Answers
a) the critical number x= N/A ,b) the absolute maximum is -16 at x= 5
c) the absolute maximum is -4 at x= 0.25
what is critical number?
The term "critical number" can have different meanings depending on the context in which it is used. Here are a few possible definitions:
In the given question,
To find the critical numbers of the function, we need to find where the derivative is either zero or undefined. Let's find the derivative of y with respect to x:
y' = 4/x²
The derivative is undefined at x = 0, but this point is not in the given interval, so we don't have to consider it. The derivative is zero when:
4/x² = 0
This equation has no real solutions, so there are no critical numbers in the interval (0.25, 5).
Since the function y = -4/x is decreasing on the interval (0.25, 5), the absolute maximum will occur at the left endpoint x = 0.25, and the absolute minimum will occur at the right endpoint x = 5. Therefore:
a) the critical number x= N/A
b) the absolute maximum is -16 at x= 5
c) the absolute maximum is -4 at x= 0.25
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Related Questions
What is the slope of the line containing (–2, 5) and (4, –4)? A. -2 B. 1 C. 1/2 D. -1/2
Answers
The slope of the line on this graph with points (2, 5) and (4, 4) is equal to: D. =1/2.
How to calculate the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, we have the following;
Slope (m) = (5 - 4)/(2 - 4)
Slope (m) = -1/2
In this context, we can reasonably infer and logically deduce that the slope of the line on this graph is equal to -0.5 or -1/2.
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In a large population of nurses, suppose 20% of the nurses would prefer the night shift. If a random sample of 10 nurses is taken, what is the probability less than 3 are nurses that prefer the night shift?
Answers
We can use the binomial probability formula:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
where X is the number of nurses in the sample who prefer the night shift.
Using the binomial probability formula, we can calculate:
P(X = 0) = (10 choose 0) * 0.2^0 * 0.8^10 = 0.1074
P(X = 1) = (10 choose 1) * 0.2^1 * 0.8^9 = 0.2684
P(X = 2) = (10 choose 2) * 0.2^2 * 0.8^8 = 0.3019
Therefore,
P(X < 3) = 0.1074 + 0.2684 + 0.3019 = 0.6777
The probability that less than 3 nurses in the sample prefer the night shift is approximately 0.6777 or 67.77%.
Please help with this
Answers
3. Create a graph that shows three linear relationships with different y-intercepts using
the following slopes, and write an equation for each line.
Slopes:
●
5/5 5/5 115
3
y
Answers
Setting x = 0, we get the y-intercept: y = 31/5. So, the equation of the line is y = 6/5x + 31/5.
What does line intersect?In geometry, a line intersect is a point where two or more lines cross or meet. When two lines intersect, they share a single point in common, which is called the point of intersection. This point of intersection is the solution to the system of equations formed by the two lines.
by the question.
To find different y-intercepts using the given slopes, we need to use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. To find the y-intercept, we can set x = 0 and solve for y.
For slope 1/5, let's choose the point (2, 3) on the line. Using the point-slope form, we get:
y - 3 = 1/5(x - 2)
y - 3 = 1/5x - 2/5
y = 1/5x + 13/5
Setting x = 0, we get the y-intercept: y = 13/5. So, the equation of the line is y = 1/5x + 13/5.
For slope 3/5, let's choose the point (4, 2) on the line. Using the point-slope form, we get:
y - 2 = 3/5(x - 4)
y - 2 = 3/5x - 12/5
y = 3/5x + 8/5
Setting x = 0, we get the y-intercept: y = 8/5. So, the equation of the line is y = 3/5x + 8/5.
For slope 6/5, let's choose the point (-1, 5) on the line. Using the point-slope form, we get:
y - 5 = 6/5(x + 1)
y - 5 = 6/5x + 6/5
y = 6/5x + 31/5
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the area of a table top is a whole number of square feet. Could the length and width be decimal numbers each one with decimal place?
Answers
Yes, the length and width can be decimal numbers each one with decimal place, but not in every case.
Define areaThe size of a two-dimensional surface or region is expressed in terms of area. Square units like square inches, square feet, or square metres are frequently used to measure it. The area of a shape or region is determined by counting the number of unit squares that can fit inside it without overlap.
for example, lets take length =2.5 feet
and width=3.2 feet
area of table top=8 feet²
Taking another case:
length =1.2 feet
and width=3.5 feet
area of table top=4.2 feet²
if the length and width are decimal numbers, then the area would also be a decimal number or whole number, But, this is not possible in every cases.
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The complete question is:
The area of Kamar’s tabletop is a whole number of square feet. Could the length and width be decimal numbers each with one decimal place? Explain your answer.
