Given:
and
are complementary angles.

To find:
The measure of
.
Solution:
According to the definition of the complimentary angles, the sum of two complementary angles is always 90 degree.
It is given that,
and
are complementary angles. So,




Therefore, the measure of
is 58°.
Answer C is the right answer.
Step-by-step explanation:
h(x) = f(x) * g(x)
h(x) = (2*3^x ) * ( 3*3^2x )
2 * 3 is easy, that will be 6.
The ground number 3 remains 3 in h(x), so that is easy too...
But with multiplying exponents, you can add them.
Let's concentrate only on the exponents of f(x) and g(x)... and add them...
x + 2x =3x
So, now combine the easy part with this new exponent, and you get <u>h(x)</u><u> </u><u>=</u><u> </u><u>6</u><u>*</u><u>(3)^(3x)</u>
<u>So</u><u> </u><u>answer C is the right answer.</u>
x+3<8
8-3 =5
X<5
any number less than 5 will work
Isn’t it 26... cuz 26x2 is 52 then subtract 7 which is 45
Answer:
The volume of the solid is 
Step-by-step explanation:
In this case, the washer method seems to be easier and thus, it is the one I will use.
Since the rotation is around the y-axis we need to change de dependency of our variables to have
. Thus, our functions with
as independent variable are:
For the washer method, we need to find the area function, which is given by:
![A=\pi\cdot [(\rm{outer\ radius)^2 -(\rm{inner\ radius)^2 ]](https://tex.z-dn.net/?f=A%3D%5Cpi%5Ccdot%20%5B%28%5Crm%7Bouter%5C%20radius%29%5E2%20-%28%5Crm%7Binner%5C%20radius%29%5E2%20%5D)
By taking a look at the plot I attached, one can easily see that for a rotation around the y-axis the outer radius is given by the function
and the inner one by
. Thus, the area function is:
![A(y)=\pi\cdot [(\sqrt{y} )^2-(y^2)^2]\\A(y)=\pi\cdot (y-y^4)](https://tex.z-dn.net/?f=A%28y%29%3D%5Cpi%5Ccdot%20%5B%28%5Csqrt%7By%7D%20%29%5E2-%28y%5E2%29%5E2%5D%5C%5CA%28y%29%3D%5Cpi%5Ccdot%20%28y-y%5E4%29)
Now we just need to integrate. The integration limits are easy to find by just solving the equation
, which has two solutions
and
. These are then, our integration limits.
