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hjlf
3 years ago
12

At what rate must $287.50 be compounded annually for it to grow to $572.86 in 8 years?

Mathematics
1 answer:
UNO [17]3 years ago
3 0
Using the compound interest formula,
572.86=287,50(1+i)^8
(1+i)^8=572.86/287.50=1.992557
1+i=(1.992557)^(1/8)=1.0899996
=> 
i=1.0899996-1=9%

Note: This problem can also be solved in the head using the rule of 72.
Since after 8 years, the amount is roughly doubled, we can say that the interest rate is approximately 72/8=9%
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Step-by-step explanation:

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Check that 2b+b and 3b have the same value when b is 1,2, and 3. Do 2b+b and 3b have the same value for all values of b? Explain
Inessa [10]

Answer:

Expression 2b+b and 3b have same values for all values of b.

Step-by-step explanation:

Given the two expression 2b+b and 3b and values of b as 1, 2 and 3.

Consider first expression that is, 2b+b.

Substituting the value of b=1,

2\left(1\right)+\left(1\right)=2+1=3 ....1

Substituting the value of b=2,

2\left(2\right)+\left(2\right)=4+2=6 ....2

Substituting the value of b=3,

2\left(3\right)+\left(3\right)=6+3=9 ....3

Consider second expression that is, 3b.

Substituting the value of b=1,

3\left(1\right)=3 ....4

Substituting the value of b=2,

3\left(2\right)=6 ....5

Substituting the value of b=3,

3\left(3\right)=9 ....6

For value of b=1, equation 1 and equation 4 are same, for value of b=2, equation 2 and equation 5 are same and for value of b=3 equation 3 and equation 6 are same.

Therefore both expression are same for all values of b.

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3 years ago
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If two lines are perpendicular, their slopes are negative reciprocals.<br> A. True<br> B.False
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the length of a rectangle is 5 times as long as its breadth and its area is 1620 m² find area of square whose perimeter is equal
Rus_ich [418]

Answer:

Area of the square is 2916 m^{2}.

Step-by-step explanation:

Let the breadth of the rectangle be represented by w. So that;

length of rectangle = 5w

Area of rectangle = length x breadth

                             = 5w x w

1620 = 5w^{2}

divide through by 5 to have,

w^{2} = 324

w = \sqrt{324}

   = 18

Thus, the breadth of the rectangle is 18 m.

length = 5 w = 5 x 18

           = 90 m

The length of the rectangle is 90 m.

Perimeter of the rectangle = 2(l + w)

                                  = 2( 90 + 18)

                                  = 216 m

Perimeter of a square = 4l

where l is the length of its side.

Given that the perimeters of the rectangle and square are equal, then;

4l = 216

l = \frac{216}{4}

 = 54

length of the side of square is 54 m.

Therefore,

Area of square = l^{2}

                         = 54^{2}

                        = 2916

Area of the square whose perimeter is equal to that of the rectangle is 2916 m^{2}.

6 0
3 years ago
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