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Studentka2010 [4]

3 years ago

10

Below is the graph of a trigonometric function. it has a maximum point at (pi/2, 1.8) and an amplitude of 4.2. what is the midli

ne equation of the function?
y=?

1 answer:

IRINA_888 [86]3 years ago

6 0

Answer:

y = -2.4

Step-by-step explanation:

y = 1.8 - 4.2 = -2.4

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√7 is between what two<br> consecutive integers?

bulgar [2K]

Answer: √7 is between 2 and 3

Step-by-step explanation:

The next lower number that is a perfect square is 4, the next higher perfect square is 9. Take the roots of those two numbers to find the integers you are looking for.

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Which number is 5.389 rounded to the nearest hundredth? A 5.4 B 5.38 © 5.39 05.399

ankoles [38]

Answer:

c) 5.39

Step-by-step explanation:

The digit that is in the hundredths place is the 8. (The hundredths are two digits to the right of the point).

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3 years ago

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 <em>P</em> 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 <em>S</em>.

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

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

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

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

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

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

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

Use the initial value to solve for <em>C</em> :

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

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

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 <em>P</em> such that

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

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3 years ago

Which expression is equivalent to this polynomial?<br> (4x + 3)(3x - 8)

abruzzese [7]

Answer:

I resolve the expression

(4x+3) (3x-8)=12x2-32x+9x-24

12x2-23x-24

the polynomial (4x+3) (3x-8) is equivalent a the expression 12x2-23x-24

7 0

3 years ago