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2 years ago

In the figure above, arc RST measures 30°

Mathematics

1 answer:

Ivenika [448]2 years ago

8 0

My brain just says this I not sure if it’s right or not but I think it’s C

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A candle in the shape of a circular cone has a base of radius r and a height of h that is the same length as the radius. which e

ladessa [460]

Answer:

$\frac{r(1-\sqrt{2})}{-3}$

Step-by-step explanation:

Volume of cone = $\frac{1}{3} \pi r^{2} h$

Since we are given that a circular cone has a base of radius r and a height of h that is the same length as the radius

= $\frac{1}{3} \pi r^{2} \times r$

= $\frac{1}{3} \pi r^{3}$

Surface area of cone including 1 base = $\pi r^{2} +\pi\times r \times \sqrt{r^2+h^2}$

Since r = h

So, area = $\pi r^{2} +\pi\times r \times \sqrt{r^2+r^2}$

= $\pi r^{2} +\pi\times r \times \sqrt{2r^2}$

= $\pi r^{2} +\pi\times r^2 \times \sqrt{2}$

Ratio of volume of cone to its surface area including base :

$\frac{\frac{1}{3} \pi r^{3}}{\pi r^{2} +\pi\times r^2 \times \sqrt{2}}$

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

$\frac{r}{3(1+\sqrt{2})}$

Rationalizing

$\frac{r}{3(1+\sqrt{2})} \times \frac{1-\sqrt{2}}{1-\sqrt{2}}$

$\frac{r(1-\sqrt{2})}{-3}$

Hence the ratio the ratio of the volume of the candle to its surface area(including the base) is $\frac{r(1-\sqrt{2})}{-3}$

8 0

2 years ago

Read 2 more answers

Use the factor theorem to determine whether the first polynomial is a factor of the second polynomial

Diano4ka-milaya [45]

Answer:

not a factor

Step-by-step explanation:

If (x - 3) is a factor then f(3) = 0

f(x) = 2x² - 4x + 30

f(3) = 2(3)² - 4(3) + 30 = 18 - 12 + 30 = 36 ≠ 0

Since f(3) ≠ 0 then (x - 3) is not a factor of f(x)

3 0

2 years ago

Use the unit circle to find the inverse function value in degrees.<br> tan^-1 sqrt 3

mr Goodwill [35]

Use the unit circle to find the inverse function value in degrees.tan^-1 sqrt 3

The correct answer would be 60 degrees. Since you are asked to find an angle that the tangent is equal to sqrt 3. The only angle that is equal to that given the interval is 60 degrees. So that is the correct answer. I hope this answer helped you.

7 0

2 years ago

What is the center and radius of a circle whose equation is x2 + y2 -2x -6y -5 = 0?

ddd [48]

x²+y²-2x-6y-5=0

x²-2x+y²-6y=5

x²-2x+1+y²-6y+9=5+1+9

(x-1)²+(y-3)²=15

(x-1)²+(y-3)²=(V15)²

-> centre of the circle: C(-1,-3)

-> radius of the circle: V15

4 0

1 year ago

How do you draw a line for this

m_a_m_a [10]

I'd do a little more than 77minutes for the 6and 7for if you could have it on 77and but you could have it in your head

8 0

2 years ago

Read 2 more answers