Which number can each term of the equation be multiplied by to eliminate the decimals before solving? –m + 0.02 + 2.1m = –1.45 – 4.81m

100

Step-by-step explanation:

If you multiply each side by 100, you'll maintain the validity of the equation and you'll get rid of the decimal values.

If you multiply by 10, you'll be able to transform "2.1m" into "21m", but you'll still have decimals left (like 14.5 and 48.1).  So, you'd have to multiply by 10 again so 100 in total.

By multiplying by 100, the equation becomes:

-100m + 2 + 210m = 145 - 481m

No decimals left.

We will multiply it by 100.

Step-by-step explanation:

Given : –m + 0.02 + 2.1m = –1.45 – 4.81m

To find : Which number can each term of the equation be multiplied by to eliminate the decimals before solving.

Solution : We have given that

–m + 0.02 + 2.1m = –1.45 – 4.81 m

We can see there is decimal upto two decimal place.

So, To remove the decimal we need to multiply it by 100.

On multiply the whole equation by 100

–m * 100 + 0.02 * 100 + 2.1m * 100 = –1.45 * 100 – 4.81 *100 m.

- 100 m + 2 + 210 m = -145 - 481 m.

Therefore, We will multiply it by 100.

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.