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artcher [175]
2 years ago
6

In a racing game, Austin has traveled 1,988 meters from the starting line. He's cruising with confidence when suddenly he slips

on a giant banana peel lying in the middle of the road, causing his position to change by −7.2 meters! How many meters must Austin drive to get back to where he was before slipping on the banana peel?
Mathematics
1 answer:
Korolek [52]2 years ago
7 0

Answer:

1987.2

Step-by-step explanation:

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Find the work done by force dield f(x,y)=x^2i+ye^xj on a particle that moves along parabola x=y^2+1 from(1,0) to (2,1)
NemiM [27]
Call the parabola P, parameterized by \mathbf r(y)=\langle y^2+1,y\rangle with 0\le y\le 1\rangle. Then the work done by \mathbf f(x,y) along P is

\displaystyle\int_P\mathbf f(x,y)\cdot\mathrm d\mathbf r=\int_{y=0}^{y=1}\mathbf f(x(y),y)\cdot\dfrac{\mathrm d\mathbf r(y)}{\mathrm dy}\,\mathrm dy
=\displaystyle\int_0^1\langle(y^2+1)^2,ye^{y^2+1}\rangle\cdot\langle2y,1\rangle\,\mathrm dy
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8 0
3 years ago
A line passes through (-2, -8) and (4, 10). What is the slope?
BigorU [14]
Answer is m= 3, hope this helps <3
7 0
3 years ago
Given that sin theta = 1/4, 0→theta→π/2, what<br>. what is the exact value of cos 8?​
natali 33 [55]
<h3>Answer: Choice B \frac{\sqrt{15}}{4}</h3>

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

Work Shown:

Angle theta is between 0 and pi/2, so this angle is in quadrant Q1.

Square both sides of the given equation

\sin \theta = \frac{1}{4}\\\\\sin^2 \theta = \left(\frac{1}{4}\right)^2\\\\\sin^2 \theta = \frac{1}{16}

Then use the pythagorean trig identity to get

\sin^2 \theta + \cos^2 \theta = 1\\\\\cos^2 \theta = 1-\sin^2 \theta\\\\\cos \theta = \sqrt{1-\sin^2 \theta} \ \ \ \text{cosine is positive in Q1}\\\\\cos \theta = \sqrt{1-\frac{1}{16}}\\\\\cos \theta = \sqrt{\frac{16}{16}-\frac{1}{16}}\\\\\cos \theta = \sqrt{\frac{16-1}{16}}\\\\\cos \theta = \sqrt{\frac{15}{16}}\\\\\cos \theta = \frac{\sqrt{15}}{\sqrt{16}}\\\\\cos \theta = \frac{\sqrt{15}}{4}\\\\

3 0
3 years ago
A water skier is towed 65 m to the south of the starting point, and then is turned 40° cast of south for another 35m. What is th
densk [106]

Using cosine law,

d^2 = 65^2 + 35^2 - 2(65)(35)cos140

= 8935.5022

d = sqrt(8935.5022)

= 94.5 m

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7 0
1 year ago
Anyone know this answer?
Tasya [4]

Answer:

16

Step-by-step explanation:

Remember to use pemdas:

8÷2(2+2)

First we do whats in parentheses.

= 8÷2(4)

Then we do multiplication and division from left to right

= 4(4)

= 16

So the answer is 16.  Remember that multiplication and division have the same priority in pemdas, and you should always do them left to right, because order does matter.

6 0
3 years ago
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