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Pie
3 years ago
6

One day, I decide to run to the park. On the way there, I run at a rate of x^2 miles per hour for 3 hours. On the way back, I ta

ke the same path and jog at a slower rate of 16 - 4x miles per hour so that it takes me 4 hours to get home. Given that x > 0, what is x? Express your answer as a common fraction.
Mathematics
2 answers:
agasfer [191]3 years ago
8 0
X would be equal to 3 over 1
Elena L [17]3 years ago
6 0

Answer:

8/3

Step-by-step explanation:

Since we know that the distance that I traveled to the park and the distance that I traveled to get back home are the same, and that distance = rate x time, we have that

(x^2)(3)=(16-4x)(4)

3x^2=64-16x

3x^2+16x-64=0

(3x-8)(x+8)=0

Solving this equation, we get the solutions x=8/3 and x=-8. Since x must be positive, we have x=8/3.

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2 years ago
12 divided into a number is wat
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Answer:

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3 0
2 years ago
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Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at miles 90 per
algol [13]
So the eastbound train travels at 90 miles per hour in the complete opposite direction to the westbound equivalent, which travels at 80 miles per hour. Therefore, per hour, they get 170 miles away from each other. Since we are working out how long it would take for them to be 204 miles apart:

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Hope I helped!
8 0
3 years ago
Find the surface area of the prism.
Mrac [35]

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8 0
3 years ago
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Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software,
grandymaker [24]

Solution:

There is no saddle point (DNE). However, there is local maximum at (1, 1/2) for the given function.

Explanation:

we have function of two variables f(x,y)= 9-2x+4y-x^2-4y^2

we will find the values by partial derivative with respect to x,y,xy

f_{x}= -2 -2x

f_{y}= 4 -8y

to find the saddle point we should first find the critical points so equate

-2 -2x=0 and   4 -8y=0

we get x= 1  and y =1/2 so, critical points are (1,1/2)

to find local maximum or minimum we have to find f_{xx},  f_{yy} and f_{xy}

formula is f_{xx} *f_{yy} - f^{2_{xy} } =0

f_{xx} = -2

f_{yy} = -8

f^{2_{xy} } =0

putting values in formula

(-2)*(-8) -0 =16 > 0, and f_{xx}< 0  and f_{yy}<0

so, here we have local maximum

we have no saddle point for this function by using the same formula we used to find extrema.



4 0
3 years ago
Read 2 more answers
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