Answer:
domain {- 5, 5 }
Step-by-step explanation:
given values in the range, that is values of y then to find the domain equate f(x) to the given values in the range, that is
x + 5 = 0 ⇒ x = - 5
x + 5 = 10 ⇒ x = 10 - 5 = 5
domain is x ∈ { - 5, 5 }
You know that

so

.
Area of a shaded region is:
![$A=\int\limits_0^k\dfrac{y^2}{4}\,dy=\frac{1}{4}\int\limits_0^ky^2\,dy=\frac{1}{4}\left[\frac{y^3}{3}\right]_0^k=\frac{1}{4}\left[\frac{k^3}{3}-\frac{0^3}{3}\right]=\frac{1}{4}\cdot\dfrac{k^3}{3}=\boxed{\frac{k^3}{12}}](https://tex.z-dn.net/?f=%24A%3D%5Cint%5Climits_0%5Ek%5Cdfrac%7By%5E2%7D%7B4%7D%5C%2Cdy%3D%5Cfrac%7B1%7D%7B4%7D%5Cint%5Climits_0%5Eky%5E2%5C%2Cdy%3D%5Cfrac%7B1%7D%7B4%7D%5Cleft%5B%5Cfrac%7By%5E3%7D%7B3%7D%5Cright%5D_0%5Ek%3D%5Cfrac%7B1%7D%7B4%7D%5Cleft%5B%5Cfrac%7Bk%5E3%7D%7B3%7D-%5Cfrac%7B0%5E3%7D%7B3%7D%5Cright%5D%3D%5Cfrac%7B1%7D%7B4%7D%5Ccdot%5Cdfrac%7Bk%5E3%7D%7B3%7D%3D%5Cboxed%7B%5Cfrac%7Bk%5E3%7D%7B12%7D%7D%20)
so k:
Answer:
<h2>77</h2>
Step-by-step explanation:
for each one of the 7 different flavors of frozen yogurt there are 11 possible different toppings
Then there are 7 × 11 = 77 possible choices for a single serving of frozen yogurt with one topping
Answer:
Volume = 42.8 cubic centimeters
Step-by-step explanation:
The volume of right circular cone is:

Where
r is the radius
h is the height
We are given height of 9.1 cm
h = 9.1
We aren't given radius explicitly, we are given circumference of 13.3, so we need to figure out radius from that. Lets do this:

So,
r = 2.12
Now, substituting in cone formula, we get the volume to be:

Rounded to nearest 10th is 1 decimal place, so
<u>Volume = 42.8 cubic centimeters</u>
Answer:
32 sticks would be in pattern number 6