All categories

3 years ago

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

Mathematics

2 answers:

lara [203]3 years ago

8 0

Answer: A

Step-by-step explanation: Center (0,0)

Vertices (+/-8,0)

Foci (+/-6.2,0)

Ronch [10]3 years ago

4 0

Answer:

Step-by-step explanation:

Answer:

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

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)

You might be interested in

What is the multiplicative rate of change of the function

mario62 [17]

Answer: B $\frac{2}{3}$

Step-by-step explanation:

From the given table

When x changes from 1 to 2 , value of y changes from 6 to 4

The multiplicative rate of change= $\frac{4}{6}=\frac{2}{3}$

Similarly we can check

When x changes from 2 to 3 , value of y changes from 4 to $\frac{8}{3}$

The multiplicative rate of change= $\frac{\frac{8}{3}}{4}=\frac{2}{3}$

When x changes from 3 to 4 , value of y changes from $\frac{8}{3}$ to $\frac{16}{9}$

The multiplicative rate of change= $\frac{\frac{16}{9}}{\frac{8}{3}}=\frac{2}{3}$

Therefore, the multiplicative rate of exponential function = $\frac{2}{3}$

5 0

3 years ago

Read 2 more answers

A high school band asked a number of students whether they would like blue, gold, or both for the uniforms for the band. The res

Anna35 [415]

Given a Venn diagram showing the number of students that like blue uniform only as 32, the number of students that like gold uniform only as 25, the number of students that like blue and gold uniforms as 12 and the number of students that like neither blue nor gold uniform as 6.

Thus, the total number of students interviewed is 75.

Recall that relative frequency of an event is the outcome of the event divided by the total possible outcome of the experiment.

From the relative frequency table, a represent the relative frequency of the students that like gold but not blue.
From the Venn, diagram, the number of students that like gold uniform only as 25, thus the relative frequency of the students that like gold but not blue is given by
$\frac{25}{75} = \frac{1}{3}=0.33=33\%$

Therefore, a = 33% to the nearest percent.

Similarly, from the relative frequency table, b represent the relative frequency of the students that like blue but not gold.
From the Venn, diagram, the number of students that like blue uniform only as 32, thus the relative frequency of the students that like gold but not blue is given by
$\frac{32}{75} = 0.427=42.7\%$

Therefore, b = 43% to the nearest percent.

7 0

3 years ago

What is the solution to this equation? 4x+x-15+3-8=13

deff fn [24]

Answer:

x = 33/5

Step-by-step explanation:

4x+x-15+3-8=13

Combine like terms

5x -20 = 13

Add 20 to each side

5x-20+20 = 13+20

5x =33

Divide by 5

5x/5 = 33/5

x = 33/5

3 0

4 years ago

A square + b square + c square equal to ab+ba+ca show that

Evgen [1.6K]

Answer:

a² + b² + c² ≠ ab + bc + ca

<h3>PLEASE MARK ME BRAINLIEST.</h3>

5 0

3 years ago

Jakes elevation decreases 350 meteors as he rides his bike to the bottom of the hill he completes the ride in 5 equal stages how

andrew-mc [135]

Answer:

70 decreases each stage

Step-by-step explanation:

350 / 5 = 70 decreases each stage

Since all decreases are equal and in 5 stages:

decreases * stages = total decreases

70 * 5 = 350

3 0

3 years ago