A car is driving at 100 kilometers per hour. How far, in meters, does it travel in 5 seconds?

Mathematics

1 answer:

Zolol [24]3 years ago

5 0

8.3333333333333333333333333333333333333 meters I recommend putting 8.3 with a bar notation over the 3

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

miskamm [114]

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) = 900 $cm^{3}$

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.

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

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7 0

3 years ago

Use four rectangles to estimate the area between the graph of the function f(x) = V3x + 5 and the x-axis on the interval[0, 4] u

yuradex [85]

Answer:

12.123

Step-by-step explanation:

You want the area under the curve f(x) = √(3x+5) on the interval [0, 4] estimated using the left sum and four subintervals.

<h3>Riemann sum</h3>

When the interval [0, 4] is divided into four equal parts, each has unit width. That means the area of the rectangle defined by the curve and the interval width will be equal to the value of the curve at the left end of the interval.

The area we want is the sum ...

f(0) +f(1) +f(2) +f(3)

As the attachment shows, that sum is ...

area ≈ 12.123 . . . square units

<em>Additional comment</em>

The table values in the attachment are rounded to 7 decimal places. Trailing zeros are not shown. Actual values used have 12 significant digits, as the total shows.

Such a sum is called a Riemann sum, named for a German mathematician. Four such sums are commonly used, and further refinements are possible. Those are the left sum (as here), the right sum, the midpoint sum, and a sum using a trapezoidal approximation of the rectangle area.

For left, right, and midpoint sums, n function values are required for n subintervals. When the trapezoidal approximation is used, n+1 function values are required.