Answer:
11.91
Step-by-step explanation:
The question says there is a new line that connects V and T. If this line is drawn, the diagram would have a right-angle triangle. This triangle is called TUV.
In triangle TUV, the side length created by the points VT is the hypotenuse.
For right-angle triangles, you can use the Pythagorean theorem to find any side.
It's in the format side² + side² = hypotenuse².
To use the formula, you need to know the length of the other two sides. The length of these sides, because they are exactly horizontal or vertical, is found by subtracting the smaller coordinate from the other (that is not the same).
The lengths of other sides:
VU:
-3 is the same. The length is 3.5 - (-5.75) = 9.25
UT:
-5.75 is the same. The length is 4.5 - (-3) = 7.5
Substitute the lengths into the Pythagorean theorem:
a² + b² = c²
9.25² + 7.5² = c² Simplify
141.8125 = c² Find the square root of both sides to isolate c
c = 11.91 Final answer, length of VT
Sin (x) = 12/13 this is because sine is opposite divided by hypotenuse.
cos (x) = 5/13 this is because cosine is adjacent divided by hypotenuse.
tan (x) = 12/5 this is because tangent is opposite divided by adjacent.
Answer:
Step-by-step explanation:
Suppose number is x
Following equation can be written from question statement
Simplifying it further
Step-by-step explanation:
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By solving the motion equations for the piano, we will see that they have 0.7 seconds to react.
<h3>
How to find the motion equation for the piano.</h3>
So the piano is in a free fall from a height of 30m.
The motion equations will be given by:
- The only force acting on the piano will be the gravitational one, thus the acceleration of the piano is the gravitational acceleration: a(t) = -9.8m/s^2 (Where the negative sign is because it is falling down).
- To get the velocity we integrate over time, because the piano has no initial velocity, the constant of integration is zero: v(t) = (-9.8m/s^2)*t
- To get the position equation we integrate again, here the initial position is 30 meters above the ground, so that will be our constant of integration: p(t) = (1/2)*(-9.8m/s^2)*t^2 + 30m
<h3>How long takes to fall?</h3>
We want to find the value of t such that the position is equal to zero, so we need to solve:
0 = (1/2)*(-9.8m/s^2)*t^2 + 30m
30m = (1/2)*(9.8m/s^2)*t^2
2*30m/(9.8m/s^2) = t^2
6.1 s^2 = t^2
√(6.1 s^2) = 2.5s = t
This means that the piano falls to the ground in 2.5 seconds.
But the workes notice it when the piano is 14 meters above the ground, it happens when:
p(t) = 14m = (1/2)*(-9.8m/s^2)*t^2 + 30m
Solving that we get:
30m - 14m = (1/2)*(9.8m/s^2)*t^2
2*16m/(9.8m/s^2) = t^2
3.27s^2 = t^2
√(3.27s^2) = t = 1.8s
So the piano falls in 2.5 seconds, and the works notice it 1.8 seconds after it starts falling, meaning that they have:
2.5 - 1.8 = 0.7 seconds to react.
If you want to learn more about motion equations, you can read:
brainly.com/question/2473092
