The rate of change is the same as the slope...u can use the slope formula : (y2 - y1) / (x2 - x1), with 2 sets of points...or....according to ur graph, they want to know how many miles u can go for 1 hr. y/x.....60/1....so they can go 60 miles in 1 hr...60/1 is ur unit rate.
Step-by-step explanation:
Words Decimal Representation Scientific Notation
ten million 10,000,000 1 x 107
one hundred million 100,000,000 1 x 108
one billion 1,000,000,000 1 x 109
ten billion 10,000,000,000 1 x 1010
Answer:
b number is a solution of in equality
Answer:
Step-by-step explanation:
f(x)=4x+1
g(x) = x^2-5
(f*g)(x) = 4x^3+x^2-20x-5
We can find this using the formula: L= ∫√1+ (y')² dx
First we want to solve for y by taking the 1/2 power of both sides:
y=(4(x+1)³)^1/2
y=2(x+1)^3/2
Now, we can take the derivative using the chain rule:
y'=3(x+1)^1/2
We can then square this, so it can be plugged directly into the formula:
(y')²=(3√x+1)²
<span>(y')²=9(x+1)
</span>(y')²=9x+9
We can then plug this into the formula:
L= ∫√1+9x+9 dx *I can't type in the bounds directly on the integral, but the upper bound is 1 and the lower bound is 0
L= ∫(9x+10)^1/2 dx *use u-substitution to solve
L= ∫u^1/2 (du/9)
L= 1/9 ∫u^1/2 du
L= 1/9[(2/3)u^3/2]
L= 2/27 [(9x+10)^3/2] *upper bound is 1 and lower bound is 0
L= 2/27 [19^3/2-10^3/2]
L= 2/27 [√6859 - √1000]
L=3.792318765
The length of the curve is 2/27 [√6859 - √1000] or <span>3.792318765 </span>units.