582.74 square inches of glass is required to construct the tank
Step-by-step explanation:
Base dimensions= 22 x 12 inches
Volume of the fish tank = 3960 cubic inches
Volume = l x w x h
3960 = 22 x 12 x h
h = 3960 /(22 x 12)
h = 3960/462
h = 8.57 inches
The glass used = lateral surface area of the rectangular prism
= 2(lh + wl)
= 2(188.57 + 102.8)
= 2(291.37)
= 582.74 square inches
582.74 square inches of glass is required to construct the tank
Step-by-step explanation:
There are a few steps to follow when you add or subtract rational expressions with unlike denominators.
To add or subtract rational expressions with unlike denominators, first find the LCM of the denominator. The LCM of the denominators of fraction or rational expressions is also called least common denominator , or LCD.
Write each expression using the LCD. Make sure each term has the LCD as its denominator.
Add or subtract the numerators.
Simplify as needed.
Answer: it will trave 56.89 meters before coming to rest.
Step-by-step explanation:
This is a geometric progression since the distance travelled (height) by the ball is reducing by a constant ratio, r. Since the number of times that the ball will bounce is infinite, then we would apply the formula for determining the sum of the terms in a geometric progression to infinity which is expressed as
S = a/(1 - r)
where
S = sum of the distance travelled by the ball
a = initial distance or height of the ball
r = common ratio
From the information given,
a = 128/9
r = (32/3)/(128/9) = 0.75
Therefore,
S = (128/9)/(1 - 0.75) = 56.89 meters
Answer:
((2 x + 1) (4 x^2 - 2 x + 1))/8
Step-by-step explanation:
Factor the following:
x^3 + 1/8
Put each term in x^3 + 1/8 over the common denominator 8: x^3 + 1/8 = (8 x^3)/8 + 1/8:
(8 x^3)/8 + 1/8
(8 x^3)/8 + 1/8 = (8 x^3 + 1)/8:
(8 x^3 + 1)/8
8 x^3 + 1 = (2 x)^3 + 1^3:
((2 x)^3 + 1^3)/8
Factor the sum of two cubes. (2 x)^3 + 1^3 = (2 x + 1) ((2 x)^2 - 2 x + 1^2):
((2 x + 1) ((2 x)^2 - 2 x + 1^2))/8
1^2 = 1:
((2 x + 1) ((2 x)^2 - 2 x + 1))/8
Multiply each exponent in 2 x by 2:
((2 x + 1) (2^2 x^2 - 2 x + 1))/8
2^2 = 4:
Answer: ((2 x + 1) (4 x^2 - 2 x + 1))/8
