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1 year ago

Which expression gives the length of the transverse axis of the hyperbola

Mathematics

1 answer:

klio [65]1 year ago

7 0

Answer:

Option (B)

Step-by-step explanation:

From the picture attached,

F1 and F2 are the focii of the hyperbola.

Point P(x, y) is x units distant from F1 and y units distant from the other focus F2.

By the definition of a hyperbola,

"Difference between the distances of a point from the focii is always constant and equals to the measure of transverse axis."

Difference in the distances of point P from focii F1 and F2 = (x - y) units

This distance is equal to the length of the transverse axis = (x - y) units

Therefore, Option (B) will be the answer.

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If cos Θ = square root 2 over 2 and 3 pi over 2 < Θ < 2π, what are the values of sin Θ and tan Θ?

KIM [24]

Answer:

The answer is

$sin(\theta)=-\frac{\sqrt{2}}{2}$

$tan(\theta)=-1$

Step-by-step explanation:

we know that

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

$sin^{2}(\theta)+cos^{2}(\theta)=1$

In this problem we have

$cos(\theta)=\frac{\sqrt{2}}{2}$

$\frac{3\pi}{2}$

The angle $\theta$ belong to the third or fourth quadrant

The value of $sin(\theta)$ is negative

Step 1

Find the value of $sin(\theta)$

Remember

$sin^{2}(\theta)+cos^{2}(\theta)=1$

we have

$cos(\theta)=\frac{\sqrt{2}}{2}$

substitute

$sin^{2}(\theta)+(\frac{\sqrt{2}}{2})^{2}=1$

$sin^{2}(\theta)=1-\frac{1}{2}$

$sin^{2}(\theta)=\frac{1}{2}$

$sin(\theta)=-\frac{\sqrt{2}}{2}$ ------> remember that the value is negative

Step 2

Find the value of $tan(\theta)$

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

we have

$sin(\theta)=-\frac{\sqrt{2}}{2}$

$cos(\theta)=\frac{\sqrt{2}}{2}$

substitute

$tan(\theta)=\frac{-\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}$

$tan(\theta)=-1$

8 0

2 years ago

Read 2 more answers

A rectangular field is enclosed by 360 feet of fencing. What is the length, in feet, of the field if it’s length is 6 feet more

Orlov [11]

Answer:

The Field's length is 93ft

Step-by-step explanation:

P=2L+2w

360=2(w+6)+2w

360=2w+12+2w

360=4w+12

348=4w

348/4=w

87=w

L=w+6

L=87+6

L=93

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2 years ago

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klemol [59]

Independent variable. It is also called abscissa.

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1 year ago

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Solve for m:<br> -3(1 – 5m) = — 38 + 8m

Solnce55 [7]

Answer:

m = - 5

Step-by-step Explanation:

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1 year ago

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Suppose x follows a continuous uniform distribution from 1 to 5. determine the conditional probability p(x >2.5 | x ≤ 4).

Rainbow [258]

Because the random variable x follows a continuous uniform distribution from x=1 to x=5, therefore
p(x) = 1/4, x=[1, 5]
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Answer: 0.375

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2 years ago