Answer:
93 feet
Step-by-step explanation:
Let us first find the time it takes to reach the maximum height. We can do this by differentiating the height function to get velocity:
dh(t)/dt = v(t) = -32t + 72
The maximum height will occur when the velocity becomes 0. Therefore, the time it takes to reach maximum height is:
0 = -32t + 72
32t = 72
t = 72/32 = 2.25 seconds
Therefore, the maximum height of the pumpkin is:
h(2.25) = -16(2.25)^2 + 72(2.25) + 12
h(2.25) = -81 + 162 + 12
h = 93 feet
<span>x=y+2
2y=x-1
substitute </span>x=y+2 into 2y=x-1
2y=x-1
2y=y+2 -1
2y - y = 1
y = 1
<span>x=y+2
</span><span>x=1+2
x=3
answer
x = 3 and y = 1</span>
Answer:
Step-by-step explanation:
If AB = 5 , then AE = 5 [Radii of the same circle]
So,
AC = AE + EC
AC = 8+5
AC = 13 units
Now, Using Pythagorean theorem to find the missing side i.e. BD because tangent strikes the circle at 90 degrees making the triangle a right angled triangle
Where c = AC , a = BD and b = AB
169 = BD² + 25
Subtracting 25 to both sides
169 - 25 = BD²
BD² = 144
Taking square root on both sides
BD = 12 units
Given that y varies inversely with x, then:
y=k/x
where
k is the constant of proportionality:
k=yx
hence, given that x=28 when y=2, then the value of k will be:
k=28×2
k=56
Answer: k=56
