Answer:
as shown in the attached file
Step-by-step explanation:
The detailed steps and application of differential equation, the use of integrating factor to generate the solution and to solve for the initial value problem is as shown in the attached file.
Answer:
9 ft
Step-by-step explanation:
Let's begin with the formula for the volume of a square pyramid. If s is the base length, then the area of the base is s^2. The volume of the pyramid is then V = (1/3)(base area)(height). We know the volume and the base length (s), and want to find the height. Solving V = (1/3)(base area)(height)
for height, we get:
3V = (base area)(height), or
3V
---------------- = height
base area
Substituting 75 ft^3 for V and (5 ft)^2 for base area, we get:
3(75 ft^3) 9 ft
height = ------------------ = ----------------- = 9 ft
25 ft^2 1
Answer:
Step-by-step explanation:
Solve for the value of 
:
-Use <u>Distributive Property</u>:
-Combine like terms:
-Add both sides by 
:
-Divide both sides by 
:
Therefore, the value of is 
.
Answer:
x = 2 /3
Step-by-step explanation:
x^3 = 8/27
Take the cube root of each side
(x^3)^1/3 = (8/27)^1/3
We know that (a/b) ^c = a^c / b^c
x = (8 ) ^1/3 / (27)^1/3
x = 2 /3
Answer:
256 ft²
Step-by-step explanation:
Net comprises: 2 equal triangles, 2 equal rectangles and 1 smaller rectangle
Area of a triangle = 1/2 x base x height
⇒ area of one triangle = 1/2 x 10 x 7 = 35 ft²
Area of a rectangle = width x length
⇒ area of larger rectangle = 6 x 12 = 72 ft²
⇒ area of smaller rectangle area = 6 x 7 = 42 ft²
⇒ Total area = (2 x 35) + (2 x 72) + 42 = 256 ft²
