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3 years ago

When adding 3 and -9, how do you know that the sum is negative?

Mathematics

1 answer:

irga5000 [103]3 years ago

7 0

You know the sum is negative because the negative integer is larger than the positive integer.

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Here are the scores that Jenna has

amid [387]

Answer:

the variance is 6.6

sry for not showing work

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2 years ago

A 75-gallon tank is filled with brine (water nearly saturated with salt; used as a preservative) holding 11 pounds of salt in so

Debora [2.8K]

Let $A(t)$ = amount of salt (in pounds) in the tank at time $t$ (in minutes). Then $A(0) = 11$ .

Salt flows in at a rate

$\left(0.6\dfrac{\rm lb}{\rm gal}\right) \left(3\dfrac{\rm gal}{\rm min}\right) = \dfrac95 \dfrac{\rm lb}{\rm min}$

and flows out at a rate

$\left(\dfrac{A(t)\,\rm lb}{75\,\rm gal + \left(3\frac{\rm gal}{\rm min} - 3.25\frac{\rm gal}{\rm min}\right)t}\right) \left(3.25\dfrac{\rm gal}{\rm min}\right) = \dfrac{13A(t)}{300-t} \dfrac{\rm lb}{\rm min}$

where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.

Then the net rate of salt flow is given by the differential equation

$\dfrac{dA}{dt} = \dfrac95 - \dfrac{13A}{300-t}$

which I'll solve with the integrating factor method.

$\dfrac{dA}{dt} + \dfrac{13}{300-t} A = \dfrac95$

$-\dfrac1{(300-t)^{13}} \dfrac{dA}{dt} - \dfrac{13}{(300-t)^{14}} A = -\dfrac9{5(300-t)^{13}}$

$\dfrac d{dt} \left(-\dfrac1{(300-t)^{13}} A\right) = -\dfrac9{5(300-t)^{13}}$

Integrate both sides. By the fundamental theorem of calculus,

$\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac1{(300-t)^{13}} A\bigg|_{t=0} - \frac95 \int_0^t \frac{du}{(300-u)^{13}}$

$\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac{11}{300^{13}} - \frac95 \times \dfrac1{12} \left(\frac1{(300-t)^{12}} - \frac1{300^{12}}\right)$

$\displaystyle -\dfrac1{(300-t)^{13}} A = \dfrac{34}{300^{13}} - \frac3{20}\frac1{(300-t)^{12}}$

$\displaystyle A = \frac3{20} (300-t) - \dfrac{34}{300^{13}}(300-t)^{13}$

$\displaystyle A = 45 \left(1 - \frac t{300}\right) - 34 \left(1 - \frac t{300}\right)^{13}$

After 1 hour = 60 minutes, the tank will contain

$A(60) = 45 \left(1 - \dfrac {60}{300}\right) - 34 \left(1 - \dfrac {60}{300}\right)^{13} = 45\left(\dfrac45\right) - 34 \left(\dfrac45\right)^{13} \approx 34.131$

pounds of salt.

7 0

1 year ago

What is the length if a right triangle with a leg that measures 16 and a hypotenuse of 20

Genrish500 [490]

Answer:

It would be 12.

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

The base of a triangular prism is an isosceles right triangle with a hypotenuse of

Setler [38]

SA= Lateral Area + Area (of base)

Lateral area = perimeter of base x height

An isosceles triangle has two congruent base segments. The hypotenuse of an isosceles right triangle is (length of base segment) x (the square root of 2). I did the math for you (shown above) to get 5 as a base.

So 5 + 5 + square root of 50 is your perimeter

Multiply the perimeter times your height (8) and you get the lateral area.

Add your lateral area to the base area (triangle = 1/2 bh)

LA = 136.568...
Area of Triangle base = 12.5

Surface area = 149.068... square cm

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2 years ago

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How long did it take the 9000 N car to reach 100 km/hr?

Veronika [31]

100 seconds. The numbers on the left are seconds.

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3 years ago