Please Hurry!!
Which polar coordinates represent the point plotted on the graph? Select all that apply and explain your answer.
Answers
Answer:
D
[tex]3. \frac{11\pi}{6} [/tex]
Step-by-step explanation:
When we determine the point's coordinates, first we have to write the polar ones (they are on the horizontal line) and then the south ones (they are around the circle)
I think this is the right answer
please help me on this question
Answers
Answer:To calculate how much money Evie will owe after 12 years, we need to use the formula:A = P(1 + r)^nWhere:
A = the amount owed after n years
P = the initial amount borrowed
r = the annual interest rate as a decimal
n = the number of yearsIn this case, P = £600, r = 24% = 0.24, and n = 12. Plugging these values into the formula, we get:A = 600(1 + 0.24)^12
A = 600(1.24)^12
A = 600(7.8905)
A = £4,734.30 (rounded to the nearest penny)Therefore, after 12 years, Evie will owe approximately £4,734.30
Step-by-step explanation: I Helped you Can You help me
(+2).(-4).(-1).(+7)=
(-5).(-6).(+3)=
Answers
Answer:
4 and the second one -8
Step-by-step explanation:
in the first one you have to 2 and take away 4 so you get a negative number and the you take one more number and then add 7
in the second one you have -5 and then take away 6 and then add 3
(1000y) -1/2 * (3/x+1) when x = 1/3 and y = 1/10
Answers
The value of simplification is 95.
What is simplification?
Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easily with calculations and solving.
Here, we have
Given: (1000y) -1/2 * (3/x+1) when x = 1/3 and y = 1/10
we have to simplify the given expression.
= (1000y) -1/2 * (3/x+1)
When x = 1/3 and y = 1/10
Now we put the value of x and y in the given equation and we get
= (1000/10) -1/2 × (3×3+1)
= 100 - 10/2
= 100 - 5
= 95
Hence, the value of simplification is 95.
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Find the interest rate for the given deposit and compound amount.
$4000 accumulating to $5994.75, compounded monthly for 7 years.
Answers
Answer:
The interest rate is 5.79% (to the nearest hundredth).
Step-by-step explanation:
To find the interest rate for the given deposit of $4000 accumulating to $5994.75, compounded monthly for 7 years, use the compound interest formula.
Compound Interest Formula[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = Final amount.P = Principal amount.r = Interest rate (in decimal form).n = Number of times interest is applied per year.t = Time (in years).Given values:
P = $4,000A = $5,994.75n = 12 (monthly)t = 7 yearsSubstitute the given values into the formula and solve for r.
[tex]\implies \sf 5994.75=4000\left(1+\dfrac{r}{12}\right)^{12 \times 7}[/tex]
[tex]\implies \sf 5994.75=4000\left(1+\dfrac{r}{12}\right)^{84}[/tex]
[tex]\implies \sf \dfrac{5994.75}{4000}=\left(1+\dfrac{r}{12}\right)^{84}[/tex]
[tex]\implies \sf \sqrt[\sf 84]{\sf \dfrac{5994.75}{4000}}=1+\dfrac{r}{12}[/tex]
[tex]\implies \sf \sqrt[\sf 84]{\sf \dfrac{5994.75}{4000}}-1=\dfrac{r}{12}[/tex]
[tex]\implies \sf r=12\left(\sqrt[\sf 84]{\sf \dfrac{5994.75}{4000}}-1\right)[/tex]
[tex]\implies \sf r=0.057937950...[/tex]
[tex]\implies \sf r=5.7937950...\%[/tex]
Therefore, the interest rate is 5.79% (to the nearest hundredth).
The following equation involves multiple angles. Solve the equation on the interval [0, 2π). cos 4x= 1/2
Answers
[tex]\cos(4x)=\cfrac{1}{2}\implies 4x=\cos^{-1}\left( \cfrac{1}{2} \right)\implies 4x= \begin{cases} \frac{\pi }{3}\\\\ \frac{5\pi }{3} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 4x=\cfrac{\pi }{3}\implies \boxed{x=\cfrac{\pi }{12}}~\hfill 4x=\cfrac{5\pi }{3}\implies \boxed{x=\cfrac{5\pi }{12}}[/tex]
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTSp
Answers
Answer:
f(x) = 3x-5
Step-by-step explanation:
Plug in the domain 0, in the other answer options
f(x) = -3x + 4 turns into f(x) = -3(0) + 4 and thats equal to 4, there is no value set to 4 in the range so that option is cancelled out
f(x) = x+2 turns into f(x) = 0+2 =2, there is no value set to 2 in the range so that option is cancelled out
f(x) = -5x + 3 turns into f(x) = -5(0) + 3, and thats equal to 3, there is no value set to 3 in the range so that option is cancelled out
f(x) = 3x-5 turns into f(x) = 3(0) - 5, and thats equal to -5, there is a value in the range that equals -5, you could also try any domain value into this equation and it would result into either -11, -5, 1, 7, or 13.
keep in mind f(x) is the range
Find the interest on deposit of 3650 from 3 January 2016 at the rate of 10% p.a up to 17 March 2016
Answers
The simple interest on a deposit of 3650 from 3 January 2016 at the rate of 10% p.a up to 17 March 2016 is given as follows:
$7.4.
