A.) To find the maximum height, we can take the derivative of h(t). This will give us the rate at which the horse jumps (velocity) at time t.
h'(t) = -32t + 16
When the horse reaches its maximum height, its position on h(t) will be at the top of the parabola. The slope at this point will be zero because the line tangent to the peak of a parabola is a horizontal line. By setting h'(t) equal to 0, we can find the critical numbers which will be the maximum and minimum t values.
-32t + 16 = 0
-32t = -16
t = 0.5 seconds
b.) To find out if the horse can clear a fence that is 3.5 feet tall, we can plug 0.5 in for t in h(t) and solve for the maximum height.
h(0.5) = -16(0.5)^2 + 16(-0.5) = 4 feet
If 4 is the maximum height the horse can jump, then yes, it can clear a 3.5 foot tall fence.
c.) We know that the horse is in the air whenever h(t) is greater than 0.
-16t^2 + 16t = 0
-16t(t-1)=0
t = 0 and 1
So if the horse is on the ground at t = 0 and t = 1, then we know it was in the air for 1 second.
Answer:
Any equation with the slope -3 and a y intercept that does not equal 5
Step-by-step explanation:
a line is parallel if the line have the same slope, and different y intercepts
3x+y=5
in slope intercept form is
y=-3x+5
slope : -3
y intercept 5
The given angles forms linear pair, and we know the angles forming linear pair are supplementary,
Therefore,
Angle MHJ + Angle MHL = 180°
Let's solve :
Value of variable m = 10°
Answer:a
Step-by-step explanation:
Answer:
The smaller number is 5.
The bigger number is 15.
Step-by-step explanation:
Let the smaller number be x and the bigger number be x+10.
x+x+10 = 4x
2x+10 = 4x
10 = 4x-2x
2x = 10
x = 10÷2
= 5
x+10 = 5+10
= 15
