Answer:
Step-by-step explanation:
Answer:
685,653 lb
Step-by-step explanation:
The weight of the liquid can be found by multiplying its volume by its density. The volume will be that of a hemisphere, which can be found using the appropriate formula.
<h3>Hemisphere volume</h3>
The volume of a hemisphere with radius r is given by ...
V = (2π/3)r³
When the radius is 15 ft, the volume is ...
V = (2π/3)(15 ft)³ = 2250π ft³
<h3>Weight</h3>
The weight of the liquid in the tank is found using the density.
W = ρV
W = (97 lb/ft³)(2250π ft³) = 218250π lb ≈ 685,653 lb
The total weight of the liquid in the tank is about 685,653 pounds.
Answer:
See below
Step-by-step explanation:
When you have 2 sides and the angle between them you use the cosine theorem or law of cosines:
After you have a side and the opposed angle (side b and angle B), you use the law of sines:
I will calculate angle A first:
![[tex]\frac{27.5}{sin36} =\frac{41}{sinA} \\sinA =\frac{41}{27.5} sin36 \\sin A = 0.876 \\A = 61.2\°](https://tex.z-dn.net/?f=%5Btex%5D%5Cfrac%7B27.5%7D%7Bsin36%7D%20%3D%5Cfrac%7B41%7D%7BsinA%7D%20%5C%5CsinA%20%3D%5Cfrac%7B41%7D%7B27.5%7D%20sin36%20%5C%5Csin%20A%20%3D%200.876%20%5C%5CA%20%3D%2061.2%5C%C2%B0)
[/tex]
Same for angle C:
The sum of the angles is 36° + 61.2° + 25.3° = 122.5°; The sum must be 180° so this isnt a triangle.
I re did the problem using B as 63° instead of 36° in case you wrote it wrong and I got a satisfactory answer.
using B = 36:
b = 36.6
angle A = 86.4°
angle C = 29.1°
A+B+C = 86.4° + 29.1° + 63° = 178.5° ~ 180°
Answer:
Length = 5
Width = 21
Step-by-step explanation:
(x)(x + 16) = 105
x^2 + 16x = 105
x^2 + 16x - 105 = 0
(x - 5) x ( x + 21) = 0
x - 10 = 0
x = 5
x + 21 = 0
x = -21
Now that we have the zeroes.
We have to find the most viable one to put in.
Using -21 would not make sense, so we will use 5.
Plug it in:
x = 5
(5) (5 + 16) = 105
5 ( 21) = 105
