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.
Two complementary angles must add to 90 degrees, and if you divide 90 into thirds (two parts for the larger angle, one for the smaller), then you get 30 degrees.
If the smaller angle is 30 degrees, then the larger is two times that, which is 60. 60 + 30 = 90, so the larger angle is equal to 60 degrees.
Answer:
1/16
Step-by-step explanation:
Answer:32 inches
Step-by-step explanation:
Using the pythagorean theorem
40²= 24²+ b²
simplify
1600 = 576 + b²
subtract 576 from both sides
1024 = b²
square root both sides
32= b
If you choose 1 scoop of ice cream from 12 flavors and any 1 topping from a choice of 8. Then the number of the different ways to make ice cream will be 96.
<h3>What are permutation and combination?</h3>
A permutation is an act of putting things or elements in the right sequence. Combinations are a method of picking things or pieces from a collection of objects or sets when the sequence of the objects is irrelevant.
If you choose 1 scoop of ice cream from 12 flavors and any 1 topping from a choice of 8.
Then the number of the different ways to make ice-cream sundaes will be
Let x be the number of the ways.
Then the number of the different ways to make ice cream will be 96.
More about the permutation and the combination link is given below.
brainly.com/question/11732255
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