Answer:
16
Step-by-step explanation:
Answer:
The rocket will reach its maximum height after 6.13 seconds
Step-by-step explanation:
To find the time of the maximum height of the rocket differentiate the equation of the height with respect to the time and then equate the differentiation by 0 to find the time of the maximum height
∵ y is the height of the rocket after launch, x seconds
∵ y = -16x² + 196x + 126
- Differentiate y with respect to x
∴ y' = -16(2)x + 196
∴ y' = -32x + 196
- Equate y' by 0
∴ 0 = -32x + 196
- Add 32x to both sides
∴ 32x = 196
- Divide both sides by 32
∴ x = 6.125 seconds
- Round it to the nearest hundredth
∴ x = 6.13 seconds
∴ The rocket will reach its maximum height after 6.13 seconds
There is another solution you can find the vertex point (h , k) of the graph of the quadratic equation y = ax² + bx + c, where h =
and k is the value of y at x = h and k is the maximum/minimum value
∵ a = -16 , b = 196
∴ 
∴ h = 6.125
∵ h is the value of x at the maximum height
∴ x = 6.125 seconds
- Round it to the nearest hundredth
∴ x = 6.13 seconds
Set it up with variables; tomatoes=t, sunflowers=s, corn=c
320=t+s+c
This year;
t=2s
c=t+40
so, replace 2s for t; c=2s+40
now we can put those factors in for 320=t+c+s
320= 2s+2s+40+s
(SIMPLIFY)---> 320=5s+40----> 5s+280----> s=56
now incorporate the s value into the other equations.
c=2s+40----> c=56(2)=40 ----> c=152
t=2s -----> t=2(56) ----> t=112
TOMATOES= 112 acres
CORN= 152 acres
SUNFLOWERS= 56 acres
To check your work: 320=t+s+c ----> 320=112+156+56
-3 because it shows the value right there