Answer: x = 6.46153846
Step-by-step explanation:
We are given the equation <em>13x - 4 +100 = 180</em>, and we must find the value of <em>x</em>. In order to do that get x on on one side by itself and a constant on the other side by itself.
This first step is to combine like terms. <em>13x</em> is by itself. <em>-4 + 100 = 96</em>. This gives us the equation <em>13x +96 = 180</em>.
In order to get <em>x </em>by itself, subtract 96 from each side of the equation. This gives us the equation 13x = 84.
Next, divide each side by 13 to find x. This gives us x = 6.46153846




Hope this helps! Have a nice day!
Answer:
Step-by-step explanation:
Samantha needs 4/5 yard of fabric to make costumes for the school play.
Let x represent the number of yards of fabric that she has
Let y represent the total number of costumes that she can make from x yards of fabric.
Since one costume require 4/5 yards of fabric, y costumes will require
x ÷ 4/5 = x×5/4 = 5x/4
The equation will be
y = 5x/4
to find how many costumes she can make with 8 yards of fabric, it becomes
y = (5×8)/4
y = 40/4 = 10
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)