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3 years ago

A square window has an area of 196

Mathematics

1 answer:

creativ13 [48]3 years ago

3 0

Answer:

14 feet

Step-by-step explanation:

s2 = 196

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Find the particular solution of the differential equation that satisfies the initial condition(s). f ''(x) = x−3/2, f '(4) = 1,

sweet [91]

Answer:

Hence, the particular solution of the differential equation is $y = \frac{1}{6} \cdot x^{3} - \frac{3}{4}\cdot x^{2} - x$ .

Step-by-step explanation:

This differential equation has separable variable and can be solved by integration. First derivative is now obtained:

$f'' = x - \frac{3}{2}$

$f' = \int {\left(x-\frac{3}{2}\right) } \, dx$

$f' = \int {x} \, dx -\frac{3}{2}\int \, dx$

$f' = \frac{1}{2}\cdot x^{2} - \frac{3}{2}\cdot x + C$ , where C is the integration constant.

The integration constant can be found by using the initial condition for the first derivative ( $f'(4) = 1$ ):

$1 = \frac{1}{2}\cdot 4^{2} - \frac{3}{2}\cdot (4) + C$

$C = 1 - \frac{1}{2}\cdot 4^{2} + \frac{3}{2}\cdot (4)$

$C = -1$

The first derivative is $y' = \frac{1}{2}\cdot x^{2}- \frac{3}{2}\cdot x - 1$ , and the particular solution is found by integrating one more time and using the initial condition ( $f(0) = 0$ ):

$y = \int {\left(\frac{1}{2}\cdot x^{2}-\frac{3}{2}\cdot x -1 \right)} \, dx$

$y = \frac{1}{2}\int {x^{2}} \, dx - \frac{3}{2}\int {x} \, dx - \int \, dx$

$y = \frac{1}{6} \cdot x^{3} - \frac{3}{4}\cdot x^{2} - x + C$

$C = 0 - \frac{1}{6}\cdot 0^{3} + \frac{3}{4}\cdot 0^{2} + 0$

$C = 0$

Hence, the particular solution of the differential equation is $y = \frac{1}{6} \cdot x^{3} - \frac{3}{4}\cdot x^{2} - x$ .

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3 years ago

A piece of metal is cut in the shape of a triangle what is the area of the piece of metal

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3 years ago

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garri49 [273]

Answer:

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2 years ago

Find the measure of angle x. Round your answer to the nearest hundredth. (please type the numerical answer only)

Alex

The value of x in the triangle is 28.1 degrees

<h3>How to solve for x?</h3>

The given triangle is a right triangle.

So, the relationship between the sides and angle x is:

sin(x) = opposite/hypotenuse

This gives

sin(x) = 8/17

Evaluate the quotient

sin(x) = 0.4706

Take the arc sin of both sides

$x = \sin^{-1}(0.4706)$

Evaluate

x = 28.1

Hence, the value of x in the triangle is 28.1 degrees