Ask question

Ask question

All categories

2 years ago

7

Mikayla is training for a half-marathon. At the beginning of her training, she is able to run 2 miles without stopping. Her goal

is to increase her distance by three quarters of a mile each week. a) Write an equation to represent the number of miles Mikayla is able to run after each week. Define your variables.

1 answer:

ivanzaharov [21]2 years ago

5 0

Alright, lets get started.

At the beginning of her training, she is able to run 2 miles without stopping means 2 will be in the addition when we will write the equation for her running miles.

Her goal is to increase her distance by three quarters of a mile each week.

Means in first week, she will add the distance = $\frac{3}{4}$ miles

Suppose she runs x weeks, so shee will add distance = $\frac{3}{4}x$

So, suppose she runs total number of miles = d, then

$d = 2 + \frac{3}{4}x$

Where d is total numer of miles she runs

x is number of weeks : Answer

Hope it will help :)

You might be interested in

An internet service provider charges $18 per month plus an initial set up fee. one customer paid a total of $81 after 2 months o

frosja888 [35]

Ok so
cost=setupfee+costused
costused=(number of months) times (cost per month)
if we represent number of months as x
we know cost per month is 18
18x is costused
and in 2 m onts, he paid 81 so
81=startup fee +18x
2 monts so x=2
81=startupfeee+36
subtract 36
45=startup fee

5 monts is x=5
45+18(5)=45+90=135

A. cost=18x+45
B. $45
C. $135

6 0

2 years ago

A factory worker can produce 28 toys in an eight hour day If there are 42 workers in total how many toys are produced every hour

katrin2010 [14]

Answer:

<em>147 toys</em>

Step-by-step explanation:

<em>for 1 person, 28toys/8hours = 3.5toys/ 1hour </em>

<em>for 42 people, 42 * 3.5toys/ 1hour = 147 toys/hour</em>

<em></em>

<em>~Hope it Helps!~</em>

3 0

2 years ago

The table shows weights for different US coins. Allen has one of each coin in his hand

Sever21 [200]

Penny- 3g
nickel-5g
dime- 2g
quarter-6g
half dollar- 11g

6 0

2 years ago

Read 2 more answers

Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D = {(x, y) |

Bas_tet [7]

Answer:

$M=168k$

$(\bar{x},\bar{y})=(5,\frac{85}{28})$

Step-by-step explanation:

Let's begin with the mass definition in terms of density.

$M=\int\int \rho dA$

Now, we know the limits of the integrals of x and y, and also know that ρ = ky², so we will have:

$M=\int^{9}_{1}\int^{4}_{1}ky^{2} dydx$

Let's solve this integral:

$M=k\int^{9}_{1}\frac{y^{3}}{3}|^{4}_{1}dx$

$M=k\int^{9}_{1}\frac{y^{3}}{3}|^{4}_{1}dx$

$M=k\int^{9}_{1}21dx$

$M=21k\int^{9}_{1}dx=21k*x|^{9}_{1}$

So the mass will be:

$M=21k*8=168k$

Now we need to find the x-coordinate of the center of mass.

$\bar{x}=\frac{1}{M}\int\int x*\rho dydx$

$\bar{x}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}x*ky^{2} dydx$

$\bar{x}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}x*y^{2} dydx$

$\bar{x}=\frac{1}{168}\int^{9}_{1}x*\frac{y^{3}}{3}|^{4}_{1}dx$

$\bar{x}=\frac{1}{168}\int^{9}_{1}x*21 dx$

$\bar{x}=\frac{21}{168}\frac{x^{2}}{2}|^{9}_{1}$

$\bar{x}=\frac{21}{168}*40=5$

Now we need to find the y-coordinate of the center of mass.

$\bar{y}=\frac{1}{M}\int\int y*\rho dydx$

$\bar{y}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}y*ky^{2} dydx$

$\bar{y}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}y^{3} dydx$

$\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{y^{4}}{4}|^{4}_{1}dx$

$\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{255}{4}dx$

$\bar{y}=\frac{255}{672}\int^{9}_{1}dx$

$\bar{y}=\frac{255}{672}8=\frac{2040}{672}$

$\bar{y}=\frac{85}{28}$

Therefore the center of mass is:

$(\bar{x},\bar{y})=(5,\frac{85}{28})$

I hope it helps you!

3 0

2 years ago

There were 567 people at a concert when a band started playing. After each song, only one-third of the people stayed to hear the

Solnce55 [7]

To write the function correctly, it is important to assign variables correctly and understand the situation of the problem clearly. For this, we let y the number of people and x as the number of songs played.

At x = 0 y = 567
at x = 1 y = 567 - 567(1/3)
at x = 2 y = 567 - 567(1/3)(1/3)
at x = 3 y = 567 - 567(1/3)(1/3)(1/3)

Therefore, the number of people left after x songs would be represented by the equation:

y = 567 - 567(1/3)x
y = 567 ( 1- x/3 )

7 0

2 years ago

Read 2 more answers