MATHEMATICS HIGH SCHOOL

A triangle T is bounded (on three sides) by the lines x = 6, y = 0, and y = 3 2 x. A rectangle of width w is inscribed inside T. Find the area of this rectangle.

Answers

Answer 1

Answer:

Answer:

33.85 units^2

Step-by-step explanation:

you must first draw the triangle on the plane using the equations (see

attached file), you will have a right angle triangle with a height of 192 and a base of 6.

then you calculate the angle with the tangent function = 88.21

Then you use the small triangle to find the value of a (see attached file).

Finally, you propose an equation for X to find one of the sides of the triangle, once you have x squared it, and you already have the area,

i attached procedure

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Which shows 54^2 − 46^2 being evaluated using the difference of squares method

Answers

We use the formula: a^2 - b^2 = (a - b )(a + b);
54^2 − 46^2 = (54 - 46)(54 + 46) = 8 x 100 = 800;

Billy stacked six pieces of wood on top of one another. If each piecewas three-quarters of a foot tall, how tall was his pile?

Answers

$6*0.75=6* (3)/(4) = (6*3)/(4) = (18)/(4) = (16+2)/(4) = (16)/(4) + (2)/(4) =4.5$

If f(3) = 15 and f(5) = 45, which of the following could be f(x)?Can anyone explain this one for me?

Answers

Just saying, but the rule COULD be:

f(x) = 15(x-2)

A taut string of length 10 inches is plucked at the center. The vibration travels along the string at a constant rate of c inches per millisecond in both directions. If x represents the position on the string from the left-most end, so that 0≤x≤10, which of the following equations can be used to find the location x of the vibration after 0.3 milliseconds? A. | x -5 | =0. 3 B. ∣cx−5∣=0.3 C. | x -0.3 | = 5 D. | x - 10 | =0.3c

Answers

Answer:

The correct option is

$A. \ (1)/(c) * \left | x - 5 \right | = 0.3$

Step-by-step explanation:

The parameters given are;

The length of the string = 10 inches

The speed or rate of travel of the wave = c inches per millisecond

The position on the string from the left-most end = x

The time duration of motion of the vibration to reach x= 0.3 milliseconds

The distance covered = Speed × Time = c×0.3

Given that the string is plucked at the middle, with the vibration travelling in both directions, the point after 0.3 millisecond is x where we have;

The location on the string where it is plucked = center of the string = 10/2 = 5 inches

Distance from point of the string being plucked (the center of the string) to the left-most end = 5 inches

Therefore, on the left side of the center of the string we have;

The distance from the location of the vibration x (measured from the left most end) to the center of the string = 5 - x = -(x -5)

On the right side of the center, the distance from x is -(5 - x) = x - 5

Therefore, the the equation that can be used to find the location of the vibration after 0.3 milliseconds is $(1)/(c) * \left | x - 5 \right | = 0.3$ or $\left | x - 5 \right | = 0.3 * c$ which gives the correct option as A

If x = 9 and y = 4, work out the value of xy/ 2

Answers

answer: 3/1

Step-by-step explanation:

This is like a puzzle, and each part tells you something. The first statement tells us that x is a negative number and y is a positive number. The next statement, x + y , is what we need to know. The first absolute value gives us x. Solve for the absolute value, that is, what is inside can be either negative or positive so either x-9 = 12 or x - 9 = -12. Solve those for x = 21 or x = -3. We know that x is negative from that first statement, , so x is -3. Do the same with the other absolute value to solve for y, then add the two together to get your final answer. hope this helps a bit!

If 4 (log3 1/27)=X what is the value of X