Cone W has a radius of 6 cm and a height of 5 cm. Square pyramid X has the same base area and height as cone W.

Paul and Manuel disagree on the reason why the volumes of cone W and square pyramid X are related. Examine their arguments. Which statement explains whose argument is correct and why?

Manuel's argument is correct. Paul used the incirrect base area to find the volume of square pyramid X

Step-by-step explanation:

step 1

Find the volume of the cone W

we know that

The volume of the cone if given by the formula

we have

substitute the given values

assume

substitute

step 2

Find the volume of the square pyramid

we know that

The volume of the pyramid is given by the formula

where

B is the area of the base

h is the height of pyramid

In this problem we have that

----> is the same that the area of the base of cone

so

----> is the same that the height of the cone

so

substitute

therefore

Manuel's argument is correct. Paul used the incirrect base area to find the volume of square pyramid X

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."

problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

i hope this !