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lions [1.4K]
3 years ago
10

Write the equation of the line that passes through (-1, 3) and is parallel to the line y = -x + 1.

Mathematics
1 answer:
ra1l [238]3 years ago
7 0

Answer:

Step-by-step explanation:

y = -x + 1......same as y = -1x + 1.....in y = mx + b form, ur slope is in the m position....so the slope of this line is -1.

a parallel line will have the same slope.

(-1,3)...x = -1 and y = 3

slope(m) = -1

y = mx + b.....we have x,y, and m....now we need to find y int (b)

3 = -1(-1) + b

3 = 1 + b

3 - 1 = b

2 = b

so ur parallel equation is : y = -1x + 2...or just y = -x + 2

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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
6. Write the factors of 36. Separate the factors with commas. ​
faltersainse [42]
1,2,3,4,6,12,18,36 are the factors!
8 0
3 years ago
8 kids bought a 3 cakes. How many equal parts will need to divide it so that everyone can have it. Easy one! ​
Vladimir79 [104]

Answer:

3/8 is your answer.

Step-by-step explanation:

Given:

<em>8 kids bought a 3 cakes.</em>

Required:

<em>How many equal parts will need to divide it so that everyone can have it.</em>

Solution:

3/8

Hope this helps ;) ❤❤❤

8 0
3 years ago
Read 2 more answers
Which is the equation for the line perpendicular to y = –5/3 x + 11 1/3 and containing P(–2, 3)?
kati45 [8]
Okay, to answer this question, 
<span>Perpendicular lines have slopes that are inverse of one another and with opposite signs so, 
If a line has a slope of m= -2 than a perpendicular line will have slope m=1/2
If a line has a slope of m= -3/4 than a perpendicular line will have slope m=4/3 If a line has a slope of m= 6 than a perpendicular line will have slope m=-1/6

So, just find the slope of your line, using it, get the slope of the line that will be perpendicular and then just get the equation for a line that has that slope and passes through point (-2,3) using: y - y1 = m(x - x1)
I hope I helped you with my answer</span>
7 0
3 years ago
What is the median of 0.8, 1.0, 2.7, 2.8, 3.1, 13.3
tresset_1 [31]

Answer:

2.75

Step-by-step explanation:

<u>Step 1:  Determine the median</u>

0.8, 1.0, 2.7, 2.8, 3.1, 13.3

The median of a set is the middle of the set.  In this instance, we have 6 numbers so we don't have a number directly in the set representing the median.  Instead, we need to find the average or middle between the 3rd and 4th number.  So we take 2.7 and 2.8, add them together to get 5.5 and then we divide by 2 to get 2.75 which is our median.

Answer:  2.75

5 0
1 year ago
Read 2 more answers
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