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3 years ago

Find the equation of the line Use exact numbers.

Mathematics

1 answer:

polet [3.4K]3 years ago

3 0

→Answer:

y = -1/4x - 6

→Step-by-step explanation:

Well it is a negative slope with a y intercept of -6.

And to spring the slope we need to use the following formula.

$\frac{y^2-y^1}{x^2-x^1}$

So we need 2 points on the line to use the formula.

(-4,-5) (0,-6)

-6 - -5 = -1

0 - -4 = 4

So the slope is -1/4.

Hence, the equation is y = -1/4x - 6

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A 100 gallon tank initially contains 100 gallons of sugar water at a concentration of 0.25 pounds of sugar per gallon suppose th

Vsevolod [243]

At the start, the tank contains

(0.25 lb/gal) * (100 gal) = 25 lb

of sugar. Let $S(t)$ be the amount of sugar in the tank at time $t$ . Then $S(0)=25$ .

Sugar is added to the tank at a rate of P lb/min, and removed at a rate of

$\left(1\frac{\rm gal}{\rm min}\right)\left(\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm gal}\right)=\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm min}$

and so the amount of sugar in the tank changes at a net rate according to the separable differential equation,

$\dfrac{\mathrm dS}{\mathrm dt}=P-\dfrac S{100}$

Separate variables, integrate, and solve for S.

$\dfrac{\mathrm dS}{P-\frac S{100}}=\mathrm dt$

$\displaystyle\int\dfrac{\mathrm dS}{P-\frac S{100}}=\int\mathrm dt$

$-100\ln\left|P-\dfrac S{100}\right|=t+C$

$\ln\left|P-\dfrac S{100}\right|=-100t-100C=C-100t$

$P-\dfrac S{100}=e^{C-100t}=e^Ce^{-100t}=Ce^{-100t}$

$\dfrac S{100}=P-Ce^{-100t}$

$S(t)=100P-100Ce^{-100t}=100P-Ce^{-100t}$

Use the initial value to solve for C :

$S(0)=25\implies 25=100P-C\implies C=100P-25$

$\implies S(t)=100P-(100P-25)e^{-100t}$

The solution is being drained at a constant rate of 1 gal/min; there will be 5 gal of solution remaining after time

$1000\,\mathrm{gal}+\left(-1\dfrac{\rm gal}{\rm min}\right)t=5\,\mathrm{gal}\implies t=995\,\mathrm{min}$

has passed. At this time, we want the tank to contain

(0.5 lb/gal) * (5 gal) = 2.5 lb

of sugar, so we pick P such that

$S(995)=100P-(100P-25)e^{-99,500}=2.5\implies\boxed{P\approx0.025}$

5 0

3 years ago

A student sketched some art on an 8.5 inch x 11 inch piece of paper. He wants to resize it to fit an 5 inch x 7 inch frame (as s

Stels [109]

The answer for this question is C. X=5.41

3 0

3 years ago

3y - 5x = 9 Y= -5/3x-12 Are the parallel

bija089 [108]

Answer:

Both lines are not parallel

Step-by-step explanation:

Given as :

Two lines equation are as :

3y - 5x = 9 And y = - $\frac{5}{3}$ x - 12

First line is now written in eq y = mx + c

Or, 3y = 5x + 9

Or, y = $\frac{5}{3}$ x + $\frac{9}{3}$

So, Slop of this line ( m 1 ) = $\frac{5}{3}$

slop of second line ( m 2) is $\frac{- 5}{3}$

∵ The slop of both lines are not equal , so the line are not parallel to each other .

Hence Both lines are not parallel Answer

6 0

3 years ago

How do i draw out that z is the mid point of FG

Minchanka [31]

Answer:

You put a dot in the middle of FG and call it z

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

798/8×41 rounded to one significant figure

Blizzard [7]

Answer:

4089

Step-by-step explanation:

798/8 x 41=

99.75 x 41 =

4089.75

Hope it helps

3 0

3 years ago