Answers
The inverse function of [tex]g'(x)=- g(x) = (sqrt(x) + 6)/(1 - sqrt(x)) is g^-1(x) = [ (x + 6)/(x + 1) ]^2.[/tex] However, the function is not invertible at x = 1 where g(x) is not defined.
What is expression ?An expression is a mathematical phrase that can contain numbers, variables, operators, and sometimes functions. Expressions are used to represent or calculate values, and they can be simple or complex. For example, "2 + 3" is a simple expression that can be evaluated to give the value 5, while "3x + 2y - 4" is a more complex expression that contains variables and can only be evaluated if values are assigned to the variables. Expressions can also be combined to form more complex expressions using operators like addition, subtraction, multiplication, and division.
According to the given information:To find the inverse function of g'(x)=- g(x) = (sqrt(x) + 6)/(1 - sqrt(x)), we can follow these steps:
Step 1: Replace g(x) with y, so that the function becomes g'(x) = -y.
Step 2: Solve the equation for y in terms of x: y = - g'(x) = - (sqrt(x) + 6)/(1 - sqrt(x)).
Step 3: Interchange x and y: x = - (sqrt(y) + 6)/(1 - sqrt(y)).
Step 4: Solve for y in terms of x:
[tex]x = - (sqrt(y) + 6)/(1 - sqrt(y))\\x(1 - sqrt(y)) = -sqrt(y) - 6\\x - x sqrt(y) = -sqrt(y) - 6\\x + 6 = (x + 1) sqrt(y)\\(x + 6)/(x + 1) = sqrt(y)\\[/tex]
[tex]y = [ (x + 6)/(x + 1) ]^2[/tex]
Therefore, the inverse function of [tex]g'(x)=- g(x) = (sqrt(x) + 6)/(1 - sqrt(x)) is:g^-1(x) = [ (x + 6)/(x + 1) ]^2[/tex]
Note that this function is defined for all x except x = 1, where the original function g(x) is not defined. Therefore, g(x) is not invertible at x = 1.
Therefore, The inverse function of [tex]g'(x)=- g(x) = (sqrt(x) + 6)/(1 - sqrt(x)) is g^-1(x) = [ (x + 6)/(x + 1) ]^2.[/tex] However, the function is not invertible at x = 1 where g(x) is not defined.
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Related Questions
Please please help
f ₁(x) = x²
Find f(x)
Answers
Answer:√x
Step-by-step explanation:
I am assuming the equation says [tex]f^{-1}(x)=x^{2}[/tex]
What you do is put x instead of [tex]f^{-1}(x)[/tex] and y² instead of x²
So x = y²
Rearrange for y
y = √x
Replace y with f(x)
f(x) = √x
NO LINKS!!! URGENT HELP PLEASE!!!!!
Please help me with 3 and 4 from another sheet please
Answers
Answer:
3. 211.6 feet
4. 59.04 degrees.
Step-by-step explanation:
3.
To find how much wire Mark Wolfman needs for the tallest tower in the park, we can use trigonometry. Let's call the height of the tower "h". We know that the wire is attached to the top of the tower and to a stake in the ground that is 44 feet away from the base of the tower. The wire makes a 78 degree angle with the flat ground.
We can use the tangent function to find the height of the tower:
tan(78) = h / 44
Multiplying both sides by 44, we get:
h = 44 * tan(78)
So the height of the tower is approximately 207 feet.
To find how much wire is needed, we can use the Pythagorean theorem:
wire length = sqrt(h^2 + 44^2)
Substituting the value we found for "h", we get:
wire length = sqrt(207^2 + 44^2)
Simplifying, we get:
wire length = 211.6
So Mark Wolfman needs approximately 211.6 feet of wire.
4.
To find the angle of depression of the swimmer's dive, we need to consider the triangle formed by the swimmer, the buoy, and the point on the lake bottom directly below the buoy. We know that the buoy is 30 feet away from the swimmer and the chain connecting it to the bottom of the lake is 50 feet down.
The angle of depression is the angle between the swimmer's line of sight and the horizontal. Since the swimmer is looking downward toward the chain, the angle of depression is the same as the angle formed by the horizontal and the line connecting the swimmer to the chain.
