area of quadrilateral = 2 (14√15) > 2 triangles make the quadrilateral
Area of quadrilateral = 28√15
Please help I need it ASAP, also needs to be rounded to the nearest 10th
Answer: AB = 16.4
Step-by-step explanation:
You can use tan x = opposite/adjacent
tan 38 = AB/21
21 tan 38 = AB
AB = 16.4
A store sells packages of comic books with a poster. A poster and 2 comics cost $7.50. A poster and 11 comics cost $16.50. Write a linear function rule that models the cost y of a package containing any number x of comic books.
Suppose another store sells a similar package, modeled by a linear function rule with initial value $5.75. Use pencil and paper. Explain which store has the better deal.
The linear function rule is y =
The linear function rule that models the cost y of a package containing any number x of comic books is y = $6.50 + $1.00x and for 10 comic books, the second store has the better deal.
What do you mean by Linear function ?A linear function is a mathematical function where the graph of the function is a straight line. It can be written in the form y = mx + b, where x and y are the variables, m is the slope of the line, and b is the y-intercept (the point where the line intersects the y-axis). The slope represents the rate of change of the function, while the y-intercept is the value of the function when x is equal to zero.
To write a linear function rule that models the cost y of a package containing any number x of comic books, we can use the given information to set up a system of equations:
Poster + 2 Comics = $7.50
Poster + 11 Comics = $16.50
We can solve for the cost of the poster and the cost of one comic book by subtracting the first equation from the second:
9 Comics = $9.00
1 Comic = $1.00
Then, we can use the cost of one comic to set up a linear function rule:
y = cost of poster + cost of x comics
y = $6.50 + $1.00x
Therefore, the linear function rule that models the cost y of a package containing any number x of comic books is y = $6.50 + $1.00x.
For the second store, the linear function rule is given as y = $5.75 + $1.00x.
To determine which store has the better deal, we can compare the cost of each package for a specific number of comic books. For example, if we want to buy 10 comic books, the cost at the first store would be:
y = $6.50 + $1.00(10) = $16.50
The cost at the second store would be:
y = $5.75 + $1.00(10) = $15.75
Therefore, for 10 comic books, the second store has the better deal. However, for a different number of comic books, the better deal may be at a different store. We can use the linear function rules to compare the costs for any number of comic books
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Emma has a wooden sculpture in the shape of a cuboid.
The sculpture is 2. 2 m high, 1. 1 m wide and 0. 55 m thick.
Emma plans to paint all the faces of the sculpture with
three coats of wood varnish.
a How many tins of wood varnish does Emma
need to buy?
b What is the total cost of the wood varnish?
varnish
$ 3. 99
(Size of tin: 100 ml)
20 m2 per litre
a) To find the total surface area of the cuboid, we need to find the area of each face and then add them up.
Area of one face = length x width
Area of top and bottom faces = 1.1 m x 0.55 m = 0.605 m² (2 faces)
Area of front and back faces = 2.2 m x 0.55 m = 1.21 m² (2 faces)
Area of side faces = 2.2 m x 1.1 m = 2.42 m² (2 faces)
Total surface area = (2 x 0.605) + (2 x 1.21) + (2 x 2.42) = 7.7 m²
Each tin of varnish covers 20 m², so Emma needs:
Number of tins = (total surface area x number of coats) / coverage per tin
Number of tins = (7.7 x 3) / 0.02 = 1155
Emma needs to buy 1155 tins of wood varnish.
b) The cost of each tin of varnish is $3.99 for 100 ml. To find the cost of 1155 tins, we first need to convert the volume of varnish needed into liters.
Volume of varnish needed = (total surface area x number of coats) / coverage per litre
Volume of varnish needed = (7.7 x 3) / 20 = 1.155 liters
The number of tins required to make up 1.155 liters of varnish is:
Number of tins = (1.155 / 0.1) = 11.55
So Emma needs to buy 12 tins of varnish. The total cost is:
Total cost = cost per tin x number of tins
Total cost = $3.99 x 12 = $47.88
The total cost of the wood varnish is $47.88.
