Answer:
<em>V = 1,568</em>
Step-by-step explanation:
<u>The Volume of a Square Pyramid</u>
Given a square-based pyramid of base side a and height h, the volume can be calculated with the formula:
We are given a square pyramid with a base side a=14 ft but we're missing the height. It can be calculated by using the right triangle shown in the image attached below, whose hypotenuse is 25 ft and one leg is 7 ft
We use Pythagora's theorem:
Solving for h:
The height is h=24 ft. Now the volume is calculated:
V = 1,568
The diagonal of a rectangle = sqrt(w^2 + l^2)
w = width
l = length
In this problem,
The diagonal = 20 in
w = x
l = 2x + 8
Let's plug our numbers into the formula above.
20in = sqrt((x)^2 + (2x + 8)^2)
Let's simplify the inside of the sqrt
20 in = sqrt(5x^2 + 32x + 64)
Now, let's square both sides.
400 = 5x^2 + 32x + 64
Subtract 400 from both sides.
0 = 5x^2 + 32x - 336
Factor
0 = (5x - 28)(x + 12)
Set both terms equal to zero and solve.
x + 12 = 0
Subtract 12 from both sides.
x = -12
5x - 28 = 0
Add 28 to both sides.
5x = 28
Divide both sides by 5
x = 28/5
The width cant be a negative number so now we know that the only real solution is 28/5
Let's plug 28/5 into our length equation.
Length = 2(28/5) + 8 = 56/5 + 8 = 96/5
In conclusion,
Length = 96/5 inches
Width = 28/5
Answer:
Total surface area of the rectangular prism is 150.88 cm^2
Step-by-step explanation:
area of base = area of top
area of base = 5 x 3.1 = 15.5 cm^2
Area of small lateral surface having dimensions 3.1 cm x 7.4 cm is
=3.1 x 7.4 = 22.94 cm^2
Area of big lateral surface having dimensions 5 cm x 7.4 cm is
=5 x 7.4 = 37 cm^2
Total area of prism = 2 x 15.5 + 2 x 22.94 + 2 x 37 = 150.88 cm^2
total surface area of the rectangular prism is 150.88 cm^2
Answer:
The answer is D. -3, 6, 11
Step-by-step explanation:
A coefficient is a number used to multiply a variable.
Example: 6z means 6 times z, and "z" is a variable, so 6 is a coefficient. Variables with no number have a coefficient of 1.
Example: x is really 1x.
