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3 years ago

The principal amount, $5500, earns 3.75% interest compounded continuously.

Mathematics

1 answer:

Eva8 [605]3 years ago

8 0

Answer:

The function that represents the value of the account at any time, t

$\:\:A=Pe^{rt}$

The total amount accrued, principal plus interest, from compound interest on an original principal of $ 5,500.00 at a rate of 3.75% per year compounded continuously over 6 years is $ 6,887.77.

Step-by-step explanation:

a. Write the function that represents the value of the account at any time, t.

The function that represents the value of the account at any time, t

$\:\:A=Pe^{rt}$

where

A represents the Future Value

P represents the Principle (Initial Value)

r represents the Interest rate

t represents the time

b) What will the value be after 6 years?

Given

The principal amount P = $5500

Annual Rate r = 3.75% = 3.75/100 = 0.0375

Time Period t = 6 years

To Determine:

The total amount A = ?

Using the formula

$\:\:A=Pe^{rt}$

substituting the values

$A\:=\:5500\left(2.71828\right)^{\left(0.0375\right)\left(6\right)}$

$A=5500\cdot \:2.71828^{0.225}$

$A = $ 6,887.77$ $

Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 5,500.00 at a rate of 3.75% per year compounded continuously over 6 years is $ 6,887.77.

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Solve:<br> 2/3x+15=17<br><br> 3x+8-x=7<br><br> 4(2x-6)=2

Volgvan

Answer:

x = 3

x = (-1)/2

x = 13/4

Step-by-step explanation:

Solve for x:

(2 x)/3 + 15 = 17

Put each term in (2 x)/3 + 15 over the common denominator 3: (2 x)/3 + 15 = (2 x)/3 + 45/3:

(2 x)/3 + 45/3 = 17

(2 x)/3 + 45/3 = (2 x + 45)/3:

1/3 (2 x + 45) = 17

Multiply both sides of (2 x + 45)/3 = 17 by 3:

(3 (2 x + 45))/3 = 3×17

(3 (2 x + 45))/3 = 3/3×(2 x + 45) = 2 x + 45:

2 x + 45 = 3×17

3×17 = 51:

2 x + 45 = 51

Subtract 45 from both sides:

2 x + (45 - 45) = 51 - 45

45 - 45 = 0:

2 x = 51 - 45

51 - 45 = 6:

2 x = 6

Divide both sides of 2 x = 6 by 2:

(2 x)/2 = 6/2

2/2 = 1:

x = 6/2

The gcd of 6 and 2 is 2, so 6/2 = (2×3)/(2×1) = 2/2×3 = 3:

Answer: x = 3

______________________________________________________

Solve for x:

3 x - x + 8 = 7

Grouping like terms, 3 x - x + 8 = (3 x - x) + 8:

(3 x - x) + 8 = 7

3 x - x = 2 x:

2 x + 8 = 7

Subtract 8 from both sides:

2 x + (8 - 8) = 7 - 8

8 - 8 = 0:

2 x = 7 - 8

7 - 8 = -1:

2 x = -1

Divide both sides of 2 x = -1 by 2:

(2 x)/2 = (-1)/2

2/2 = 1:

Answer: x = (-1)/2

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Solve for x:

4 (2 x - 6) = 2

Divide both sides of 4 (2 x - 6) = 2 by 4:

(4 (2 x - 6))/4 = 2/4

4/4 = 1:

2 x - 6 = 2/4

The gcd of 2 and 4 is 2, so 2/4 = (2×1)/(2×2) = 2/2×1/2 = 1/2:

2 x - 6 = 1/2

Add 6 to both sides:

2 x + (6 - 6) = 1/2 + 6

6 - 6 = 0:

2 x = 1/2 + 6

Put 1/2 + 6 over the common denominator 2. 1/2 + 6 = 1/2 + (2×6)/2:

2 x = 1/2 + (2×6)/2

2×6 = 12:

2 x = 1/2 + 12/2

1/2 + 12/2 = (1 + 12)/2:

2 x = (1 + 12)/2

1 + 12 = 13:

2 x = 13/2

Divide both sides by 2:

x = (13/2)/2

2×2 = 4:

Answer: x = 13/4

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3 years ago

In Exercises 8-10, sketch the figure described.

Lunna [17]

The sketch answers to question 8, 9 and 10 is given in the image attached.

<h3>What is an intersecting lines?</h3>

A link is known to be intersecting if two or more lines are said to have cross one another in a given plane.

Note that the intersecting lines are known to be one that often share a common point, and it is one that can be seen on all the intersecting lines, and it is known to be the point of intersection.

Looking at the image attached, you can see how plane A and line c intersecting at all points on line c and also GM and GH and line CD and plane X as they are not intersecting

Therefore, The sketch answers to question 8, 9 and 10 is given in the image attached.

Learn more about intersecting lines from

brainly.com/question/2065148

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2 years ago

What is an equation of the line that passes through the point (8,-5) and is parallel

HACTEHA [7]

Answer:

y=-5/4x+5

Step-by-step explanation:

Hi there!

We're given the line 5x+4y=24 and we want to find the line parallel to it that passes through (8,-5)

Parallel lines have the same slopes

First, we need to find the slope of 5x+4y=24.

We'll do that by converting 5x+4y=24 from standard form (ax+by=c where a, b, and c are integers) to slope-intercept form (y=mx+b where m is the slope and b is the y intercept)

subtract 5x from both sides

4y=-5x+24

divide by 4 on both sides

y=-5/4x+6

since -5/4 is in the place where m should be, it is the slope.

So the equation of the line parallel to it will also have -5/4 as the slope

Here's the equation so far in slope-intercept form:

y=-5/4x+b

we need to find b

because the equation will pass through (8,-5), we can use it to solve for b

substitute 8 as x and -5 as y

-5=-5/4(8)+b

multiply

-5=-10+b

add 10 to both sides

5=b

substitute 5 as b into the equation

That's the equation of the line parallel to 5x+4y=24.

Hope this helps!

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3 years ago

Last week, the price of apples at a grocery store was $1.06 per pound. This week, apples at the store are on sale at a 10% disco

olga2289 [7]

Answer: $6.48

Step-by-step explanation:

1.60 * 0.1 = $0.16

1.60 - 0.16 = $1.44

1.44 * 4.5 = $6.48

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kupik [55]

Answer:

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Step-by-step explanation:

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