I need help please!!!!!!

A rectangular prism has a base area 56 ft.² and a volume of 840 ft.³ the length of the base is longer than the width if the sum

suter [353]

Answer:

The length of the base in feet is 8 ft.

Step-by-step explanation:

The volume V of the rectangular prism is given by

V = l × w × h

But Area, A = l × w

∴ V = A × h

Where A is the base area and h is the height

From the question

A = 56 ft.² and V = 840 ft.³

∴ 840 ft.³ = 56 ft.² × h

840 ft.³ / 56 ft.² = h

15 ft. = h

∴ h = 15 ft.

Hence, the height of the rectangular prism is 15 ft.

Also, from the question

the sum of the length and the width of the base is equal to the height

i.e l + w = h

where l is the length of the base and w is the width of the base

Then, l + w = 15 ------ (1)

Also, A = l × w

Then, 56 = l × w ------- (2)

From equation (1)

l + w = 15

Then, w = 15 - l ------- (3)

Substitute this into equation (2)

56 = l × w

56 = l × (15-l)

56 = 15l - l²

Then,

l²- 15l + 56 = 0

l² -8l -7l + 56 = 0

l(l - 8) -7(l - 8) = 0

(l - 7)(l - 8) = 0

l - 7 = 0 OR l - 8 = 0

∴ l = 7 OR l = 8

Substitute the values of l into equation (3)

w = 15 - l

when l = 7

w = 15 - 7

w = 8

and when l = 8

w = 15 - 8

w = 7

From the question, the length of the base is longer than the width

∴ l = 8 and w = 7

Hence, the length of the base in feet is 8 ft.

6 0

3 years ago

Help plz!!!!!!<br> −3(4 − a) = 6

inn [45]

Answer:

a = 6

Step-by-step explanation:

use distribution method:

-3(4-a) = 6

-12+3a = 6

3a = 6+12

3a = 18

a = 18/3 = 6

3 0

4 years ago

Read 2 more answers

Explain why a recursive rule alone does not define one sequence.

OverLord2011 [107]

In the recursive rule, there's a variable where you plug in the number of times you need the sequence to repeat, but you don't put 1 in that slot because there's another formula/rule you use to find that answer (I can't remember the name of the other rule right now I apologize I hope this makes sense)

5 0

4 years ago

The sum of the lengths of any two sides of a triangle must be greater than the third side. if a triangle has one side that is 11

vfiekz [6]

2a+2a-1>11, a>3, b=2a-1

6 0

3 years ago

A supplier of heavy construction equipment has found that new customers are normally obtained through customer requests for a sa

ziro4ka [17]

Answer:

The probability that it will take fewer than six customer contacts to clear the inventory is 0.8%.

Step-by-step explanation:

We have a probability of making an individual sale of p=0.15.

We have 4 units, so the probability of clearing the inventory with n clients can be calculated as:

$P=\dbinom{n}{4}p^4q^{n-4}=\dbinom{n}{4}0.15^4\cdot 0.85^{n-4}$

As we see in the equation, n has to be equal or big than 4.

In this problem we have to calculate the probability that less than 6 clients are needed to sell the 4 units.

This probability can be calculated adding the probability from n=4 to n=6:

$P=\sum_{n=4}^6P(n)=\sum_{n=4}^6 \dbinom{n}{4}0.15^4^\cdot 0.85^{n-4}\\\\\\P=0.15^4(\dfrac{4!}{4!0!}\cdot 0.85^{4-4}+\dfrac{5!}{4!1!}\cdot0.85^{5-4}+\dfrac{6!}{4!2!}0.85^{6-4})\\\\\\P=0.15^4(1\cdot0.85^0+5\cdot0.85^1+15\cdot0.85^2)\\\\\\P=0.00051(1+4.25+10.84)\\\\\\P=0.00051\cdot16.09\\\\\\P=0.008$

5 0

3 years ago