Answer:
46.57
Step-by-step explanation:
Given that:
h(t) = 37t - 4.9t²
When the ball reaches the ground, then the height is zero;
So, we equate h(t) to zero and solve for t
37t - 4.9t² = 0
t = 0, 7.55
Let the Initial time be a = t = 0
The time the ball reaches the ground be b = 7.55
So, the average height can now be calculated as:
Average height = ![\frac{1}{b-a}\int\limits^b_a {h(t)} \, dt](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bb-a%7D%5Cint%5Climits%5Eb_a%20%7Bh%28t%29%7D%20%5C%2C%20dt)
= ![\frac{1}{7.55-0}\int\limits^{7.55}_0 (37t-4.9^2) dt](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B7.55-0%7D%5Cint%5Climits%5E%7B7.55%7D_0%20%2837t-4.9%5E2%29%20%20%20dt)
= ![\frac{1}{7.55-0}\ (\frac{37(7.55)^2}{2} - \frac {4.9(7.55)^3}{3})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B7.55-0%7D%5C%20%28%5Cfrac%7B37%287.55%29%5E2%7D%7B2%7D%20-%20%5Cfrac%20%7B4.9%287.55%29%5E3%7D%7B3%7D%29)
= ![\frac{1}{7.55-0}\ (351.6104208)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B7.55-0%7D%5C%20%28351.6104208%29)
= 46.57091665
≅ 46.57 to (2 decimal places)
The quadriatic portion of a quadriatic equation is actually the term x^2. On the other hand, the constant in a quadriatic equation are a, b, c, or whatever letter except for x, which is a variable.
Answer:
You didn't list the answers, but here are some conversions:
Step-by-step explanation:
14.794 cups
.925 gallons
3500 milliliters
118.349 fluid ounces
7.397 pints
3.698 quarts
236.698 tablespoons
710.094 teaspoons
Answer:
x=8
Step-by-step explanation:
If the value of x varies directly as the value of y we can say they are directly proportional. This implies that when y increases x will increase too, and when y decreases x will also decrease.
If x=16 when y=3/4 we can write their relation as:
x/y = 16/(3/4) = 16*(4/3) = 64/3
So, for every value of y, the ratio x/y must maintain equal to 64/3 because both values are proportional.
Now we can see what happens to x when y varies. If y=3/8:
x/(3/8) = 64/3
Multiply both sides by 3/8 to eliminate the 3/8 in the denominator.
x/(3/8) * (3/8) = (64/3) * (3/8)
See that we have a 3 multiplying and another dividing, we can eliminate them.
x = 64/8
x = 8
So, if y decreases to 3/8 x will decrease to 8. Notice that y is decreasing in a half as 3/8 is the half of 3/4, and x is also decreasing in a half from 16 to 8, what makes sense.
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