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3 years ago

What is the value of x? Enter your answer in the box. x = [ ]

Mathematics

1 answer:

zhenek [66]3 years ago

4 0

<h2>Answer:</h2>

Since both angles are vertical angles, we need to set them equal to each other.

$2(x + 10) = 3x - 30\\\\2x + 20 = 3x - 30\\\\5x + 20 = 30\\\\5x = 50\\\\x = 10$

The final answer is <em>x = 10</em>.

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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

Question 9 of 10

Aleks04 [339]

Answer:

A is the answer

// x = -2(y + 3)2-1

4 0

2 years ago

4/5 divided 8/7 HELP ASAP !!!

Leno4ka [110]

Answer:

7/10

Step-by-step explanation:

You can either use a calculator, or make both fractions have the denominator of 35 and change the two fractions to be,

$\frac{28}{35}$ and $\frac{40}{35}$ then divide.

Hope that helps and have a great day!

6 0

3 years ago

Read 2 more answers

Please help this is due in about three minutes

mihalych1998 [28]

Answer:

13) Constant

14) Variable

15) Coefficient

16) Exponent

6 0

3 years ago

Assume that you assign the following subjective probabilities for your final grade in your econometrics course (the standard GPA

rodikova [14]

Answer:

$E(X) = 4*0.2 +3*0.5+ 2*0.2 +1*0.8+ 0*0.02= 2.78$

So then the best answer for this case would be:

C. 2.78

Step-by-step explanation:

For this case we have the following probabability distribution function given:

Score P(X)

A= 4.0 0.2

B= 3.0 0.5

C= 2.0 0.2

D= 1.0 0.08

F= 0.0 0.02

______________

Total 1.00

The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.

If we use the definition of expected value given by:

$E(X) = \sum_{i=1}^n X_i P(X_I)$

And if we replace the values that we have we got:

$E(X) = 4*0.2 +3*0.5+ 2*0.2 +1*0.8+ 0*0.02= 2.78$

So then the best answer for this case would be:

C. 2.78

3 0

3 years ago

What is the value of x? Enter your answer in the box. x = [ ]​

What is the value of x? Enter your answer in the box. x = [ ]