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:
The answer is 2.5
Step-by-step explanation:
each cube has a volume of 0.125 and the cube can hold 20 of them.
0.125 * 20 = 2.5
<h3>
Answer:</h3>
(x, y) = (7, -5)
<h3>
Step-by-step explanation:</h3>
It generally works well to follow directions.
The matrix of coefficients is ...
![\left[\begin{array}{cc}2&4\\-5&3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%264%5C%5C-5%263%5Cend%7Barray%7D%5Cright%5D)
Its inverse is the transpose of the cofactor matrix, divided by the determinant. That is ...
![\dfrac{1}{26}\left[\begin{array}{ccc}3&-4\\5&2\end{array}\right]](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B26%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%26-4%5C%5C5%262%5Cend%7Barray%7D%5Cright%5D)
So the solution is the product of this and the vector of constants [-6, -50]. That product is ...
... x = (3·(-6) +(-4)(-50))/26 = 7
... y = (5·(-6) +2·(-50))/26 = -5
The solution using inverse matrices is ...
... (x, y) = (7, -5)
Answer:
x = 11
Step-by-step explanation:
Using Secants ad Segments Theorem we can say;
(x + 7) (7) = (15 + 6) (6)
7x + 49 = (21) (6)
7x + 49 = 126
7x = 77
x = 11
Hope this helps!
Answer: 2 calls
Step-by-step explanation:
4 mins/2 minutes per call
