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3 years ago

Write an inequality for the given statement: The sum of x and 25 is less than 75.

1 answer:

4 0

That statement would be best express by " x + 25 < 75 ". Since the statement says the sum of x and 25, thus, it will be x + 25. Then it also states that the sum is less than 75, so the best expression would be " < 75".

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Find the value of tan(sin^-1(1/2))

suter [353]

If you know that $\sin\dfrac\pi3=\dfrac12$ , then you know right away

$\tan\left(\sin^{-1}\dfrac12\right)=\tan\dfrac\pi3=\dfrac1{\sqrt}3=\dfrac{\sqrt3}3$

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Otherwise, you can derive the same result. Let $\theta=\sin^{-1}\dfrac12$ , so that $\sin\theta=\dfrac12$ . $\sin^{-1}$ is bounded, so we know $-\dfrac\pi2\le\theta\le\dfrac\pi2$ . For these values of $\theta$ , we always have $\cos\theta\ge0$ .

So, recalling the Pythagorean theorem, we find

$\cos^2\theta+\sin^2\theta=1\implies\cos\theta=\sqrt{1-\sin^2\theta}=\sqrt{1-\left(\dfrac12\right)^2}=\dfrac{\sqrt3}2$

Then

$\tan\theta=\tan\left(\sin^{-1}\dfrac12\right)=\dfrac{\sin\theta}{\cos\theta}=\dfrac{\frac12}{\frac{\sqrt3}2}=\dfrac1{\sqrt3}=\dfrac{\sqrt3}3$

as expected.

5 0

3 years ago

Read 2 more answers

What functions have a range of {y £ R | -

Fudgin [204]

Answer:

the second and the fourth have a range of real no

4 0

2 years ago

-2

zloy xaker [14]

Answer is

gradient=change in y/change in X

(10--2)/(4--2)=2

7 0

3 years ago

The number of E.coli bacteria cells in a pond of stagnant water can be represented by the function below, where A represents the

liq [111]

Answer:

Option B. 59%

Explanation:

The function that represents the number of E.coli bacteria cells per 100 mL of water as the time t years elapses is:

$A(t)=136(1.123)^{4t}$

The base, 1.123, represents the multiplicative constant rate of change of the function, so you just must substitute 1 for t in the power part of the function:

$rate=(1.123)^{4t}=(1.123)^4=1.590$

Then, the multiplicative rate of change is 1.590, which means that every year the number of E.coli bacteria cells per 100 mL of water increases by a factor of 1.590, and that is 1.59 - 1 = 0.590 or 59% increase.

8 0

3 years ago

Comparing Fractions Choose the correct symbol to compare the fractions please see attached image

Elza [17]

Answer:

Step-by-step explanation:

Given: $\frac{1}{2} ? \frac{1}{3}$