Answer:
k=24
Step-by-step explanation:
The tangent of the function f at x=a, can be found by differentiating f w.r.t. x and then replacing x with a.
f=-x^2+8x+20
Differentiating both sides:
f'=(-x^2+8x+20)'
By sum rule:
f'=(-x^2)'+(8x)'+(20)'
By constant multiple rule:
f'=-(x^2)'+8(x)'+(20)'
By constant rule:
f'=-(x^2)+8(x)'+0
By power rule:
f'=-2x+8
f' at x=a is -2a+8
This is the slope of any tangent line to the curve f.
The slope of g is 4 if you compare it to slope intercept form y=mx+b.
So we gave -2a+8=4.
Subtracr 8 on both sides: -2a=-4
Divide both sides by -2: a=2
The tangent line to the curve at x=2 is y=4x+k.
To tind y we must first know the y-coordinate of the point of tangency.
If x=2, then
f(2)=-(2)^2+8(2)+20=-4+16+20=12+20=32
So the point is (2,32).
g(x)=4x+k and we know g(2)=32.
This gives us:
32=4(2)+k
32=8+k
k=32-8
k=24
Answer:
149
Step-by-step explanation:
One foot = 0.3048 meters
so 60 feet = 0.3048 * 60 = 18.29 meters to nearest 1/100
Answer:
Identity property
Step-by-step explanation:
Given :
On average, a refrigerator door is opened 99 times each day.
Len has two refrigerators in his house.
To Find :
How many times in a 8−week period are the refrigerator doors opened.
Solution :
Number of times door opened for 2 refrigerator , n = 99×2 = 198.
Number of days in 8 week , d = 8×7 = 56 days.
So, total number of times doors open in a period of 8-week is :
Therefore, refrigerator doors are opened about 11088 times.
Hence, this is the required solution.
