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2 years ago

Verify the identity. tan (x + pi/2) = -cot x

1 answer:

5 0

$\tan\left(x+\dfrac\pi2\right)=\dfrac{\sin\left(x+\frac\pi2\right)}{\cos\left(x+\frac\pi2\right)}=\dfrac{\sin x\cos\frac\pi2+\cos x\sin\frac\pi2}{\cos x\cos\frac\pi2-\sin x\sin\frac\pi2}=\dfrac{\cos x}{-\sin x}=-\cot x$

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Answer:

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Step-by-step explanation:

You just have to divide then multiple by 100

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3 years ago

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Kelli is walking to raise money for a local shelter. A neighbor gives her $20. Her uncle donates $2 per kilometer. Write an equa

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2 years ago

Jim is trying to improve his speed on the track so he can qualify for the State Championships. As he is running, he goes from 70

kumpel [21]

Answer:

His acceleration is $\frac{1}{15}$ meters per seconds²

Step-by-step explanation:

Acceleration is the rate of change of the speed

The formula of acceleration is $a=\frac{v_{f}-v_{i}}{t}$ , where

$v_{f}$ is the final speed
$v_{i}$ is the initial speed
The unit of the acceleration is meters/second²

∵ Jim goes from 70 meters/minute (beginning speed) to

106 meters/minute (final speed) in 9 seconds

∴ His initial speed $v_{i}$ = 70 meters/minute

- Change it the meter per second

∵ 1 minute = 60 seconds

∴ $\frac{70}{(1)(60)}=\frac{70}{60}=\frac{7}{6}$ meters/second

∴ $v_{i}$ = $\frac{7}{6}$ meters/second

∵ His final speed $v_{f}$ = 106 meters/minute

- Change it the meter per second

∴ $\frac{106}{(1)(60)}=\frac{106}{60}=\frac{53}{30}$ meters/second

∴ $v_{f}$ = $\frac{53}{30}$ meters/second

∵ The time of the change of his speed is 9 seconds

∴ t = 9

∵ The formula of acceleration is $a=\frac{v_{f}-v_{i}}{t}$

- Substitute the values of t, $v_{i}$ and $v_{f}$ in the formula above

∴ $a=\frac{\frac{53}{30}-\frac{7}{6}}{9}=\frac{1}{15}$

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3 years ago

The Expression 4x^2-p(x)+7 leaves a remainder of -2 when divided by (x-3) find the value of p

Romashka-Z-Leto [24]

Answer:

(c) For p = 15, $4x^2-p(x)+7$ leaves a remainder of -2 when divided by (x-3).

Step-by-step explanation:

Here, The dividend expression is $4x^2-p(x)+7$ = E(x)

The Divisor = (x-3)

Remainder = -2

Now, by <u>REMAINDER THEOREM</u>:

Dividend = (Divisor x Quotient) + Remainder

If ( x -3 ) divides the given polynomial with a remainder -2.

⇒ x = 3 is a solution of given polynomial E(x) - (-2) =

$E(x) - (-2) = 4x^2-p(x)+7 -(-2) = 4x^2-p(x)+9$ = S(x)

Now, S(3) = 0

⇒ $4x^2-p(x)+9 = 4(3)^2 - p(3) + 9 = 0\\\implies 36 - 3p + 9 = 0\\\implies 45= 3p , \\or p =15$

or, p =1 5

Hence, for p = 15, $4x^2-p(x)+7$ leaves a remainder of -2 when divided by (x-3).

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2 years ago

A kitten was given to a child as a birthday present when she was two years old. The cat lived a good life, but eventually became

Katyanochek1 [597]

Answer: 14 years

Step-by-step explanation:

Let the cat's age when it died = x.

Therefore, the child's age is 2 + x because he/she got the cat when he/she was 2 years old.

We can set up an equation.

x + (2+x) = 30

2x + 2 = 30

2x = 28

Therefore, x = 14

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2 years ago

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