Using trigonometry, we can find the tangent of this angle:
tan(angle of depression) = opposite / adjacent
tan(angle of depression) = 50 / 30
tan(angle of depression) = 5/3
Taking the arctangent of both sides, we get:
angle of depression = arctan(5/3)
Using a calculator, we find that the angle of depression is approximately 59.04 degrees.
Hi i need help with this question
Answers
The angles of the given Rhombus are:
= 31°= 90°= 59°= 59°= 31°= 59°The above are arrived at using the qualities of a Rhombus and the theorem of alternate angles.
What are the properties of a rhombus?A rhombus is a quadrilateral with certain properties that distinguish it from other types of quadrilaterals. The key properties of a rhombus are:
All sides are congruent (i.e., have the same length).Opposite angles are congruent (i.e., have the same measure).Diagonals bisect each other (i.e., they intersect at their midpoint), creatign 90° angles.The diagonals are perpendicular to each other (i.e., they form a right angle where they intersect).It is a parallelogram (i.e., opposite sides are parallel).So we stated that ∠ = 31° because ∠KNM have been dissected into two equal halves by diagonal, LN.∠2 = 90° because Diagonals bisect each other (i.e., they intersect at their midpoint), creating 90° angles.Since we know ∠2 and ∠LNM = 31° (both of which are angles in ΔN2M), ∠3 = 180 -31-90 = 59° (Sum of Angles in a Triangle)because Diagonals bisect each other (i.e., they intersect at their midpoint), creating 90° angles, ∠4 is also equal to 59°Since ∠L2M = 90°, ∠5 = 180 - 90 - 59° = 31° ∠6 = ∠3 = 59° (Alternate angles)Learn more about Rhombus;
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how many tickets are there when it weighs 135 grams
Answers
Answer:
about like 4-5
Step-by-step explanation:
its 4 or 5
Suppose that the value of a stock varies each day from $10.82 to $33.17 with a uniform distribution. Find the upper quartile; 25% of all days the stock is above what value?
Answers
Answer:
The range of the stock prices is from $10.82 to $33.17. To find the upper quartile, we need to find the value of the stock price that is greater than 75% of the data.
The distance between the minimum value and the maximum value is:
$33.17 - $10.82 = $22.35
To find the upper quartile, we need to find the value that is three-quarters of the distance above the minimum value:
$10.82 + 0.75($22.35) = $26.69
Therefore, the upper quartile of the stock price is $26.69.
To find the value above which the stock price is higher 25% of the time, we need to find the value that is 75% of the distance above the minimum value:
$10.82 + 0.25($22.35) = $15.62
Therefore, 25% of the time, the stock price is above $15.62.
To find the upper quartile, we need to first find the median of the stock prices, which is the value that divides the distribution into two equal parts. The midpoint of the distribution is:
Midpoint = (10.82 + 33.17) / 2 = 22.995
Now, we can find the upper quartile, which is the median of the upper half of the distribution. The upper half of the distribution ranges from the midpoint to the highest value of 33.17. Therefore, we calculate the median of this range as follows:
Upper quartile = (22.995 + 33.17) / 2 = 28.0825
So, the upper quartile of the stock prices is $28.08.
To find the value above which the stock is priced 25% of the time, we need to find the 75th percentile of the distribution. Since the distribution is uniform, we can use the formula for the percentile as follows:
Percentile rank = (percentile / 100) = (value - minimum) / (maximum - minimum)
Solving for the value, we get:
value = minimum + percentile rank x (maximum - minimum)
For the 75th percentile, we have:
value = 10.82 + 0.75 x (33.17 - 10.82) = 28.49
Therefore, the stock is priced above $28.49 on 25% of all days.
Annie is concerned over a report that "a woman over age 40
40
has a better chance of being killed by a terrorist than of getting married." A study found that the likelihood of marriage for a never-previously-wed, 40
40
-year-old university-educated American woman was 3.4%
3.4
%
. To demonstrate that this percentage is too small, Annie uses her resources at the Baltimore Sun to conduct a simple random sample of 407
407
never-previously-wed, university-educated, American women who were single at the beginning of their 40
40
s and who are now 45
45
. Of these women, 20
20
report now being married. Does this evidence support Annie’s claim, at the 0.01
0.01
level of significance, that the chances of getting married for this group is greater than 3.4%
3.4
%
?
