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EastWind [94]
3 years ago
7

Write the differential equation model that fits the given description. (a) The rate of change of the volume of a snowball (due t

o melting) is proportional to the square of the volume at time t. Initially, the snowball has a volume of 900 cm3 . (b) For an insect moving along some path, the velocity at time t is proportional to the square root of its position.
Mathematics
1 answer:
miskamm [114]3 years ago
7 0

Answer:

a) he rate of change of the volume of a snowball (due to melting) is proportional to the square of the volume at time t. Initially, the snowball has a volume of 900 cm3

\frac{dV(t)}{dT} = A*V(t)^{2} \\ and V(0) = 900cm^{3}

where A is a real constant, it appears because it says that the change i volume (dV/dt) is "proportional" to V(t)^{2}. Furthermore, we should assume that A is a negative number, because the volume of the snowball will decrease as the time pasese by.

(b) For an insect moving along some path, the velocity at time t is proportional to the square root of its position.

\frac{dr(t)}{dt}  = B*\sqrt{r(t)}

Here again appears a constant B for the "proportional" part. And i wrote the velocity as \frac{dr(t)}{dt} "the rate of change of the position with respect to te time".

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Write the slope intercept form of the equation given the point (-2,4) and a slope of 3
Hitman42 [59]

Given the points:

(x, y) ==> (-2, 4)

slope, m = 3

To write the slope intercept form, use the form below:

y = mx + b

Where m = slope and b = y-intercept.

Now, substitute -2 for x, 4 for y, and m for 3 in the equation above to solve for b.

We have:

y = mx + b

4 = 3(-2) + b

4 = -6 + b

Add 6 to both sides:

4 + 6 = -6 + 6 + b

10 = b

b = 10

Therefore, the slope intercept form of the equation is:

y = 3x + 10

ANSWER:

y = 3x + 10

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1 year ago
How to simplify the square root of 9/245
lana66690 [7]
<span><span>the exact answer is 3 over
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3 years ago
Help please asap algebra 2
timurjin [86]
X = approximately 633

Steps:
lnx + ln3x = 14

ln3x^2 = 14 : Use the log property of addition which is to multiply same log                           together so you multiply x and 3x because they have log in                                common

  (ln3x^2) =  (14)  : take base of e on both sides to get rid of the log
e                e

3x^2 = e^14  : e cancels out log on the left side and the right side is e^14 

x^2 = e^14 / 3 : divide both sides by 3

√x^2 = <span>√(e^14 / 3) : take square root on both sides to get rid of the square 2                                  on x
</span>
x = √(e^14) / <span>√3 : square root cancels out square 2 leaving x by itself

x = e^7 / </span>√3 : simplify the √(e^14) so 14 (e^14) divide by 2 (square root) = 7<span>

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4 0
2 years ago
If x=5, evaluate x^5 * x^-3
Artyom0805 [142]

Answer: 25

Step-by-step explanation:

Plug in x to the expression.

5^5 * 5^{-3}\\

When there is the same base of exponents is being multiplied the exponents add together and the base stays the same.

So this simplifies to, 5^2.

This then solves to 25.

3 0
3 years ago
A line includes the points (0,0) and (1,5). What is its equation in slope-intercept form
Kipish [7]

9514 1404 393

Answer:

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The equation of the line is ...

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