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Nitella [24]
3 years ago
12

Given that y=x^(1/3) , use calculus to determine an approximate value for ∛8030

Mathematics
1 answer:
Alex777 [14]3 years ago
8 0
F(x) = x^(1/3)
f(8000) = 8000^(1/3) = 20

f'(x) = 1/3 * x^(-2/3)
f'(x) = 1/(3x^(2/3))
f'(8000) = 1/(3*8000^(2/3)) = 1/(3*400) = 1/1200

Linear approximation for f(x) about x = 8000
L(x) = f(8000) + f'(8000) (x−8000)
L(x) = 20 + 1/1200 (x−8000)

8030^(1/3) ≈ L(8030)
= 20 + 1/1200 (8030−8000)
= 20 + 30/1200
= 20 + 1/40
= 20.025
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Can someone give me the answers plz:)
Alborosie

Remark

There is no short way to do this problem and no obvious way to get the answer other that to solve each part.  

Solve

A

\dfrac{x + 1.6}{2} =\text{x + 0.1}                    Multiply by 2

x + 1.6 = 2(x + 0.1)                                         Remove the brackets

x + 1.6 = 2x + 0.1*2                                        

x + 1.6 = 2x + 0.2                                          Subtract x from both sides

1.6 = x + 0.2                                                  Subtract 0.2 from both sides  

1.6 - 0.2 = x                        

1.4 = x

Circle A

B

Subtract 2x from both sides.

3x - 2x = 1.4

Circle B

C

Remove the brackets.

4x + 6 = 2x - 6           Add 6 to both sides

4x + 12 = 2x               Subtract 4x from both sides.

12 = -2x                      Divide by - 2

12/-2 = x

x = - 6                         Don't circle C

D

I'm going to be very scant in my solution of this. You can fill in the steps.

3x = 4.2

x = 4.2/3

x = 1.4

Circle D

5 0
3 years ago
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Factor 20 please explain factors and answer I'm really bad at math
Leona [35]
<span>1, 2, 4, 5,10, and 20.</span>
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3 years ago
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Lesechka [4]

Answer:

B. 0.602%

Step-by-step explanation:

Probability is essentially (# times specific event will occur) / (# times general event will occur). Here, we have a few specific events: draw a quarter, draw a second quarter, draw a penny, and draw another penny. The general event will just be the number of coins there are to choose from.

The probability that the first draw is a quarter will be 4 / (4 + 8 + 9) = 4/21.

Since we've drawn one now, there's only 21 - 1 = 20 total coins left. The probability of drawing a second quarter is: (4 - 1) / (21 - 1) = 3/20.

The probability of drawing a penny is: 9 / (20 - 1) = 9/19.

The probability of drawing a second penny is: (9 - 1) / (19 - 1) = 8/18.

Multiply these four probabilities together:

(4/21) * (3/20) * (9/19) * (8/18) = 864 / 143640 ≈ 0.602%

The answer is B.

8 0
3 years ago
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5. Evaluate the function for the given variables.
UkoKoshka [18]

Answer:

C. f(5) = 13 and f(-3) = -3

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS

Step-by-step explanation:

<u>Step 1: Define</u>

f(x) = 2x + 3

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x = -3

<u>Step 2: Evaluate</u>

x = 5

  1. Substitute:                    f(5) = 2(5) + 3
  2. Multiply:                        f(5) = 10 + 3
  3. Add:                              f(5) = 13

x = -3

  1. Substitute:                    f(-3) = 2(-3) + 3
  2. Multiply:                        f(-3) = -6 + 3
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SVETLANKA909090 [29]

Answer:

10 (10.34 rounded down)

Step-by-step explanation:

11% is the same as .11

Multiply by 94 for your answer.

.11 x 94 = 10.34

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