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bulgar [2K]
2 years ago
7

The volume of a rectangular box with a square base remains constant at 500 cm3 as the area of the base increases at a rate of 6

cm2/sec. Find the rate at which the height of the box is decreasing when each side of the base is 15 cm long.
Mathematics
1 answer:
Andre45 [30]2 years ago
7 0

Answer:

the rate at which the height of the box is decreasing is -0.0593 cm/s

Step-by-step explanation:

Given the data in the question;

Constant Volume of a rectangular box with a square base = 500 cm³

area of the base increases at a rate of 6 cm²/sec

so change in the area of the base with respect to time dA/dt = 6 cm²/sec

each side of the base is 15 cm long

so Area of the base = 15 cm × 15 cm = 225 cm²

the rate at which the height of the box is decreasing = ?

Now,

V = Ah

dv/dt = 0 ⇒ Adh/dt + hdA/DT = 0

⇒ dh/dt = -hdA/dt / A

we substitute

dh/dt = [ -( 500 / 225 ) × 6 ] / 225

dh/dt = [ -(2.22222 × 6)  ] / 225

dh/dt = [ -13.3333 ] / 225

dh/dt = -0.0593 cm/s

Therefore, the rate at which the height of the box is decreasing is -0.0593 cm/s

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Answer:

A and C

Step-by-step explanation:

solving the equations

A

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x² = 4 ( take square root of both sides )

x = ± \sqrt{4} = ± 2 ← required solution

B

x² = - 4 ← has no real solutions

C

4x² = 16 ( divide both sides by 4 )

x² = 4 ( take square root of both sides )

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D

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Solution

             To    find   Which two numbers on the number line have  sn  

            absolute value of 1.75  .

            Absolute   value   means    " how  far   a  number    is   from  

            zero "  .

           "1.75"    is    1.75   away   from   zero  .

           and  " -1.75"   is  also   1.75    away   from  zero  .

          i.e

               |  0  - 1.75 |   =   1.75

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           So ,  the  absolute   value  of   "1.75"    is  1.75  

          similarly  , absolute  value  of  "1.75"   is   1.75  .

          Hence  , the  two  numbers   are   -1.75  and  1.75  .

                 

           

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Answer:

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Step-by-step explanation:

* Lets revise the rules of simple interest

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 A = P(1 + rt)

- Where:

• A = Total amount (principal + interest)  future amount

• P = Principal Amount

• I = Interest Amount

• r = Rate of Interest per year in decimal; r = R/100

• t = Time Period involved  

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* Lets solve the problem

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∵ P = $3600.00

∵ R = 4%

∵ t = 3 month

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Step-by-step explanation:

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Step-by-step explanation:

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