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SVETLANKA909090 [29]
2 years ago
11

14

Mathematics
2 answers:
lutik1710 [3]2 years ago
7 0

Answer:

2.5lbs. per year

Step-by-step explanation:

So you have 12 year difference

And 30 pound difference

So divide 30 by 12

30/12

2.5

LenKa [72]2 years ago
4 0

Answer:2.5 pounds per year

Step-by-step explanation:

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9 minus t equals t plus 3
Zarrin [17]
9-t=t+3
Subtract t on both sides
-2t=-6
Divide by -2 to leave the variable by itself
t=3
8 0
3 years ago
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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
Simplify the expression
Reil [10]

Answer:453rft

Step-by-step explanation:

5 0
3 years ago
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If a drug has a concentration of 8.22 mg per 3.039 mL, how many mL are needed to give 7.469 gram of the drug? Round to 1 decimal
aalyn [17]

Answer:

2.8 litres

Step-by-step explanation:

8.22 mg per 3.039 mL

2.704 mg per 1 mL

7.469 gram = 7469 milligrams

7469 milligrams per 2,761.34927mL

= 2.761 litres = 2.8 litres

7 0
3 years ago
I need it step by step​
elena-s [515]

Answer:

Step-by-step explanation:

we want y by itself...sooo

y - 19 = - \frac{6}{10}(x - (-5))

y - 19 = - \frac{6}{10}(x+5)

y - 19 =  - \frac{6}{10}x - \frac{6}{2}

y = - \frac{6}{10}x - 3 +19

y = - \frac{6}{10}x + 16

4 0
3 years ago
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