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Rus_ich [418]
3 years ago
7

4. A horizontal ellipse, centered at the origin has a major axis of 10 units and minor axis of 8 units. Write the

Mathematics
1 answer:
s2008m [1.1K]3 years ago
5 0

Answer:

\frac{x^2}{25} +\frac{y^2}{16} =1

Step-by-step explanation:

For ellipses, the length of the major axis is represents as:

Major axis = 2a

where a is called the semi-major axis.

In this case since the major axis is equal to 10 units:

10=2a

solving for the semi-major axis a :

a=10/2\\a=5

and also the minor axis of an ellipse is represented as:

Minor axis = 2b

where b  is called the semi-minor axis.

Since the minor axis has a length of 8 units:

8=2b

solving for b:

b=8/2\\b=4

Now we can use the equation for an ellipse centered at the origin (0,0):

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

and substituting the values for a and b:

\frac{x^2}{5^2} +\frac{y^2}{4^2} =1

and finall we simplify the expression to get the equation of the ellipse:

\frac{x^2}{25} +\frac{y^2}{16} =1

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andriy [413]

Answer:

1. Steve's age is 18 and Anne's age is 8.

2. Max's age is 17 and Bert's age is 11.

3. Sury's age is 19 and Billy's age is 9.

4. The man's age is 30 and his son's age is 10.

Step-by-step explanation:

1. Let us assume that:

S = Steve's age now

A = Anne's age now

Therefore, in four years, we have:

S + 4 = (A + 4)2 - 2

S + 4 = 2A + 8 - 2

S + 4 = 2A + 6 .................. (1)

Three years ago, we have:

S - 3 = (A - 3)3

S - 3 = 3A - 9 ................................ (2)

From equation (2), we have:

S = 3A - 9 + 3

S = 3A – 6 …………. (3)

Substitute S from equation (3) into equation (1) and solve for A, we have:

3A – 6 + 4 = 2A + 6

3A – 2A = 6 + 6 – 4

A = 8

Substitute A = 8 into equation (3), we have:

S = (3 * 8) – 6

S = 24 – 6

S = 18

Therefore, Steve's age is 18 while Anne's age is 8.

2. Let us assume that:

M = Max's age now

B = Bert's age now

Therefore, five years ago, we have:

M - 5 = (B - 5)2

M - 5 = 2B - 10 .......................... (4)

A year from now, we have:

(M + 1) + (B + 1) = 30

M + 1 + B + 1 = 30

M + B + 2 = 30 .......................... (5)

From equation (5), we have:

M = 30 – 2 – B

M = 28 – B …………………… (6)

Substitute M from equation (6) into equation (4) and solve for B, we have:

28 – B – 5 = 2B – 10

28 – 5 + 10 = 2B + B

33 = 3B

B = 33 / 3

B = 11

Substituting B = 11 into equation (6), we have:

M = 28 – 11

M = 17

Therefore, Max's age is 17 while Bert's age is 11.

3. Let us assume that:

S = Sury's age now

B = Billy's age now

Therefore, now, we have:

S = B + 10 ................................ (7)

Next year, we have:

S + 1 = (B + 1)2

S + 1 = 2B + 2 .......................... (8)

Substituting S from equation (7) into equation (8) and solve for B, we have:

B + 10 + 1 = 2B + 2

10 + 1 – 2 = 2B – B

B = 9

Substituting B = 9 into equation (7), we have:

S = 9 + 10

S = 19

Therefore, Sury's age is 19 while Billy's age is 9.

4. Let us assume that:

M = The man's age now

S = His son's age now

Therefore, now, we have:

M = 3S ................................... (9)

Five years ago, we have:

M - 5 = (S - 5)5

M - 5 = 5S - 25 ................ (10)

Substituting M from equation (9) into equation (10) and solve for S, we have:

3S - 5 = 5S – 25

3S – 5S = - 25 + 5

-2S = - 20

S = -20 / -2

S = 10

Substituting S = 10 into equation (9), we have:

M = 3 * 10

M = 30

Therefore, the man's age is 30 and his son's age is 10.

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Simplify 9 to the power of 2 over 9 to the power of 7
coldgirl [10]

Answer:heya

Step-by-step explanation:

it is in the form... a raise to the power n / a raise to the power m = a raise to the power n-m..........

so 9 raise to the power 2/9 raise to the power 7= 9 raise to the power(2-7)

=9 raise to the power -5

=1/9 raise to the power 5

hope it helps

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