Answers
The answer is no. As the p-value is more than 0.01, evidence does not support Annie's claim that the chances of getting married for this group is greater than 3.4%.
What is null hypothesis?It assumes that the observed result is due to chance and there is not any difference between specified populations.
To determine this, we must calculate the p-value.
The number of successes in the sample is 20 and the number of observations is 407.
The sample proportion = 0.049. (20/407)
The hypothesis is that the percentage of women who got married is greater than 3.4%.
The null hypothesis is that the percentage is 3.4%.
We can use the z-test statistic to test this hypothesis.
The z-test statistic is calculated as:
z = (0.049-0.034)/(√(0.034(1-0.034)/407))
= 1.66.
The p-value is calculated as:
p-value = Φ/(1.66)
= 0.97.
This is more than 0.01 ,so we can not reject the null hypothesis.
This evidence does not support Annie's claim that the chances of getting married for this group is greater than 3.4%.
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What is the value of x?
Answers
Answer:
x = 26
Step-by-step explanation:
the 3 angles lie on the straight line DAC and sum to 180° , that is
4x - 8 + 34 + 76 - x = 180
3x + 102 = 180 ( subtract 102 from both sides )
3x = 78 ( divide both sides by 3 )
x = 26
Find the surface area of a rectangular prism with a height of 6 inches, a width of 7 inches, and a length of 13 inches.
Answers
Answer:
A fast and easy surface area of a rectangular prism calculator to find just what its name suggests.
Step-by-step explanation:
l=13in
w=7
h=6
A=422in squared
I WILL GIVE BRAINLYEST!! ALGEBRA 1 HW
Answers
Answer:☠️☠️☠️☠️do ur hw lil bro u actually need to learn this fr fr dont let me catch u slippin on foenem
Step-by-step explanation:
b. 650 because in the directions it says for groups of more than ( > ) 8 people they charge a FIXED fee of 650 so it's not 75 times 9 which would have been 675
Step-by-step explanation:
C(n) = {
75n, if n <= 8
650, if n > 8 and n <= 12
}
This function states that for groups of 8 people or fewer, the total cost is 75n, while for groups of 9 to 12 people, the total cost is a fixed $650.
b. To determine the total cost of a 1-hour private guided tour with 9 people, we can simply plug n = 9 into the equation we derived in part a:
C(9) = {
75*9, if 9 <= 8
650, if 9 > 8 and 9 <= 12
}
Since 9 is greater than 8 but less than or equal to 12, we use the second case:
C(9) = 650
Therefore, the total cost of a 1-hour private guided tour with 9 people is $650.
ChatGPT
In a class of 60 students, 40 are Democrats, 10 are business majors, and 4 of the business majors are Democrats. If one student is randomly
selected from the class, find the probability of choosing a Democrat or a business major.
P(Democrat or business major) =
Answers
In conclusion, the probability of selecting a Democrat or a business major is 11/15.
How to solve?
To find the probability of selecting a Democrat or a business major, we need to add the probabilities of selecting a Democrat and selecting a business major, and then subtract the probability of selecting a student who is both a Democrat and a business major (since we would be double counting this student).
So, let's calculate each of these probabilities:
Probability of selecting a Democrat: There are 40 Democrats out of 60 students, so the probability of selecting a Democrat is 40/60 = 2/3.
Probability of selecting a business major: There are 10 business majors out of 60 students, so the probability of selecting a business major is 10/60 = 1/6.
Probability of selecting a student who is both a Democrat and a business major: We know that there are 4 business majors who are also Democrats, so the probability of selecting one of these students is 4/60 = 1/15.
Now we can calculate the probability of selecting a Democrat or a business major:
P(Democrat or business major) = P(Democrat) + P(business major) - P(Democrat and business major)
= 2/3 + 1/6 - 1/15
= 11/15
Therefore, the probability of selecting a Democrat or a business major is 11/15.
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The number of years from the start of the Great Depression to the first presidential election of Richard Nixon is six years less than three times Raul’s age. Nixon’s first presidential election happened 39 years after the Great Depression. Using the given information, write an equation to find Raul’s age, r.
