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3 years ago

Talisa plans a 30-foot deep pond. While digging, she hits rock 25 feet down. How can Talisa modify

Mathematics

1 answer:

Natali [406]3 years ago

6 0

9514 1404 393

Answer:

multiply the radius by √1.2 ≈ 1.0954

Step-by-step explanation:

Let the original depth and radius be represented by 30 and r. Let the modified depth and radius be represented by 25 and r'. Assuming the pond is uniform depth, the formula for the volume of a cylinder applies. The volume of a cylinder is given by ...

V = πr²h

In this application, we want the original and modified volumes to be the same.

πr²(30) = π(r')²(25)

(r')² = r²(30/25) = r²(6/5)

r' = r√(6/5)

The radius can be multiplied by √1.2 to maintain the original volume of the pond.

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Identify each matrix A such that A^2 has identical diagonal elements?

Maksim231197 [3]

Answer:

The correct matrices are:

Matrix:

7 1 5

1 5 7

5 7 1

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Matrix:

9 18 27

27 -9 18

18 27 9

all diagonal elements of A^2 are: 9^2 + 27*18 + 18*27 or (-9)^2

Matrix:

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all diagonal elements of A^2 are: 8^2 + 6*1 + 1*6

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4 years ago

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Nat2105 [25]

Answer:

Step-by-step explanation:

In the first part the given polynomial is $3x^{3}-2x^{2}+x-1$ , we have to divide this polynomial by (x-1) using synthetic division.

Here are the steps of synthetic division

Step 1: Set up the synthetic division table in which the coefficients are written in descending power of x.

Step 2: Drop down the leading coefficient i.e the coefficient of highest power of x to the bottom row.

Step 3: Multiply a by the value just written on the bottom row and write this value just down of the number written next of leading coefficient. Here, a is 1(taken from divisor)

Step 4: Add the column made in step 3. Repeat these steps until the last column reached.

In the second part,

It is given that divisor polynomial is the factor of given polynomial then we have to tell the remainder which is 0 because if divisor polynomial is the factor the it will completely divide the given polynomial which gives remainder 0.

In the third part,

Given when one uses the synthetic division to divide by (x-3) then what number is used to multiply each term that is dropped down or added.

As explained the steps of synthetic division in first part

x-3=0 ⇒ x=3 which is a

In step 3, Multiply a by the value just written on the bottom row and write this value just down of the number written next of leading coefficient. So, 3 is multiplied.

As explained in Step 2: Drop down the leading coefficient i.e the coefficient of highest power of x to the bottom row.

The columns which is formed by above steps are added.