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Bess [88]
3 years ago
5

Multiple Choice

Mathematics
2 answers:
Lesechka [4]3 years ago
7 0

Answer:

c-b

Step-by-step explanation:

Rainbow [258]3 years ago
3 0
Thirty over eighty and six over eighteen
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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
2 years ago
Which value is equivalent to cos 10°?<br> sin 30°<br> O sin 25°<br> O sin 70°<br> O sin 80°
Sauron [17]

Answer:

13

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Common factor and HCF of 10m squared,15mk​
Anton [14]

Answer:

Step-by-step explanation:

10m^2 and 15mk

common factor is 5m

HCF is 5m

5 0
3 years ago
In the diagram below,AB is the diameter of the circle with centre P.Point C lies on the y-axis.Given the coordinates of A and B
Step2247 [10]

Answer:

<em>The coordinates of P are (-2,0)</em>

<em>The radius of the circle is 5.</em>

Step-by-step explanation:

<u>Analytic geometry</u>

The diagram shows a circle with center P, and two points A(-6,3) and B(2,-3) that form the diameter of the circle.

a)

The center of the circle lies at the midpoint of A and B. The midpoint (xm,ym) can be calculated by:

\displaystyle x_m=\frac{x_1+x_2}{2}

\displaystyle y_m=\frac{y_1+y_2}{2}

Substituting x1=-6, x2=2, y1=3, y2=-3:

\displaystyle x_m=\frac{-6+2}{2}=\frac{-4}{2}=-2

\displaystyle y_m=\frac{3-3}{2}=0

Thus, the coordinates of P are (-2,0)

b) The radius of the circle is the distance from the center to any point in its circumference. We can use the distance from P to A or B indistinctly.

Given two points A(x1,y1) and P(x2,y2), the distance between them is:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Substituting x1=-6, x2=-2, y1=3, y2=0:

r=\sqrt{(-2+6)^2+(0-3)^2}

r=\sqrt{4^2+(-3)^2}

r=\sqrt{16+9}=\sqrt{25}=5

The radius of the circle is 5.

4 0
3 years ago
Name a value for x that will complete the inequality that is shown. Then, explain why the value makes the inequality true.
Alex17521 [72]
<h3>Answer:    0.157</h3>

========================================================

Explanation:

Convert the fraction 9/50 to decimal form. You can use either long division or a calculator.

You should find that 9/50 = 0.18 which is the same as 0.180

So the original compound inequality is the same as saying 0.125 < x < 0.180

This tells us that x is between 0.125 and 0.180 where x is not equal to either endpoint. We simply need to pick anything in this interval. It can be anything you want (I recommend to use a number line to help pick a value). One such value is 0.157. There are infinitely many values you can select from.

The number 0.157 is between 0.125 and 0.180, ie  0.125 < 0.157 < 0.180

It's very similar to saying 157 is between 125 and 180, ie 125 < 157 < 180.

7 0
3 years ago
Read 2 more answers
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