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2 years ago

F(x)=x^3-x^2+4x+2. is this even, odd or neither? (solve algebraically. will mark brainliest :)

Mathematics

1 answer:

Gwar [14]2 years ago

5 0

Answer:

Neither even nor odd

Step-by-step explanation:

If f(x) = f(- x) then f(x) is even

If f(- x) = - f(x) then f(x) is odd

Given f(x) = x³ - x² + 4x + 2, then

f(- x) = (- x)³ - (- x)² + 4(- x) + 2 = - x³ - x² - 4x + 2

Since f(x) ≠ f(- x) then f(x) is not even

- f(x) = - (x³ - x² + 4x + 2) = - x³ + x² - 4x - 2

Since f(- x) ≠ - f(x) then f(x) is not odd

Thus f(x) is neither even nor odd

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3 years ago

14. Higher Order Thinking Does Cavalieri's Principle apply to the volumes of the cones shown? Explain

AleksAgata [21]

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Step-by-step explanation:

At each height above the base, the cross section of each cone shown is the same (a circle with the same diameter), so Yes, Cavalieri's Principle applies.

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2 years ago

What’s the volume of the cylinder with a radius of 10 and a height of 30?

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3 years ago

1. S(–4, –4), P(4, –2), A(6, 6) and Z(–2, 4) a) Apply the distance formula for each side to determine whether SPAZ is equilatera

Aleksandr [31]

Answer:

a) SPAZ is equilateral.

b) Diagonals SA and PZ are perpendicular to each other.

c) Diagonals SA and PZ bisect each other.

Step-by-step explanation:

At first we form the triangle with the help of a graphing tool and whose result is attached below. It seems to be a paralellogram.

a) If figure is equilateral, then SP = PA = AZ = ZS:

$SP = \sqrt{[4-(-4)]^{2}+[(-2)-(-4)]^{2}}$

$SP \approx 8.246$

$PA = \sqrt{(6-4)^{2}+[6-(-2)]^{2}}$

$PA \approx 8.246$

$AZ =\sqrt{(-2-6)^{2}+(4-6)^{2}}$

$AZ \approx 8.246$

$ZS = \sqrt{[-4-(-2)]^{2}+(-4-4)^{2}}$

$ZS \approx 8.246$

Therefore, SPAZ is equilateral.

b) We use the slope formula to determine the inclination of diagonals SA and PZ:

$m_{SA} = \frac{6-(-4)}{6-(-4)}$

$m_{SA} = 1$

$m_{PZ} = \frac{4-(-2)}{-2-4}$

$m_{PZ} = -1$

Since $m_{SA}\cdot m_{PZ} = -1$ , diagonals SA and PZ are perpendicular to each other.

c) The diagonals bisect each other if and only if both have the same midpoint. Now we proceed to determine the midpoints of each diagonal:

$M_{SA} = \frac{1}{2}\cdot S(x,y) + \frac{1}{2}\cdot A(x,y)$

$M_{SA} = \frac{1}{2}\cdot (-4,-4)+\frac{1}{2}\cdot (6,6)$

$M_{SA} = (-2,-2)+(3,3)$

$M_{SA} = (1,1)$

$M_{PZ} = \frac{1}{2}\cdot P(x,y) + \frac{1}{2}\cdot Z(x,y)$

$M_{PZ} = \frac{1}{2}\cdot (4,-2)+\frac{1}{2}\cdot (-2,4)$

$M_{PZ} = (2,-1)+(-1,2)$

$M_{PZ} = (1,1)$

Then, the diagonals SA and PZ bisect each other.

8 0

2 years ago

the length of a rectangle is 14 meters. the perimeter of the rectangle is 44 meters. what is the width?

fomenos

Answer:

Step-by-step explanation:

6 0

2 years ago

F(x)=x^3-x^2+4x+2. is this even, odd or neither? (solve algebraically. will mark brainliest :)​

F(x)=x^3-x^2+4x+2. is this even, odd or neither? (solve algebraically. will mark brainliest :)