How to obtain the balance using simple interest?The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are listed and explained as follows:
A(t) is the final balance.P is the value of the initial deposit.r is the interest rate, as a decimal.t is the time in years.The interest accrued is modeled as follows:
I(t) = Prt.
The parameter values for this problem are given as follows:
P = 3650.r = 0.1.t = 74/365 -> there are 74 days from Jan 3 2016 to March 17 2016.Then the interest accrued is given as follows:
I = 365 x 0.1 x 74/365
I = $7.4.
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Kayne runs a specialty running store. Last year, he earned $50,000 in revenue and had explicit costs of $20,000. Kayne could have made $42,000 selling video games on the Internet and received an additional $5,000 if he rented out the store and equipment. Calculate Kayne’s implicit costs.
Answers
economic profit = total revenue - explicit costs - implicit costs
We are given that Kayne earned $50,000 in revenue and had explicit costs of $20,000. We also know that if he had sold video games on the Internet, he could have made $42,000, and if he had rented out the store and equipment, he could have received an additional $5,000. These represent the opportunity costs of running his specialty running store.
So, we can calculate Kayne's implicit costs as follows:
implicit costs = opportunity cost of selling video games + opportunity cost of renting out the store and equipment
implicit costs = $42,000 + $5,000
implicit costs = $47,000
Now, we can substitute this value into the economic profit formula:
economic profit = $50,000 - $20,000 - $47,000
economic profit = -$17,000
The negative value indicates that Kayne did not earn a positive economic profit, meaning that his explicit and implicit costs were greater than his revenue.
PLEASE ANSWER THIS ASAP What is the exact surface area of a cylindrical propane tank with a radius of 1 m and a height of 10 m?
2π m²
20π m²
22π m²
24π m²
Answers
22π m² is the exact surface area of a cylindrical propane tank.
What are volume and surface area?
The entire area of all the faces makes up the surface area of a three-dimensional form. We measure the areas of each face and put them together to determine the surface area of a shape.
The surface-area-to-volume ratio, also known as the surface-to-volume ratio or abbreviated as SA:V, refers to how much surface area there is in each unit volume of an object or collection of objects.
A=2πrh+2πr²
=2π * 1* 10 +2π* 1²
= 2π( 10 + 1)
= 2π * 11
= 22π m²
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The cost of renting a chain saw is $3.90 per hour plus $6.50 for a can of gas. Find the cost of using the chain saw for 7.5 hours.
Equation and Answer
Answers
Answer:
$35.75----------------------------
The total cost is the cost for a can of gas plus rental cost per number of hours.
So the total cost is:
6.50 + 7.5*3.90 = 6.50 + 29.25 = 35.75Which statement is true?
Answers
The correct statement about diagram is m∠1 > m∠4. So correct option is D.
Describe Angles?In mathematics, an angle is a measure of the amount of rotation between two rays or line segments that share a common endpoint, known as the vertex. The rays or line segments are typically referred to as the sides of the angle.
Angles are usually measured in degrees or radians, with a full rotation or circle being 360 degrees or 2π radians. Angles can be classified into different types based on their degree of rotation, such as acute angles, which are less than 90 degrees, right angles, which are exactly 90 degrees, obtuse angles, which are greater than 90 degrees but less than 180 degrees, and straight angles, which are exactly 180 degrees.
Angles can be added, subtracted, multiplied, and divided, and they can be used to solve a wide range of problems in geometry and trigonometry. For example, angles are used to calculate the measurements of geometric shapes, such as triangles, circles, and polygons, and they are also used to calculate distances and heights using trigonometric functions such as sine, cosine, and tangent.
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100 points!!
f (x) = −√x + 2 + 3
Fully explain the three transformations required to produce this function from the
parent function.
