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3 years ago

Find the product (2x-1)(-x+2)

Mathematics

1 answer:

DaniilM [7]3 years ago

7 0

Answer:

2x^2+4x+x-2

Step-by-step explanation:

use FOIL (first, outside, inside, last)

(2x-1)(-x+2)

2x(-x)=-2x^2

2x(2)=4x

-1(-x)=x

-1(2)=-2

2x^2+4x+x-2

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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

Solve the following equation. Then place the correct number in box provided.

Pepsi [2]

x is equal to 0 because 6 is already equal to 6

so there shouldnt be another number unless its 0

0+6=6

7 0

3 years ago

kramer

Value of y= 18 and value of x= 9 root3
therefore answer is D

7 0

3 years ago

Will mark Brainliest! You MUST explain step-by-step how you solved the problem.

sergiy2304 [10]

Answer:

choice C) 30 ft

Step-by-step explanation:

tan 41° = height/34

0.8693 = height/34

height = 29.56 or rounded to 30 ft

3 0

2 years ago

Bill charges $12 per hour for a plumbing job. Write the equation that shows the relationship between the numbers of hours Bill w

yarga [219]

Answer:

m = 12h

Step-by-step explanation:

Since Bill charges $12 per hour, it implies for every hour he charges $12. Therefore, the amount of money he makes, m, is dependent on the number of hours he works, h. The higher the number of hours, the more his money. And vice versa.

So that;

m = 12h

Thus if Bill works for 6 hours, his amount of money would be;

m = 12 (6)

= 72

m = $72

Bill would make $72 after working for 6 hours.

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3 years ago