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)
First things first.. What type of triangle
If u are taking about a normal triangle here is some:
∠60+∠60+∠60
∠30+∠90+∠60
∠11+∠82+∠87
Answer:
The height of the pole is 167 m
Step-by-step explanation:
The given parameters are;
Increase in the length of the shadow = 90 m
Initial angle of elevation of the Sun = 58°
Final angle of elevation of the Sun = 36°
We have a triangle formed by the change in the length of the shadow and the rays from the two angle of elevation to the top of the pole giving an angle 22° opposite to the increase in the length of the shadow
We have by sin rule;
90/(sin (22°) = (Initial ray from the top of the pole to the end of the shadow's length)/(sin(122°)
Let the initial ray from the top of the pole to the end of the shadow's length = l₁
90/(sin (22°) = l₁/(sin(122°)
l₁ = 90/(sin (22°) ×(sin(122°) = 283.3 m
Therefore;
The height of the pole = 283.3 m × sin(36°) = 166.52 m
The height of the pole= 167 m to three significant figures.
Answer:
Step-by-step explanation: to progress gradually and carefully from one stage to the nex
Answer:
1.5$
Step-by-step explanation:
10 cupcakes =15$
so, 1 cupcake = 15/10
i.e. 1.5
.: 1cupcake cost = 1.5$