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.
Let the first be x and the second be x + 4
x+ x + 4 = 56
2x+4 = 56
2x = 52
∴x= 26
please mark as brainliest
Answer:
Step-by-step explanation:
Using the addition formulae for cosine
cos(x ± y) = cosxcosy ∓ sinxsiny
---------------------------------------------------------------
cos(120 + x) = cos120cosx - sin120sinx
= - cos60cosx - sin60sinx
= - 
cosx - 
sinx
squaring to obtain cos² (120 + x)
= 
cos²x + sinxcosx + 
sin²x
--------------------------------------------------------------------
cos(120 - x) = cos120cosx + sin120sinx
= -cos60cosx + sin60sinx
= - cosx + sinx
squaring to obtain cos²(120 - x)
= cos²x - sinxcosx + sin²x
--------------------------------------------------------------------------
Putting it all together
cos²x + cos²x + sinxcosx + sin²x + cos²x - sinxcosx + sin²x
= cos²x + cos²x + sin²x
= cos²x + sin²x
= (cos²x + sin²x) =
I believe the answer should be 77
Given:
First side(A): 2B - 7
Second side(B): B
Third side(C): B + 4
Plug in values:
A + B + C = 80
2B - 7 + B + B + 4 = 80
If you look at the coefficients only, you can rewrite the equation like this:
2B + B + B - 7 + 4 = 80
This means that 4B - 7 + 4 = 80
=4B - 3 = 80
= 4B = 80 + 3
B = 83/4, so you can either write B as 83/4 or as 20.75.
Checking your work:
A: 2(20.75) - 7 = 34.5
B: 20.75
C: 4 + 20.75 = 24.75
34.5 + 20.75 + 24.75 = 80cm.
Hope this helped.
