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➷ Substitute -3 into g(x)
g(-3) = 2(-3) + 4
Solve:
g(x) = -2
Substitute this value into f(x)
f(-2) = 3(-2)^2
Solve:
f(-2) = 12
The answer is B. 12
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Answer:
k = 11.
Step-by-step explanation:
y = x^2 - 5x + k
dy/dx = 2x - 5 = the slope of the tangent to the curve
The slope of the normal = -1/(2x - 5)
The line 3y + x =25 is normal to the curve so finding its slope:
3y = 25 - x
y = -1/3 x + 25/3 <------- Slope is -1/3
So at the point of intersection with the curve, if the line is normal to the curve:
-1/3 = -1 / (2x - 5)
2x - 5 = 3 giving x = 4.
Substituting for x in y = x^2 - 5x + k:
When x = 4, y = (4)^2 - 5*4 + k
y = 16 - 20 + k
so y = k - 4.
From the equation y = -1/3 x + 25/3, at x = 4
y = (-1/3)*4 + 25/3 = 21/3 = 7.
So y = k - 4 = 7
k = 7 + 4 = 11.
Acceleration due to gravity is 32.2 ft/s^2
68=32.2t
t=2.11 seconds
h=68t-32.2/2*t^2
h(2.11)=68*2.11-32.2/2*2.11^2
h=71.8 feet
Answer:

Step-by-step explanation:
Given: 
To find: c
Solution:
At
:
(i)
At
:
(ii)
At
:
(iii)
On subtracting (i) and (ii),
(iv)
On subtracting (i) and (iii),

On subtracting (iv) and (v),

Put a=3 in (iv)

Put
in (iii)

Answer:
B: 32 cm
Step-by-step explanation:
Add together only the outside lengths
6+6+4+4+3+3+3+3=32 cm