Answers
Answer:
Raul is 15 years old.
Step-by-step explanation:
The number of years from the start of the Great Depression to Nixon's election is six years less than three times Raul's age: 3r-6
If then Nixon's first election happened 39 years after the Great Depression, then: 3r-6=39
3r-6=39 Add six to both sides so the 6 on the left side gets canceled out (positive and negative cancel each other out) so the equation will now look like this: 3r=45
Then divide 3 on both sides (multiplication and division also cancel each other out), then the equation looks like this: r=15
And so, Raul is 15 years old.
The image shows a point and a line. Suppose we create a parabola using the point as the focus and the line as the directrix. Decide whether each point on the list is on this parabola.
A (-1.5) True or False
B.(3.3) True or False
C. (5,5) True or false
D. (7,5) True or false
E. (3,9) True or false
Answers
The correct answers for the equation of parabola with (3,5) are:
A. True
B. False
C. True
D. True
E. True
EquationsUsing the vertex form equation of the parabola with vertex (h, k) and p = 2,
[tex](y-4)^{2}[/tex] = 8(x - 3)
[tex]y^{2}-10y+25[/tex] = 8x - 24
[tex]y^{2}-10y+49[/tex] = 8x
A. (-1, 5): Substitute x = -1 and y = 5 into the equation:
25 - 10(5) + 49 = 8(-1)
-16 = -16
This is true, so the point (-1, 5) is on the parabola.
B. (3, 3): Substitute x = 3 and y = 3 into the equation:
9 - 10(3) + 49 = 8(3)
-8 = 8
This is false, so the point (3, 3) is not on the parabola.
C. (5, 5): Substitute x = 5 and y = 5 into the equation:
25 - 10(5) + 49 = 8(5)
9 = 9
This is true, so the point (5, 5) is on the parabola.
D. (7, 5): Substitute x = 7 and y = 5 into the equation:
25 - 10(5) + 49 = 8(7)
25 = 25
This is true, so the point (7, 5) is on the parabola.
E. (3, 9): Substitute x = 3 and y = 9 into the equation:
81 - 10(9) + 49 = 8(3)
1 = 1
This is true, so the point (3, 9) is on the parabola.
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Help asap ty !!!!! Thanks
Answers
So, we have an equation relating the volume of the prism to the dimensions of the base. However, we still need more information to solve for x. Then x is 2.5 xyxx
What is height?Height generally refers to the distance from the base of an object, such as a person or a building, to the highest point of that object. In the case of a person, height is typically measured in feet and inches or centimeters and is a measurement of how tall someone is from the top of their head to the soles of their feet. In the case of a building or structure, height is typically measured in meters or feet and is a measurement of how tall the structure is from its base to its highest point, such as its roof or antenna. Height can also refer to the vertical distance between two points, such as the height of a mountain or the height of a wave in the ocean.
by the question.
Volume = base area x height
Since the bases of the prism are right triangles, we can calculate their area using the formula:
base area = 1/2 x base x height
where base is the length of the base of the triangle and height is the height of the triangle.
Let's assume that the length of the base of each right triangle is x, and that the height of each right triangle is y. Then we can write:
base area = 1/2 x y
The total volume of the prism is given as So. Therefore, we can write:
So = base area x height
Substituting the expression for base area and the given value for height, we get:
So = 1/2 x y x 5
Simplifying this equation, we get:
So = 2.5 x y x x
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Janelle makes fruit punch by mixing the ingredients listed below.
•5 pints of orange juice
•6 cups of grape juice
•8 cups of apple juice
How many quarts of fruit punch does Janelle make?
TIPS:
1 quart is 2 pints
1 pint is 2 cups
1 cup is 8 fluid ounces
Answers
Answer:
6 quarts
Step-by-step explanation:
2 pints = 1 quart
4 cups = 1 quart
• 5 pints of orange juice
5 pints = 5/2 =>2.5 quarts
• 6 cups of grape juice
6 cups = 6/4 => 1.5 quarts
• 8 cups of apple juice
8 cups = 2 quarts
2.5 + 1.5 + 2 = 6 quarts
es calculo del %
38% de 1610
Answers
1610(0.38)=611.8
38/100=0.38
Carla buys a bag of 12 apples for $1.44. How much is each apple worth?
