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3 years ago

Solve the equation for t. (t-7)^2+18=9

Mathematics

1 answer:

Anika [276]3 years ago

4 0

Answer:

t = 7 + 3i

Step-by-step explanation:

(t-7)^2 + 18 = 9

(t-7)^2 = 9 - 18

(t-7)^2 = -9

(t-7) = sqrt(-9) = |3| sqrt(-1)

t = 7 + 3i

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identify all of the central angles. please help me asap. i have to have this done soon! :( thann you so much!

vova2212 [387]

Answer:

see explanation

Step-by-step explanation:

Central angles are angles at the centre of the circle subtended by 2 radii

Angles that meet this criteria are

∠AOB, ∠BOC, ∠AOC

8 0

3 years ago

Which expression is equivalent to -9-(-4 1/3)

qaws [65]

Note that two negatives = one positive

- (-4 1/3) = + 4 1/3

Subtract

-9 + 4 1/3 = -4 2/3

-4 2/3 is your answer

hope this helps

3 0

4 years ago

If an object is dropped from a height of 144 feet, the function h(t)=-16t^2+144 gives the height of the object after t seconds.

shtirl [24]

Answer:

A. 3s

Step-by-step explanation:

The height of the object after t seconds is given by:

$h(t) = -16t^2 + 144$

When will the object hit the ground?

It hits the ground after t seconds, and t is found when $h(t) = 0$ . So

$h(t) = -16t^2 + 144$

$0 = -16t^2 + 144$

$16t^2 = 144$

$t^2 = \frac{144}{16}$

$t^2 = 9$

$t = \sqrt{9}$

$t = 3$

3 seconds, so the correct answer is given by option a.

5 0

3 years ago

Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.47 and a standard deviation of 1.5. U

alex41 [277]

Answer:

2.5% of American women have shoe sizes that are greater than 11.47.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 8.47

Standard deviation = 1.5

The normal distribution is symmetric, which means that half the measures are below the mean, and half are above the mean.

What percentage of American women have shoe sizes that are greater than 11.47?

11.47 = 8.47 + 2*1.5

This means that 11.47 is two standard deviations above the mean.

Of those measures below the mean, none are greater than 11.47.

Of those measures above the mean, 95% are between the mean and 11.47, and 5% are above. So

0.5*0.05 = 0.025

2.5% of American women have shoe sizes that are greater than 11.47.

8 0

3 years ago

I need to get the left side to equal the right side. Keeping the right side alone and not changing it.

likoan [24]

<u>To prove the trigonometric equation:</u>

$\sin ^{3} x+\cos ^{3} x=(\sin x+\cos x)(1-\sin x \cos x)$

$RHS=(\sin x+\cos x)(1-\sin x \cos x)$

We know that $\sin^2x +\cos^2x=1$ , substitute this in place of 1.

$=(\sin x+\cos x)(\sin^2x +\cos^2x-\sin x \cos x)$

Multiply each term of the first term with each term of the 2nd term.

$=\sin^3x + \sin x \cos^2x-\sin^2 x \cos x+\cos x \sin^2 x + \cos^3 x-\sin x\cos^2 x$

Group like terms together.

$=\sin^3x +( \sin x \cos^2x-\sin x\cos^2 x)+(\cos x \sin^2 x-\sin^2 x \cos x) + \cos^3 x$

$=\sin^3x +( 0)+(0) + \cos^3 x$

$=\sin^3x + \cos^3 x$

= LHS

RHS = LHS

$\sin ^{3} x+\cos ^{3} x=(\sin x+\cos x)(1-\sin x \cos x)$

Hence proved.

7 0

4 years ago