Find the measure of x. (to the nearest tenth)
1 answer:
For the given triangle, x measures A) 25.7 units.
Step-by-step explanation:
Step 1:
In the given triangle, the angle is 56°. The adjacent side has a length of x units and the hypotenuse of the triangle measures 46 units.
To calculate the value of x, we determine the cos of the triangle where we divide the length of the adjacent side by the length of the hypotenuse.
Step 2:
The length of the adjacent side = x units.
The length of the hypotenuse = 46 units.
The angle of the triangle = 56°.
So x = 25.7186 units, rounding this is off we get option A.
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Answer:
0.98 seconds
Step-by-step explanation:
We assume the height of the volleyball is described by the equation for ballistic motion. We want to find the time it takes for the height to become zero.
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<h3>motion equation</h3>The general form of the equation of height for ballistic motion is ...
The coefficient 16 in the equation is an approximation of 1/2g, where g is the acceleration due to gravity in ft/s². This means the units of time and distance are expected to be seconds and feet.
For the problem at hand, the initial velocity and height are 10.5 ft/s and 5 ft. Then the height equation is ...
h(t) = -16t² +10.5t +5
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<h3>reaction time</h3>Marsha has until the ball hits the ground to react to the serve. To find out how long that is, we need to solve the height equation for t when h=0. This is most easily done using the quadratic formula with ...
- a = -16
- b = 10.5
- c = 5
The solution is ...
The positive solution is ...
t ≈ 0.976327 ≈ 0.98
Marsha has about 0.98 seconds to react before the volleyball hits the ground.
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<em>Additional comment</em>
After about 0.33 seconds, Marsha knows she doesn't need to react at all. The serve will not clear the net. Its maximum height is about 6' 8 5/8". A women's volleyball net is 7' 4 1/8" high. Jennifer's serve velocity must be at least 12.3 ft/s for the ball to go over the net. With that upward velocity, Marsha has about 1.06 seconds to react.