Answers
Answer:
Each apple is worth $0.12
Step-by-step explanation:
Total of 12 apples ÷ Quantity of Apples = Cost of each apple
1.44 ÷ 12 = 0.12
35,617 minus by 15,624
Answers
Answer:
19, 993
Step-by-step explanation:
35, 617
15, 624
19, 993
Answer:
Step-by-step explanation:
20,047 using simple subtraction
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answers
Answer:
Step-by-step explanation: ??? There is no picture
Find the percent of each number What is 59% of 640?
Answers
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{59\% of 640}}{\left( \cfrac{59}{100} \right)640}\implies 377.6[/tex]
Answer:
377.6
Step-by-step explanation:
640÷10=64 to find 10%
64×5=320 to find 50%
640÷100=6.4 to find 1%
6.4×9=57.6 to find 9%
320+57.6=377.6
answer: 377.6
Emir, Katherine, Dylan and Anna Who earned enough money to attend the festival?
Answers
Therefore , the solution of the given problem of unitary method comes out to be able to afford the festival because 120 is larger than 70.
What is an unitary method?To accomplish the task, one may use this generally accepted ease, preexisting variables, as well as any significant components from the original Diocesan customizable query. If so, there might be an opportunity to interact with the item once more. Otherwise, every significant factor that affects how algorithmic evidence behaves will be gone.
Here,
The following chart allows us to determine each person's earnings:
=> Person 1: 2 hours times $8 per hour = $16
=> Person 2: $4 hours x $8 per hour = $32 per person
=>Person 3: 3 hours x $8 per hour = $24 per person.
=> Person 4: 5 hours x $8 per hour = $40.
=> Person 5: One hour times $8 per hour equals $8.
Each person needs to bring at least $70 in order to join the festival. As a result, the disparity shown below can be used to describe this circumstance:
=> 16 + 32 + 24 + 40 + 8 ≥ 70
Simplifying the inequality's left side, we obtain:
=> 120 ≥ 70
We can infer that all of the friends were able to afford the festival because 120 is larger than 70.
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twice the difference between two numbers is 44. three times their sum is 96
Answers
Answer:
Step-by-step explanation:
Let's say the two numbers are x and y.
From the first statement "twice the difference between two numbers is 44", we can set up the equation:
2(x-y) = 44
Simplifying this equation, we get:
x - y = 22 (dividing both sides by 2)
From the second statement "three times their sum is 96", we can set up the equation:
3(x+y) = 96
Simplifying this equation, we get:
x + y = 32 (dividing both sides by 3)
Now we have two equations:
x - y = 22
x + y = 32
We can solve for x and y by adding the two equations together:
2x = 54
x = 27
Substituting x = 27 in either of the two equations, we get:
y = 5
Therefore, the two numbers are 27 and 5.
x = 27;
y = 5.
Step-by-step explanation:1. Name the number as variables.Say "x" is the first number.
Say "y" is the second number.
2. Form the first equation from the statements.First statement: "twice the difference between two numbers is 44".
Difference of the numbers:[tex]x-y[/tex]
Twice the difference: [tex]2(x-y)[/tex]
Twice the difference between two numbers is 44: [tex]2(x-y)=44[/tex]
3. Form the second equation from the statements.Second statement: "three times their sum is 96".
Sum of the numbers: [tex](x+y)[/tex]
3 times the sum: [tex]3(x+y)[/tex]
3 times the sum is 96: [tex]3(x+y)=96[/tex]
4. Simplify the equations.Use the distributive property of multiplication to simplify each equation as follows (check this property in the attached image).
