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3 years ago

In a solution,the ratio of salt water by volume is 1:4 .What is the percent of salt in the total solution?

Mathematics

1 answer:

mojhsa [17]3 years ago

8 0

I believe its 20% salt to water ratio since theres 5 pieces all together

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Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produ

SOVA2 [1]

$y=\ln(6+x^3)\implies y'=\dfrac{3x^2}{6+x^3}$

The arc length of the curve is

$\displaystyle\int_0^5\sqrt{1+\frac{9x^4}{(6+x^3)^2}}\,\mathrm dx$

which has a value of about 5.99086.

Let $f(x)=\sqrt{1+\frac{9x^4}{(6+x^3)^2}}$ . Split up the interval of integration into 10 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], ..., [9/2, 5]

The left and right endpoints are given respectively by the sequences,

$\ell_i=\dfrac{i-1}2$

$r_i=\dfrac i2$

with $1\le i\le10$ .

These subintervals have midpoints given by

$m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}4$

Over each subinterval, we approximate $f(x)$ with the quadratic polynomial

$p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m_i)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}$

so that the integral we want to find can be estimated as

$\displaystyle\sum_{i=1}^{10}\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx$

It turns out that

$\displaystyle\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx=\frac{f(\ell_i)+4f(m_i)+f(r_i)}6$

so that the arc length is approximately

$\displaystyle\sum_{i=1}^{10}\frac{f(\ell_i)+4f(m_i)+f(r_i)}6\approx5.99086$

5 0

3 years ago

-2x-2y=4 solve this

Ierofanga [76]

Y=4-x that's the answer

6 0

3 years ago

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Midpoints of segment with endpoints. (-4,2) and (2,4)

sashaice [31]

Well! See ,If the endpoints are (x1,y1) & (x2,y2) then mid-point is given by (x1+x2)/2,

(y1+y2)/2

Here in this question endpoints given for the line segment are (-4,2) , (2,4) so we have to find mid-point for x and y co-ordinates by applying above rule.

So, the mid-point we get is (-4+2)/2 , (2+4)/2.

i.e. (-1,3) which lies in 2nd Co-ordinate!

Hope it helps!!

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3 years ago

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Which equation can be used to solve a – 5 = 30?

kari74 [83]

Answer:

last one

a = 30 + 5

a - 5 = 30

Step-by-step explanation:

here is your answer

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2 years ago

Solve for z<br> answer correctly

Lorico [155]

Z=1 eventually you get 15 divided by 15 giving you Z=1 it’s a long equation

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2 years ago

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