In analytical geometry, there are already derived equations to find the distance of lines and points as well as the angle made between two lines. As special case is when the other line is one of the coordinate axis. Then, the formula can be simplified to
tan θ =m, where m is the slope of the equation
In the next step, we also incorporate operations of calculus. Since the slope is equal to Δy/Δx, this is equivalent to dy/dx in calculus. Therefore, you can find the slope by differentiating the equation in terms of x.
<span>y-2x=7
y = 2x+7
dy/dx = 2 =m
So,
tan </span>θ = 2
θ = tan⁻¹(2)
θ = 63.43°
Answer:
2,742.50
Step-by-step explanation:
2194 x 1.25 = 2742.50
Answer:
V = 115.3 ft³
Step-by-step explanation:
The left part of the figure shows a cube of side length 4.2 ft. The volume of a cube is V = s³, where s is the side length. Hence, the volume of this particular cube is V = (4.2 ft)³ = 74.088.
The volume of a pyramid is V = (1/3)(base area)(height).
Here V = (1/3)(4.2 ft)²(7 ft) = 41.16 ft³.
Summing up the two distinct areas, we get V = 41.16 ft³ + 74.088 ft³, or
V = 115.3 ft³ after rounding up to the nearest tenth.
First you ask yourself, can 8 go into 1? The answer is no. Can 8 go into 12? Yes, 1 time. So you put 1 on top of the 2 and subtract 8 from 12. That gives you 4. Then you pull down the 8 from 128 and ask how many times can 8 go into 48? The answer is 6. So your answer is 16. Hope I helped!
Answer:
a)
, n = 15 , X=3.4 , S=1.5 , α = .05
Formula : 
p- value = 0.607(using calculator)
α = .05
p- value > α
So, we failed to reject null hypothesis
b)
, n =75 , X=20.12 , S=2.1 , α = .10
Formula :
p- value = 0.000412(using calculator)
α = .1
p- value< α
So, we reject null hypothesis
(c) 
, n = 36, p-value = 0.061.
Assume α = .05
p-value = 0.061.
p- value > α
So, we failed to reject null hypothesis
