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3 years ago

8

Did the old version of the instrument triangle have a different sound because of the open corner and different triangle shape of

isosceles triangle, instead of the equilateral triangle shape used today?

1 answer:

eduard3 years ago

7 0

Yes the old version has different sounds

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Let S be the solid beneath z = 12xy^2 and above z = 0, over the rectangle [0, 1] × [0, 1]. Find the value of m > 1 so that th

jonny [76]

Answer:

The answer is $\sqrt{\frac{6}{5}}$

Step-by-step explanation:

To calculate the volumen of the solid we solve the next double integral:

$\int\limits^1_0\int\limits^1_0 {12xy^{2} } \, dxdy$

Solving:

$\int\limits^1_0 {12x} \, dx \int\limits^1_0 {y^{2} } \, dy$

$[6x^{2} ]{{1} \atop {0}} \right. * [\frac{y^{3}}{3}]{{1} \atop {0}} \right.$

Replacing the limits:

$6*\frac{1}{3} =2$

The plane y=mx divides this volume in two equal parts. So volume of one part is 1.

Since m > 1, hence mx ≤ y ≤ 1, 0 ≤ x ≤ $\frac{1}{m}$

Solving the double integral with these new limits we have:

$\int\limits^\frac{1}{m} _0\int\limits^{1}_{mx} {12xy^{2} } \, dxdy$

This part is a little bit tricky so let's solve the integral first for dy:

$\int\limits^\frac{1}{m}_0 [{12x \frac{y^{3}}{3}}]{{1} \atop {mx}} \right.\, dx =\int\limits^\frac{1}{m}_0 [{4x y^{3 }]{{1} \atop {mx}} \right.\, dx$

Replacing the limits:

$\int\limits^\frac{1}{m}_0 {4x(1-(mx)^{3} )\, dx =\int\limits^\frac{1}{m}_0 {4x-4x(m^{3} x^{3} )\, dx =\int\limits^\frac{1}{m}_0 ({4x-4m^{3} x^{4}) \, dx$

Solving now for dx:

$[{\frac{4x^{2}}{2} -\frac{4m^{3} x^{5}}{5} ]{{\frac{1}{m} } \atop {0}} \right. = [{2x^{2} -\frac{4m^{3} x^{5}}{5} ]{{\frac{1}{m} } \atop {0}} \right.$

Replacing the limits:

$\frac{2}{m^{2} }-\frac{4m^{3}\frac{1}{m^{5}}}{5} =\frac{2}{m^{2} }-\frac{4\frac{1}{m^{2}}}{5} \\ \frac{2}{m^{2} }-\frac{4}{5m^{2} }=\frac{10m^{2}-4m^{2} }{5m^{4}} \\ \frac{6m^{2} }{5m^{4}} =\frac{6}{5m^{2}}$

As I mentioned before, this volume is equal to 1, hence:

$\frac{6}{5m^{2}}=1\\m^{2} =\frac{6}{5} \\m=\sqrt{\frac{6}{5} }$

3 0

3 years ago

A craft store buys 50 yards of satin ribon for $12.50. The store sells the ribbon by the foot. A customer can purchase 5 feet of

amm1812

Answer:

$8.1

Step-by-step explanation:

Convert 45 yards of ribbon to feet through proper conversion factor.

(45 yards)(3 ft / 1 yard) = 135 feet

Divide this number by 5 to determine the number of 5-ft ribbon that customers can purchased.

n = 135 ft / 5 ft = 27

Then, multiply by $0.80.

R = (27)($0.80) = $21.6

The profit is equal to $21.6 and $13.50,

P = $21.6 - $13.50 = $8.1

Answer: $8.1

8 0

3 years ago

What are the ordered pairs of the

Sholpan [36]

Answer:

its definitvely 6

Step-by-step explanation:

2 by 4 by the 3 empfs and by the 123 divided by the 360 and by the iscoceles and the 4 cohedrons

5 0

3 years ago

What is the effect in the time required to solve a problem when you double the size of the input from n to 2n, assuming the numb

kobusy [5.1K]

Answer:

Go to this site

https://www.slader.com/discussion/question/what-is-the-effect-in-the-time-required-to-solve-a-problem-when-you-double-the-size-of-the-input-fro/

there should the your answer

Step-by-step explanation:

3 0

3 years ago

Example: y= -2x and y= x + 3<br> Does the point (0,4) make either equation true?

Alinara [238K]

Answer:

No it does not make either equation true

Step-by-step explanation:

If you substitute x, (0) and y (4) into the equation and solve, It doesn't end with a true statement.

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3 years ago