MATHEMATICS HIGH SCHOOL

The function of f(x) varies directly with x, and f(x)=48 when x=8.
Evaluate f(x) when x=2

Answers

Answer 1
Answer: Here's the equation for direct variation. k=y/x    [ f(x)=y]
Find k
k= 48/8=6
6=y/2
y=12
Hope this helps. 

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Tell whether 807 is divisible by 2, 3, 4, 5, 6, 9, and 10.a. Divisible by 2, 3, 4, 6, and 10
c. Divisible by 3
b. Divisible by 5 and 9
d. Divisible by 2, 4, 5, 6, 9, and 10

Answers

c.divisible by three

Question 2 (Matching Worth 10 points)(08.05 LC)

Match   Term   Definition

Triangle                 A) perpendicular cross section of a cylinder

Rectangle             B) perpendicular cross section of a pyramid

Circle                    C) shape created when a right triangle is rotated about the y-axis

Cylinder                D) parallel cross section of a sphere

Answers

Answer:

Part A) Rectangle

Part B) Triangle

Part C) Cone

Part D) Circle

Step-by-step explanation:

Part A) Perpendicular cross section of a cylinder

The perpendicular cross section of a cylinder is a rectangle

The base of the rectangle is equal top the diameter of the circular base of cylinder and the height of the rectangle is equal to the height of the cylinder

Part B) Perpendicular cross section of a pyramid

Cross sections perpendicular to the base and through the vertex of a pyramid will be triangles

Part C) Shape created when a right triangle is rotated about the y-axis

When a right triangle is rotated about the y-axis, then it forms a cone.

The vertical leg of the triangle becomes the height of the cone.

The horizontal leg of the triangle becomes the radius of the cone.

The hypotenuse of the triangle becomes the slant height

Part D) Parallel cross section of a sphere

The parallel cross section of a sphere is a circle

All cross sections of a sphere are circles

Abigail played an arcade game 5 times. Her scores were 80, 95, 100, 85, and 80.What is the mode of her scores for the 5 games?

Answers

The mode is the score that she scored most frequently.  All the scores where attained once except 80, thus 80 is the mode.

Find the solution to the following equation by transforming it into a perfect square trinomial. x2 – 10x = 39

Answers

x^2-10x=39\n\nx^2-2\cdot x\cdot5=39\ \ \ \ /+5^2\n\n\underbrace{x^2-2\cdot x\cdot5+5^2}_((*))=39+5^2\n\n(x-5)^2=39+25\n\n(x-5)^2=64\iff x-5=\pm√(64)\n\nx-5=-8\ or\ x-5=8\n\nx=-8+5\ or\ x=8+5\n\nx=-3\ or\ x=13

Work out the value of (-2)2

Answers

Answer:

this is one of the property

Step-by-step explanation:

(-2)×2=(-4)

hope it helps

Consider the function f(x)=sin(2x)-1 and g(x)= 2 cos^2(x), both with domain [0,phi]. the line x = p intersects the graph of f in point A and the graph of g in point B. calculate the value of p for which the length of segment AB is maximal. Thank you please kindly answer this question

Answers

I think the correct value of p is 2.9 when dealing with this question.  Since AB is a vertical line between f(x) and g(x), you know you subtract the upper function by the lower function to find the distance between them.  In other words you are tying to find the x value (which can also be thought of as p) that produces the greatest value when g(x) is subtracted from f(x). The reason why g(x) is subtracted by f(x) is that g(x) is above f(x) over the domain of 0 to pi. 
I found p by making the function d(x)=g(x)-f(x).  Then I took the derivative of d(x) and found when the derivative of d(x) equals 0 since that indicates a maximum or a minimum of the function d(x).  their ended up being 2 points from 0 to pi where the derivative of d(x) equaled 0.  one at 2.9 and the other at 1.34.  The value at 1.34 is a minimum and therefore can't be the right answer.  The value at 2.9 is a maximum and is therefore the correct answer.
By the way I did all of my work on a graphing calculator which makes these types of questions a lot easier since it makes it so that you don't have to do it by hand. 
I hope this helps. Let me know if I got anything wrong in the comments so that I can try to fix it.
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