Answer: $3
Step-by-step explanation: 6*2=12 5*3=15
15-12=3
Answer:
Formula for the volume of a rectangular prism:
V = length x width x height
To solve, substitute the dimensions given in the problem and multiply.
Answer:
Step-by-step explanation:
Consider the graphs of the 
and 
.
By equating the expressions, the intersection points of the graphs can be found and in this way delimit the area that will rotate around the Y axis.
then 
o 
. Therefore the integration limits are:
and 
The inverse functions are given by:
and 
. Then
The volume of the solid of revolution is given by:
![\int\limits^{64}_ {0} \, [2\sqrt{y} - \frac{y}{4}]^{2} dy = \int\limits^{64}_ {0} \, [4y - y^{3/2} + \frac{y^{2}}{16} ]\ dy = [2y^{2} - \frac{2}{5}y^{5/2} + \frac{y^{3}}{48} ]\limits^{64}_ {0} = 546.133 u^{2}](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B64%7D_%20%7B0%7D%20%5C%2C%20%5B2%5Csqrt%7By%7D%20-%20%5Cfrac%7By%7D%7B4%7D%5D%5E%7B2%7D%20%20dy%20%3D%20%5Cint%5Climits%5E%7B64%7D_%20%7B0%7D%20%5C%2C%20%5B4y%20-%20y%5E%7B3%2F2%7D%20%2B%20%5Cfrac%7By%5E%7B2%7D%7D%7B16%7D%20%5D%5C%20%20dy%20%3D%20%5B2y%5E%7B2%7D%20-%20%5Cfrac%7B2%7D%7B5%7Dy%5E%7B5%2F2%7D%20%2B%20%5Cfrac%7By%5E%7B3%7D%7D%7B48%7D%20%5D%5Climits%5E%7B64%7D_%20%7B0%7D%20%3D%20546.133%20u%5E%7B2%7D)
Answer:
f(x) = { x, -5 ≤ x < 0 and 3x - 3, 1 ≤ x < 5
Step-by-step explanation:
The equation of one line is y = x
The equation of the other line is y = 3x - 3
Altogether,
f(x) = { x, -5 ≤ x < 0 and 3x - 3, 1 ≤ x < 5
Answer:
<em>x = 32</em>
Step-by-step explanation:
This is an isosceles triangle since two sides have length 10. The angles opposite the congruent sides are congruent. There is an angle measuring 116 deg, and two angles measuring x. The sum of the measures of the angles of a triangle is 180.
x + x + 116 = 180
2x + 116 = 180
2x = 64
x = 32
