Find where the curve intersects the <em>x</em>-axis; this happens when <em>y</em> = 0:
<em>y</em> = <em>t</em> - <em>t</em> ² = 0 → <em>t</em> (1 - <em>t</em> ) = 0 → <em>t</em> = 0, <em>t</em> = 1
Then the area of the bounded region is
(you can compute the integral by parts)
Answer:
D
Step-by-step explanation:
6*2=12
6*3=18..........
<h2>
Answer:</h2><h3>False</h3><h2>
Step-by-step explanation:</h2>
Let's find the inverse function of 
to know whether this function has an inverse function ![f^{-1}(x)=-3+\sqrt[3]{x+4}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D-3%2B%5Csqrt%5B3%5D%7Bx%2B4%7D)
. So let's apply this steps:
a) Use the Horizontal Line Test to decide whether 
has an inverse function.
Given that f(x) is a cubic function there is no any horizontal line that intersects the graph of at more than one point. Thus, the function is one-to-one and has an inverse function.
b) Replace 
by 
in the equation for .
c) Interchange the roles of 
and and solve for
![x=(y-3)^3+4 \\ \\ \therefore x-4=(y-3)^3 \\ \\ \therefore (y-3)^3=x-4 \\ \\ \therefore y-3=\sqrt[3]{x-4} \\ \\ \therefore y=\sqrt[3]{x-4}+3](https://tex.z-dn.net/?f=x%3D%28y-3%29%5E3%2B4%20%5C%5C%20%5C%5C%20%5Ctherefore%20x-4%3D%28y-3%29%5E3%20%5C%5C%20%5C%5C%20%5Ctherefore%20%28y-3%29%5E3%3Dx-4%20%5C%5C%20%5C%5C%20%5Ctherefore%20y-3%3D%5Csqrt%5B3%5D%7Bx-4%7D%20%5C%5C%20%5C%5C%20%5Ctherefore%20y%3D%5Csqrt%5B3%5D%7Bx-4%7D%2B3)
d) Replace by 
in the new equation.
![f^{-1}(x)=\sqrt[3]{x-4}+3](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5Csqrt%5B3%5D%7Bx-4%7D%2B3)
So this is in fact the inverse function and it isn't the same given function. Therefore, the statement is false
Answer:
20x+9y
Step-by-step explanation:
add the numbers that have the same variable(x in this problem)this is also called combining like terms. Then put the other numbers that have different variables. hope this helped
Answer:
X=3
Step-by-step explanation:
4x-12+1=1
4x=1-1+12
4x=12
x=12/4
x=3
