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
S_A_V [24]
3 years ago
12

The volume v of a cylinder is computed using the values 2.2 m for diameter and 6.8 m for height. use the linear approximation to

estimate the maximum error in v if each of these values has a possible error of at most 5% (use decimal notation. give your answer to three decimal places.)
Mathematics
1 answer:
geniusboy [140]3 years ago
4 0

A linear approximation to the error in volume can be written as

... ∆V = (∂V/∂d)·∆d + (∂V/∂h)·∆h

For V=(π/4)·d²·h, this is

... ∆V = 2·(π/4)·d·h·∆d + (π/4)·d²·∆h

Using ∆d = 0.05d and ∆h = 0.05h, this becomes

... ∆V = (π/4)·d²·h·(2·0.05 + 0.05) = 0.15·V

The nominal volume is

... V = (π/4)·d²·h = (π/4)·(2.2 m)²·(6.8 m) = 25.849 m³

Then the maximum error in volume is

... 0.15V = 0.15·25.849 m³ ≈ 3.877 m³

_____

Essentially, the error percentage is multiplied by the exponent of the associated variable. Then these products are added to get the maximum error percentage.

You might be interested in
Is My answer correct?
Licemer1 [7]
Yes,  you are correct!
6 0
3 years ago
Consider the population regression of log earnings [Yᵢ, where Yᵢ= ln(Earningsᵢ)] against two binary variables:
puteri [66]

Answer:

A) allows the population effect on log earnings of being married to depend on gender

Step-by-step explanation:

The regression equation of a dependent variable based on two or more independent variables is of the form:

Y=b_{0}+b_{1}X_{1} +b_{2}X_{2}+b_{3}X_{1}X_{2}

Here,

<em>Y</em> = dependent variable

X_{1} and X_{2} = independent variables

X_{1}X_{2} = interaction term

b_{1},\ b_{2}\ and \ b_{3} = regression coefficients.

If there is a significant interaction effect present then this implies that the effect of one independent variable (X_{1} orX_{2} ) on the dependent variable (<em>Y</em>) differs every time with different value of the other independent variable  (X_{1} orX_{2} ) .

The provided regression equation is:

Y_{i}=\beta _{0}+\beta _{1}D_{1i}+\beta_{2}D_{2i}+\beta _{3}D_{1i}D_{2i}+u_{i}

Y_{i} = dependent variable

D_{1i} and D_{2i} = independent variables

In this case the interaction term is defined as follows:

The effect of being married on log earnings is dependent on different values of the variables D_{2i}, i.e. the gender of the i^{th}person.

Thus, the correct option is (A).

3 0
3 years ago
Cindy earned 35 bonus points. Farid earned b more bonus points than Cindy. Write an expression that shows how many bonus points
arlik [135]
# of points Farid has = b+35.

So the expression would be b+35.
4 0
3 years ago
Read 2 more answers
What is the solution to the system of linear equations graphed below? On a coordinate plane, 2 lines intersect at (negative 2.5,
Vitek1552 [10]

Answer:

D. (Negative 2 and one-half, negative 2)

Step-by-step explanation:

The intersection of the two lines is the solution to the system of linear equations. The two lines intersect at (-2.5, -2), then the solution to the system is x = -2.5 and y = -2

3 0
3 years ago
Sally invests £8000 in a savings account. The account pays 2.8% compound interest per year work out the value of her investment
Alborosie

Answer: the value of her investment after 4 years is £8934.3

Step-by-step explanation:

The formula for determining compound interest is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount invested.

t represents the duration of the investment in years.

From the information given,

P = 8000

r = 2.8% = 2.8/100 = 0.028

n = 1 because it was compounded once in a year.

t = 4 years

Therefore,

A = 8000(1+0.028/1)^1 × 4

A = 8000(1+0.028)^4

A = 8000(1.028)^4

A = £8934.3 to the the nearest penny

6 0
3 years ago
Other questions:
  • Graph the inequality -6&lt;d
    5·1 answer
  • How much money will you have if you started with $ 50, and put it in an account that earned 9.7% every year for 15 years?
    8·1 answer
  • Simplify 3 - (4x - 5) + 6.<br><br><br>A)12x + 21 <br>B) 4x + 14 <br>C) 4x + 4<br>D) -4x + 14
    8·2 answers
  • Write an equation of the direct variation that includes the given point (-8, -4)
    6·2 answers
  • Given f(x) = 3x2 + 10x - 8 and g(x) = 3x2 - 2x<br>What is (f/g)(x)?​
    5·1 answer
  • Can someone help me with this fast please?<br> Thank You
    14·1 answer
  • Will give the big brain award for answers
    10·2 answers
  • A girl work a works a basic week of 40 hours,and her basic rate is 6.25per hour .calculate her basic wage for that week
    5·2 answers
  • 11 take away 2 times minus 7 plus 4
    13·1 answer
  • Find the Unit Rate
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!