Answer:
x= 1/3 its a fraction but i couldnt put the answer in fraction form.
Step-by-step explanation:
Answer:c
Step-by-step explanation:just did the test
Answer:
12.7
Step-by-step explanation:
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
1615/170
We first need to convert this into a proper fraction. Which means that the denominator must be larger than the numerator for it to be proper. Also, since 1615 is BIGGER than 170, we will end up with a mixed fraction. A mixed fraction always has a whole number.
1615 can go into 170 how many times?
9 times
170*9 = 1530
Now subtract.
1615 - 1530 = 85
Now we have our mixed fraction: 9 85/170
Now we must simplify the fraction.
85/5 = 17
170/5 = 34
17/34 is the smallest possible fraction we can get.
9 17/34
Final answer: