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tekilochka [14]
3 years ago
6

What is the measure of x?

Mathematics
1 answer:
bogdanovich [222]3 years ago
8 0

Answer:

22

Step-by-step explanation:

This is a right angle so the sum of those would be equal to 90 degrees

x + 7 + 3x - 5 = 90 add like terms

4x + 2 = 90 subtract 2 from both sides

4x = 88 divide both sides by 4

x = 22

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In a circus performance, a monkey is strapped to a sled and both are given an initial speed of 3.0 m/s up a 22.0° inclined track
Aloiza [94]

Answer:

Approximately 0.31\; \rm m, assuming that g = 9.81\; \rm N \cdot kg^{-1}.

Step-by-step explanation:

Initial kinetic energy of the sled and its passenger:

\begin{aligned}\text{KE} &= \frac{1}{2}\, m \cdot v^{2} \\ &= \frac{1}{2} \times 14\; \rm kg \times (3.0\; \rm m\cdot s^{-1})^{2} \\ &= 63\; \rm J\end{aligned} .

Weight of the slide:

\begin{aligned}W &= m \cdot g \\ &= 14\; \rm kg \times 9.81\; \rm N \cdot kg^{-1} \\ &\approx 137\; \rm N\end{aligned}.

Normal force between the sled and the slope:

\begin{aligned}F_{\rm N} &= W\cdot  \cos(22^{\circ}) \\ &\approx 137\; \rm N \times \cos(22^{\circ}) \\ &\approx 127\; \rm N\end{aligned}.

Calculate the kinetic friction between the sled and the slope:

\begin{aligned} f &= \mu_{k} \cdot F_{\rm N} \\ &\approx 0.20\times 127\; \rm N \\ &\approx 25.5\; \rm N\end{aligned}.

Assume that the sled and its passenger has reached a height of h meters relative to the base of the slope.

Gain in gravitational potential energy:

\begin{aligned}\text{GPE} &= m \cdot g \cdot (h\; {\rm m}) \\ &\approx 14\; {\rm kg} \times 9.81\; {\rm N \cdot kg^{-1}} \times h\; {\rm m} \\ & \approx (137\, h)\; {\rm J} \end{aligned}.

Distance travelled along the slope:

\begin{aligned}x &= \frac{h}{\sin(22^{\circ})} \\ &\approx \frac{h\; \rm m}{0.375}\end{aligned}.

The energy lost to friction (same as the opposite of the amount of work that friction did on this sled) would be:

\begin{aligned} & - (-x)\, f \\ = \; & x \cdot f \\ \approx \; & \frac{h\; {\rm m}}{0.375}\times 25.5\; {\rm N} \\ \approx\; & (68.1\, h)\; {\rm J}\end{aligned}.

In other words, the sled and its passenger would have lost (approximately) ((137 + 68.1)\, h)\; {\rm J} of energy when it is at a height of h\; {\rm m}.

The initial amount of energy that the sled and its passenger possessed was \text{KE} = 63\; {\rm J}. All that much energy would have been converted when the sled is at its maximum height. Therefore, when h\; {\rm m} is the maximum height of the sled, the following equation would hold.

((137 + 68.1)\, h)\; {\rm J} = 63\; {\rm J}.

Solve for h:

(137 + 68.1)\, h = 63.

\begin{aligned} h &= \frac{63}{137 + 68.1} \approx 0.31\; \rm m\end{aligned}.

Therefore, the maximum height that this sled would reach would be approximately 0.31\; \rm m.

7 0
3 years ago
COMMON CORE REVIEW
masha68 [24]

Answer:

146.9

Step-by-step explanation:

I'm not sure of the answer but if I'm wrong tell me I'll continue trying it is a pleasure to help you.

7 0
3 years ago
3. The box-and-whisker plot below shows the heights,in inches, of the students in a 7th grade class.What percentage of the heigh
Fantom [35]
(3) 62.5% cuz u take the total number of the students and u divide it by the number of students between 60 to 65
7 0
3 years ago
What is the volume of a rectangular prism with a length of 7m, a hight of 9m and a width of 11m
vazorg [7]
Hello!

To find the Volume of the Rectangular Prism, you'll need to multiply all of the measurements together. So you'll need to multiply 7, 9, and 11 together.

V=7*9*11

First, you'll need to multiply 7 and 9. Once you've multiplied 9 and 7 together, you should have 63. Now you should multiply 63 and 11 together. Once you've multiplied 63 and 11 together, you should have a Volume of 693

You should have a Volume of 693m³

I hope this helps!
5 0
3 years ago
Does anyone know???!
jok3333 [9.3K]

Answer:

#8 might be y= -3x + 5

Step-by-step explanation:

This may help

5 0
3 years ago
Read 2 more answers
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