Write and solve an inequality that models the situation. suppose you can get a higher interest rate on your savings if you maintain a balance of at least $1000 in your savings account. the balance in your savings account is now $1053. you deposit $44.50 into your account. what is the greatest amount that you can withdraw and still get the higher interest rate?

$99.50

Step-by-step explanation:

Given that only if a minimum balance of 1000 dollars is maintained it will attract high interest.

To enjoy the privilege of high interest, it should be ensured that the balance does not go below 1000 dollars at any point of time.

Keeping the above in mind, we see that

Balance as of now   ..    1053 dollars

Deposit                     ..        44.50 dollars

Balance after deposit  ..   1097.50 dollars

Minimum balance        ..    1000 dollars

Maximum amount

that can be withdrawn   ..  1097.50 -1000 = 97.50 dollars.

answer: slight chance that it will happen

step-by-step explanation:

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.