A.) Since there are no restrictions as to the dimensions of the candle except that their volumes must equal 1 cubic foot and that each must be a cylinder, we have the freedom to decide the candles' dimensions.
I decided to have the candles equal in volume. So, 1 cubic foot divided by 8 gives us 0.125 cubic foot, 216 in cubic inches.
With each candle having a volume of 216 cubic inches, I assign a radius to each: 0.5 in, 1.0 in, 1.5 in, 2.0 in, 2.5 in, 3.0 in, 3.5 in, and 4.0 in. Then, using the formula of the volume of a cylinder, which is:
V=pi(r^2)(h)
we then solve the corresponding height per candle. Let us let the value of pi be 3.14.
Hence, we will have the following heights (expressed to the nearest hundredths) for each of the radius: for
r=2.5 in: h=11.01 in
r=3.0 in: h= 7.64 in
r=3.5 in: h= 5.62 in
r=4.0 in: h= 4.30 in
r=4.5 in: h= 3.40 in
r=5.0 in: h= 2.75 in
r=5.5 in: h= 2.27 in
r=6.0 in: h= 1.91 in
b. each candle should sell for $15.00 each
($20+$100)/8=$15.00
c. yes, because the candles are priced according to the volume of wax used to make them, which in this case, is just the same for all sizes
Using the Sine Rule:-
20 /sin 45 = BC / sin 30
BC = 20 sin 30 / sin45
= 20 * 1/2 / 1 / sqrt2
= 20 * 1/2 * sqrt2
= 10 sqrt2 answer
To answer this question you will set up the proportion shown in the attached picture.
There are 2 ways to solve this.
1. You can create an equivalent ratio by determining the factor that will take you from 1 cm to 2 cm and apply his factor to the 19 miles.
The answer would be 19 x 2= 38 miles for 2 centimeters.
2. The second strategy is to use cross products to get an answer. You multiply the number diagonal from each other. See picture for this work.
Answer:
Step-by-step explanation:
Smaller perfect squares near 99 is 81
Larger perfect square near 99 is 100
First step would be to find the two perfect squares that lies between on the number line. I could then think about the number 99 and how close it is to the smaller perfect square and the larger perfect square. That could tell me how far above or below the of the two perfect squares 99 lies on the number line. I could then take the square root of the perfect squares to see how I would estimate the square root of 99. The √99 is almost 10.
81 < 99 < 100
√81 < √99 < √100
8 < √99 < 10
So, √99 is almost 10.