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3 years ago

The diagonal of a rectangle is 30 inches and the length of the rectangle is 24 inches.

Mathematics

1 answer:

RoseWind [281]3 years ago

6 0

Answer:

area=432

Step-by-step explanation:

use the Pythagoras theory now that you know the width and you'll get the length and the width then you multiply both of them hope it helps you.

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If the area of a baseball diamond (shape of a square) is 8100 ft squared, how would you find the distance from 1st base to 3rd b

Readme [11.4K]

Answer:

Exact distance = $90\sqrt{2}$ feet
Approximate distance = 127.2792 feet.

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Explanation:

The area of the square is 8100 square feet, abbreviated ft^2.

Apply the square root to find the distance from any base to its adjacent counterpart (eg: from 1st to 2nd base). So we get sqrt(8100) = 90 ft as that side distance. Notice that 90*90 = 8100.

If you were to draw a line from 1st base to 3rd base, then you would split the square into two congruent right triangles. Each right triangle is isosceles (the two legs being 90 ft each).

Use the pythagorean theorem to find the hypotenuse.

$a^2 + b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{90^2+90^2}\\\\c = \sqrt{2*90^2}\\\\c = \sqrt{2}*\sqrt{90^2}\\\\c = \sqrt{2}*90\\\\c = 90\sqrt{2} \ \text{ ... exact distance}\\\\c \approx 127.2792 \ \text{ ... approximate distance}\\\\$

The distance from 1st to 3rd base is roughly 127.2792 feet.

5 0

2 years ago

(b) dy/dx = (x - y+ 1)^2

Elanso [62]

Substitute $v(x)=x-y(x)+1$ , so that

$\dfrac{\mathrm dv}{\mathrm dx}=1-\dfrac{\mathrm dy}{\mathrm dx}$

Then the resulting ODE in $v(x)$ is separable, with

$1-\dfrac{\mathrm dv}{\mathrm dx}=v^2\implies\dfrac{\mathrm dv}{1-v^2}=\mathrm dx$

On the left, we can split into partial fractions:

$\dfrac12\left(\dfrac1{1-v}+\dfrac1{1+v}\right)\mathrm dv=\mathrm dx$

Integrating both sides gives

$\dfrac{\ln|1-v|+\ln|1+v|}2=x+C$

$\dfrac12\ln|1-v^2|=x+C$

$1-v^2=e^{2x+C}$

$v=\pm\sqrt{1-Ce^{2x}}$

Now solve for $y(x)$ :

$x-y+1=\pm\sqrt{1-Ce^{2x}}$

$\boxed{y=x+1\pm\sqrt{1-Ce^{2x}}}$

3 0

3 years ago

Can (5z+3)(-5z-3) result in a difference of squares

castortr0y [4]

Answer:

no, it cannot

Step-by-step explanation:

a difference of square is: a² - b² = (a - b)(a + b)

looking at the expression (5z+3)(-5z-3), we see that it does not fit the criteria of the breakdown of a perfect square, as (-5z-3) has a negative <em>a</em> term (-5z)

if we FOILed (5z+3)(-5z-3) out, we would get:

-25z² - 30z - 9, which is not a difference of squares

8 0

2 years ago

How do I write these ratios 10/20 and 2/2 in y=kx form

hodyreva [135]

You would write it 2=10(20+2)

6 0

3 years ago

What is the y coordinate?

wel

Answer:

Step-by-step explanation:

3 0

2 years ago