Hello from MrBillDoesMath!
Answer:
27 x^2 sqrt(x^3) sin(x^3) - 9/2 sqrt(x^1/2) sin(x^1/2)*x^(-1/2)
Discussion:
Let f(t) - 9 sqrt(t) sin(t), then
y' = f(x^3) * d(x^3)/dx - f(sqrt(x)) * d(x^1/2)/dx
= (9 sqrt(x^3)sin(x^3)) * 3x^2 - (9 sqrt(x^1/2)sin(x^1/2)) * (1/2) x^-(1/2)
= 27 x^2 sqrt(x^3) sin(x^3) - 9/2 sqrt(x^1/2) sin(x^1/2)*x^(-1/2)
Hope I didn't make a "bozo" error differentiating things!
Thank you,
MrB
Answer:
B
Step-by-step explanation:
To solve this, we use ratio.
Firstly, we need to know the number of hours traveled. The total number of hours traveled = x+y
Ratio of this used by high speed train = x/(x +y).
Total distance traveled before they meet = [x/(x + y)] × z
For low speed train = [y/(x + y)] × z.
The difference would be distance by high speed train - distance by low speed train.
= z [ (x - y)/x + y)]
Answer:
Style A shoes sold : <u>152</u>
Style B shoes sold : <u>88</u>
Step-by-step explanation:
Let :
- Style A shoes = x
- Style B shoes = y
Forming equations :
- x = 2y - 24
- 66.95x + 84.95y = 17,652
Substitute the value of x from 1 in 2.
- 66.95 (2y - 24) + 84.95y = 17,652
- 133.90y - 1606.80 + 84.95y = 17,652
- 218.85y = 19258.80
- <u>y = 88</u>
<u />
Finding x :
- x = 2(88) - 24
- x = 176 - 24
- <u>x = 152</u>
<u />
Solution :
- Style A shoes sold : <u>152</u>
- Style B shoes sold : <u>88</u>
Let's consider each of the options;
A) The range is the values that y can be of the function f(x). We can see that no matter what x values you put in, f(x)>0. It will never be negative. Although, if you put (1/2)^2, you can get a y value of (1/4) so this statement is incorrect.
B) It would have to put in the x or y value into the function and check. f(0)=(1/2)^0
You know that anything to the zero-th power gives 1, therefore, this statement is correct.
C) Again, if you put in a value such as (1/2)^2, you would be getting a number that is smaller than 1/2, so it isn't always increasing.
D) Again, it is possible to input any value in x and you would still be getting a positive y-value, therefore, this statement is incorrect.
Hope I helped :)
To answer this, let's first describe the two areas and obtain the pertinent dimensions from them.
The area of the square hole is 5 cm^2. Since A = s^2, where s is the length of a side of the square, s = +√5 in this situation. +√5 is approx. 2.24 cm.
The area of the round peg is 5 cm^2 also, but the area is calculated using a different formula: A = πr^2, where r is the radius of the circle. Solving for r^2, we get:
r^2 = A/π. Here, r^2 = (5 cm^2)/π = 5π, so that:
r = +√(5π). This is approx. 3.96 cm, and so the diameter is twice that, or 7.93 cm.
So there's plenty of room for the round peg to enter the square hole, but not the other way around!
