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svetoff [14.1K]
3 years ago
15

Find the standard equation for the ellipse, using the given characteristic or characteristics. vertices:(0,+-7) foci: (0,+-√33)

Mathematics
1 answer:
Alexxx [7]3 years ago
8 0

Answer:

=\frac{x^2}{16} +\frac{y^2}{49}=1

Step-by-step explanation:

The equation of this ellipse is

\frac{(x-h)^2}{b^2} +\frac{y-k)^2}{a^2} =1

for a vertical oriented ellipse where;

(h,k) is the center

c=distance from center to the foci

a=distance from center to the vertices

b=distance from center to the co-vertices

You know center of an ellipse is half way between the vertices , hence the center (h,k) of this ellipse is (0,0) and its is vertical oriented ellipse

Given that

a= distance between the center and the vertices, a=7

c=distance between the center and the foci, c=√33

Then find b

a^2-b^2=c^2\\\\b^2=a^2-c^2\\\\\\b^2=7^2-(\sqrt{33} )^2\\\\\\b^2=49-33=16\\\\\\b^2=16

The equation for the ellipse will be

\frac{(x-0)^2}{16} +\frac{(y-0)^2}{49} =1\\\\\\=\frac{x^2}{16} +\frac{y^2}{49} =1

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Answer:

180 sq.cm

Step-by-step explanation:

A = 10 x 10 + 16 x 5 x 1/2 x 2

A = 100 + 16 x 5

A = 100 + 80

A = 180 square cm

Hope that helps!

8 0
3 years ago
Read 2 more answers
EXPERTS AND ABOVE ONLY
yawa3891 [41]
1. This must be greater than or equal to 0 (there can't be any negatives!)
8 - .5t ≥ 0.
8 ≥ .5t 
t ≤ 16
D. 

2. 4(2x-1) = 2x + 35
8x - 4 = 2x + 35
6x = 39
x = 6.5
H.

3. c = .8(x-15) = .8x-12
A.

4. m = number of marble cupcakes
s = number of strawberry shortcake cupcakes

6m + 8.5s = 391
m = 1/2s
6(.5s)+8.5s = 391
11.5s = 391
s = 34
m = 17
F.

5. B
6. Use substitution
2x + 3x = 10
5x = 10
x = 2

7.  (sorry I'm not sure!)

8. G
9. L = number of balls
B = number of bats
L + B = 100
B = 100 - L
4.5L+20B = 822
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10. J

8 0
3 years ago
Which two ratios represent quantities that are proportional?
vesna_86 [32]

Answer:

B

Step-by-step explanation:

4 0
3 years ago
what is the product of 4x/x-1 and x^2-1/3x+3 expressed in simplest form? A. 4x/3, B.4x^2/3, C. 4x^2/3x(x+1), D. 4(x+1)/3​
zvonat [6]

Answer:

Step-by-step explanation:

7 0
3 years ago
An ice chest contains cans of apple juice, cans of grape juice, cans of orange juice, and cans of mango juice. Suppose that you
mel-nik [20]

Answer:

4.9%

Step-by-step explanation:

This question is incomplete. However; it can be found on search engines. The complete question is  as follows :

An ice chest contains cans of six apple juice, eight cans of grape juice, four cans of orange juice, and two cans of mango juice. Suppose that you reach into the container and randomly select three cans in succession. Find the probability of selecting three cans of grape juice.

Solution :

In an ice chest there are different cans of juice. Among them

Number of cans of apple juice = 6

Number of cans of grape juice = 8

Number of cans of orange juice = 4

Number of cans of mango juice = 2

Total number of cans of juice = 6 + 8 + 4 + 2 = 20

Let A, B and C are the event of selecting of three cans.  The events A, B and C are dependent.

Probability of selecting three cans of juice

P = \frac{\text{number of grape cans}}{\text {total number of cans}}

P (A) = \frac{8}{20}

P (B) = \frac{7}{19}

P (B) = \frac{6}{18}

P = \frac{8}{20} × \frac{7}{19} × \frac{6}{18}

  = \frac{336}{6840}

  = 0.049 or 4.9%

Probability of selecting three cans of grape juice is 4.9%

5 0
3 years ago
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