Answer:
Part A: Kimberly
Part B:
Becca = 22.5 miles, Kimberly = 25 miles
Step-by-step explanation:
Part A:
Given that Becca runs at a constant speed of 4.5 miles per hour, use the table to find the constant speed that Kimberly runs, and compare who runs faster.
Let x = time
y = distance
k = speed = y/x
Equation for each person can be written as: y = kx
Therefore:
✔️Equation for Becca if k = 4.5
y = 4.5x
✔️Find k (speed) of Kimberly using (2, 10):
Speed (k) = y/x
k = 10/2
k = 5 miles per hour
Equation for Kimberly would be:
y = 5x
Comparing their speed, Kimberly runs faster because she covers more miles per hour than Becca does.
Part B:
For Becca, substitute x = 5 into Becca's equation, y = 4.5x
Thus:
y = 4.5*5 = 22.5 miles
For Kimberly, substitute x = 5 into Kimberly's equation, y = 5x
Thus:
y = 5*5 = 25 miles
Answer:
![\tan 3x=\frac{\sqrt{3} }{3} =\frac{1}{\sqrt{3} } =tan\frac{\pi }{6} =tan (n\pi +\frac{\pi }{6} )\\3x=n\pi +\frac{\pi }{6} =\frac{(6n+1)\pi }{6} \\x=\frac{(6n+1)\pi }{18} \\where~x~is~an~integer.](https://tex.z-dn.net/?f=%5Ctan%203x%3D%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B3%7D%20%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%20%7D%20%3Dtan%5Cfrac%7B%5Cpi%20%7D%7B6%7D%20%3Dtan%20%28n%5Cpi%20%2B%5Cfrac%7B%5Cpi%20%7D%7B6%7D%20%29%5C%5C3x%3Dn%5Cpi%20%2B%5Cfrac%7B%5Cpi%20%7D%7B6%7D%20%3D%5Cfrac%7B%286n%2B1%29%5Cpi%20%7D%7B6%7D%20%5C%5Cx%3D%5Cfrac%7B%286n%2B1%29%5Cpi%20%7D%7B18%7D%20%5C%5Cwhere~x~is~an~integer.)
Step-by-step explanation:
tan 3x=\frac{\sqrt{3} }{3} =\frac{1}{\sqrt{3} } =tan\frac{\pi }{6} =tan (n\pi +\frac{\pi }{6} )\\3x=n\pi +\frac{\pi }{6} =\frac{(6n+1)\pi }{6} \\x=\frac{(6n+1)\pi }{18} \\
where~x~is~an~integer.
The ratio a:b is 3:8
Step-by-step explanation:
In simple words, the ratio a:b means the fraction a/b.
So we will have to solve the given equation for a/b
Given
![8a=3b](https://tex.z-dn.net/?f=8a%3D3b)
Dividing both sides by 8
![\frac{8a}{8}=\frac{3b}{8}\\a=\frac{3b}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B8a%7D%7B8%7D%3D%5Cfrac%7B3b%7D%7B8%7D%5C%5Ca%3D%5Cfrac%7B3b%7D%7B8%7D)
Dividing both sides by b
![\frac{a}{b}=\frac{3b}{8*b}\\\frac{a}{b} =\frac{3}{8}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bb%7D%3D%5Cfrac%7B3b%7D%7B8%2Ab%7D%5C%5C%5Cfrac%7Ba%7D%7Bb%7D%20%3D%5Cfrac%7B3%7D%7B8%7D)
The ratio a:b is 3:8
Keywords: Ratios, Fractions
Learn more about ratios at:
#LearnwithBrainly
That would be 644.8 / 31 = 20.8 feet / second
Assuming the equation is x^2 + y^2 = 1, then that's a circle, with radius 1, centered on the origin [0,0].
So there are two tangents at x = 0. They are y = 1, and y = -1 (horizontal lines).
There is one tangent at x = 1. It is x = 1 (a vertical line).
There is no tangent at x = 35, because the original equation has no solution at x = 35.