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
We have consecutive odd numbers for the sides of a triangle, perimeter 201. We could write an equation, but clearly the middle side is 201/3 = 67, so the other two sides are 65 and 69.
This is almost an equilateral triangle, angles around 60 degrees, so not obtuse, meaning one angle over 90 degrees.
Scalene means the sides are all different lengths; we didn't even have to solve the problem to know this is true.
Smallest side 61, false.
Largest side 69, true.
This last one doesn't make much sense to me. What's a unit here? Dilation of 1/3 means all the linear measures become 1/3 as big, including the perimeter. It would decrease much more than 3 inches, since it would go from 201 inches to 67 inches. If I have to answer I'd go with false.
Follow the steps in order how to know how to divide
1st find the averages of each one:
Elizabeth average of reading in min =(18+36+15+45+88+57+12)/7 =38.71 min
Sam average of reading in min =(17+52+48+35+13+71+16)/7 =36 min
question:
1) No
2) YES. [the range is te difference between the largest & the smallest)
Eliz Range = 88-12 =76 & Sam's= 71-13 = 58
3) NO. Sam 71 min & Eliz 88 min
4) YES. Median Eliz =45 min. Median Sam =35 min
