Answer:
Time = 3secs
Max height = 56m
Step-by-step explanation:
Given the height reached by the rocket modeled by the equation;
h(x) = -5(x - 3)² + 56 where;
x is in seconds
The rocket velocity at its maximum height is zero.
Hence dh/dx = 0
dh/dx = 2(-5)(x-3)
dh/dx = -10(x-3)
Since dh/dx = 0
0 = -10(x-3)
0 = -10x + 30
10x = 30
x = 3secs
<em>Hence it takes 3 secs to reach the maximum height.</em>
Get the maximum height reached by the rocket. Substitute x = 3 into the equation given;
Recall that:
h(x) = -5(x - 3)² + 56
If x = 3
h(3) = -5(3 - 3)² + 56
h(3) = 0 + 56
h(3) = 56
<em>Hence the maximum height that the rocket reaches is 56m</em>
The function's input value is 2.
f(x) = 2x² + 3x + 5
f(x) = 2(2)² + 3(2) + 5
f(x) = 2(4) + 6 + 5
f(x) = 8 + 11
f(x) = 19
9514 1404 393
Answer:
B) biker at 12 mph
Step-by-step explanation:
Distance is proportional to time when velocity is constant. It is not constant in the case of stop-and-go traffic, a baseball*, or a slowing car. The speed of the person biking is given as a constant 12 mph, so that person is traveling a distance proportional to time.
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<em>Additional comment</em>
* It depends. The usual assumption is that horizontal speed is constant, in which case the distance from the hitter along the ground is proportional to time. If you are modeling the real world, the ball slows due to air resistance, so distance is not proportional to time.
If you are concerned with the actual distance the baseball travels through the air, the ball's speed slows as it gains height, then increases again as it falls to the ground. The speed is not constant during any part of that travel.
Since 5 winning numbers are draw and there are exactly 2 winning numbers, the other 3 numbers chosen have to be incorrect.
The 2 numbers picked right, there are 5C2=10 different possibilities.
The other 3 numbers are just picked from the rest of the 32 numbers. Getting there are 32C3=4960 different possibilities.
For each set of 2 correct winning numbers, you could have the 4960 different losing numbers to match up to make a unique set. This meant that there are 4690*10=46900 different total possibilities.
Now the total different outcomes of how you can choose the numbers are 37C5=435897 outcomes.
Now the way to find probabilities is want/total
The want is 46900 and the total is 435897
Doing the division you get the number rounded to the nearest thousandths as 0.107 or in percent form as
10.759% chance of picking exactly 2 winning numbers.
This seems like a competition problem of some sort therefore I assume that you already know what combinations in form nCk and permutation in form nPk means.
