1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Harrizon [31]
3 years ago
6

You are taking a trip at the same time as another family. Your family traveled 1,900 miles in 2 days, their family traveled 2,70

0 in 3 days. Who is traveling faster?
Mathematics
1 answer:
makkiz [27]3 years ago
6 0
The other family is traveling at 900 miles per day while your family is traveling at 950 miles per day. So your family is traveling faster.
You might be interested in
(x^2y+e^x)dx-x^2dy=0
klio [65]

It looks like the differential equation is

\left(x^2y + e^x\right) \,\mathrm dx - x^2\,\mathrm dy = 0

Check for exactness:

\dfrac{\partial\left(x^2y+e^x\right)}{\partial y} = x^2 \\\\ \dfrac{\partial\left(-x^2\right)}{\partial x} = -2x

As is, the DE is not exact, so let's try to find an integrating factor <em>µ(x, y)</em> such that

\mu\left(x^2y + e^x\right) \,\mathrm dx - \mu x^2\,\mathrm dy = 0

*is* exact. If this modified DE is exact, then

\dfrac{\partial\left(\mu\left(x^2y+e^x\right)\right)}{\partial y} = \dfrac{\partial\left(-\mu x^2\right)}{\partial x}

We have

\dfrac{\partial\left(\mu\left(x^2y+e^x\right)\right)}{\partial y} = \left(x^2y+e^x\right)\dfrac{\partial\mu}{\partial y} + x^2\mu \\\\ \dfrac{\partial\left(-\mu x^2\right)}{\partial x} = -x^2\dfrac{\partial\mu}{\partial x} - 2x\mu \\\\ \implies \left(x^2y+e^x\right)\dfrac{\partial\mu}{\partial y} + x^2\mu = -x^2\dfrac{\partial\mu}{\partial x} - 2x\mu

Notice that if we let <em>µ(x, y)</em> = <em>µ(x)</em> be independent of <em>y</em>, then <em>∂µ/∂y</em> = 0 and we can solve for <em>µ</em> :

x^2\mu = -x^2\dfrac{\mathrm d\mu}{\mathrm dx} - 2x\mu \\\\ (x^2+2x)\mu = -x^2\dfrac{\mathrm d\mu}{\mathrm dx} \\\\ \dfrac{\mathrm d\mu}{\mu} = -\dfrac{x^2+2x}{x^2}\,\mathrm dx \\\\ \dfrac{\mathrm d\mu}{\mu} = \left(-1-\dfrac2x\right)\,\mathrm dx \\\\ \implies \ln|\mu| = -x - 2\ln|x| \\\\ \implies \mu = e^{-x-2\ln|x|} = \dfrac{e^{-x}}{x^2}

The modified DE,

\left(e^{-x}y + \dfrac1{x^2}\right) \,\mathrm dx - e^{-x}\,\mathrm dy = 0

is now exact:

\dfrac{\partial\left(e^{-x}y+\frac1{x^2}\right)}{\partial y} = e^{-x} \\\\ \dfrac{\partial\left(-e^{-x}\right)}{\partial x} = e^{-x}

So we look for a solution of the form <em>F(x, y)</em> = <em>C</em>. This solution is such that

\dfrac{\partial F}{\partial x} = e^{-x}y + \dfrac1{x^2} \\\\ \dfrac{\partial F}{\partial y} = e^{-x}

Integrate both sides of the first condition with respect to <em>x</em> :

F(x,y) = -e^{-x}y - \dfrac1x + g(y)

Differentiate both sides of this with respect to <em>y</em> :

\dfrac{\partial F}{\partial y} = -e^{-x}+\dfrac{\mathrm dg}{\mathrm dy} = e^{-x} \\\\ \implies \dfrac{\mathrm dg}{\mathrm dy} = 0 \implies g(y) = C

Then the general solution to the DE is

F(x,y) = \boxed{-e^{-x}y-\dfrac1x = C}

5 0
3 years ago
A university is building a new student center that is two- thirds the distance from the arts center to the residential complex.
Natasha2012 [34]

Answer:

C = (\frac{21}{5},\frac{33}{5})

Step-by-step explanation:

Given

Points: (1, 9) and (9, 3)

Ratio = 2/3

Required

Determine the coordinate of the center

Represent the ratio as ratio

Ratio = 2:3

The new coordinate can be calculated using

C = (\frac{mx_2 + nx_1}{n + m},\frac{my_2 + ny_1}{n + m})

Where

(x_1,y_1) = (1, 9)

(x_2, y_2) = (9, 3)

m:n = 2:3

Substitute these values in the equation above

C = (\frac{2 * 9 + 3 * 1}{3 + 2},\frac{2 * 3 + 3 * 9}{2 + 3})

C = (\frac{18 + 3}{5},\frac{6 + 27}{5})

C = (\frac{21}{5},\frac{33}{5})

Hence;

<em>The coordinates of the new center is </em>C = (\frac{21}{5},\frac{33}{5})<em></em>

7 0
2 years ago
4. Bobby is 12 years old. His grandfather is 60 years old, what percent of Bobby's
Lina20 [59]

Answer: 12/60 as a percentage is 20%

Step-by-step explanation: boby is 12 and his grandfather is 60 so Bobby’s age is 12/60 of his grandfather and as a percentage it’s 20%

5 0
2 years ago
Read 2 more answers
Show a diagram or picture why 1/2 of 60 is not the same as 1/2 of 24
antoniya [11.8K]
Look at the picture..............

6 0
3 years ago
Sam and Bethan share £54 in the ratio of 5:4 work out how much each gets
Sindrei [870]
Answer:
Sam gets £30 and Bethan gets £24.
Why?
When dealing with ratios, add up the numbers in the ratio.
5 + 4 = 9
Now, divide the total amount of money by that number.
£54/9 = 6
Now you have the base rate. Multiply each quantity in the ratio by this number.
5*6 = 30
4*6 = 24
Now, the ratio is (in euro) 30:24. This means that Sam has £30 and Bethan has £24.
Check:
30 + 24 = 54
6 0
3 years ago
Other questions:
  • I need.help please
    5·2 answers
  • A 20 foot ladder is lean against a building. The foot of the ladder is 6 feet from the building. Find the
    6·1 answer
  • Can anyone help me with this? I'll mark brainliest for best answer
    10·1 answer
  • A Microgates Industries bond has a 10 percent coupon rate and a $1,000 face value. Interest is paid semiannually, and the bond h
    7·1 answer
  • ) Si on multiplie les deux membres d'une inégalité par un même nombre négatif non nul, on obtient une inégalité de même sens.
    5·1 answer
  • What is the value of k in the product of powers below?<br> 1<br> 0<br> -1<br> -3
    13·2 answers
  • Given: WX congruent to XY congruent to YZ congruent to ZW Prove: angle W and angle Y are congruent
    10·1 answer
  • With a.b.c=1 and a+b+c=1<br> Prove that:
    15·1 answer
  • Find the volume of the irregular<br> figure.
    15·1 answer
  • Y +3 = x<br> 3x + 4y = 16
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!