Answer:
B
Step-by-step explanation:
f(0) - f(-3) = area under f'(x) from x=0 to x=3.
We can find the area under f'(x) in this interval by finding the area of the triangle formed by the line.
A = 1/2 b h
A = 1/2 (3) (3)
A = 4.5
f(0) - f(-3) = 4.5
Since f(0) = 7:
7 - f(-3) = 4.5
f(-3) = 7 - 4.5
f(-3) = 2.5
Answer:
t = 2.28 s
Step-by-step explanation:
h = 105 - 9t - 16t ^ 2
0 ft = 105 ft - 9t -16^t
To find the roots of a quadratic function we have to use the Bhaskara formula
, the roots will give us the time it takes to reach zero height
ax^2 + bx + c = 0
-16^t - 9t + 105 ft = 0 ft
a = -16 b = -9 c = 105
t1 = (-b + √ b^2 - 4ac)/2a
t2 =(-b - √ b^2 - 4ac)/2a
t1 = (9 + √(-9^2 - (4 * (-16) * 105)))/2 * (-16)
t1 = (9 + √(-81 + 6720))/ -32
t1 = (9 + √6639)/ -32
t1 = (9 + 81.84)/ -32
t1 = 90.84 / -32
t1 = -2.83 s
t2 = (9 - √(-9^2 - (4 * (-16) * 105)))/2 * (-16)
t2 = (9 - √(-81 + 6720))/ -32
t2 = (9 - √6639)/ -32
t2 = (9 - 81.84)/ -32
t2 = -72.84 / -32
t2 = 2.28 s
we have two possible values, we are only going to take the positive one, beacause we are talking about time
t2 = 2.28 s
Answer:
18 L
Step-by-step explanation:
Given : she must mix a solution of 67% herbicide with a solution of 46% herbicide to form 42 liters of a 55% solution.
To Find: How much of the 67% solution must she use?
Let x = amount of 67% solution needed
Then 42-x=amount of 46% solution needed
Now we know that the pure herbicide in the 67% solution
So, pure herbicide = (0.67x)
The amount of pure herbicide in the 46% solution (0.46(42-x))
Now 42 liters of a 55% solution = (0.46(42-x))
So,
Amount of 67% solution + Amount of 46% solution = 42 liters of a 55% solution
⇒0.67x+0.46(42-x)=0.55*42
⇒0.67x+19.32-0.46x=23.1
⇒0.21x=3.78
⇒
⇒x = 18 liters
Hence she use 18 liters of the 67% solution
Answer:
Step-by-step explanation:
8 x 6 = 48 because you just add a 1
Answer:
The integers are 52 and 54
Step-by-step explanation:
x = first even integer
x + 2 = next integer that is even
x + x + 2 = 106
2x + 2 = 106
2x = 104
x = 52
x + 2 = 54
