In 1980, the united states' national debt exceeded $9 billion dollars. express the exact dollar amount in scientific notation. use complete sentences to explain, step by step, how to convert a number from standard form to scientific notation. you may use your answer to question #1 to you explain the process. calculate, in scientific notation, how many times greater the recorded debt in 2010 is compared to the recorded debt in 1960. express your answer in proper scientific notation

$9 billion has 9 zeros so would be written as 9,000,000,000

 to write in scientific notation move the decimal point 9 places to the left so the number becomes 9

now that would be multiplied by 10 to an exponent. The exponent is equal to the number of spaced you moved the decimal point. In this case you moved it 9 places

 so scientific notation is 9x10^9

 1960 debt was 2.86x10^9, 2010 debt was 1.3562*10^13 -= 2.1x10^4 times more

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.