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Reptile [31]
3 years ago
8

Write this equation in standard form of each line passing through the two given points (2,3);(1,-2)

Mathematics
1 answer:
Len [333]3 years ago
7 0
The given points
(x₁,y₁) = (2,3)
(x₂,y₂) = (1,-2)

There are 2 formulas we will use.
The first is formula to find the slope, and the second is formula to find the line equation.
To find the slope
m = (y₂ - y₁)/(x₂ - x₁)
To find the line equation
y - y₁ = m(x - x₁)

Find the slope, input the numbers to the formula
m = (y₂ - y₁)/(x₂ - x₁)
m = (-2-3) / (1-2)
m = -5/-1
m = 5

Find the line equation, input the numbers to the formula
y - y₁ = m(x - x₁)
y - 3 = 5(x - 2)
5(x - 2) = y - 3
5x + 10 = y - 3
5x - y = -3 - 10
5x - y = -13

The equation of the line is
5x - y = -13
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3 years ago
Find an explicit solution of the given initial-value problem. (1 + x4) dy + x(1 + 4y2) dx = 0, y(1) = 0
MissTica

Answer:

a solution is 1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) + π/4

Step-by-step explanation:

for the equation

(1 + x⁴) dy + x*(1 + 4y²) dx = 0

(1 + x⁴) dy  = - x*(1 + 4y²) dx

[1/(1 + 4y²)] dy = [-x/(1 + x⁴)] dx

∫[1/(1 + 4y²)] dy = ∫[-x/(1 + x⁴)] dx

now to solve each integral

I₁= ∫[1/(1 + 4y²)] dy = 1/2 *tan⁻¹ (2*y) + C₁

I₂=  ∫[-x/(1 + x⁴)] dx

for u= x² → du=x*dx

I₂=  ∫[-x/(1 + x⁴)] dx = -∫[1/(1 + u² )] du = - tan⁻¹ (u) +C₂ =  - tan⁻¹ (x²) +C₂

then

1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) +C

for y(x=1) = 0

1/2 *tan⁻¹ (2*0) = - tan⁻¹ (1²) +C

since tan⁻¹ (1²) for π/4+ π*N and tan⁻¹ (0) for  π*N , we will choose for simplicity N=0 . hen an explicit solution would be

1/2 * 0 = - π/4 + C

C= π/4

therefore

1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) + π/4

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3 years ago
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svp [43]

Answer:

eight people drink 6 glasses of water

Step-by-step explanation:

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Klio2033 [76]

The key calculation in this problem is figuring out <em>how many times 80 goes into 1,000,000</em>. I'll build up in steps here.

80 x 5 = 400. This gives us a building block on our way to 1,000,000. From here, we can go further and say that 400 x 5 = 2,000; that 2,000 x 5 = 10,000; and finally that 10,000 x 100 = 1,000,000. Altogether, starting from 80, that's

80 x 5 x 5 x 5 x 100 = 80 x 25 x 500 = <em>80 x 12,500</em>

So, since 80 goes into one million 12,500 times, it takes 12,500 minutes for the animal's heart to beat that 1,000,000 times.

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