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
Olenka [21]
3 years ago
12

Use a linear approximation (or differentials) to estimate the given number. (Round your answer to five decimal places.) 3 217

Mathematics
1 answer:
Soloha48 [4]3 years ago
6 0

Answer:

f(216) \approx 6.0093

Step-by-step explanation:

Given

\sqrt[3]{217}

Required

Solve

Linear approximated as:

f(x + \triangle x) \approx f(x) +\triangle x \cdot f'(x)

Take:

x = 216; \triangle x= 1

So:

f(x) = \sqrt[3]{x}

Substitute 216 for x

f(x) = \sqrt[3]{216}

f(x) = 6

So, we have:

f(x + \triangle x) \approx f(x) +\triangle x \cdot f'(x)

f(215 + 1) \approx 6  +1 \cdot f'(x)

f(216) \approx 6  +1 \cdot f'(x)

To calculate f'(x);

We have:

f(x) = \sqrt[3]{x}

Rewrite as:

f(x) = x^\frac{1}{3}

Differentiate

f'(x) = \frac{1}{3}x^{\frac{1}{3} - 1}

Split

f'(x) = \frac{1}{3} \cdot \frac{x^\frac{1}{3}}{x}

f'(x) = \frac{x^\frac{1}{3}}{3x}

Substitute 216 for x

f'(216) = \frac{216^\frac{1}{3}}{3*216}

f'(216) = \frac{6}{648}

f'(216) = \frac{3}{324}

So:

f(216) \approx 6  +1 \cdot f'(x)

f(216) \approx 6  +1 \cdot \frac{3}{324}

f(216) \approx 6  + \frac{3}{324}

f(216) \approx 6  + 0.0093

f(216) \approx 6.0093

You might be interested in
Mrs. martina wants to put a wire fence around her garden which is 15 feet long and 8 feet wide. how much fencing does she need?
dlinn [17]
The answer is D 46 ft ( 15+15+8+8)
6 0
3 years ago
Read 2 more answers
Solve each equation.<br>1. 9/2x+18+3x=11/2<br>2. (x+6)-(2x=7)-3x=-9
zzz [600]
1.\\\frac{9}{2}x+18+3x=\frac{11}{2}\ \ \ \ \ |Multiply\ by\ 2\\\\&#10;9x+36+6x=11\\\\&#10;15x+36=11\ \ \ |Subtract\ 36\\\\&#10;15x=-25\ \ \ |Divide\ by\ 15\\\\&#10;x=-1\frac{2}{5}\\\\&#10;2.\\&#10;(x+6)-(2x-7)-3x=-9\\\\&#10;x+6-2x+7-3x=-9\\\\&#10;-4x+13=-9\ \ \ |Subtract\ 13\\\\&#10;-4x=-22\ \ \ |Divide\ by\ -4\\\\&#10;x=5,5
3 0
3 years ago
Which of the following sets of inequalities​
Ludmilka [50]

Inequalities help us to compare two unequal expressions. The correct options are 2 and 3.

<h3>What are inequalities?</h3>

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The inequality for the red portion is,

slope, m = (-2/-4) = 1/2

y-intercept is 2.

y ≤ (1/2)x + 2

The inequality for the blue portion is,
slope, m = (5-0)/(3-0.5) = 2

y-intercept is -1.

y > 2x - 1

Hence, the correct options are 2 and 3.

Learn more about Inequality:

brainly.com/question/19491153

#SPJ1

7 0
1 year ago
PLS EXPLAIN IN FULL DETAIL
elena-14-01-66 [18.8K]

Answer:

1.50x=18

x=12

Step-by-step explanation:

You have to divide 1.50 on both sides and 1.50x/1.50= x and 18/1.50=12 so x=12

3 0
2 years ago
Read 2 more answers
Help on this algebra 2 question!!!!!!
prisoha [69]

Answer:

C.

Ax + 1 = x A + 1

Bx + 2 = x B + 2

Cx + 3 = x C + 3

A = x C + 3

B = x C + 3

C = x C + 3

<em>I'm </em><em>not </em><em>really</em><em> </em><em>sure </em><em>about</em><em> </em><em>the </em><em>answer</em><em> </em><em> </em><em>but </em><em>i </em><em>hope </em><em>it </em><em>helps </em>

8 0
2 years ago
Other questions:
  • What is a situation in which you might locate points on a coordinate grid?
    9·1 answer
  • In a certain​ country, the true probability of a baby being a girlgirl is 0.4810.481. among the next sixsix randomly selected bi
    11·1 answer
  • How do I solve f+4/g=6 for f showing my work
    10·1 answer
  • Giselle pays $220 in advance on her account at the athletic club. Each time she uses the club,
    12·1 answer
  • I'm Sure no one will see or answer this correctly like always...
    9·1 answer
  • 19. Higher Order Thinking The hands of
    12·1 answer
  • Anyone know what the answer would be?
    14·1 answer
  • Can someone please answer this!!
    10·1 answer
  • Spencer has a bank account with a balance of $75.00. Spencer owes $30.00 to her credit card and she owes $50.00 for a LCD TV. Wh
    11·2 answers
  • Giải phương trình vi phân<br> x=y′2−y′+2
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!