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Over [174]
3 years ago
8

Estimate the difference by rounding each number to the nearest half or whole. 7 1/15 - 3 4/5

Mathematics
1 answer:
bearhunter [10]3 years ago
3 0
7 1/15 to the nearest whole would be 7. 3 4/5 to the nearest whole would be 4.

7 – 4 = 3
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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
What is the point slope form of Y=1/2X-2
vagabundo [1.1K]
Point-slope form of a line: We need a point (x₀,y₀) and the slope "m";
y-y₀=m(x-x₀)

We have the next equation of line:
y=1/2 x-2  (slope-intercept form y=mx+b)

the slope of this line is 1/2  (m=1/2)
And any one point could be:
if x=0; then y=1/2 (0)-2=-2  (0,-2)

Therefore, we already have the point (0-,2) and the slope (m=1/2)
y-y₀=m(x-x₀)
y+2=1/2(x-0)

Answer: the point slope form of y=1/2 x-2; would be:
y+2=1/2(x-0)
8 0
3 years ago
The number of adults going on a field trip was the largest prime number less than 50. How many adults were going on the field tr
Vilka [71]

Answer:

47

Step-by-step explanation:

Well 47 is the highest prime number that is smaller than 50

4 0
2 years ago
Solve for the variable
krek1111 [17]

Answer:

G = 2/3

Step-by-step explanation:

-13G + 10 = 2(-5G + 4)  Distribute the 2 to (-5G + 4)

-13G + 10 = -10G + 8  

+13G           +13G         Add 13G to both sides

10 = 3G + 8

-8           -8                  Subtract 8 from both sides

2 = 3G                          Divide both sides by 3

2/3 = G

If this answer is correct, please make me Brainliest!

5 0
3 years ago
16.748 rounded to the nearest hundredths
bagirrra123 [75]
The answer is 17.000
3 0
3 years ago
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