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VMariaS [17]
3 years ago
10

Rafael can run 5 laps around the track in 16 minutes. If he runs at the same rate, which of the following proportions can be use

d to find the number of minutes, m, it takes him to run 20 laps?
A) 25/16=20/m
B) 5/20=m/16
C) 5/16=m/20
D) 5/16=20/m
Mathematics
1 answer:
kari74 [83]3 years ago
3 0
The best answer is D) 5/16=20/m
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You are parasailing for the first time. The rope that connects you to the boat is 38 feet long. The distance along the water bet
Xelga [282]

Answer:

About 30.98386677 ft above the water.

Step-by-step explanation:

Use pythagorean theorem, a^2+b^2=c^2.

So when you plug in the numbers it would be x^2+22^2=38^2. Move 22^2 to the right side giving you x^2=38^2-22^2. Then subtract and take the square root of x^2.

5 0
2 years ago
Suppose a and b are both non zero real numbers. Find real numbers c and d such that 1/a+ib= c+id
Thepotemich [5.8K]

\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}

Explanation

\frac{1}{a+bi}=c+di

Step 1

multiplicate by the conjugate

\begin{gathered} \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(bi)^2} \\ \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(-b^2)}=\frac{a-bi}{a^2+b^2} \end{gathered}

notice that

\begin{gathered} \frac{1}{a+bi}=\frac{a-bi}{a^2+b^2}=\frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i \\ \frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i=c+di \\ so \\  \end{gathered}\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}

I hope this helsp you

6 0
1 year ago
How to find the hypotenuse of a right angled triangle using trigonometry?
Ghella [55]
It depends on whether you have "Perpendicular" or "base"
If you have perpendicular then, you can use the formula:
sin Ф = P / H

If you have base then, you can use the formula:
cos Ф = B/ H

Hope this helps!
4 0
3 years ago
Which equation represents a proportional relationship?
asambeis [7]

Given:

Four equations in the options.

To find:

The equation which represents a proportional relationship.

Solution:

If y is proportional to x, then

y\propto x

y=kx

where, k is the constant of proportionality.

In this case if x=0, then y=0. It means the graph of a proportional relationship passes through the origin.

From the given options, only option B, i.e., y=\dfrac{1}{4}x, is of the y=kx, where, k=\dfrac{1}{4}.

So, the equation y=\dfrac{1}{4}x represents a proportional relationship.

Therefore, the correct option is B.

6 0
3 years ago
(08.01 MC)
Juli2301 [7.4K]

Answer:

d. 27 cubic feet

Step-by-step explanation:

volume of cube = s^3 = B * s

volume of pyramid = (1/3) * B * h

The volume of a pyramid is 1/3 of the area of the base multiplied by the height. The volume of a cube is the area of the base multiplied by the height. Since the volume of a pyramid has the fraction 1/3 and the volume of the cube does not, then the volume of a cube is 3 times greater than the volume of a pyramid that fits inside and has the same base area.

volume of pyramid = 9 cu ft

volume of cube = 3 * 9 cu ft = 27 cu ft

Answer: d. 27 cubic feet

4 0
3 years ago
Read 2 more answers
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