1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Artyom0805 [142]
2 years ago
13

1Determine the value of k if g(x)=4x+k is a tangent to f(x)=-x²+8x+20​

Mathematics
1 answer:
tangare [24]2 years ago
6 0

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

You might be interested in
Solve for A R=x(A+B)
julia-pushkina [17]
R=x(A+B)
divide both sides by x
R/x=A+B
minus B both sides
(R/x)-B=A
A=(R/x)-B
5 0
3 years ago
On a winter day in Alaska, the temperature at noon was -0.6°C. From noon to 3:00, the temperature increased by 1.2°C. From 3:00
vazorg [7]
The expression is -6 + 1.2 + -0.4 + -0.6


7 0
3 years ago
Find the value of f(1) and f(0)​
sergeinik [125]

Answer:

Step-by-step explanation:suppose

Our equation be x^2+2x +1

When f(x)= 1

Substitute 1 in our equation. 1+2+1 /( we get like this)

=4

When f(0)= 0+0+1. =1

Thank you

5 0
3 years ago
Round 6.14 to the nearest tenth <br> (this is 5th grade math)
Liula [17]

Answer:

<h2>6.14 rounded to the nearest tenth is 6.1.</h2><h2></h2><h2>I hope it helps.</h2><h2>Have a great day.</h2>

6 0
3 years ago
VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.
Sonbull [250]

Answer: (4,-11)

Step-by-step explanation: To perform a 180 degree rotation we switch the signs of the coordinates

5 0
2 years ago
Read 2 more answers
Other questions:
  • A group of students stood in a circle to play a game. The circle had a diameter of 22 meters. Which measurement is closest to th
    13·1 answer
  • Evaluate x2/y + x2/z for x = 6, y = -4, and z = -2.
    6·2 answers
  • BRAINLIEST LOVES!!!!!
    14·2 answers
  • Please help with this word problem would be a huge help!!
    10·1 answer
  • I think i found the right one but I let her go thru my things but she wont lemme go thru her stuff what does that mean :( I want
    12·2 answers
  • List the first 5 terms of the sequence -3n -2.<br>​
    8·2 answers
  • while walking in the woods Molly's is a deer grazing as she creeps forward to get a better look molly steps on a Twink that snap
    11·2 answers
  • Which order is correct? 0.8. 1 2 3' 3 1. 0 -0.8, 2 1 1. 1 3 3 1 o 1 3. -0.8, 2 3 1 1 IN 1 -0.8 1​
    14·2 answers
  • **Round to the nearest tenth Level ll: John missed 14 points on an 80 point science test. What percentage did he get?​
    11·1 answer
  • Which statement describes how to solve Equation. Square both sides and then solve the resulting quadratic equation.
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!