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Estimate the area under the curve f(x)=1/x on [1,2] by using 4 approximating rectangles with a) left endpoints, b) right endpoints, then c) take the average.
our final estimate for the area under the curve f(x)=1/x on [1,2] using 4 approximating rectangles and taking the average of the left and right endpoints is 0.76.
To estimate the area under the curve f(x)=1/x on [1,2], we can use 4 approximating rectangles.
a) Using left endpoints, the width of each rectangle is (2-1)/4 = 0.25. The left endpoints of the rectangles are 1, 1.25, 1.5, and 1.75. The height of each rectangle is f(x) evaluated at the left endpoint.
So, the heights are f(1) = 1/1 = 1, f(1.25) = 1/1.25 = 0.8,
f(1.5)=1/1.5 = 0.67, and f(1.75) = 1/1.75 = 0.57.
The area of each rectangle is width times height, so the areas are
0.25*1 = 0.25, 0.25*0.8 = 0.2, 0.25*0.67 = 0.1675, and 0.25*0.57 = 0.1425.
Adding these areas together, we get an estimate of the total area under the curve as
0.25 + 0.2 + 0.1675 + 0.1425 = 0.76.
b) Using right endpoints, the width of each rectangle is the same as before. The right endpoints of the rectangles are
1.25, 1.5, 1.75, and 2.
The heights are f(x) evaluated at the right endpoint. So, the heights are
f(1.25) = 0.8, f(1.5) = 0.67, f(1.75) = 0.57, and f(2) = 0.5.
The areas of the rectangles are the same as before, so adding them up, we get an estimate of the total area as
0.2 + 0.1675 + 0.1425 + 0.25 = 0.76,
which is the same as before.
c) To get the average of the two estimates, we add them together and divide by 2:
(0.76+0.76) / 2 = 0.76.
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Casey recently purchased a sedan and a pickup truck at about the same time for a new business. The value of the sedan S, in dollars, as a function of the number of years t after the purchase can be represented by the equation S(t)=24,400(0. 82)^t. The equation P(t)=35,900(0. 71)^t/2 represents the value of the pickup truck P, in dollars, t years after the purchase. Analyze the functions S(t) and P(t) to interpret the parameters of each function, including the coefficient and the base. Then use the interpretations to make a comparison on how the value of the sedan and the value of the pickup truck change over time
Based on the given situation we can conclude that the sedan retains its value better than the pickup truck over time.The functions S(t) and P(t) represent the values of the sedan and pickup truck, respectively, as a function of the number of years t after their purchase.
The coefficient 24,400 in the function S(t) represents the initial value of the sedan, which is the value of the car at t=0. The base 0.82 represents the decay rate or the percentage decrease in the value of the sedan each year. Similarly, in the function P(t), the coefficient 35,900 represents the initial value of the pickup truck and the base 0.71 represents the decay rate of the value of the pickup truck.
Since the base of the sedan's value decay is 0.82, it indicates that the value of the sedan decreases by 18% each year. Whereas the base of the pickup truck's value decay is 0.71, indicating that the value of the pickup truck decreases by 29% each year. Therefore, we can observe that the value of the pickup truck depreciates faster than the sedan. After two years, the value of the sedan would be approximately $16,650, and the value of the pickup truck would be approximately $14,161. After five years, the value of the sedan would be approximately $9,237, and the value of the pickup truck would be approximately $6,155.
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Nick is building a kaleidoscope by making a cylinder case with height of 11 inches and a diameter of 2 3/4 inches. What is the volume of the cylinder in cubic inches? Round to the nearest tenth. ( Use 3. 14 for pi ) Right Awnser will be marked brainliest!!
The volume 33.5 cubic inches
To calculate the volume of the cylinder, we need to use the formula:
V = π[tex]r^2[/tex]h
where V is the volume, π is the constant pi, r is the radius of the base (which is half the diameter), and h is the height.
