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2 years ago

10

The ratio of the heights of two similar solids is 6:11. Find the ratio of their surface areas.

1 answer:

vaieri [72.5K]2 years ago

8 0

Answer:

The ratio of surface areas is 36:121.

Step-by-step explanation:

We have, the ratio of the heights of two similar solids is 6:11. It is required to find the ratio of their surface areas. As the two solids are similar, it means that the ratio of surface areas of solids is directly proportional to the square of their heights such that,

$\dfrac{S_1}{S_2}=(\dfrac{h_1}{h_2})^2\\\\\dfrac{S_1}{S_2}=(\dfrac{6}{11})^2\\\\\dfrac{S_1}{S_2}=\dfrac{36}{121}$

So, the ratio of surface areas is 36:121.

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The ellipse with x-intercepts (2, 0) and (-2, 0); y-intercepts (0, 4) and (0, -4).

masya89 [10]

Answer:

$\dfrac{x^2}{4}+\dfrac{y^2}{16}=1$

Step-by-step explanation:

If the ellipse has its x-intercepts at points (2, 0) and (-2, 0) and y-intercepts at points (0, 4) and (0, -4), then its symmetric across the y-axis and across the x-axis.

Moreover,

$a=2\\ \\b=4$

The equation of such ellipse is

$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$

Hence, the equation of the ellipse is

$\dfrac{x^2}{2^2}+\dfrac{y^2}{4^2}=1\\ \\ \\\dfrac{x^2}{4}+\dfrac{y^2}{16}=1$

3 0

2 years ago

Kelly plans to put her graduation money into an account and leave it there for 4 years while she goes to college. she recieves $

Firlakuza [10]

Answer:

C) $877.50

Step-by-step explanation:

Time t = 4 years

Principal, p = $750

rate, r = 4.25% = 0.0425

Amount that will be in her account in four years =

Simple interest (prt/100) + principal

750 * 4.25* 4 / 100 + 750

127.5 + 750

= $877.50

7 0

2 years ago

A(0, 1), B(4,1), C(1, 2), D(1,6): AB and CD

Ivanshal [37]

The answer is D because I took the test

8 0

2 years ago

25 POINTS AVAILABLE

myrzilka [38]

Answer:

$\large\boxed{1.\ (-3, 0),\ r = 3}\\\boxed{2.\ (x+4)^2+(y-3)^2=36}\\\boxed{3.\ (x-2)^2+(y-1)^2=(\sqrt{34})^2}$

Step-by-step explanation:

The equation of a circle in standard form:

$(x-h)^2+(y-k)^2=r^2$

(h, k) - center

r - radius

1. We have the equation:

$(x+3)^2+y^2=9\\\\(x-(-3))^2+(y-0)^2=3^2$

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2. We have the center (-4, 3) and the radius r = 6. Substitute:

$(x-(-4))^2+(y-3)^2=6^2\\\\(x+4)^2+(y-3)^2=36$

3. We have the endpoints of the diameter: (-1, 6) and (5, -4).

Midpoint of diameter is a center of a circle.

The formula of a midpoint:

$\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)$

Substitute:

$h=\dfrac{-1+5}{2}=\dfrac{4}{2}=2\\\\k=\dfrac{6+(-4)}{2}=\dfrac{2}{2}=1$

The center is in (2, 1).

The radius length is equal to the distance between the center of the circle and the endpoint of the diameter.

The formula of a distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substitute the coordinates of the points (2, 1) and (5, -4):

$r=\sqrt{(5-2)^2+(-4-1)^2}=\sqrt{3^2+(-5)^2}=\sqrt{9+25}=\sqrt{34}$

Finally we have:

$(x-2)^2+(y-1)^2=(\sqrt{34})^2$

7 0

2 years ago

I need help on this question!

agasfer [191]

Answer:

I think its 1234.

sorry if im wrong

4 0

2 years ago

Read 2 more answers