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3 years ago

Solve y = -1/2x + 6 create an equation of a line parallel and perpendicular to this line that goes

Mathematics

1 answer:

SCORPION-xisa [38]3 years ago

6 0

Answer:

y = -½x + 12; y = 2x + 2

Step-by-step explanation:

1. Solve the equation

y = -½x + 6

(a) Let x = 0

y = -½(0) + 6

y = 0 + 6

y = 6

(b) Let y = 0

0 = -½x + 6 Subtract 6 from each side

-6 = -½x Multiply each side by -2

x = 12

The line passes through the points (0, 6) and (12, 0).

2. Equation for parallel line

The line passes through (4, 10).

y = mx + b

m = -½

10 = -½(4) + b

10 = -2 + b Add 1 to each side

b = 12

The equation for the parallel line is y = -½x + 12.

3. Equation for perpendicular line

(a). Find the slope (m₁) of the original line

The equation for the original line is

y = -½x + 6

slope = m₁ = -½

(b). Find the slope (m₂) of the perpendicular line

m₂ = -1/m₁ Substitute the value of m₁

m₂ = 2

(c). Find the equation for the perpendicular line

y = mx + b Substitute the value of m₂

y = 2x + b

The line passes through (4,10).

10 = 2 × 4 + b

10 = 8 + b Subtract 8 from each side

b = 2

y = 2x + 2

In the image, below, the red line is the graph of your original equation.

The green line passing through (4, 10) is the parallel line.

The black line passing through (4, 10) is the perpendicular line.

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3 years ago

A tank with a capacity of 1600 L is full of a mixture of water and chlorine with a concentration of 0.0125 g of chlorine per lit

Veronika [31]

Answer:

y(t) = 20 [1600^(-5/3)] x (1600-24t)^ (5/3)

Step-by-step explanation:

1) Identify the problem

This is a differential equation problem

On this case the amount of liquid in the tank at time t is 1600−24t. (When the process begin, t=0 ) The reason of this is because the liquid is entering at 16 litres per second and leaving at 40 litres per second.

2) Define notation

y = amount of chlorine in the tank at time t,

Based on this definition, the concentration of chlorine at time t is y/(1600−24t) g/ L.

Since liquid is leaving the tank at 40L/s, the rate at which chlorine is leaving at time t is 40y/(1600−24t) (g/s).

For this we can find the differential equation

dy/dt = - (40 y)/ (1600 -24 t)

The equation above is a separable Differential equation. For this case the initial condition is y(0)=(1600L )(0.0125 gr/L) = 20 gr

3) Solve the differential equation

We can rewrite the differential equation like this:

dy/40y = - (dt)/ (1600-24t)

And integrating on both sides we have:

(1/40) ln |y| = (1/24) ln (|1600-24t|) + C

Multiplying both sides by 40

ln |y| = (40/24) ln (|1600 -24t|) + C

And simplifying

ln |y| = (5/3) ln (|1600 -24t|) + C

Then exponentiating both sides:

e^ [ln |y|]= e^ [(5/3) ln (|1600-24t|) + C]

with e^c = C , we have this:

y(t) = C (1600-24t)^ (5/3)

4) Use the initial condition to find C

Since y(0) = 20 gr

20 = C (1600 -24x0)^ (5/3)

Solving for C we got

C = 20 / [1600^(5/3)] = 20 [1600^(-5/3)]

Finally the amount of chlorine in the tank as a function of time, would be given by this formula:

y(t) = 20 [1600^(-5/3)] x (1600-24t)^ (5/3)

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3 years ago

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user100 [1]

The sum of their age is "s" years? Please fix the typo. Then I might be able to help :D

4 0

3 years ago

Read 2 more answers

Find the distance between the points (-9,2) and (-1,4). Round to the nearest tenth if necessary.

AlekseyPX

Answer:

The answer to the nearest tenth is 8.2

Step-by-step explanation:

In order to find the distance between any two points, you must use the distance formula. when you plug in the points into the formula you end up with 8.246, rounded to the nearest tenth would be 8.2. I hope this helps!

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3 years ago

TotCo is developing a new deluxe baby bassinet. If the length of a newborn baby is normally distributed with a mean of 50 cm and

slavikrds [6]

Answer:

91.63 cm is the interior length of the bassinet to ensure that 99 percent of newborn babies will fit, with a safety margin of 15 cm on each end of the bassinet.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 50 cm

Standard Deviation, σ = 5 cm

We are given that the distribution of length of a newborn baby is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$