Answers
Answer: the first thing is your answer :)
thx for the points
Step-by-step explanation:
g
(
x
)
=
x
2
−
3
The parent function is the simplest form of the type of function given.
f
(
x
)
=
x
2
The transformation being described is from
f
(
x
)
=
x
2
to
g
(
x
)
=
x
2
−
3
.
f
(
x
)
=
x
2
→
g
(
x
)
=
x
2
−
3
The horizontal shift depends on the value of
h
. The horizontal shift is described as:
g
(
x
)
=
f
(
x
+
h
)
- The graph is shifted to the left
h
units.
g
(
x
)
=
f
(
x
−
h
)
- The graph is shifted to the right
h
units.
In this case,
h
=
0
which means that the graph is not shifted to the left or right.
Horizontal Shift: None
The vertical shift depends on the value of
k
. The vertical shift is described as:
g
(
x
)
=
f
(
x
)
+
k
- The graph is shifted up
k
units.
g
(
x
)
=
f
(
x
)
−
k
- The graph is shifted down
k
units.
Vertical Shift: Down
3
Units
The graph is reflected about the x-axis when
g
(
x
)
=
−
f
(
x
)
.
Reflection about the x-axis: None
The graph is reflected about the y-axis when
g
(
x
)
=
f
(
−
x
)
.
Reflection about the y-axis: None
Compressing and stretching depends on the value of
a
.
When
a
is greater than
1
: Vertically stretched
When
a
is between
0
and
1
: Vertically compressed
Vertical Compression or Stretch: None
Compare and list the transformations.
Parent Function:
f
(
x
)
=
x
2
Horizontal Shift: None
Vertical Shift: Down
3
Units
Reflection about the x-axis: None
Reflection about the y-axis: None
Vertical Compression or Stretch: None
image of graph
Part 1
Use the Pythagorean theorem to find the unknown side of the right triangle.
Answers
Answer:
Hypotenuse length = 37Step-by-step explanation:
According to the question we are given with a right traingle Where base is 35 and the perpendicular is 12.
We need to find the unknown side that is the longest side (Hypotenuse) .
By using pythagoras theorem :
[tex]\longrightarrow \rm \: \: (H)^2 = (B)^2 + (P)^2 \\ [/tex]
here,
H represents hypotenuseB represents base P represents Perpendicular.Putting the required values in the Pythagoras theorem we will get,,
[tex]\longrightarrow \rm \: \: (H)^2 = (35)^2 + (12)^2 \\ \\ \longrightarrow \rm \: \:(H)^2 =1225 + 144 \\ \\ \longrightarrow \rm \: \:(H)^2 = 1369 \\ \\ \longrightarrow \rm \: \:H = \sqrt{1369} \\ \\ \longrightarrow \rm \: \:H = 37 \\ [/tex]
Therefore, Unknown side of the right triangle i.e hypotenuse is 37 .
Friends ordered a large circular pizza of a certain diameter, however the diameter of the baked pizza was 10% smaller than the one ordered. By the way percentage of the area of the cooked pizza is smaller than the one ordered?
Answers
Answer:
19% smaller
Step-by-step explanation:
A=πr^2
r=d/2
A=pi(d/2)^2
A=pi(.9d/2)^2=
81% of original
100%-81%=19%=Give this answer a like!
Can you please help me with this problem
Answers
Answer:
X = 35°
Y = 72.5°
Step-by-step explanation:
x is vertically opposite to 35° so x = 35°
35 × 2 = 70
360 - 70 = 290
290 / 4 = 72.5
Y = 72.5°
Answer:
x = 35
y = 72.5
Step-by-step explanation:
At your level, it is assumed that those lines are straight. Keeping this in mind, we can find the answer to this problem.
First, we have to find x.
x = 35º because opposite angles are equal (xº is opposite to 35º).
Then, we have to calculate y.
You should know that angles in a straight line add up to 180º.
So: yº + yº + 35º = 180º
You know have to solve this equation (solve for y).
y + y + 35 = 180
y + y = 180 - 35
y + y = 145
2y = 145
y = 145 / 2
y = 72.5
Check: 72.5 + 72.5 + 35 = 180
for both of these graphs i need help finding the equations of the functions
also need help describing the transformation from its parent function (both graphs)
(120 points)
Answers
The equations of the transformed graphs are f(x) = -√(x - 2) and f(x) = -(x + 3)² - 1, while the descriptions are added below
How to describe the functions from the parent function and the equationGraph 1
This function is a square root function
The parent function is the square root function, which is denoted as
f(x) = √x
The function is first reflected across the x-axis to give
f(x) = -√x
Next, the function is shifted to the right by 2 units
So, we have
f(x) = -√(x - 2)
This means that the function description is a reflection about the x-axis. followed by a horizontal shift to the right by 2 units
Graph 2
This function is a quadratic function
The parent function is the square root function, which is denoted as
f(x) = x²
The function is first reflected across the x-axis to give
f(x) = -x²
Next, the function is shifted down and left by 1 and 3 units respectively
This means that
f(x) = -(x + 3)² - 1
This means that the function description is a reflection about the x-axis. followed by a horizontal shift to the down and left by 1 and 3 units
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Given the graph of y = a sin b(x + c) +d, determine the amplitude.
