An even degree power function has a negative leading coefficient. which answer correctly describes the function's end behavior?

1st option is the correct choice.

Step by step explanation:

We have been given that an even degree power function has a negative leading coefficient. We are asked to find the correct option representing the end behavior of our given function.

Since we know that end behavior means, how the graph of function behaves at the end of x-axis. The end behavior is determined by the degree and the leading coefficient.

We know that the square of a very large positive number will be more large positive value and the square of a large negative number is also a very positive number.

So when we will multiply a very large positive number by a negative number, then the resulting number will be a very large negative number.

Upon looking at our given choices we can see that 1st option is the correct choice as when x approaches positive or negative infinity our function will approach negative infinity.

Therefore, 1st option is the correct choice.

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

ratio is 2 : 9

the answer is three

13.5 : 3