Answer: ![\cos^{-1} \left(\frac{-37}{\sqrt{7298}} \right) \approx 115.665^{\circ}](https://tex.z-dn.net/?f=%5Ccos%5E%7B-1%7D%20%5Cleft%28%5Cfrac%7B-37%7D%7B%5Csqrt%7B7298%7D%7D%20%5Cright%29%20%5Capprox%20115.665%5E%7B%5Ccirc%7D)
Step-by-step explanation:
![u \cdot v=(1)(8)+(-9)(5)=-37\\\\|u|=\sqrt{1^{2}+(-9)^{2}}=\sqrt{82}\\\\|v|=\sqrt{8^{2}+5^{2}}=\sqrt{89}\\\\\cos \theta=\frac{-37}{\sqrt{82}\sqrt{89}}\\\\\theta=\cos^{-1} \left(\frac{-37}{\sqrt{82}\sqrt{89}} \right)\\\\\theta=\boxed{\cos^{-1} \left(\frac{-37}{\sqrt{7298}} \right) \approx 115.665^{\circ}}](https://tex.z-dn.net/?f=u%20%5Ccdot%20v%3D%281%29%288%29%2B%28-9%29%285%29%3D-37%5C%5C%5C%5C%7Cu%7C%3D%5Csqrt%7B1%5E%7B2%7D%2B%28-9%29%5E%7B2%7D%7D%3D%5Csqrt%7B82%7D%5C%5C%5C%5C%7Cv%7C%3D%5Csqrt%7B8%5E%7B2%7D%2B5%5E%7B2%7D%7D%3D%5Csqrt%7B89%7D%5C%5C%5C%5C%5Ccos%20%5Ctheta%3D%5Cfrac%7B-37%7D%7B%5Csqrt%7B82%7D%5Csqrt%7B89%7D%7D%5C%5C%5C%5C%5Ctheta%3D%5Ccos%5E%7B-1%7D%20%5Cleft%28%5Cfrac%7B-37%7D%7B%5Csqrt%7B82%7D%5Csqrt%7B89%7D%7D%20%5Cright%29%5C%5C%5C%5C%5Ctheta%3D%5Cboxed%7B%5Ccos%5E%7B-1%7D%20%5Cleft%28%5Cfrac%7B-37%7D%7B%5Csqrt%7B7298%7D%7D%20%5Cright%29%20%5Capprox%20115.665%5E%7B%5Ccirc%7D%7D)
The simplified answer is: 43046721<span>
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Answer:
She can finish 4 puzzles.
Step-by-step explanation:
3/4+3/4=1 1/2
1 1/2+ 1 1/2= 3(hours)
That means that there are four 3/4s and that also means she does 4 puzzles in 3 hours.
Hope this helps!^_^
<span>A
ladder is leaned against a building. the bottom of the ladder is 11
feet from the building. the top of the ladder is 19 feet above the
ground.
a. what is the slope of the ladder?
slope = rise / run = height / base = 19 feet / 11 feet = 19 /11
b. what does the slope of the ladder mean in the real world?
The slope is the inclination of the ladder. The higher the slope the more leaned is the ladder.
c. if the ladder were set closer to the building, would it be harder or
easier to climb? explain in terms of the slope of the ladder.
if the ladder were closer to the building the base would be lower and the heigth would be higher, so the slope would be higher, which means that the ladder would be steeper, therefore harder to climb.
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Answer:
at twice the father's rate of speed. At this rate; how many miles would the bicycle rider travel in 9 hours?
Step-by-step explanation:
at twice the father's rate of speed. At this rate; how many miles would the bicycle rider travel in 9 hours?