Ex 3.7
12. find the area between the curve y=x³-2 and the y-axis between y= -1 and y=25

Answers

Answer 1

Answer: $y=x^3-2\nx^3=y+2\nx=\sqrt[3]{y+2}\n\n\int \limits_(-1)^(25)\sqrt[3]{y+2}\, dy=\n\int \limits_(-1)^(25)(y+2)^{\tfrac{1}{3}}\, dy=\n\left[\frac{(y+2)^{\tfrac{4}{3}}}{(4)/(3)} \right]_(-1)^(25)=\n$
$\left[(3)/(4)(y+2)^{\tfrac{4}{3}} \right]_(-1)^(25)=\n\left[(3)/(4)(y+2)\sqrt[3]{y+2} \right]_(-1)^(25)=\n(3)/(4)(25+2)\sqrt[3]{25+2}-\left((3)/(4)(-1+2)\sqrt[3]{-1+2}\right)=\n(3)/(4)\cdot27\sqrt[3]{27}-\left((3)/(4)\sqrt[3]{1}\right)=\n(3)/(4)\cdot27\cdot3-(3)/(4)=\n(3)/(4)(81-1)=\n(3)/(4)\cdot 80=\n3\cdot20=\n60$

Answer 2

Answer: Yeah, you'd have to use the inverse function to produce this result.

Let's get the inverse function first:

$y={ x }^( 3 )-2\n \n { x }^( 3 )=y+2\n \n x=\sqrt [ 3 ]{ y+2 }$

$\n \n \therefore \quad { f }^( -1 )\left( x \right) =\sqrt [ 3 ]{ x+2 }$

Now, we can solve the problem using:

$\int _( -1 )^( 25 ){ \sqrt [ 3 ]{ x+2 } } dx$

But to solve the problem more easily we make u=x+2, therefore du/dx=1, therefore du=dx.

When x=25, u=27.

When x=-1, u=1.

Now:

$\int _( 1 )^( 27 ){ { u }^{ \frac { 1 }{ 3 } } } du\n \n ={ \left[ \frac { 3 }{ 4 } { u }^{ \frac { 4 }{ 3 } } \right] }_( 1 )^( 27 )$

$\n \n =\frac { 3 }{ 4 } \cdot { 27 }^{ \frac { 4 }{ 3 } }-\frac { 3 }{ 4 } \cdot { 1 }^{ \frac { 4 }{ 3 } }\n \n =\frac { 3 }{ 4 } { \left( { 3 }^( 3 ) \right) }^{ \frac { 4 }{ 3 } }-\frac { 3 }{ 4 }$

$\n \n =\frac { 3 }{ 4 } \cdot { 3 }^( 4 )-\frac { 3 }{ 4 } \n \n =\frac { 3 }{ 4 } \left( { 3 }^( 4 )-1 \right)$

$\n \n =\frac { 3 }{ 4 } \cdot 80\n \n =60$

Answer: 60 units squared.

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Answer this question please!
A quarterback completed 68% of his passes in a game. He threw 25 passes. How many passes did the quarterback complete?
Simplify. (15/x-5)-5 = (21/x-6)-7
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Calculate the measure of each exterior angle of a 90 sided regular polygon. Explain.

Answers

90 sides give us 90 angles

sum of all inside angels is (n-2) * 180 deg. where n is number of angels

so one inside angle is
(90-2)*180 deg / 90 = 88* 2 deg = 176 deg.

measure of exterior angle is 360 - 176 = 184 deg.

The diagonals of a parallelogram QRST, TR And QS, Intersect at point U, if RS = 10 , ST=12,And RU=9.5 , Find The Perimeter Of The parallelogram QRST.A. 39
B. 44
C. 88
D.100

Answers

Answer:

(B)44

Step-by-step explanation:

It is given that The diagonals of a parallelogram QRST, TR And QS, Intersect at point U, if RS = 10 , ST=12,And RU=9.5.

Now, Since, RS =10, then RS=QT=10 (Opposite sides of parallelogram are equal).

And, ST=12, then ST=QR=12 (Opposite sides of parallelogram are equal)

Thus, The perimeter of the parallelogram QRST is given as:

Perimeter=Sum of all the sides

Perimeter=QR+RS+ST+TQ

Perimeter=12+10+12+10

Perimeter=44

Therefore, the perimeter of the given parallelogram QRST is 44 units.

Hence, option B is correct.

The answer is B. 44

Raquel and Van live in two different cities. As part of a project, they each record the lowest prices for a gallon of gas at gas stations around their cities on the same day. Raquel’s data reflect a mean price of $3.42 with a standard deviation of 0.07. Van’s data reflect a mean price of $3.78 with a standard deviation of 0.23.Which statement is true about their gas-price data?
A- Raquel’s data are most likely closer to $3.42 than Van’s data are to $3.78.
B- Van’s data are most likely closer to $3.42 than Raquel’s data are to $3.78.
C- Raquel’s data are most likely closer to $3.78 than Van’s data are to $3.42.
D- Van’s data are most likely closer to $3.78 than Raquel’s data are to $3.42.

Answers

the standard deviation shows the dispersion (how close) of the data. Therefore the correct statement is A:
A- Raquel’s data are most likely closer to $3.42 than Van’s data are to $3.78.

A is the answer my folks.

What is the product?(2x – 1)(x + 4)

2x2 – 4
2x2 + 4
2x2 + 7x – 4
2x2 – 7x – 4

Answers

the answer is the third one 2x^2+7x-4

Answer:

the answer is the c. 2x^2+7x-4

Step-by-step explanation:

Which of the following graphs represent functions Circle your answers. If it is a function, state the domainand range. If the graph is not included, make a table and graph the function by hand.

Answers

Answer:

Step-by-step explanation:

A). y = |2x - 3| + 1

Domain of function is defined by the x-values (Input values) and Range by the y-values(Output values).

From the graph,

Domain : (-∞, ∞)

Range : [1, ∞)

B). Table of the input-output values of the function,

y = x² - 2x + 1

x -2 -1 0 1 2

y 9 4 1 0 1

By graphing the function as attached,

Domain of the function : (-∞, ∞)

Range of the function : [0, ∞)

C). x² + y² = 3²

Domain of the function : [-3, 3]

Range of the function : [-3, 3]

D). x = 5

Domain of the line : [5, 5]

Range of the line : (-∞, ∞)

How do you classify the slope of a line ?

Answers

y=mx+b

slope= rise
run
If its already graphed then you find where the line meets the y- line ( thats the b in the equation) from there you go up or down on the y- line to the point where the line next meets directly over another vertical line on the grid, the number of times you moved up or down is the "rise" in the equation for slope. After finding rise your move left or right from that point on the y-line until you meet the point where the line is and that will be the run. That fraction or number once you simplify the equation is you slope. Hope that helps.

Answer:

Easy the equation will always be y=mx+b

mx is the slope in the equation and b is the y intercept and always remember rise over run

Step-by-step explanation:

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