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3 years ago

Which equation represents a hyperbola with a center at (0, 0), a vertex at (−48, 0), and a focus at (50, 0)?

2 answers:

8 0

<span>The center, vertex, and focus all lie on the line y = 0. Then we know that the equation of a hyperbola is a^2 + b^2 = c^2 . a^2 represents the x part of the equation and the y part will be subtracted. We know that the vertex is 48 units from the center and that the focus is 50 units from the center. Then we have that b^2 = 2500 - 2304 = 196 . Thus the equation that represents the hyperbola is x^2/2304 - y^2/196 = 1 or 49x^2 -576y^2 - 112896 = 0</span>

KiRa [710]3 years ago

8 0

Its B im sure. i just took the test

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Kitty [74]

a. The volume of prism 1 is 8346.562 ft³

b. The surface area of the white eraser is 13 cm²

The question has to do with scale factor

<h3>What is scale factor?</h3>

Scale factor is the ratio of two similar quantities

<h3>a. How to find the volume of Prism 1.</h3>

Since

Prism 1 has a surface area of A = 289 ft² and
Prism 2 has a surface area of A' = 529 ft².

Let

L be the length of side of prism 1 and
L' the length of side of prism 2

We have that scale factor = A/A'

Also,

A/A' = (L/L')²

L/L = √(A/A') = √( 289 ft²/ 529 ft²) = √0.49 = 0.7

Since

prism 1 has a volume of V and
prism 2 has a volume of V' = 24334 ft³. We have that

V/V' = (L/L')³

So, V = (L/L')³V'

So, substituting the values of the variables into the equation, we have

V = (L/L')³V'

V = (0.7)³24334 ft³

V = 0.343 × 24334 ft³

V = 8346.562 ft³

So, the volume of prism 1 is 8346.562 ft³

<h3>b. How to find the surface area of the white eraser?.</h3>

Since

The white eraser has volume of V = 2 cm³ and
The yellow eraser has volume of V' = 16 cm³.

Let

L be the length of side of white eraser and
L' the length of side of yellow eraser

We have that scale factor = V/V'

Also, V/V' = (L/L')³

L/L = ∛(V/V')

= ∛( 2 cm³/16 cm³)

= ∛(1/8)

= 1/2

Since

White eraser has a surface area of A and
Yellow eraser has a surface area of A = 52 cm² . We have that

A/A' = (L/L')²

So, A = (L/L')²A'

So, substituting the values of the variables into the equation, we have

A = (L/L')²A'

A = (1/2)²52 cm²

A = 1/4 × 52 cm²

A = 13 cm²

So, the surface area of the white eraser is 13 cm²

Learn more about scale factor and surface area here:

brainly.com/question/26161002

#SPJ1

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