Answer:
the answer would be c
Step-by-step explanation: Because the values inside of the parenthesis don't have the same variable, they cannot be combined. Using the 9 on the outside of the parenthesis you would multiply 9 by 3r, which gives you 27r, and 9 by -4 to create -36. The new equation would be 27r - 36, which is equivalent to the equation shown next to it.
(3/6)^-1 negative exponent flips the fraction
(6/3)
2
v = √16 · √d
d = 300 ft
v = √16 · √300
v = √16 · √100 · √3
v = 4 · 10 · √3
<em>v = 40√3 ft/sec </em> <== simplified radical form
That's about 69.3 feet per sec, or 47.2 miles per hour.
It costs $3.63 more for the gold die than the gold plated die.
The volume of each half of the die is given by the formula
V=1/3s³.
This means the total volume is V = 2(1/3s³) = 2(1/3(2³)) = 16/3 = 5.33 mm³.
For the solid gold die, we know that it weighs 0.02g per mm³:
5.33(0.02) = 0.1066g
Gold costs $40.38 per gram:
40.38(0.1066) = $4.30
For the plastic die, plastic weighs 0.01 g per mm³:
0.01(5.33) = 0.0533g
Plastic costs $10 per gram:
0.0533(10) = 0.533 ≈ $0.54.
We also need to find the surface area, as it will be painted. Each face is an equilateral triangle; the area of a triangle is given by the formula
A = 1/2bh
We need to use the Pythagorean theorem to find the height. The height will be one leg and 1/2 of the base will be the other; the slanted side will be the hypotenuse:
h² + (1/2(2))² = 2²
h² + 1² = 2²
h² + 1 = 4
h² = 3
h = √3
The area of the triangle would then be A = 1/2bh = 1/2(2)(√3) = √3. There are 8 such faces on the die, so the total surface area would be 8√3 = 13.86mm².
Paint costs $0.01 per mm²:
13.86(0.01) = 0.1386 ≈ $0.14
Together the cost for the plastic is 0.14+0.53 = $0.67.
The difference between it and the cost for the gold die is 4.30 - 0.67 = $3.63.
