Answer:
red= about 324°
blue= 360°
Green=about 144°
Step-by-step explanation:
Answer:
-1/2
Step-by-step explanation:
The slope of a line parallel is to another line is the same.
So the line in the picture has a slope of -1/2, and since the other line is parallel to the first one, its slope is also -1/2
Answer:
0
Step-by-step explanation:
g[f(x)] = x^2 - 3
= 3x^2
if gf(0) = 3(0)^2
= 0
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.
Answer:
scale factor 3 is the answer.
Step-by-step explanation:
Length = 18 in
Breadth = 3 in
height = 10 in
Volume of cuboid = l × b × h
V = 18 × 3 × 10
V = 540 in³
540 in³ is the original volume. The volume needs to be tripled, so multiply the original volume with 3
V = 540 × 3 = 1620 in³
∴ 1620 in³ will be the new volume if it's tripled and the scale factor is 3.
