Assuming that the triangle is a right triangle, we can reverse engineer the Pythagorean theorem (a^2+b^2=c^2).
60^2 + x^2 = 61^2
3600 + x^2 = 3721
x^2 = 3600 - 3721
x^2 = 121
x = sqrt121
x = 11
Answer:
8
x
−
3
Hope this helps, if it does please give brainliest
D. -2, if the lines are parallel then the slope is the same but the y-int is different
Answer:
Exponential function: a*b^x
if B is less than 1, it is a decay function
if B is more than 1, then it is a growth function
if B is 0, then the function neither decreases nor increases
Example 1: 100*0.14^x
The y-intercept is decreasing by 86%
Example 2: 3000*1.14^x
The y-intercept is increasing by 14%
Example 3: 400*0
The y-intercept is neither decreasing nor increasing
Going back to the function, <u>a</u> is the y-intercept, and <u>b</u> is the rate
<u>I hope this will help you, I just started to learn about exponential functions..</u>
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.
