New Workshop: 4,134,232,638,937
Old Workshop: 22,912,546,992
New/Old = 180.435
The new workshop can produce approximately 180 times as many toys as the old workshop.
For this problem, I think there is no need for the details of 12 inches width and 4 inches length. This is because an equation is already given. It was clearly specified that A as a function of θ represents the area of the opening. Then, we are asked to find exactly that: the area of opening. Moreover, the value of θ was also given. Therefore, I am quite sure that the initial details given are for the purpose of red herring only.
So, all we have to do is substitute θ=45° to the function given.
A = 16 sin 45° ⋅ (cos 45° + 1)
The angle 45° is a special angle in trigonometry. So, it would be easy to remember trigonometric functions of this angle. Sine of 45° is equal to √2/2 while cosine of 45° is also √2/2.
A = 16(√2/2) ⋅ (√2/2 + 1)
A = 8+8√2
A = 19.31 square inches
Answer:
1 ± √47
Step-by-step explanation:
Combine like terms in 2x^2 +3 x-7 =x^2 +5x +39:
2x^2 - x^2 = x^2 (first term);
3x - 5x = -2x (second term);
-7 - 39 = -46 (third term)
Then we have, all on the left side, x^2 - 2x - 46, which is a quadratic equation. Here the coefficients are a = 1, b = -2 and c = -46.
Then the discriminant, b^2 - 4ac, is:
(-2)^2 - 4(1)(-46) = 4 + 184.
The roots are:
-(-2) ±√188 2 ± √4√47
------------------- = -------------------
2 2
= 1 ± √47 (last of the answer choices)
=
x = ------------------
37.4 Gallons of gas should be your answer! Hope i helped!
If $1 is 5%, 100% would be $1 times 100/5= $1 times 20 = $20
