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Anarel [89]
3 years ago
12

Find the equation of the tangent to the curve

Mathematics
1 answer:
12345 [234]3 years ago
4 0

9514 1404 393

Answer:

  y = -x/16 +1

Step-by-step explanation:

The slope is at any point x is ...

  y' = -4/x^2

so, at x=8, the slope is ...

  m = -4/8^2 = -4/64 = -1/16

The point-slope form of the equation of the line is ...

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

Then the line with slope -1/16 through point (8, 1/2) is ...

  y - 1/2 = -1/16(x -8)

  y = -1/16x +1/2 + 1/2 . . . . . eliminate parentheses, add 1/2

  y = -1/16x +1 . . . . . equation of the tangent line

You might be interested in
What are the vertex and axis of symmetry of the parabola y = x2 – 16x + 63?
jonny [76]

Answer:

A

Step-by-step explanation:

Remember that the x-value of the vertex when an equation is given in standard form can be found with the equation \frac{-b}{2a}. So, we can take the coefficients from the equation and plug them in.

\frac{-b}{2a} \\\frac{-(-16)}{2(1)}\\\\\frac{16}{2}\\\\8

Now we know that the x-value of the vertex is 8. Next, the equation for the y-value is c-ah^2, where h is the x-value of the vertex (8).

(63)-(1)(8)^2\\63-64\\-1

So the vertex is (8,-1).

Finally, the axis of symmetry is the x-value of the vertex, also called h.

Final answer, vertex: (8,-1) and axis of symmetry: x=8

Hope this helps!

3 0
3 years ago
What is the slope of the line through (-3,0) and (-4,-2)?
rodikova [14]

AnswerY=-10/3x+11:

Step-by-step explanation:

M=0--2/-3-4= -10/3

Y-1=-10/3(x-3)

-10/3x+10+1

Y=-10/3x+11

4 0
3 years ago
Is the following statement a good definition? Why? An integer is divisible by 100 if and only if its last two digits are zeros.
kifflom [539]
The given statement is:
An integer is divisible by 100 if and only if its last two digits are zeros

The two conditional statements that can be made are:

1) If an integer is divisible by 100 its last two digits are zeros.

This is a true statement. If a number is divisible by 100, it means 100 must be a factor of that number. When 100 will be multiplied by the remaining factors, the number will have last two digits zeros. 

2) If the last two digits of an integer are zeros, it is divisible by 100.

This is also true. If last two digits are zeros, this means 100 is a factor of the integer. So the number will be divisible by 100.

Therefore, the two conditional statements that are formed are both true.

So, the option A is the correct answer.
Yes, it is. When the definition is separated into two conditional statements, both of the statements are true
6 0
3 years ago
a park is 9/10 mile long and 4/5 mile wide. What is the area of the park? ENTER ANSWER AS A FRACTION FOR EXAMPLE: 4/10.​
ASHA 777 [7]

The park formed like a rectangle so :

Area = length × width

Area = ( 9/10 ) × ( 4/5 )

Area = 9 × 4 / 10 × 5

Area = 9 × 2 × 2 / 5 × 5 × 2

Area = 18 / 25

3 0
2 years ago
Can someone help me with this math homework please!
lapo4ka [179]

Answer:

x = 48.125

Step-by-step explanation:

Explanation in progress! (●'◡'●)

7 0
3 years ago
Read 2 more answers
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