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.
Huhvgujvdthb friend gf t if y h iutzyreRx it’s g. Ttussuesru. G h
(9m - 6)7
Distribute 7 to both sides
63m - 42
Add 42 to get 63m by itself
63m = 42
Divide both sides by 63
m = 42/63 or simplified, 2/3
Answer:
see below
Step-by-step explanation:
Every vertex moves twice as far from the center of dilation as it is in the pre-image.
Perhaps the easiest image point to find is the one at lower left. In the pre-image it is 2 units left of the center of dilation, so the image point will be 2×2 = 4 units left of the center of dilation. It will be located at (-6, -2).
Other points on the image can be found either by reference to the center of dilation, or by reference to known image points. For example, the next point clockwise is 1 left and 4 up in the pre-image, so will be 2 left and 8 up from (-6, -2) in the image. That is, the pre-image point (-5, 2) becomes image point (-8, 6). You will note that (-5, 2) is 3 left and 4 up from the center of dilation, and that (-8, 6) is 6 left and 8 up from the center of dilation (twice as far away).
The following sequence shown up top is arithmetic sequence
