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3 years ago

A family took a road trip and traveled west a distance of 350 kilometers in 7 hours. What was their velocity during this

Mathematics

2 answers:

yanalaym [24]3 years ago

6 0

Answer:

50 km/h

Step-by-step explanation:

so you traveled total of 350 (km) in 7 (hours) right?, just take 350, divide it by 7, which will give you km/h. (or 50 km/h) and then when you add a direction it like "west" it's no longer a speed it's a velocity.

Marina86 [1]3 years ago

4 0

Displacement given (in metres) = (350 × 1000)m.

Displacement = 350000 metres.

Time = (7× 3600) seconds

Time = 25200 seconds.

Velocity = Displacement / Time

Velocity = 350000 / 25200

Velocity = 13.89m/s

Approximately, Velocity = 14m/s.

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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).

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2 years ago

45 children attend preschool the number of two-year-olds is 1/2 the number of three-year-olds the number for your old is the sam

Mkey [24]

There are 9 two-year-olds and 18 each of 3 and 4 year olds.

To solve this we could write and solve the equation below, letting x be the number of 3 and 4 year olds.

x/2 + x + x = 45
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From here, we just divide 18 by 2 to get the number of 2 year olds.

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3 years ago

1. Write the solution set in interval notation: 3x-2 > x-4 or 7x-5 < 3x+3

Yakvenalex [24]

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3 years ago

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A light bulb consumes 1440 watt-hours per day. How many watt-hours does it consume in 4 days and 18 hours.

dimaraw [331]

Answer:

6840

Step-by-step explanation:

Well we know there's 24 hours in a day so dividing that by 1440 we get 60. Now we know that it consumes 60 watts ever hour. so now we just have to figure out how many hours there are and times that by 60. So there are 96 hours in 4 days plus 28=114. So times that by 60 ( watts) 114×60=6840

So that's your awnser.

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2 years ago

Dayren is driving to visit family. She drives at a average of 65 miles per hour. She drives 227.5 miles before lunch. And then 9

Kitty [74]

Answer:

5 hours

Step-by-step explanation:

First, add the miles together

Next, divide 65 into the sum of 227.5 and 97.5(which is 325)

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3 years ago

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