Answer:
Step-by-step explanation:
Find the slope of the line AB.
<u>The slope:</u>
- m = (11 - 9)/(11 - 7) = 2/4 = 1/2
Since the altitude is perpendicular to AB, it has a slope of -2.
The line with the slope of -2 and passes through point C(6, 16).
<u>Use point-slope equation to find the line:</u>
- y - 16 = -2(x - 6)
- y - 16 = -2x + 12
- y + 2x = 16 + 12
- 2x + y = 28
A = 2, B = 1, C = 28
Triangle A
hypotenuse: 3y + x
leg: y - x
Triangle B
hypotenuse: y + 5
leg: x + 5
Congruency => 3y + x = y + 5 and y - x = x + 5
Solve the system
3y + x = y + 5 -> 2y + x = 5
y - x = x + 5 -> y - 2x = 5
2y + x = 5
-2y + 4x = -10
5x = -5
x = -1
y = (5 -(-1)) / 2 = 6/2 = 3
Verify:
hypotenuses
3y + x = 9 - 1 = 8
y + 5 = 3 + 5 = 8
Legs:
y - x = 3 -(-1) = 3 + 1 = 4
x + 5 = -1 + 5 = 4.
Then both hypotenuses and both legs are congruent.
Answer: x = -1 and y = 3
Answer:
174 square centimetres
Step-by-step explanation:
The formula for finding the surface area of a rectangular prism is
SA = 2LW + 2LH + 2HW
Therefore surface area will be
= 2(11*5) + 2(11*2) +2(2*5)
= 2 * 55 + 2 * 22 + 2 * 10
= (110 + 44 + 20) square cm
Which gives you 174 square centimetres.
Answer:

Step-by-step explanation:
In order to solve this problem we can make use of the following formula:

where θ is the total angle the basket has turned, ω is the angular velocity and t is the time.
Generally theta is written in radians and omega is written in radians per second. Now, since the revolutions are directly related to the radians and they want us to write our answer in revolutions, we can directly use the provided speeds in the formula, so we can rewrite it as:

where n represents the number of revolutions and f is the frequency at which the basket is turning.
The movement of the cylindrial basket can be split in two stages, when it accelerates and when it decelerates. So let's analye the first stage:

and now let's analyze the second stage, where it decelerates, so we get:

So now that we know how many revolutions the cylindrical basket will take as it accelerates and as it decelerates we can add them to get:
n=18rev+26rev=44rev
So the basket will turn a total of 44 revolutions during this 22s interval.
Answer:
80%
Step-by-step explanation:
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