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3 years ago

How do you find the radius of a cylinder when you only know the surface area?

1 answer:

7 0

The surface area of a cylinder with circular bases of radius r and height h is equal to the sum of the areas of the two circular faces and the area of the rectangular lateral surface:

A = 2πr² + 2πrh

If you know the height h, then you can solve the quadratic equation for r.

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Use a half-angle identity to find the exact value

Tatiana [17]

Given:

$\cos 15^{\circ}$

To find:

The exact value of cos 15°.

Solution:

$$\cos 15^{\circ}=\cos\frac{ 30^{\circ}}{2}$

Using half-angle identity:

$$\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos (x)}{2}}$

$$\cos \frac{30^{\circ}}{2}=\sqrt{\frac{1+\cos \left(30^{\circ}\right)}{2}}$

Using the trigonometric identity: $\cos \left(30^{\circ}\right)=\frac{\sqrt{3}}{2}$

$$=\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}$

Let us first solve the fraction in the numerator.

$$=\sqrt{\frac{\frac{2+\sqrt{3}}{2}}{2}}$

Using fraction rule: $\frac{\frac{a}{b} }{c}=\frac{a}{b \cdot c}$

$$=\sqrt{\frac {2+\sqrt{3}}{4}}$

Apply radical rule: $\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$

$$=\frac{\sqrt{2+\sqrt{3}}}{\sqrt{4}}$

Using $\sqrt{4} =2$ :

$$=\frac{\sqrt{2+\sqrt{3}}}{2}$

$$\cos 15^\circ=\frac{\sqrt{2+\sqrt{3}}}{2}$

5 0

3 years ago

Can someone pls help me? :)

erastova [34]

Step-by-step explanation:

1 t=16/21

2.m=2

3.n=13/7

4.a=2

5.x=6/17

6.x=15

7.s=21/4

8. t=7/3

9. s=1

10. s=6/61

11. x=1/3

12. r=27/16

13. c=−1

14.m=9/5n

15. j=−117/58

8 0

3 years ago

Plane A is descending toward the local airport, and plane B is ascending from the same airport. Plane A is descending at a rate

Bas_tet [7]

Answer: 2 minutes

Step-by-step explanation:

Given the following :

Plane A's descent :

y = -2,500x + 14,000

Plane B's Ascent :

y = 4,000x + 1,000

where y = altitude x = minute

Time to be at the same altitude :

Being at the same altitude means ;

Plane A's descent = Plane B's Ascent

-2,500x + 14,000 = 4,000x + 1,000

-2500x - 4000x = 1000 - 14000

-6500x = - 13000

x = 13000 / 6500

x = 2

x = 2minutes.

5 0

3 years ago

Find the greatest number that divides451, 328 and 673 leaving 1, 4 and 1,respectively as remainders.

Vesna [10]

You're looking for the largest number x such that

x ≡ 1 (mod 451)

x ≡ 4 (mod 328)

x ≡ 1 (mod 673)

Recall that

x ≡ a (mod m)

x ≡ b (mod n)

is solvable only when a ≡ b (mod gcd(m, n)). But this is not the case here; with m = 451 and n = 328, we have gcd(m, n) = 41, and clearly

1 ≡ 4 (mod 41)

is not true.

So there is no such number.

4 0

3 years ago

The population of current statistics students has ages with mean muμ and standard deviation sigmaσ. samples of statistics studen

Aleonysh [2.5K]

What does the central limit theorem tell us about the distribution of those mean ages?

A. Because n>30, the sampling dist of the mean ages can be approximated by a normal dist with a mean u and a SD o/sqrt 54,

Whenever n>30 the central limit theory applies.

6 0

3 years ago