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notsponge [240]
2 years ago
3

Translate and solve: 51 more than y is greater than −204. Write your solution in interval notation.

Mathematics
2 answers:
Vlad1618 [11]2 years ago
7 0

Answer:

(-255, \infty)

S=\{y\in\mathbb{R}| y>-255 \}

Step-by-step explanation:

We have the inequality:

51+y>-204

y>-255

The interval is:

(-255, \infty)

antoniya [11.8K]2 years ago
6 0

Answer:

y > -255, or (-255, infinity)

Step-by-step explanation:

y + 51 > - 204

Solve for y:  subtract 51 from both sides, obtaining:

y > -255, or (-255, infinity)

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This can be solved using trigonometric functions. The distance x serves as one leg of a triangle, and makes an angle q with the hypotenuse. The distance from the tip of the rocket to the ground make up the other leg of the triangle. So solving this:

tan q = y / x

Where: y = distance from the tip of the rocket to the ground

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Simplify sin θ / square root 1 - sin^2 θ
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Recall that

\cos^2\theta+\sin^2\theta=1

which means

\dfrac{\sin\theta}{\sqrt{1-\sin^2\theta}}=\dfrac{\sin\theta}{\sqrt{\cos^2\theta}}

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\dfrac{\sin\theta}{\sqrt{1-\sin^2\theta}}=\dfrac{\sin\theta}{\cos\theta}=\tan\theta

or if it's negative,

\dfrac{\sin\theta}{\sqrt{1-\sin^2\theta}}=\dfrac{\sin\theta}{-\cos\theta}=-\tan\theta

7 0
2 years ago
A company makes wax candles in the shape of a solid sphere. Suppose each candle has a diameter of 15 cm. If
jekas [21]

We have been given that a company makes wax candles in the shape of a solid sphere. Each candle has a diameter of 15 cm. We are asked to find the number of candles that company can make from 70,650 cubic cm of wax.

To solve our given problem, we will divide total volume of wax by volume of one candle.

Volume of each candle will be equal to volume of sphere.

V=\frac{4}{3}\pi r^3, where r represents radius of sphere.

We know that radius is half the diameter, so radius of each candle will be \frac{15}{2}=7.5 cm.

\text{Volume of one candle}=\frac{4}{3}\cdot 3.14\cdot (7.5\text{ cm})^3

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Now we will divide 70,650 cubic cm of wax by volume of one candle.

\text{Number of candles}=\frac{70,650\text{ cm}^3}{1766.25\text{ cm}^3}

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8 0
2 years ago
7. If W = 3Z, and Z is 30% of R, then W is what
dem82 [27]

Answer:

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Since, Z = 30% of R

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7 0
2 years ago
One factor of the polynomial 2x^3 - 3x^2 - 3x + 2 is ( x - 2 ). Which expression represents the other factor, or factors, of the
Georgia [21]

Answer:

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2 |  2     -3       -3       2    

 

    <u>         4         2      -2          </u>

     2      1         -1        0

Therefore, other factor of the given polynomial is (2x² + x - 1)

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Option (D) will be the answer.

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2 years ago
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