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Alla [95]
3 years ago
11

Consider a circular cone of radius 3 and height 5, which we view horizontally as pictured in Figure 6.8. Our goal in this activi

ty is to use a definite integral to determine the volume of the cone.
(a) Find a formula for the linear function y = f(x) that is pictured in Figure 6.8.

(b) For the representative slice of thickness (x that is located horizontally at a location x (somewhere between x = 0 and x = 5), what is the radius of the representative slice? Note that the radius depends on the value of x.

(c) What is the volume of the representative slice you found in (b)?

(d) What definite integral will sum the volumes of the thin slices across the full horizontal span of the cone? What is the exact value of this definite integral?

(e) Compare the result of your work in (d) to the volume of the cone that comes from using the formula V(cone) = (1/3) * pi * r^2 * h.

Mathematics
1 answer:
brilliants [131]3 years ago
4 0

Answer:

a) Y = -3x/5 + 15

b) Y = 3 - 0.6x

d) Volume = 15Pi

e) Volume of cone = 15pi

Step-by-step explanation:

The detailed steps and appropriate integration is as shown in the attached file.

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QUESTION
garri49 [273]

Answer:

45

Step-by step

What do we already know about the equation?

We know that they EACH bought a hockey puck($17) and 2 shirts

Half of 214 is 107. So they had to have spent 107 separately

So we make the equation and let s represent shirts

2s + 17 = 107

    - 17            -17

2s= 90.    DIVIDE by 2

s = 45

3 0
3 years ago
Read 2 more answers
The sum of two positive integers, a and b, is at least 30. The difference of the two integers is at least 10. If b is th
Dafna11 [192]

Answer:

a + b \geq 30

b - a \geq 10

Step-by-step explanation:

Given

The sum of the two positive integer a and b is at least 30, this means the sum of the two positive integer is 30 or greater than 30, so we write the inequalities as below.

a + b \geq 30

The difference of the two integers is at least 10, if b is the greater integer then we subtract integer a from integer b, so we write the inequality as below.

b - a \geq 10

Therefore, the following system of inequalities could represent the values of two positive integers a and b.

a + b \geq 30

b - a \geq 10

6 0
3 years ago
Express this decimal as a fraction.<br><br> 1.21212121.......
katovenus [111]
I think it's <span>121212121/100000000 but I'm not sure...

</span>
8 0
3 years ago
Consider the leading term of the polynomial function. What is the end behavior of the graph? 2x^7-8x^6-3x^5-3
jeyben [28]

Answer:

\lim_{x \to -\infty}y = -\infty\\ \lim_{x \to \infty}y = \infty

Step-by-step explanation:

Due to the fact that the degree of the polynomial is odd, we know one end must go up and the other down. Because the leading coefficient is even, we know that as x approaches negative infinity, y approaches negative infinity as well. As x approaches positive infinity, y approaches positive infinity.

8 0
3 years ago
3500∙(−2)∙(−5)
xeze [42]
3500*10= 35,000 the answer to the question
8 0
3 years ago
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