Answer:
See image
Step-by-step explanation:
It helps a lot to draw a triangle. Sin is OPPOSITE/ HYPOTENUSE. You can use Pythagorean thm to find the third side. Then use cos = ADJ/HYP
tan = OPP/HYP
Then, find reciprocal functions. Reciprocal just means you are flipping the ratios over.
csc = HYP/OPP
sec = HYP/ADJ
tan = ADJ/OPP
The only tricky remaining part is that you cant leave a radical (the square root symbol) on the bottom of a ratio. So you have to fix those. See image.
Answer:
Volume = 16 unit^3
Step-by-step explanation:
Given:
- Solid lies between planes x = 0 and x = 4.
- The diagonals rum from curves y = sqrt(x) to y = -sqrt(x)
Find:
Determine the Volume bounded.
Solution:
- First we will find the projected area of the solid on the x = 0 plane.
A(x) = 0.5*(diagonal)^2
- Since the diagonal run from y = sqrt(x) to y = -sqrt(x). We have,
A(x) = 0.5*(sqrt(x) + sqrt(x) )^2
A(x) = 0.5*(4x) = 2x
- Using the Area we will integrate int the direction of x from 0 to 4 too get the volume of the solid:
V = integral(A(x)).dx
V = integral(2*x).dx
V = x^2
- Evaluate limits 0 < x < 4:
V= 16 - 0 = 16 unit^3
Answer:
The domain is all real numbers. The range is {y|y ≤ 16}.
Step-by-step explanation:
The vertex of a parabola is given by
.
As a = -1, b = -2, c= 15 here, then the vertex is at (1,16).
As a is negative, it opens downward, so the range is {y|y ≤ 16}.
Meanwhile, all parabolic functions have a domain of 
.
Answer:
-30 feet
Step-by-step explanation:
What we know:
The rollercoaster first rose 210 feet, so after rise 1, the height is +210 feet.
After that, it dropped 240 feet. This is greater than the 210 feet it initially rose, so the number is now negative. The height is now -30 feet.
210 - 240 = -|240-210| = -|30| = -30 feet
After that, it rose another 80 feet. That outdoes the eariler -30 feet, so we're back to a positive height. After that rise, the height is now +50 feet.
-30 + 80 = |80 - 30| = |50| = 50 feet
Then the last two drops combine for a 80-foot drop. This is greater than the +50-foot height it was at, so we're back at -30 feet.
50 - 80 -|80 - 50| = -|30| = -30 feet after the last drop
Answer:
-The answer is 
.
Step-by-step explanation:
When you divide numbers/variables with exponents, the exponents will subtract each other:
