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Allushta [10]
4 years ago
12

james has $3000 in credit card debt, which charges 14% interest. how long will it take to pay off the card if he makes the minim

um payment of $60.00 a month?
Mathematics
1 answer:
GREYUIT [131]4 years ago
7 0

Answer:

The answer is approx 75 months.

Step-by-step explanation:

We have P = 3000

r = 14%

Monthly payment = $60

We will use the formula :

[(0.14/12) \times3000] / [1- (1+(0.14/12)^{-12n}]

Solving this we get n = approx 75 months. After 75 months few dollars will be left. And in the 76th month the balance will become negative.

For easy and better understanding, I have attached an excel sheet.

The answer is approx 75 months.

Download xlsx
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The area of the rhombus is 540 cm2; the length of one of its diagonals is 4.5 dm. What is the distance between the point of inte
malfutka [58]

1. The area of the rhombus can be found by the formula

A=\dfrac{d_1\cdot d_2}{2}, where d_1,\ d_2 are rhombus's diagonals.

Note that d_1=4.5\ dm=45\ cm, then

540=\dfrac{45\cdot d_2}{2},\\ \\540\cdot 2=45d_2,\\ \\d_2=24\ cm.

2. The diagonals of rhombus are perpendicular and are bisectors of each other. Then the triangle formed with halfs of diagonals is right triangles with legs

\dfrac{d_1}{2}=22.5\ cm,\ \dfrac{d_2}{2}=12\ cm.

The hypotenuse of this triangle is the rhombus's side. By the Pythagorean theorem

\text{rhombus's side}^2=(22.5)^2+12^2=506.25+144=650.25,\\ \\\text{rhombus's side}=25.5\ cm.

3. The distance between the point of intersection of the diagonals and the side of the rhombus is the height of right triangle considered above.

Use twice the Pythagorean theorem to find this height:

\left\{\begin{array}{l}x^2+h^2=12^2\\(25.5-x)^2+h^2=22.5^2,\end{array}\right.

where x is projection of leg 12 cm and h is height.

Subtract the first equation from the second:

(25.5-x)^2+h^2-x^2-h^2=22.5^2-12^2,\\ \\650.25-51x=506.25-144,\\ \\51x=650.25-362.25=288,\\ \\x=\dfrac{96}{17}\ cm.

Then

h^2=144-\left(\dfrac{96}{17}\right)^2=144-\dfrac{9216}{289}=\dfrac{32400}{289},\\ \\h=\dfrac{180}{17}\ cm.

Answer: h=\dfrac{180}{17}\ cm.

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12. Dreams of driving. Suppose you drive to school. If you
Orlov [11]

Answer: 12 miles

Step-by-step explanation:

Ok, we know that:

Distance = Time*Speed.

or:

D = T*S

The distance between the house and the school is constant, and suppose that T is the exact time such that you arrive just in time, then:

" If you  drive at an average speed of 45 mph, you arrive 1 min early  for the first bell. "

We can write this as:

D = (T - 1min)*45mi/h.

"If you drive at an average speed 40 mph,  you arrive 1 min late."

We can write this as:

D = (T + 1min)*40mi/h.

So we have a system of linear equations:

D = (T - 1min)*45mi/h.

D = (T + 1min)*40mi/h.

First, 1 hour has 60 mins, then 1 min = (1/60) hours.

We do this change because in the system of equations we have minutes and hours, and we can only work with one unit, now we can write the equations as:

D = (T - (1/60)h)*45mi/h.

D = (T + (1/60)h)*40mi/h.

now, we can write:

D = (T - (1/60)h)*45mi/h. = (T + (1/60)h)*40mi/h.

Now we can solve this for T.

(T - (1/60)h). = (T + (1/60)h)*(40/45)

T = (T + (1/60)h)*(40/45) + (1/60)h

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T*(1 - 40/45) = 0.031 h

T = 0.031h/(1 - 40/45) = 0.283... hours

Now, to find the distance to the school we can replace this time in one of the equations:

D = (T + (1/60)h)*40mi/h. = (0.283...h + (1/60)h)*40mi/h = 12 miles.

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