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Iteru [2.4K]
3 years ago
12

What are the quotient and remainder of (3x^3-2x^2-8)/(x+5)

Mathematics
2 answers:
MA_775_DIABLO [31]3 years ago
7 0

Answer:

Quotient 3x^2 - 17x + 85   remainder -433.

Step-by-step explanation:

Perform Long Division:

        3x^2 - 17x + 85   <---------Quotient

        ----------------------

x + 5) 3x^3 -  2x^2 + 0x  - 8

         3x^3 + 15x^2

                  - 17x^2 + 0 x

                  - 17x^2 -85x

                               85x   -   8

                                85x + 425

                                            -433  <------ Remainder.

MAXImum [283]3 years ago
5 0

Answer:

The quotient : 3x^2 — 17x + 85

The remainder = — 433

Step-by-step explanation:

3x^3-2x^2-8)/(x+5)

The above can be solved by following the illustration in the attached file.

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3 years ago
This is the pond in a shape of a prism, it is completely full of water. Colin uses a pump to empty the pond. The level goes down
AnnZ [28]

Answer:

150 minutes

Step-by-step explanation:

P.S - The exact question is -

Given - This is the pond in a shape of a prism, it is completely full of

             water. Colin uses a pump to empty the pond. The level goes

             down by 20 cm in the first 30 min.

To find - Work put how many minutes Colin has to wait for the pond

               to completely empty.

Proof -

Given that,

Height of prism = 1 m

Also,

Base of the prism is trapezium and

Sides of the trapezium are 0.6 m and 1.4 m

Height of trapezium is 2 m

We know that,

Area of trapezium = \frac{1}{2}× (sum of sides)× height

                             =  \frac{1}{2}× (0.6 + 1.4)× 2

                             =  \frac{1}{2}× (2)× 2

                             =  2 m²

⇒Area of trapezium = 2 m²

Now,

Volume of prism = Area of trapezium × height of prism

                          = 2 m² × 1 m

                          = 2 m³

⇒Volume of prism = 2 m³

Now,

Given that the level goes down by 20 cm in the first 30 min

We know

100 cm = 1 m

⇒1 cm = \frac{1}{100} m = 0.01 m

⇒20 cm = 20×0.01 m = 0.2 m

⇒The level goes down by 0.2 m in the first 30 min.

Also,

we know that height of water = height of prism = 1 m

So, the remaining water left in the pond = 1 m - 0.2 m = 0.8 m

Also,

Volume of Remaining water = Area of trapezium × height

                                           = 2 m² × 0.8 m

                                           = 1.6 m³

⇒Volume of Remaining water = 1.6 m³

Now,

Volume of emptied water = Total Volume - Volume of Remaining water

                                       = 2 m³ - 1.6 m³

                                       = 0.4 m³

⇒Volume of emptied water = 0.4 m³

Now,

0.4 m³ water will be empty in 30 minutes

⇒ 1 m³ water will be empty in \frac{30}{0.4} = 75 minutes

⇒1.6 m³ water will be empty in 1.6 × 75 = 120 minutes

∴ we get

The remaining water is empty in 120 minutes

So,

Total pond is empty in 120 + 30 minutes

⇒Total pond is empty in 150 minutes

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V125BC [204]

Answer:

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Step-by-step explanation:

we have

x+y=2 -----> equation A

y=-2x-1 ------> equation B

Solve the system by substitution

Substitute the equation B in equation A and solve for x

x+(-2x-1)=2

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y=-2x-1

y=-2(-3)-1

y=5

therefore

The solution of the system is the point (-3,5)

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