[tex]2(x-y)=44\\ \\2x-2y=44[/tex]
[tex]3(x+y)=96\\ \\3x+3y=96[/tex]
5. Solve one of the equations for one of the variables.Let's solve the second equation for "x".
[tex]3x+3y-3y=96-3y\\ \\3x=96-3y\\ \\x=\frac{96-3y}{3} \\ \\x=\frac{96}{3} -\frac{3y}{3} \\ \\x=32-y[/tex]
7. Use the calculated value of "x", plug it in the other equation and calculate.[tex]2((32-y)-y)=44\\ \\2(32-y-y)=44\\ \\2(32-2y)=44\\ \\(2)(32)+(2)(-2y)=44\\ \\64+(-4y)=44\\ \\64-4y=44\\ \\-4y=44-64\\ \\-4y=-20\\ \\y=\frac{-20}{-4} \\ \\y=5[/tex]
8. Find the value of "x".Use any equation to find a value for "x" by substituting "y" by "5" and solving for "x".
[tex]3(x+(5))=96\\ \\3(x+5)=96\\ \\3x+15=96\\ \\3x=96-15\\ \\3x=81\\ \\x=\frac{81}{3} \\ \\x=27[/tex]
9. Verify the answers.To see if the answers are correct, plug in the values of "x" and "y" on each formula and see if they return the correct values (44 and 96).
[tex]2(x-y)=44\\ \\2((27)-(5))=44\\ \\2(22)=44\\ \\44=44[/tex]
Correct.
[tex]3((27)+(5))=96\\ \\3(32)=96\\ \\96=96[/tex]
Correct.
The numbers returned the correct values when evaluated in both opf the equation. Therefore, they are the correct answers.
x = 27;
y = 5.
See the graphic solution to this problem in the second attached image.
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Given the volume of a sphere formula: V =
³
Find the volume of spheres with the following radii. Rewrite the equations and show your substitutions.
Remember to include units. LEAVE YOUR ANSWER IN TERMS OF TT.
1. r = 12 ft
Answers
Answer:
The volume of the sphere is 2304π ft³.
Step-by-step explanation:
The formula for the volume of a sphere is:
[tex]\boxed{V=\dfrac{4}{3}\pi r^3}[/tex]
where r is the radius of the sphere.
Given the radius of the sphere is 12 feet, substitute r = 12 into the formula and solve for V:
[tex]\begin{aligned}\implies V&=\dfrac{4}{3} \cdot \pi \cdot 12^3\\\\&=\dfrac{4}{3} \cdot \pi \cdot 1728\\\\&=\dfrac{6912}{3} \cdot \pi \\\\&=2304\pi\; \sf ft^3 \end{aligned}[/tex]
Therefore, the volume of the sphere in terms of π is 2304π ft³.
how long does it take for a population that is growing with a constant relative growth rate of 10% per year to triple. Show work.
Answers
It takes 11.52 years for a population that is growing with a constant relative growth rate of 10% per year to triple.
The formula for calculating the time it takes a population to triple with a constant relative growth rate of 10% per year is:
Time (in years) = ln(3) / ln(1.10)
The natural logarithm of 3 (ln(3)) is 1.09861228866811, and the natural logarithm of 1.10 (ln(1.10)) is 0.095310179804325.
Therefore, the calculation of the time it takes a population to triple with a constant relative growth rate of 10% per year is:
Time (in years) = 1.09861228866811 / 0.095310179804325 = 11.52
It takes 11.52 years for a population that is growing with a constant relative growth rate of 10% per year to triple.
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please help find the area
Answers
Answer:
85.6 cm²
Step-by-step explanation:
You can divide this shape with a horizontal line: trapezoid and a rectangle
Total Area = Area of trapezoid + Area of rectangle
= (1/2)(b₁ + b₂)(h) + (b)(h)
= (1/2)(6+10)(7.2) + (10)(2.8)
= 57.6 + 28
= 85.6 cm²
solve the following equations by graphical method: 2x+y=7 and x-y=1
Answers
Answer:
Step-by-step explanation:
can you solve this question?
y=?
(?,?)
Answers
Answer:
The tangent line is: y = 8x - 58
The tangent point is at (7, -2)
===================================================
Explanation:
One of the definitions of derivatives is
[tex]\displaystyle f'(a) = \lim_{x\to a} \frac{f(x)-f(a)}{x-a}[/tex]
where f ' (a) represents the derivative evaluated at x = a.
The value of f ' (a) will get us the slope of the tangent at x = a.
The idea is that x is getting closer and closer to 'a'. In doing so, the secant lines slowly approach the tangent line.
Keep in mind that x will never reach 'a' itself (if it did, then we'd have a division by zero error).
