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GaryK [48]
3 years ago
15

F(x) = x^-1, x=.9. Use linear approximation to estimate answer

Mathematics
1 answer:
Angelina_Jolie [31]3 years ago
8 0
L(x) = f'(a)(x - a)
f(x) = x^(-1), f'(x) = -x^(-2)
Let a = 1, f'(a) = -(1)^(-2) = -1
L(0.9) = f'(1)(0.9 - 1) = -1(-0.1) = 0.1

Therefore, linear approximation of f(x) = x^(-1) for x = 0.9 is 0.1
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In the year 1987, an investment was worth $29,800. In the year 1997, this
Veseljchak [2.6K]

Answer:

a) 46.98%

b) increasing rate of change

Step-by-step explanation:

In year 1987, investment worth $29800

In year 1997, investment worth $43800

Rate of change = 1997investment - 1987investment / 1987investment × 100

Rate of change = 43800 - 29800/29800 × 100

= 14000/29800 × 100

= 0.46979 × 100

= 46.98%

Therefore, the rate of change of the investment during the time period is 46.98%.

b) The rate of change of the investment is increasing. This is as a result of the following reasons. First, the value of rate of change is positive. Second, there is no value for rate of change for period before the time period so we cannot compare rate of change.

8 0
3 years ago
If the perimeter of a square is 236 inches, how long is each side?
Degger [83]

Answer:

59 inches

Step-by-step explanation:

a square has 4 equal sides

if the sum of all sides(perimeter) is 236 you can do the inverse of that and divide by 4

so your answer should be 59

5 0
3 years ago
Read 2 more answers
You need to buy some pencils and an eraser. You can spend no more than $5. The eraser cost $1 and the pencil cost $0.25 each. Wr
vekshin1
5≤1e+ .25p 
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6 0
3 years ago
-3x+10y=-20 <br> -8x+2y=11 elimination method
Semenov [28]
(-75/37, -193/74) is your answer .-.
5 0
3 years ago
Please help. I don’t understand and don’t know what do to.
Bingel [31]

9514 1404 393

Answer:

  72

Step-by-step explanation:

The triangles are said to be similar. (ΔNPQ ~ ΔRSQ) That means corresponding sides have the same ratio:

  NP/RS = NQ/RQ = PQ/SQ = 24/32 = 21/28 = 3/4

This ratio, or scale factor, also applies to the perimeters of the two triangles.

  perimeter NPQ / perimeter RSQ = 3/4

Using the given expressions for the perimeters, we have ...

  (7x +2)/(10x -4) = 3/4

We can solve this equation in the usual way to find the value of x. Then we can use that value to find the perimeter of ΔNPQ.

  4(7x +2) = 3(10x -4) . . . . . multiply both sides by 4(10x -4)

  28x +8 = 30x -12 . . . . . eliminate parentheses

  20 = 2x . . . . . . . . . . . add 12-28x to both sides

  10 = x . . . . . . . . . . . divide both sides by 10

The perimeter of ΔNPQ is ...

  7x +2 = 7(10) +2 = 72

The perimeter of triangle NPQ is 72 units.

7 0
3 years ago
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