Answer:
The answer should be 350 calories
Answer:
The number of times over the Weekend that:
Ashley watched TV = x = 12 hours
Gabby watched TV = y = 6 hours
Step-by-step explanation:
Let us represent:
The number of times
Ashley watched TV = x
Gabby watched TV = y
Together, Ashley and Gabby watched a total of 14 hours of television over the weekend.
= x + y = 14..... Equation 1
x = 14 - y
Ashley watched 6 times as many hours as Gabby.
x = 6y
Using substitution method
We substitute 14 - y for x
14 - y = 6y
14 = 6y + y
14 = 7y
y = 14/7
y = 2 hours
Solving for x
x = 14 - y
x = 14 - 2
x = 12 hours
Therefore:
The number of times over the Weekend that:
Ashley watched TV = x = 12 hours
Gabby watched TV = y = 6 hours
Answer:
the first option 40 degrees
Step-by-step explanation:
the outward angle at the center of the circle between the two tangential points is 220 degrees.
that means that the inward angle between them is
360 - 220 = 140 degrees.
now consider that there is a triangle between the center of the circle, one of the tangential points (it does not matter which one, as the upper and the lower triangles are equal) and the point R.
we know the angle at the tangential point : 90 degrees by definition (otherwise it would not be a tangent).
and we know the angle at center of the circle, which is half of the inward angle
140 / 2 = 70 degrees.
and at point R we have half of the full angle R.
we can calculate that half by using the fact that the sum of all angles in a triangle is always 180 degrees.
180 = 90 + 70 + R/2
180 = 160 + R/2
20 = R/2
R = 40 degrees
Answer: 1308m
Step-by-step explanation:
Top and Bottom: 19 x 16 x 2 = 608
Sides: 16 x 10 x 2 = 320
Front and Back: 19 x 10 x 2 = 380
608 + 320 + 380 = 1308
Answer:
V = 8.06 cubed units
Step-by-step explanation:
You have the following curves:
In order to calculate the solid of revolution bounded by the previous curves and the x axis, you use the following formula:
![V=\pi \int_a^b [(g(x))^2-(f(x))^2]dx](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5Cint_a%5Eb%20%5B%28g%28x%29%29%5E2-%28f%28x%29%29%5E2%5Ddx)
(1)
To determine the limits of the integral you equal both curves f=g and solve for x:
Then, the limits are a = -1 and b = 1
You replace f(x), g(x), a and b in the equation (1):
![V=\pi \int_{-1}^{1}[(\frac{13}{9}-x^2)^2-(\frac{4}{9}x^2)^2]dx\\\\V=\pi \int_{-1}^1[\frac{169}{81}-\frac{26}{9}x^2+x^4-\frac{16}{81}x^4]dx\\\\V=\pi \int_{-1}^1 [\frac{169}{81}-\frac{26}{9}x^2+\frac{65}{81}x^4]dx\\\\V=\pi [\frac{169}{81}x-\frac{26}{27}x^3+\frac{65}{405}x^5]_{-1}^1\\\\V\approx8.06\ cubed\ units](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5Cint_%7B-1%7D%5E%7B1%7D%5B%28%5Cfrac%7B13%7D%7B9%7D-x%5E2%29%5E2-%28%5Cfrac%7B4%7D%7B9%7Dx%5E2%29%5E2%5Ddx%5C%5C%5C%5CV%3D%5Cpi%20%5Cint_%7B-1%7D%5E1%5B%5Cfrac%7B169%7D%7B81%7D-%5Cfrac%7B26%7D%7B9%7Dx%5E2%2Bx%5E4-%5Cfrac%7B16%7D%7B81%7Dx%5E4%5Ddx%5C%5C%5C%5CV%3D%5Cpi%20%5Cint_%7B-1%7D%5E1%20%5B%5Cfrac%7B169%7D%7B81%7D-%5Cfrac%7B26%7D%7B9%7Dx%5E2%2B%5Cfrac%7B65%7D%7B81%7Dx%5E4%5Ddx%5C%5C%5C%5CV%3D%5Cpi%20%5B%5Cfrac%7B169%7D%7B81%7Dx-%5Cfrac%7B26%7D%7B27%7Dx%5E3%2B%5Cfrac%7B65%7D%7B405%7Dx%5E5%5D_%7B-1%7D%5E1%5C%5C%5C%5CV%5Capprox8.06%5C%20cubed%5C%20units)
The volume of the solid of revolution is approximately 8.06 cubed units