---------------
The given limit we have is
[tex]\displaystyle \lim_{x\to 7} \frac{f(x)+2}{x-7} = 8[/tex]
and that is equivalent to
[tex]\displaystyle \lim_{x\to 7} \frac{f(x)-(-2)}{x-7} = 8[/tex]
and also equivalent to
[tex]\displaystyle \lim_{x\to 7} \frac{f(x)-f(7)}{x-7} = 8[/tex]
Compare that to the template I mentioned at the top to see that
a = 7f(a) = f(7) = -2f ' (a) = f ' (7) = 8Therefore, we can say the tangent slope is 8 and the tangent touches the f(x) curve at (x,y) = (a, f(a)) = (7,f(7)) = (7,-2)
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[tex]m = 8 = \text{slope}\\\\(x_1,y_1) = (7,-2) = \text{tangent point}\\\\[/tex]
Let's use that info to determine the equation of the tangent line.
I'll use point-slope form to isolate y.
[tex]y-y_1 = m(x-x_1)\\\\y-(-2) = 8(x-7)\\\\y+2 = 8x-56\\\\y = 8x-56-2\\\\y = 8x-58\\\\[/tex]
That's the equation of the tangent line to the point (7,-2).
solve the area of bottom of tiffin box is 0.30m(sq) and weight is 60n=?
Answers
The pressure exerted (in N/m²) by the box on the shelf given that the bottom of the box has an area of 0.30 m² and weighs 60 N, is 200 N/m²
How do i determine the pressure exerted by the box?Pressure is defined a force per unit area. Mathematically, it is written as
Pressure (P) = force (F) / area (A)
P = F / A
With the above formular, we can obtain the pressure exerted by the box as follow:
Area of box (A) = 0.30 m² Weight of box (W) = 60 NPressure exerted (P) =?Pressure exerted (P) = Weight of box (W) / Area of box (A)
Pressure exerted = 60 / 0.30
Pressure exerted = 200 N/m²
Thus, we can conclude that the pressure exerted is 200 N/m²
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Complete question:
The area of the bottom of a tiffin box is 0.30 sq. m and weight is 60 N, Calculate the pressure exerted by the box on the shelf in N/sq. m *
Area and Square Units
Area is amount of surface covered by a figure.
It is measured in square units.
Model each figure.
Answers
The area of the given figures is 1) 4 sq. units; 2) 16 sq units; 3) 6 sq units.
Define area and perimeter.
The distance around a closed figure is its perimeter, while the area is the portion of the surface that it occupies. The size of a plane or the space it encloses is expressed in square meters.
1. In this figure, the longest side has 4 units and the smallest one has 1 unit.
Area of the rectangular figure(A) = 4 * 1 = 4 sq units
Perimeter(P) = 4 + 1 + 4 + 1 = 10 units.
2. In this figure, the longest side has 4 units and the smallest one has 4 units.
Area of the rectangular figure(A) = 4 * 4 = 16 sq units
Perimeter(P) = 4 + 4 + 4 + 4 = 16 units.
3. In this figure, the longest side has 4 units, 3 units, then 2 units the smallest one has 1 unit.
Area of the rectangular figures combinely (A) = 4 * 1 + 2 * 1= 6 sq units
Perimeter(P) = 4 + 3 + 2 + 2 + 1 = 12 units.
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Jose has 4 ants in his house and his discovers that those ants will double every day how many ants he will have after 2 weeks.
Answers
8 because 4 ants doubled (4x2)
14 because 7 days a week + another week
A parabola opening up or down has vertex (-1, 2) and passes through (-14, - 153/8)
Write its equation in vertex form.
Simplify any fractions.
Answers
The quadratic equation is:
y = (149/1,800)*(x + 1)² + 2
What is the equation of the parabola?Remember that if the parabola has a vertex (h, k) and a leading coefficient a can be written as:
y = a*(x - h)² + k
Here we know that the vertex is (-1, 2), then we will get the following equation:
y = a*(x + 1)² + 2
And we know it passes through (-14, - 153/8), then we will get:
-153/8 = a*(14 + 1)² + 2
-153/8 = a*225 + 2
a = (153/8 - 2)/225 =
a = 149/1,800
The quadratic is:
y = (149/1,800)*(x + 1)² + 2
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