We have that
F(x) = x^3 and <span>G(x) = (4x)^3 − 5
so
</span>G(x) = F(4x) -5
the visual effect is
1) shrink horizontally by 1/4
2) shift down by 5
therefore
the answer is the option
<span>D.The graph of G(x) is the graph of F(x) compressed horizontally and shifted 5 units down.</span>
If <em>y</em> = <em>y(x)</em>, then the slope of the tangent line to (1, 1) is equal to the value of the derivative d<em>y</em>/d<em>x</em> when <em>x</em> = 1 and <em>y</em> = 1.
Compute the derivative using implicit differentiation:
d/d<em>x</em> [<em>xy</em> ^2 + <em>y</em>] = d/d<em>x</em> [2<em>x</em>]
d/d<em>x</em> [<em>xy</em> ^2] + d/d<em>x</em> [<em>y</em>] = 2 d/d<em>x</em> [<em>x</em>]
(<em>x</em> d/d<em>x</em> [<em>y</em> ^2] + d/d<em>x</em> [<em>x</em>] <em>y</em> ^2) + d<em>y</em>/d<em>x</em> = 2
2<em>xy</em> d<em>y</em>/d<em>x</em> + <em>y</em> ^2 + d<em>y</em>/d<em>x</em> = 2
(2<em>xy</em> + 1) d<em>y</em>/d<em>x</em> = 2 - <em>y</em> ^2
d<em>y</em>/d<em>x</em> = (2 - <em>y</em> ^2) / (2<em>xy</em> + 1)
Plug in <em>x</em> = 1 and <em>y</em> = 1 :
slope = d<em>y</em>/d<em>x</em> = (2 - 1^2) / (2*1*1 + 1) = 1/3
Now use the point-slope formula to get the equation of the line:
<em>y</em> - 1 = 1/3 (<em>x</em> - 1)
<em>y</em> = <em>x</em>/3 + 2/3
We are asked to evaluate the limit of (e^-2x)*cosx as x approaches infinity. we can rewrite the equation into cos x / e ^2x. we substitute x with infinity. This is equal to 1/infinity. a number divided by infinity is equal to zero. Hence the answer to this problem is zero
Answer:
65°
Step-by-step explanation:
Answer: 18 parent volunteers and 4 buses.
Step-by-step explanation: In order to solve this problem you must first calculate how many student will be going on the trip.
There are 8 classes of 20 students and 90% are attending, so the formula is 8 x 20 x .9 = 144 students are going.
Part A: If one parent needs to go for each 8 students you need to divide 144 by 8 = 18 parent volunteers.
Part B: The total people attending are 144 students, 18 parent volunteers and 4 teachers is a total 166 total attending to ride the bus. You need to divide 166 people by 44 on each bus = 166/44 = 3.7 buses, so they need to reserve 4 buses.
