What times 3 equals 4?

If point A is located at (5,-7) and there are 8 points between A and B, what could be the possible coordinates for point B?

aleksandr82 [10.1K]

Answer: The possible cordinates (X,Y) of B can be found with the formula Y = √(8^2 - (X- 5)^2) - 7 where -3 ≤ X ≤ 13

Step-by-step explanation:

The point A is located at (5, -7)

And we know that we have 8 units of difference between A and B.

The equation of a circle centerd in the point (x0, y0) is:

(x - x0)^2 + (y - y0)^2 = r2

where r is the radius of the circle

So we can draw a circle of 8 units around A, and get:

(X - 5)^2 + (Y - (-7))^2 = 8^2

So from this equation we can find all the possible values of B, for this we can isolate one of the variables in one side and get a function.

Y = √(8^2 - (X- 5)^2) - 7

So for a given value of X, you can find the value of Y. where you need to remember that (8^2 - (X-5)^2) can not be a negative number, so we must have that:

8^2 ≥ (X - 5)^2

So X can go from -3 (because (-3 - 5)^2 = 8^2)

to X = 13 (because (13 - 5)^2 = 8^2)

So X is in the range {-3, 13}

4 0

2 years ago

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At 10 percent interest, how long does it take to quadruple your money?

horsena [70]

It takes about 14.55 years for quadruple your money

Solution:

Given that,

At 10 percent interest, how long does it take to quadruple your money

Rule of 144:

The Rule of 144 will tell you how long it will take an investment to quadruple

Here,

Rate of interest = 10 %

Therefore, number of years to quadruple your money is obtained by dividing 144 by 10

Rule of 144 Formula:

$N = \frac{144}{R}$

Where:

N = Number of many years times.

144 = Is the constant variable.

R = Rate of interest.

$\rightarrow N = \frac{144}{10} = 14.4$

Thus it takes about 14.4 years for quadruple your money.

Another method:

If initial amount is $ 1 and it if quadruples it should be $ 4

We have to find the number of years if rate of interest is 10 %

Let "n" be the number of years

Then we can say,

$Amount = Principal(1+\frac{R}{100})^n$

$4 = 1(1+\frac{10}{100})^n$

$4 = 1(1+0.1)^n\\\\4= 1(1.1)^n\\\\4 = 1.1^n\\\\We\ know\ that,\\\\(1.1)^{14.55} = 1.1^n\\\\We\ know\ that\\\\If\ a^m = a^n\ then\ m = n\\\\Therefore,\\\\14.55 = n\\\\n = 14.55$

Thus Option D 14.55 years is correct

7 0

3 years ago

a ramp measures 6 feet long. if the ramp is 12 inches tall, what is the horizontal distance it covers? i'll give brainliest to w

luda_lava [24]

we know that

1 ft--------> is equals to 12 in

the ramp is 12 inches tall----------> 1 ft tall

A ramp measures------------------> 6 ft long

applying the Pythagorean theorem

c²=a²+b²

where

c-----> 6 ft long

a----> horizontal distance

b-----> 1 ft tall

a²=c²-b²------> a²=6²-1²-----> a²=35------> a=√35------> a=5.92 ft

the answer is

5.92 ft

6 0

2 years ago

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The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 se

Dominik [7]

Answer: the price of a senior citizen's ticket is $8.

the price of a child's ticket is $14

Step-by-step explanation:

Let x represent the price of a senior citizen's ticket.

Let y represent the price of a child's ticket.

On the first day of ticket sales, the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. It means that

3x + y = 38- - - - - - - - - - - -1

The school took in $52 on the second day by selling 3 senior citizen and 2 child tickets. It means that

3x + 2y = 52- - - - - - - - - - - -2

Subtracting equation 2 from equation 1, it becomes

- y = - 14

y = 14

Substituting y = 14 into equation 1, it becomes

3x + 14 = 38

3x = 38 - 14 = 24

x = 24/3

x = 8

6 0

3 years ago

At the fair the 'Twirly Tea Cups'ride can hold nine people per tea cup.If the ride has seven tea cups,how many total people can

Kamila [148]

63 people should be able to fit in because 7 times 9 is 63.

If I'm wrong, contact me.

6 0

3 years ago

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