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Degger [83]
2 years ago
15

The base of a solid is bounded by x^2 + y^2 = 16. Cross sections perpendicular to the x-axis are right isosceles triangles with

one leg located in the base. Which definite integral represents the volume of this solid?

Mathematics
1 answer:
SVETLANKA909090 [29]2 years ago
4 0

The equation for the base is that of a circle, so the cross sections will have a leg of length equal to the vertical distance between its halves.

x² + y² = 16   ⇒   y = ±√(16 - x²)

⇒   length = √(16 - x²) - (-√(16 - x²)) = 2 √(16 - x²)

Cross sections with thickness ∆x have a volume of

1/2 length² ∆x = 1/2 (2 √(16 - x²))² ∆x = (32 - 2x²) ∆x

since they are isosceles triangles and so their bases and heights are equal.

Then the total volume would be (D)

\displaystyle \int_{-4}^4 \frac12 \left(2 \sqrt{16-x^2}\right)^2 \, dx

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5 0
3 years ago
Is 20 a prime or composite number.​
STALIN [3.7K]

Answer: It is a composite number since it has more factors than just itself and 1.

Step-by-step explanation:

1x20=20

2x10=20

4x5=20

6 0
3 years ago
Read 2 more answers
Misha deposited $3,725 into a savings account 22 years ago. The account has an interest rate of 2.2% and the balance is currentl
Annette [7]
The compounding equation is A=P(1+ \frac{r}{n}) ^{nt}. So
 
6012.37 = 3725(1+ \frac{0.022}{n}) ^{22n}    Divide by 3725

1.6141= (1+ \frac{0.022}{n}) ^{22n}

Daily      = (1+ \frac{0.022}{365}) ^{22*365}
              = (1.000060274) ^{8030}
              = 1.6225
Monthly  = (1+ \frac{0.022}{12}) ^{22*12}
              = (1.0018333) ^{264}
              = 1.6218
Quarter  = (1+ \frac{0.022}{4}) ^{22*4}
              = (1.0055) ^{88}
              = 1.6204
Yearly  = (1+ \frac{0.022}{1}) ^{22*1}
              = (1.022) ^{22}
              = 1.6141

The answer is yearly.





5 0
3 years ago
Need answers ASAP
andrew-mc [135]
Data:
r (radius) = 14 m
h (height) = 6 m
v (volume) = ?

Formula:
V =  \pi *r^2*h

Solving:
V = \pi *r^2*h
V =  \pi *14^2*6
V =  \pi *196*6
\boxed{\boxed{V = 1176 \pi\:m^3}}\end{array}}\qquad\quad\checkmark
4 0
3 years ago
Aiden owns a food truck that sells tacos and burritos. He sells each taco for $4.75 and each burrito for $7. Yesterday Aiden mad
nevsk [136]

Number of tacos sold is 65 and number of burritos sold is 40

<h3><u>Solution:</u></h3>

Given that Aiden sells each taco for $4.75 and each burrito for $7

Let the number of tacos sold be "t" and number of burritos sold be "b"

Given that Aiden sold 25 more tacos than burritos

t = b + 25 ---- eqn 1

Also given that yesterday Aiden made a total of $588.75 in revenue

number of tacos sold x cost of each tacos + number of burritos sold x cost of each burritos = 588.75

t \times 4.75 + b \times 7 = 588.75

4.75t + 7b = 588.75  ----- eqn 2

Substitute eqn 1 in eqn 2

4.75(b + 25) + 7b = 588.75

4.75b + 118.75 + 7b = 588.75

11.75b = 470

b = 40

Substitute b = 40 in eqn 1

t = 40 + 25

t = 65

Thus the number of tacos sold is 65 and number of burritos sold is 40

5 0
3 years ago
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