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Mandarinka [93]

3 years ago

9

Asian began painting his house on Monday He work 5 hrs. longer on Tuesday than he work on Monday. On Wednesday he worked 4 hrs.

less than Tuesday. on Thursday he pained 6 hrs more than Wednesday. He painted 11 hrs on Thursday. How long did he paint on Monday?

2 answers:

jek_recluse [69]3 years ago

8 0

He worked 4 hours on monday.

sergeinik [125]3 years ago

6 0

The answer is either 9 or 4 hours on Monday. Hope this helps!

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Is h(x)=3x^3+2x^2+5 even, odd, or neither?

pochemuha

Answer:

Neither even or odd

Step-by-step explanation:

4 0

2 years ago

Set up the integral that represents the arc length of the curve f(x) = ln(x) + 5 on [1, 3], and then use Simpson's Rule with n =

marta [7]

Answer:

The integral for the arc of length is:

$\displaystyle\int_1^3\sqrt{1+\frac{1}{x^2}}dx$

By using Simpon’s rule we get: 1.5355453

And using technology we get: 2.3020

The approximation is about 33% smaller than the exact result.

Explanation:

The formula for the length of arc of the function f(x) in the interval [a,b] is:

$\displaystyle\int_a^b \sqrt{1+[f'(x)]^2}dx$

We need the derivative of the function:

$f'(x)=\frac{1}{x}$

And we need it squared:

$[f'(x)]^2=\frac{1}{x^2}$

Then the integral is:

$\displaystyle\int_1^3\sqrt{1+\frac{1}{x^2}}dx$

Now, the Simposn’s rule with n=4 is:

$\displaystyle\int_a^b g(x)}dx\approx\frac{\Delta x}{3}\left( g(a)+4g(a+\Delta x)+2g(a+2\Delta x) +4g(a+3\Delta x)+g(b) \right)$

In this problem:

$a=1,b=3,n=4, \displaystyle\Delta x=\frac{b-a}{n}=\frac{2}{4}=\frac{1}{2},g(x)= \sqrt{1+\frac{1}{x^2}}$

So, the Simposn’s rule formula becomes:

$\displaystyle\int_1^3\sqrt{1+\frac{1}{x^2}}dx\\\approx \frac{\frac{1}{3}}{3}\left( \sqrt{1+\frac{1}{1^2}} +4\sqrt{1+\frac{1}{\left(1+\frac{1}{2}\right)^2}} +2\sqrt{1+\frac{1}{\left(1+\frac{2}{2}\right)^2}} +4\sqrt{1+\frac{1}{\left(1+\frac{3}{2}\right)^2}} +\sqrt{1+\frac{1}{3^2}} \right)$

Then simplifying a bit:

$\displaystyle\int_1^3\sqrt{1+\frac{1}{x^2}}dx \approx \frac{1}{9}\left( \sqrt{1+\frac{1}{1^2}} +4\sqrt{1+\frac{1}{\left(\frac{3}{2}\right)^2}} +2\sqrt{1+\frac{1}{\left(2\right)^2}} +4\sqrt{1+\frac{1}{\left(\frac{5}{2}\right)^2}} +\sqrt{1+\frac{1}{3^2}} \right)$

Then we just do those computations and we finally get the approximation via Simposn's rule:

$\displaystyle\int_1^3\sqrt{1+\frac{1}{x^2}}dx\approx 1.5355453$

While when we do the integral by using technology we get: 2.3020.

The approximation with Simpon’s rule is close but about 33% smaller:

$\displaystyle\frac{2.3020-1.5355453}{2.3020}\cdot100\%\approx 33\%$

8 0

3 years ago

Pllllllease help me asap

marishachu [46]

Answer & Step-by-step explanation:

When we see the phrase "rate of change" then it means that we are looking for the slope. So, we will need to know the formula for finding slope or the rate of change.

$slope=\frac{y_2-y_1}{x_2-x_1}$

Now, let's use this equation to solve for the rate of change of each question.

<u>Problem 1:</u>

$Slope=\frac{2-\frac{4}{3}}{0-(-1)}\\\\Slope=\frac{\frac{2}{3}}{1}\\\\Slope=\frac{2}{3}$

<em>The rate of change of this equation is 2/3</em>

<u>Problem 2:</u>

<u></u> $Slope=\frac{4-2}{1-0}\\\\Slope=\frac{2}{1}\\\\Slope=2$ <u></u>

<em>The rate of change for this equation is 2</em>

<u>Problem 3:</u>

<u></u> $Slope=\frac{10-4}{2-1}\\\\Slope=\frac{6}{1}\\\\Slope=6$ <u></u>

<em>The rate of change for this equation is 6</em>

4 0

3 years ago

$2000 borrowed with 10% interest rate, got additional 1000 on the same rate for the same period of repayment. How much would he

nekit [7.7K]

Answer:

nothing

Step-by-step explanation:

Loan payments are <em>linear in the loan amount</em> for a given rate and period, so the payments for loans of $2000 and $1000 sum to the amount of payments for a loan of $3000.

The only possible savings (or cost) might come from rounding to the nearest cent. (In any event, the final payment on each loan should make up for any differences due to rounding.)

5 0

3 years ago

Simplify (3v^3)^2/15v^7

leonid [27]

<span>Combine like terms : (v2 - 5) x (3v + 7)</span>

8 0

3 years ago

Read 2 more answers