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Dima020 [189]
2 years ago
5

Mr. Harper's car used 5 gallons of gasoline to travel 150 miles. After he had some work done on the cars engine ,it used it used

6 gallons of gasoline to travel 210 miles. If the price of gasoline was $3.50 per gallon, how much money did Mr. Harper save per mile after the work was done on the cars engine? (Round your answers to the nearest cent.)
Mathematics
1 answer:
Iteru [2.4K]2 years ago
6 0

Answer:

He saves $0.0175 per mile

Step-by-step explanation:

Before the work done on the car´s engine, it took 0.033 gallons to travel one mile ( 5 gallons /150miles =0.033). After this work, the car spends 0.028 gallons to travel one mile (6 gallons/210 miles =0.028). The difference between this two is:

0.033 gallons/mile-0.028 gallons/mile= 0.005 gallons per mile.

Now Mr.Harper´s saves 0.005 gallons per mile.

In money he saves:

$3,50/gallon*0.005 gallon/mile= $0.0175/mile (the unit of "gallon" cancel each other)

Rounded to the nearest cent:

He saves $0.0 per mile.

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(-31/2)-(-41/4)=-7/2-(17/4)=
Andrew [12]
Just forget about the first half, and just do the second half. It’s way easier. Answer is -7.75
6 0
2 years ago
Find the absolute extrema for f(x,y)=4-x^2-y^4+1/2y^2 over the closed disk D:x^2+y^2 is less than or equal to 1
algol [13]

Find the critical points of f(x,y):

\dfrac{\partial f}{\partial x}=-2x=0\implies x=0

\dfrac{\partial f}{\partial y}=y-4y^3=y(1-4y^2)=0\implies y=0\text{ or }y=\pm\dfrac12

All three points lie within D, and f takes on values of

\begin{cases}f(0,0)=4\\f\left(0,-\frac12\right)=\frac{65}{16}\\f\left(0,\frac12\right)=\frac{65}{16}\end{cases}

Now check for extrema on the boundary of D. Convert to polar coordinates:

f(x,y)=f(\cos t,\sin t)=g(t)=4-\cos^2-\sin^4t+\dfrac12\sin^2t=3+\dfrac32\sin^2t-\sin^4t

Find the critical points of g(t):

\dfrac{\mathrm dg}{\mathrm dt}=3\sin t\cos t-4\sin^3t\cos t=\sin t\cos t(3-4\sin^2t)=0

\implies\sin t=0\text{ or }\cos t=0\text{ or }\sin t=\pm\dfrac{\sqrt3}2

\implies t=n\pi\text{ or }t=\dfrac{(2n+1)\pi}2\text{ or }\pm\dfrac\pi3+2n\pi

where n is any integer. There are some redundant critical points, so we'll just consider 0\le t< 2\pi, which gives

t=0\text{ or }t=\dfrac\pi3\text{ or }t=\dfrac\pi2\text{ or }t=\pi\text{ or }t=\dfrac{3\pi}2\text{ or }t=\dfrac{5\pi}3

which gives values of

\begin{cases}g(0)=3\\g\left(\frac\pi3\right)=\frac{57}{16}\\g\left(\frac\pi2\right)=\frac72\\g(\pi)=3\\g\left(\frac{3\pi}2\right)=\frac72\\g\left(\frac{5\pi}3\right)=\frac{57}{16}\end{cases}

So altogether, f(x,y) has an absolute maximum of 65/16 at the points (0, -1/2) and (0, 1/2), and an absolute minimum of 3 at (-1, 0).

5 0
2 years ago
PLS EXPLAIN HOW THESE SEQUNCE IS FORMED<br><br>ALL ODD NUMBERS
scoundrel [369]

Answer:

7,21,27,81,87, 261, 267....

Step-by-step explanation:

All odd number series from the given figure is

7, 21, 27, 81 , 87....

We can write this series as

7, 7 x 3 , (7x3)+6, ((7x3)+6)x3, (((7x3)+6)x3)+6....

7, 21, 21+6 , 27 x 3, 81+6...

Now, the next term of the series will be

=((((7x3)+6)x3)+6) x 3

= 87 x 3

= 261

And another term of the series will be

= 261 +6

= 267

7,21,27,81,87, 261, 267....

8 0
3 years ago
If kevin makes c toys in m minutes, how many toys can he make per hour
mina [271]

Answer:

\frac{60c}{m}

Step-by-step explanation:

We can use the unity rule to solve this problem.

Number of toys made in m minutes = c

Number of toys made in 1 minute = \frac{c}{m}

Number of toys made in 60 minutes = \frac{c}{m} \times 60 = \frac{60c}{m}

Since 60 minutes = 1 hours, we can write:

Number of toys made in 1 hour = \frac{60c}{m}

Therefore, we can say that Kevin makes \frac{60c}{m} toys per an hour.

7 0
3 years ago
How do you solve 3/x^2+5x+6 + x-1/x+2= 7/x+3
gulaghasi [49]

Answer:

it equal 69 is a arat with 24 legs and 5+5=30

Step-by-step explanation:

8 0
3 years ago
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