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3 years ago

What is the form of the Pythagorean triple generator?

Mathematics

2 answers:

stepladder [879]3 years ago

4 0

Answer:(x^2+y^2)^2=(x^2+y^2)(x^2+y^2)

Step-by-step explanation:

We can rewrite left side into right side form

(x^2+y^2)^2=(x^2+y^2)(x^2+y^2)

we can expand it

(x^2+y^2)^2=x^4+x^2y^2+x^2y^2+y^4

(x^2+y^2)^2=x^4+y^4+2x^2y^2

we can add and subtract 2x^2y^2

(x^2+y^2)^2=x^4+y^4+2x^2y^2+2x^2y^2-2x^2y^2

(x^2+y^2)^2=x^4-2x^2y^2+y^4+2x^2y^2+2x^2y^2

(x^2+y^2)^2=x^4-2x^2y^2+y^4+4x^2y^2

(x^2+y^2)^2=x^4-2x^2y^2+y^4+(2xy)^2

(x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2

andrey2020 [161]3 years ago

3 0

The form of the Pythagorean triple is
a^2+b^2=c^2

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2 years ago

Kryptonite is a material found on the planet Krypton and has various effects, most importantly on Superman. The most common type

Rashid [163]

Answer:

The maximum amount of red kryptonite present is 33.27 g after 4.93 hours.

Step-by-step explanation:

dy/dt = y(1/t - k)

separating the variables, we have

dy/y = (1/t - k)dt

dy/y = dt/t - kdt

integrating both sides, we have

∫dy/y = ∫dt/t - ∫kdt

㏑y = ㏑t - kt + C

㏑y - ㏑t = -kt + C

㏑(y/t) = -kt + C

taking exponents of both sides, we have

$\frac{y}{t} = e^{-kt + C} \\\frac{y}{t} = e^{-kt}e^{C} \\\frac{y}{t} = Ae^{-kt} (A = e^{C})\\y = Ate^{-kt}$

when t = 1 hour, y = 15 grams. So,

$y = Ate^{-kt}\\15 = A(1)e^{-kX1}\\15 = Ae^{-k}$ (1)

when t = 3 hours, y = 30 grams. So,

$y = Ate^{-kt}\\30 = A(3)e^{-kX3}\\30 = 3Ae^{-3k}$ (2)

dividing (2) by (1), we have

$\frac{30}{15} = \frac{3Ae^{-3k}}{Ae^{-k}} \\2 = 3e^{-2k}\\\frac{2}{3} = e^{-2k}$

taking natural logarithm of both sides, we have

-2k = ㏑(2/3)

-2k = -0.4055

k = -0.4055/-2

k = 0.203

From (1)

$A = 15e^{k} \\A = 15e^{0.203} \\A = 15 X 1.225\\A = 18.36$

Substituting A and k into y, we have

$y = 18.36te^{-0.203t}$

The maximum value of y is obtained when dy/dt = 0

dy/dt = y(1/t - k) = 0

y(1/t - k) = 0

Since y ≠ 0, (1/t - k) = 0.

So, 1/t = k

t = 1/k

So, the maximum value of y is obtained when t = 1/k = 1/0.203 = 4.93 hours

$y = 18.36(1/0.203)e^{-0.203t}\\y = \frac{18.36}{0.203}e^{-0.203X1/0.203}\\y = 90.44e^{-1}\\y = 90.44 X 0.3679\\y = 33.27 g$

<u>So the maximum amount of red kryptonite present is 33.27 g after 4.93 hours.</u>

3 0

3 years ago

The table shows some

valentinak56 [21]

Answer:

<u>For 1 quart of orange juice:</u>

Calories = 448

Vitamin C = 387.6 mg

Carbohydrates = 107.56 mg

Step-by-step explanation:

The following information is given about 1 CUP of orange juice:

<h2>Calories</h2><h3>112</h3><h2>Vitamin C</h2><h3>96.9 mg</h3><h2>Carbohydrates</h2><h3>26.89 mg</h3>

Now, we have to estimate the 3 values for 1 quart of orange juice. Remember, 4 cups is 1 quart, so we need to multiply each value by 4 to get the values for 1 quart.

Calories = 112 * 4 = 448

Vitamin C = 96.9 * 4 = 387.6 mg

Carbohydrates = 26.89 * 4 = 107.56 mg

6 0

2 years ago

What is the form of the Pythagorean triple generator?​

What is the form of the Pythagorean triple generator?