First, we need to convert the diameter of the cylinder to inches:
2 3/4 inches = (2*4 + 3)/4 inches = 11/4 inches
The radius of the cylinder is half the diameter, so:
r = (11/4)/2 = 11/8 inches
Now we can plug in the values into the formula:
V = π[tex](11/8)^2[/tex](11) cubic inches
V ≈ 33.5 cubic inches (rounded to the nearest tenth)
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can someone help with this please
Answer:
shape a is 20 cm squared
Step-by-step explanation:
shape a is a parallogram, A =b×h. 5x4=20
shape b is a trapezoid. The picture is cut off but here are the steps for you to solve. A=0.5h(base1+base2) count the number of squares on the top and bottom of the shape. I can see the top is 2, you will need to tfind the length of the bottom base.then count the height, how far to get from the bottom to top, here it is 4.
area=0.5*4(2+bottom base) simply and that's your answer! Don't forget your units
Consider the following. g(x) = 8e⁶·⁵x; h(x) = 8(6.5ˣ) (a) Write the product function. = f(x) = (b) Write the rate-of-change function. f'(x) = Consider the following. g(x) = 9e- ˣ + In(x); h(x) = 4x²·⁷(a) Write the product function. f(x) = (b) Write the rate-of-change function. f'(x) =
For the Following the product function is f(x) = g(x) * h(x) = (9e^{-x} + ln(x)) * 4x^{2.7} and rate of change of function is f'(x) = 43.2x^{1.7}e^{-x} + 10.8x^{1.7}ln(x) - 36e^{-x}
For g(x) = 9e^{-x} + ln(x) and h(x) = 4x^{2.7}, we have:
(a) The product function is: f(x) = g(x) * h(x) = (9e^{-x} + ln(x)) * 4x^{2.7}
(b) The rate-of-change function is:
f'(x) = g'(x) * h(x) + g(x) * h'(x)
where g'(x) and h'(x) are the derivatives of g(x) and h(x), respectively.
Taking derivatives, we have:
g'(x) = -9e^{-x} + 1/x
h'(x) = 10.8x^{1.7}
Substituting into the formula for f'(x), we get:
f'(x) = (-9e^{-x} + 1/x) * 4x^2.7 + (9e^{-x} + ln(x)) * 10.8x^{1.7}
Simplifying, we get:
f'(x) = 43.2x^{1.7}e^{-x} + 10.8x^{1.7}ln(x) - 36e^{-x}
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please help with the question in the image !!
Answer:
image dosent load
Step-by-step explanation:
Answer:
a = 80°, b = 100°, c = 80°, d = 100°
Step-by-step explanation:
You know a + b + c + d = 360°.
Plugging b + c + d = 280° into the formula above:
a + 280° = 360°.
a = 80°.
You know a + d = 180° because of angles on a straight line. Solve for d:
80° + d = 180°.
d = 100°.
For the same reason, you know a + b = 180°. b must be equal to d, which is 100°.
Lastly, c + d = 180° because they make up the second line. Solve for c:
c + 100° = 180°.
c = 80°.
a = 80°, b = 100°, c = 80°, d = 100°.
Please hurry I need it ASAP
Answer:
x = 18
Step-by-step explanation:
We Know
(10x - 4) + (x - 14) must equal 180°
Find the value of x.
Let's solve
10x - 4 + x - 14 = 180
11x - 18 = 180
11x = 198
x = 18
So, x = 18 is the answer.
Choose the function that the graph represents.
Click on the correct answer.
y = f(x) = log7x
y = f(x)=x7
y = f(x) = 7x
Answer:
y=f(x) = log7x
Just trust me
The graph best represents the function y = f(x) = 7x, an exponential function.
The graph represents the function y = 7x, which is an exponential function. In an exponential function, the variable x is the base, and the exponent is a constant, which in this case is 7. This means that the function grows rapidly as x increases, creating a steep curve on the graph.
The other two options, y = f(x) = log7x and y = f(x) = x7, are not represented by the given graph.
The function y = f(x) = log7x is a logarithmic function, which has a different shape on the graph, with a horizontal asymptote and the x-axis acting as its asymptote.
The function y = f(x) = x7 is a polynomial function, where x is raised to the power of 7, and it would have a different pattern on the graph compared to the exponential function shown.
