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melamori03 [73]
3 years ago
6

Juan and his little brother Miguel ran around a circular track together. Juan ran on the inner track, which has a radius of 30 f

eet. Miguel ran on the outer track which has a radius of 40 feet. How much farther did Miguel run than Juan?
Mathematics
1 answer:
eduard3 years ago
8 0

Answer:

80pi-60pi

Step-by-step explanation:

To find how much Juan ran, we must find the circumference.

pi *30*2=60*pi  (which is how much Juan ran.)

pi*40*2=80*pi (which is how much Miguel ran)

80pi-60pi would be how much farther Miguel ran than Juan.

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What are the zeros of the polynomial function f(x) = x3 + 2x2 − 24x?
Alik [6]

You may notice that all of the terms have a common factor: x. So, let's take the x out of all the terms. This gives us:

x(x^2 + 2x - 24) = 0


Using the Zero Product Property, we can say that both x = 0 and x^2 + 2x - 24 = 0.

Let's solve both. x = 0 is obvious, but we still need to solve our other term:

x^2 + 2x - 24 = 0

  • Set up

(x + 6)(x - 4) = 0

  • Factor

x = -6, 4

  • Apply the Zero Product Property

Our answer is x = -6, 0, 4.


4 0
3 years ago
A toy manufacturer makes lightweight balls for indoor play. The large basketball uses 4 ounces of foam and 20 minutes of labor a
trapecia [35]

Answer:

(24, 224 ) i.e. 24 basketball and 224 footballs

Step-by-step explanation:

<em>Basketball :</em>

uses 4 ounces of foam

20 minutes of labor

profit = $2.50

<em>Football :</em>

uses 3 ounces of foam

30 minutes of labor

profit = $2

Manufacturer has :

768 ounces of foam , 120 labor hours per week,

<u>using the simplex method to determine the optimal production schedule so as to maximize profits </u>

lets assume

x = number of basketball

y = number of footballs

maximize = 2.5 x + 2y  from a linear programming problem

attached below is the detailed solution

6 0
3 years ago
Finding an irrational number between which given pair of numbers supports the idea that irrational numbers are dense
Fittoniya [83]

Answer:

3.33 and 1/3

Step-by-step explanation:

"Dense" here means that there are infinite irrational numbers between two rational numbers. Also, there are infinite rational numbers between two rational numbers. That's the meaning of dense. Actually, that can be apply to all real numbers, there always is gonna be a number between other two.

But, to demonstrate that irrationals are dense, we have to based on an interval with rational limits, because the theorem about dense sets is about rationals, and the dense irrational set is a deduction from it. That's why the best option is 2, because that's an interval with rational limits.

8 0
3 years ago
The formula d = rt can be used to calculate the distance (d) an object travels using its rate of speed (r) and the time it trave
riadik2000 [5.3K]
Start with d=rt. Now, solve for r by isolating it. since r is multiplied by t, divide both sides by t. d/t=r. So your answer would be the 2nd choice.
3 0
3 years ago
Please help ASAP....
sesenic [268]

Answer:

C

Step-by-step explanation:

All the other answers are changing direction at some point so the sign of velocity is changing. The only one that is not changing is C, so C is correct.

8 0
3 years ago
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