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satela [25.4K]
2 years ago
14

Find the amount in a continuously compounded account for the following condition. ​Principal, ​$​4000; Annual interest​ rate, 5.

7​%; ​time, 3 years
Mathematics
1 answer:
soldi70 [24.7K]2 years ago
7 0
<h3>Answer:  4745.96 dollars</h3>

=======================================================

Explanation:

We have this given info

  • P = 4000 = principal
  • r = 0.057 = annual interest rate in decimal form
  • t = 3 = number of years

Use this to plug into the formula below

A = Pe^{r*t}\\\\A = 4000*e^{0.057*3}\\\\A \approx 4,745.96299608713\\\\A \approx 4,745.96\\\\

You'll need your calculator, and the calculator needs the "e" button.

The "e" refers to the special constant 2.718... which is similar to pi = 3.14...

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A 20-sided regular polygon has an angle measure represented as 3gº.
Andre45 [30]

The value of g in the 20 sided regular polygon is 54.

<h3>How to find the angles of a regular polygon?</h3>

If all the polygon sides and interior angles are equal, then they are known as regular polygons.

The polygon given is a 20 sided regular polygon and the measure of each angle is 3g degrees.

Therefore, let's find g.

The sum of interior angles of a 20 sided polygon is as follows:

180(n - 2) = 180(20 - 2) = 180(18) = 3240

Therefore,

each angle = 3240 / 20 = 162

Hence,

162 = 3g

g = 162 / 3

Therefore,

g = 54

learn more on regular polygon here: brainly.com/question/16992545

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8 0
1 year ago
Find the area of the part of the plane 3x 2y z = 6 that lies in the first octant.
gavmur [86]

The area of the part of the plane 3x 2y z = 6 that lies in the first octant  is  mathematically given as

A=3 √(4) units ^2

<h3>What is the area of the part of the plane 3x 2y z = 6 that lies in the first octant.?</h3>

Generally, the equation for is  mathematically given as

The Figure is the x-y plane triangle formed by the shading. The formula for the surface area of a z=f(x, y) surface is as follows:

A=\iint_{R_{x y}} \sqrt{f_{x}^{2}+f_{y}^{2}+1} d x d y(1)

The partial derivatives of a function are f x and f y.

\begin{aligned}&Z=f(x)=6-3 x-2 y \\&=\frac{\partial f(x)}{\partial x}=-3 \\&=\frac{\partial f(y)}{\partial y}=-2\end{aligned}

When these numbers are plugged into equation (1) and the integrals are given bounds, we get:

&=\int_{0}^{2} \int_{0}^{3-\frac{3}{2} x} \sqrt{(-3)^{2}+(-2)^2+1dxdy} \\\\&=\int_{0}^{2} \int_{0}^{3-\frac{3}{2} x} \sqrt{14} d x d y \\\\&=\sqrt{14} \int_{0}^{2}[y]_{0}^{3-\frac{3}{2} x} d x d y \\\\&=\sqrt{14} \int_{0}^{2}\left[3-\frac{3}{2} x\right] d x \\\\

&=\sqrt{14}\left[3 x-\frac{3}{2} \cdot \frac{1}{2} \cdot x^{2}\right]_{0}^{2} \\\\&=\sqrt{14}\left[3-\frac{3}{2} \cdot \frac{1}{2} \cdot x^{2}\right]_{0}^{2} \\\\&=\sqrt{14}\left[3.2-\frac{3}{2} \cdot \frac{1}{2} \cdot 3^{2}\right] \\\\&=3 \sqrt{14} \text { units }{ }^{2}

In conclusion,  the area is

A=3 √4 units ^2

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5 0
1 year ago
NEED HELP ASAP !! WILL MARK BRAINLEAST<br> SHOW WORK TOO !!!
irinina [24]

Step-by-step explanation:

(1 +  \cos(x) )(1 -  \cos(x) )

1  -  \cos {}^{2} (x)

=  \sin {}^{2} (x)

b.

\frac{1}{ \cot {}^{2} (x) }  -  \frac{1}{ \cos {}^{2} (x) }

\frac{1}{ \frac{ \cos {}^{2} (x) }{ \sin { }^{2} (x) } }  -  \frac{1}{ \cos {}^{2} (x) }

\frac{1}{ \cot {}^{2} (x) }  -  \frac{   \csc {}^{2} (x)   {} }{ \cot {}^{2} (x) }

\frac{ -  \cot {}^{2} (x) }{ \cot {}^{2} (x) }

- 1

c.

\sec {}^{2} ( \frac{\pi}{2} - x ) )( \sin {}^{2} (x)  -  \sin {}^{4} (x))

( \csc {}^{2} (x) )( \sin {}^{2} (x)  -  \sin {}^{4} (x  )

\csc {}^{2} (x) ( \frac{1}{ \csc {}^{2} (x) }  -  \frac{1}{  \csc {}^{4}  (x) } )

1 -  \frac{1}{ \csc {}^{2} (x) }

1 -  \sin {}^{2} (x)

\cos {}^{2} (x)

3 0
2 years ago
Find the least whole number that can replace _ to make the statement true<br><br> _ ÷ 7 &gt; 800
Sloan [31]
7 goes into 6,300 900 times so your answer is 6,300
3 0
3 years ago
How do you find your answer step-by-step?
WARRIOR [948]
5.68 x 6.02 ( 10^9)


same base 10 so add the exponent together

4 0
3 years ago
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