Ask question

Ask question

All categories

andreyandreev [35.5K]

1 year ago

14

Find the volume of the resulting solid if the region under the curve y = 10/(x2 + 3x + 2) from x = 0 to x = 1 is rotated about t

he x-axis and the y-axis.

1 answer:

alexgriva [62]1 year ago

5 0

Answer:

Step-by-step explanation:

Check attachment for solution

You might be interested in

Emily is observing the velocity of a cyclist at different times. After four hours, the velocity of the cyclist is 14 km/h. After

lina2011 [118]

Assume that Emily starts from rest so that the velocity is zero at 0 hours.

Define the function v(t) for velocity in km/h, and t in hours.

Part A
From t=0 to t=4, v changes from 0 to 14.
Let v(t) = mt + b
The slope is
m = 14/4 = 3.5, and the y-intercept is
b = 0.
Therefore
v(t) = 3.5t, for 0 ≤ t ≤ 4

Fromt=4 to t=9, changes from 14 to 4.
Let v(t) = mt + b
The slope is
m = (4 - 14)/(9 - 4) = -2
Therefore
v = -2t + b
When t=4, v=14, therefore
14 = -2*4 + b = -8 + b
22 = b
v(t) = -2t + 22, for 4 < t ≤ 9.

Answer:
The equation for the velocity is
v(t) = 3.5t, 0 ≤ t ≤ 4
= -2t + 22, 4 < t ≤ 9

Part B
The equation for velocity is a piecewise function that is graphed as shown below. If we assume that the second part of the equation is valid at t=10, then
v(10) = -2*10 + 22 = 2 km/h

3 0

1 year ago

Jack and Walter work in a store's gift-wrapping department. Jack can wrap 28 boxes in 2 hours, while Walter takes 3 hours to wra

iVinArrow [24]

J = 14h
w = 12h
h = jw65

4 0

1 year ago

Complete the table of values

Agata [3.3K]

Both problems give you a function in the second column and the x-values. To find out the values of a through f, you need to plug in those x-values into the function and simplify!

You need to know three exponent rules to simplify these expressions:
1) The negative exponent rule says that when a base has a negative exponent, flip the base onto the other side of the fraction to make it into a positive exponent. For example, $3^{-2} =
\frac{1}{3^{2} }$ .
2) Raising a fraction to a power is the same as separately raising the numerator and denominator to that power. For example, $(\frac{3}{4}) ^{3} = \frac{ 3^{3} }{4^{3} }$ .
3) The zero exponent rule<span> says that any number raised to zero is 1. For example, $3^{0} = 1$ .
</span>

Back to the Problem:
Problem 1
The x-values are in the left column. The title of the right column tells you that the function is $y = 4^{-x}$ . The x-values are:
<span>1) x = 0
</span>Plug this into $y = 4^{-x}$ to find letter a:
$y = 4^{-x}\\
y = 4^{-0}\\
y = 4^{0}\\
y = 1$
<span>
2) x = 2
</span>Plug this into $y = 4^{-x}$ to find letter b:
$y = 4^{-x}\\ 
y = 4^{-2}\\ 
y = \frac{1}{4^{2}} \\ 
y= \frac{1}{16}$
<span>
3) x = 4
</span>Plug this into $y = 4^{-x}$ to find letter c:
$y = 4^{-x}\\ 
y = 4^{-4}\\ 
y = \frac{1}{4^{4}} \\ 
y= \frac{1}{256}$
<span>

Problem 2
</span>The x-values are in the left column. The title of the right column tells you that the function is $y = (\frac{2}{3})^x$ . The x-values are:
<span>1) x = 0
</span>Plug this into $y = (\frac{2}{3})^x$ to find letter d:
$y = (\frac{2}{3})^x\\
y = (\frac{2}{3})^0\\
y = 1$
<span>
2) x = 2
</span>Plug this into $y = (\frac{2}{3})^x$ to find letter e:
$y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^2\\ y = \frac{2^2}{3^2}\\
y = \frac{4}{9}$
<span>
3) x = 4
</span>Plug this into $y = (\frac{2}{3})^x$ to find letter f:
$y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^4\\ y = \frac{2^4}{3^4}\\ y = \frac{16}{81}$
<span>
-------

Answers:
a = 1
b = </span> $\frac{1}{16}$ <span>
c = </span> $\frac{1}{256}$
d = 1
e = $\frac{4}{9}$
f = $\frac{16}{81}$

5 0

2 years ago

Consider the system of inequalities and its graph. y ≤ –0.75x y ≤ 3x – 2 In which section of the graph does the actual solution

lora16 [44]

We need to assign a value for x to check the possible values of y. 1st inequality: y < -0.75x X = - 1 ; y < -0.75(-1) ; y < 0.75 possible coordinate (-1,0.75) LOCATED AT THE 2ND QUADRANT X = 0 ; y < -0.75(0) ; y < 0 possible coordinate (0,0) ORIGIN X = 1 ; y < -0.75(1) ; y < -0.75 possible coordinate (1,-0.75) LOCATED AT THE 4TH QUADRANT 2nd inequality: y < 3x -2 X = -1 ; y < 3(-1) – 2 ; y < -5 possible coordinate (-1,-5) LOCATED AT THE 4TH QUADRANT X = 0 ; y < 3(0) – 2 ; y < -2 possible coordinate (0,-2) LOCATED AT THE 4TH QUADRANT X = 1 ; y < 3(1) – 2 ; y <<span> 1 possible coordinate (1,1) LOCATED AT THE 1ST QUADRANT The actual solution to the system lies on the 4TH QUADRANT. </span>

3 0

1 year ago

Read 2 more answers

500 grams of tomatoes cost £1.76 how much will 1.75kg cost??

ValentinkaMS [17]

500 grams equals 0.50 kg so multiply 1.76 3 times to get 5.28, then divide 1.76 by 2 to get .88 add the two together to get 6.16

3 0

1 year ago