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3 years ago

If $3,000,000 is invested at 6% interest compounded continuously, how much

Mathematics

1 answer:

g100num [7]3 years ago

3 0

Answer:

$24,498,509.74

Step-by-step explanation:

The formula for the value as a function of time is ...

V(t) = P·e^(rt)

Filling in the numbers and doing the arithmetic, we have ...

V(35) = 3,000,000·e^(0.06·35) ≈ 24,498,509.74

Compounded continuously for 35 years, the investment will be worth $24,498,509.74.

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You are filling up a cylindrical tank with a radius of 5m with water at a rate of 3 cm^3/min. Unbeknownst to you the tank has a

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dh/dt = 3/25π m/min

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3 years ago

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3 years ago

The coordinates of the vertices of a rectangle are (-4, 3), (-1, 5),(3, – 1), and (0, – 3).

SCORPION-xisa [38]

Answer:

Perimeter of rectangle is 23.34

Step-by-step explanation:

The coordinates of the vertices of a rectangle are (-4, 3), (-1, 5),(3, – 1), and (0, – 3).

What is the perimeter of the rectangle?

The formula to find perimeter of rectangle is: $Perimeter=2(l+w)$

We need to find length and width first using the coordinates (-4, 3), (-1, 5),(3, – 1), and (0, – 3).

Let A=(-4, 3) B=(-1, 5) C=(3, – 1) and D=(0, – 3) according to the figure attached.

So, If we find distance of point AB it can be considered length of rectangle and distance of point AC can be considered width of rectangle

The formula used to find distance is: $Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Finding distance AB, we have $x_1=-4, y_1=3, x_2=-1, y_2=5$

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(-1-(-4))^2+(5-3)^2}\\Distance=\sqrt{(-1+4)^2+(5-3)^2}\\Distance=\sqrt{(3)^2+(2)^2}\\Distance=\sqrt{9+4}\\Distance=\sqrt{13}\\Distance=3.61$

So distance between point A and B is 3.61

Finding distance AC, we have $x_1=-4, y_1=3, x_2=3, y_2=-1$

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(3-(-4))^2+(-1-3)^2}\\Distance=\sqrt{(3+4)^2+(-1-3)^2} \\Distance=\sqrt{(7)^2+(-4)^2} \\Distance=\sqrt{49+16} \\Distance=\sqrt{65}\\Distance=8.06$

So, distance between point A and C is 8.06

We have length = 3.61 and width = 8.06

Using formula of perimeter

$Perimeter=2(l+w)\\Perimeter=2(3.61+8.06)\\Perimeter=2(11.67)\\Perimeter=23.34$

So, Perimeter of rectangle is 23.34

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3 years ago