Thus, the graph best represents the function y = f(x) = 7x, an exponential function.
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Clarissa is cutting construction paper into rectangles for a project. She needs to cut one rectangle that is 10 inches × 14 1/2
inches. She needs to cut another rectangle that is 10 1/4
inches by 10 1/2 inches. How many total square inches of construction paper does Clarissa need for her project?
Clarissa needs a total of 251.25 square inches of construction paper for her project.
To find the total area of construction paper needed, we need to find the area of each rectangle and add them together.
The first rectangle has an area of 10 inches × 14.5 inches = 145 square inches.
The second rectangle has an area of 10.25 inches × 10.5 inches = 107.625 square inches.
Adding these two areas together, we get a total of 145 + 107.625 = 252.625 square inches.
Therefore, Clarissa needs a total of 251.25 square inches (rounded to two decimal places) of construction paper for her project.
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A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 600 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.04 cents per square centimeter. The top will be made of glued paper, costing 0.05 cents per square centimeter. Find the dimensions for the package that will minimize production cost.
The dimensions of the cylinder that minimize the production cost are:
radius = approximately 2.78 cm
height = 600 / (πr^2) ≈ 7.14 cm
paper top radius = 2.5 cm
Let's start by finding the formula for the cost of the container in terms of its dimensions.
The volume of the cylinder is given as 600 cubic centimeters, so we have:
πr^2h = 600
where r is the radius of the cylinder and h is its height. Solving for h, we get:
h = 600 / (πr^2)
The surface area of the cylinder is given by:
A = 2πrh + 2πr^2
Substituting h in terms of r, we get:
A = 2πr(600/(πr^2)) + 2πr^2
= 1200/r + 2πr^2
The cost of the container is the sum of the cost of the styrofoam sides and bottom and the cost of the paper top. Let's call the radius of the paper top R, and assume that the height of the cylinder is greater than or equal to the radius of the paper top, so that the top can be completely covered with paper. Then the cost of the container is:
C = 0.04(2πrh + πr^2) + 0.05(πR^2)
Substituting h in terms of r, we get:
C = 0.08πr(600/(πr^2)) + 0.04πr^2 + 0.05πR^2
= 4.8/r + 0.04πr^2 + 0.05πR^2
To minimize the cost, we need to find the values of r and R that minimize the cost function C. To do this, we take the partial derivatives of C with respect to r and R, and set them equal to zero:
dC/dr = -4.8/r^2 + 0.08πr = 0
dC/dR = 0.1πR = 0
Solving for r and R, we get:
r = ∛(60/π) ≈ 2.78 cm
R = 2.5 cm
We can check that these values give us a minimum by checking the second derivatives:
d^2C/dr^2 = 9.6/r^3 + 0.08π > 0 (minimum)
d^2C/dR^2 = 0.1π > 0 (minimum)
Therefore, the dimensions of the cylinder that minimize the production cost are:
radius = approximately 2.78 cm
height = 600 / (πr^2) ≈ 7.14 cm
paper top radius = 2.5 cm
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The volume of the cylinder displayed is approximately 9. 4 cubic feet. What is the approximate volume for a cone with the same height and radius? Whats the answer
The volume of the cone is approximately one-third the volume of the
cylinder
:V(cone) ≈ 1/3 V(cylinder) = 1/3 (9.4) ≈ 3.1 cubic feet.
The volume of a cone with the same height and radius as the given
cylinder, we can use the formula:
[tex]V = 1/3 πr²h[/tex]
where V is the volume, r is the radius, and h is the height.
Since the cylinder has a volume of approximately 9.4 cubic feet, we can
use the formula for the volume of a cylinder
:V = πr²hand solve for the radius:
[tex]r = √(V/πh) = √(9.4/πh)[/tex]
Now we can substitute this expression for the radius into the formula for
the volume of a cone:
[tex]V = 1/3 π(√(V/πh))²h[/tex]
Simplifying this expression gives:
[tex]V = 1/3 π(V/πh)hV = 1/3 V[/tex]
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