A -1
C 6
B
3
D 12
- 27
9 Y
2T
Answers
Answer:
Step-by-step explanation:
The general equation for a sinusoidal function of the form y = a sin b(x + c) + d is:
a is the amplitude (the maximum displacement from the midline).
b determines the period (the distance between two consecutive peaks or troughs).
c is the horizontal shift (the amount by which the graph is shifted horizontally).
d is the vertical shift (the amount by which the graph is shifted vertically).
From the given information, we can see that:
The amplitude is not given.
b = 3, which means the period is 2π/3.
c = 6, which means the graph is shifted 6 units to the left.
d = 9, which means the graph is shifted 9 units up.
Since the amplitude is not given, we need to look at the graph to determine it. However, the graph is not provided, so we cannot determine the amplitude with the given information.
can somebody please help me with these problems !
Answers
Answer:
divide figure in many parts.
Then, find volume of each divided figure :- v= l*b*h
Then add volume of all divided figure
6. Find the first three terms of the expansion of the following in acceding powers of
x
2
1
2
x
x
Answers
The first three terms in decreasing powers of X are as follows.
x5−10x4X−1+40x3X−2+…
What are functions?A relation is any subset of a Cartesian product.
As an illustration, a subset of is referred to as a "binary connection from
A to B," and more specifically, a "relation on A."
A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.
Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).
A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).
Every function, as you can see from these definitions, is a relation from X.
Hence, The first three terms in decreasing powers of X are as follows.
x5−10x4X−1+40x3X−2+…
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How do you convert 72 kilograms to pounds? show the mathmatical steps
Answers
1 kilogram = 2.20462 pounds
To convert 72 kilograms to pounds, you can multiply 72 by 2.20462 as follows:
72 kilograms = 72 x 2.20462 pounds
72 kilograms = 158.73264 pounds (rounded to five decimal places)
Therefore, 72 kilograms is equal to approximately 158.73264 pounds.
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please answer it asap.
Answers
Answer:
8^2
Step-by-step explanation:
noah is filling a tank with water at a constant rate of 0.5 gallons per minute. what is the rate of filling in minutes per gallon?
Answers
Noah is consistently adding 0.5 gallons of water every minute to a tank. 2 minutes are spent filling a gallon.
The rate of filling is the amount of water that is filled per unit of time. In this instance, Noah is consistently adding 0.5 gallons of water each minute to the tank.
To determine the rate of filling in minutes per gallon, we can simply take the reciprocal of the rate of filling in gallons per minute.
That is:
Rate of filling in minutes per gallon = 1 / Rate of filling in gallons per minute
So, the rate of filling in minutes per gallon is:
1 / 0.5 gallons per minute = 2 minutes per gallon
Therefore, Noah is filling the tank at a rate of 2 minutes per gallon.
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A pool can be filled by one pipe in 4 hours and by a second pipe in 5 hours. How long will it take using both pipes to fill the pool?
Answers
Step-by-step explanation:
Rate A = 1 pool / 4 hrs = 1/4 pool/hr
Rate B = 1 pool / 5 hrs = 1/5 pool / hr
Now combine the rates to fill 1 pool
1 pool / ( 1/4 pool/hr + 1/5 pool / hr) = 1 / ( 1/4 + 1/5) hr = 2.22 hrs
( or 2 hrs 13.3 min)
please help…………………………….
Answers
The shaded area above the line y = -x + 3 and below the line -2x + y = -1 is the solution region of the system that is option A.
What is graph?A graph is a visual representation of data or mathematical concepts. It is a diagram that shows how variables or quantities relate to each other, often using points, lines, bars, or other symbols. In mathematics, a graph can be used to represent a set of points or a function, where the x-axis represents the input values and the y-axis represents the output values. A graph can show the shape of a function, its range, its domain, and other important features.
Here,
To graph the system, we can first graph the boundary lines of the two inequalities.
For the first inequality, y > -x + 3, we can draw the line y = -x + 3 and shade the area above the line. This is because the inequality is y > -x + 3, which means that all points above the line satisfy the inequality.
Next, for the second inequality, -2x + y < -1, we can draw the line -2x + y = -1 and shade the area below the line. This is because the inequality is -2x + y < -1, which means that all points below the line satisfy the inequality.
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