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Tanzania [10]
3 years ago
9

Find the center, vertices, and foci for the ellipse 25x^2 + 64y^2 = 1600

Mathematics
1 answer:
Alisiya [41]3 years ago
7 0

Answer:

The answer to your question is below

Step-by-step explanation:

Data

Equation               25x² + 64y² = 1600

Process

1.- Divide all the equation by 1600

                             25x²/1600 + 64y²/ 1600 = 1600/1600

-Simplify

                              x²/64 + y²/ 25 = 1

2.- Equation of a horizontal ellipse

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

3.- Find a, b and c

    a² = 64             a = 8

    b² = 25             b = 5

-Calculate c with the Pythagorean theorem

                   a² = b² + c²

-Solve for c

                   c² = a² - b²

-Substitution

                   c² = 8² - 5²

-Simplification

                  c² = 64 - 25

                  c² = 39

-Result

                  c = √13

4.- Find the center

          C = (0, 0)

5.- Find the vertices

          V1 = (-8, 0)     V2 = (8, 0)

6.- Find the foci

          F1 = (-√13, 0)   F2 = (√13, 0)

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Using interval notation, the domain off is [- 3, 5] and the domain of g is [- 2, 7] . On what domain is f defined
Scorpion4ik [409]

Note: I am assuming you mean ''on what domain is f+g is defined''.

Answer:

We conclude that

  • Dom(f+g) = [-2, 5]

Step-by-step explanation:

Given the domain of f

[-3, 5]

Given the domain of g

[-2, 7]

  • The domain of a composition f+g would include the intersection of both domains.

In other words, the domain of a composition f+g includes all the inputs of x-values that are in the domain of both functions i.e. f and g.

so

Domain of f = [-3, 5]

The x-values lie in the domain of f interval are:

x = -3, -2, 1, 0, 1, 2, 3, 4, 5

Domain of g = [-2, 7]

The x-values lie in the domain of g interval are:

x = -2, 1, 0, 1, 2, 3, 4, 5, 6, 7

Therefore, the common x-values in both f and g would be:

-2, 1, 0, 1, 2, 3, 4, 5

Thus, we conclude that

  • Dom(f+g) = [-2, 5]
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3 years ago
the area of the surface of the swimming pool is 210 feet . what is the length d of the deep end ( in feets )?
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Step-by-step explanation:

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X<br> For f(x)=0.01(2) , find the average rate of change from x=3 to x=8.
NikAS [45]
  • Answer:

Option b. 0.496

  • Step-by-step explanation:

we know that

f(x)=0.01(2^{x})

The average rate of change is equal to

\frac{f(b)-f(a)}{b-a}

where

a=3

b=8

f(a)=f(3)=0.01(2^{3})=0.08

f(b)=f(8)=0.01(2^{8})=2.56

Substitute

\frac{2.56-0.08}{8-3}

\frac{2.48}{5}

0.496

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2 years ago
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