(-9 x -3) + 27 integers

Two cyclists, Alan and Brian, are racing around oval track of length 450m on the same direction simultaneously from the same poi

skelet666 [1.2K]

Answer:

Alan: 200 m/min

Brian: 150 m/min

Step-by-step explanation:

Given : Two cyclists, Alan and Brian, are racing around oval track of length 450m on the same direction simultaneously from the same point. Alan races around the track in 45 seconds before Brian does and overtakes him every 9 minutes.

To find : What are their rates, in meters per minute?

Solution :

Let n represent the number of laps that Alan completes in 9 minutes.

Then n-1 is the number of laps Brian completes.

45 seconds = 3/4 minutes.

The difference in their lap times in minutes per lap is

$\frac{9}{(n -1)}-\frac{9}{n} =\frac{3}{4}$

Solving the equation we get,

$\frac{9n-9n+9}{n(n -1)} =\frac{3}{4}$

$9\times 4=3\times n(n -1)$

$36=3\times n(n -1)$

$n^2-n-12=0$

$n^2-4n+3n-12=0$

$n(n-4)+3(n-4)=0$

$(n-4)(n+3)=0$

$n=4,-3$

Neglecting n=-3

So, n=4

Then Alan's speed in m/min is

$S=\frac{D}{T}$

$S_a=\frac{4\times 450}{9}$

$S_a=200 m/min$

Brian completes 3 laps in that 9-minute time, so his rate is

$S_b=\frac{3\times 450}{9}$

$S_b=150 m/min$

Therefore, Alan: 200 m/min

Brian: 150 m/min

4 0

3 years ago

Find the solution of the system of equations.

Alex17521 [72]

Answer:

the answer is Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(−17/2, -7)

Equation Form:x=-17/2 y=-7

5 0

2 years ago

Read 2 more answers

PLEASE HELP

shtirl [24]

Answer:

70 m

Step-by-step explanation:

AB makes a 30-60-90 triangle with the wall.

AC makes a 45-45-90 triangle with the wall.

In a 30-60-90 triangle, the short leg (opposite of the 30° angle) is half the hypotenuse.

In a 45-45-90 triangle, the legs are the same length.

So the distance between the left wall and the laser is 60/2 = 30 m.

The distance between the right wall and the laser is 40 m.

The total distance is therefore 70 m.

6 0

2 years ago

A circular garden has a circumference of

omeli [17]

This solution to this problem is predicated on the fact that the circumference is just: $2\pir$ . A straight line going through the center of the garden would actually be the diameter, which is well known to be two times the radius of the circle, so we can say that the circumference is just:

$d\pi$

So, solving for both the radius and the diameter gives us:

$d\pi=8xy^2\pi\\ d=8xy^2\\ \\ 2\pi r=8xy^2\pi\\ r=4xy^2$

So, the length of thes traight path that goes through the center of the guardain is just $8xy^2$ , and we can use the radius for the next part of the problem.

The area of a circle is $\pi r^2$ , which means we can just plug in the radius and find our area:

$A=\pi r^2 \implies \\ A=\pi (4xy^2)^2\implies \\ A= 16\pi x^2y^4$

So, we have found our area( $16 \pi x^2 y^4$ ) and the problem is done.

6 0

3 years ago

How do you find the cube root

zvonat [6]

Use a calculator to find the cube root of positive or negative numbers. Given a number x, the cube root of x is a number a such that a3 = x. If x positive a will be positive, if x is negative a will be negative. Cube roots is a specialized form of our common radicals calculator.

Example Cube Roots:The 3rd root of 64, or 64 radical 3, or the cube root of 64 is written as $ \sqrt[3]{64} = 4 $.The 3rd root of -64, or -64 radical 3, or the cube root of -64 is written as $ \sqrt[3]{-64} = -4 $.The cube root of 8 is written as $ \sqrt[3]{8} = 2 $.The cube root of 10 is written as $ \sqrt[3]{10} = 2.154435 $.

The cube root of x is the same as x raised to the 1/3 power. Written as $ \sqrt[3]{x} = x^{\frac{1}{3}} $. The common definition of the cube root of a negative number is that 
(-x)1/3 = -(x1/3).[1] For example:

The cube root of -27 is written as $ \sqrt[3]{-27} = -3 $.The cube root of -8 is written as $ \sqrt[3]{-8} = -2 $.The cube root of -64 is written as $ \sqrt[3]{-64} = -4 $.

This was not copied from a website or someone else. This was from my last year report.


f -64, or -64 radical 3, or the cube root of -64 is written as $ \sqrt[3]{-64} = -4 $.The cube root of 8 is written as $ \sqrt[3]{8} = 2 $.The cube root of 10 is written as $ \sqrt[3]{10} = 2.154435 $.

The cube root of x is the same as x raised to the 1/3 power. Written as $ \sqrt[3]{x} = x^{\frac{1}{3}} $. The common definition of the cube root of a negative number is that 
(-x)1/3 = -(x1/3).[1] For example:

The cube root of -27 is written as $ \sqrt[3]{-27} = -3 $.The cube root of -8 is written as $ \sqrt[3]{-8} = -2 $.The cube root of -64 is written as $ \sqrt[3]{-64} = -4 $.

6 0

2 years ago