Answer:
We conclude that the set of numbers x satisfying -7 ≤ x ≤ 4 is an interval that contains -7, 4, and all numbers in between.
Thus, the domain of g is: -7 ≤ x ≤ 4
Step-by-step explanation:
We know that the domain of a function is the set of inputs or argument values for which the function is defined.
From the given graph, it is cleared that the function g starts from the x-value x = -7 and ends at x = 4.
It means the function is defined for the set of input values from x = -7 to x = 5 for which the function is defined.
Therefore, we conclude that the set of numbers x satisfying -7 ≤ x ≤ 4 is an interval that contains -7, 4, and all numbers in between.
Thus, the domain of g is: -7 ≤ x ≤ 4
Answer:
A) √3
Step-by-step explanation:
The tangent of an angle can be found by dividing the leg opposite the angle over the leg adjacent to it.
So, we have to find them.
The 30-60-90 rule says that in a right triangle with the angles 30°, 60° and 90°, the sides opposite those angles will have the ratio of 1:√3:2.
That means the side adjacent to 60° is 2 units long and the one opposite is 2√3 units long.
Dividing those two gives us (2√3)/2, which can be simplified to √3.
3/4 = 3/4*1
3/4 = 3/4 * 3/3 = 9/12
Box is 9/12 full after heba ate 1/12 of a box of cereal
Initial fraction will be 9/12+1/12
=10/12= 5/6
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.
