There are $528 available to fence in a rectangular garden. the fencing for the side of the garden facing the road costs $9 per foot, and the fencing for the other three sides costs $3 per foot. the picture on the right depicts this situation. consider the problem of finding the dimensions of the largest possible garden.

  22 ft by 44 ft, with 22 ft parallel to the road

Step-by-step explanation:

Problems in optimizing rectangular area for a given perimeter or perimeter cost all have a similar solution: the length (or cost) of one pair of opposite sides is equal to that of the other pair of opposite sides.

Here, that means that the sides perpendicular to the road will have a total cost of $528/2 = $264, so will have a total length of $264/($3/ft) = 88 ft. Since it is a rectangle, the dimension perpendicular to the road is 44 ft.

Likewise, the sides parallel to the road will have a total cost of $264. If x is the length in that direction, this means ...

  9x +3x = 264

  12x = 264

  264/12 = x = 22

The length of the garden parallel to the road is 22 ft.

If you solve this directly, you get the same result. Let x be the distance parallel to the road. Then the cost of fence for the two sides parallel to the road is (3x +9x) = 12x.

The length of fence perpendicular to the road will use the remaining cost, so that length will be (528 -12x)/(2·3). (Half of the remaining fence is used on each of the two parallel sides.) This expression for length simplifies to (88-2x).

Then the area of the garden will be the product of its length and width:

  area = x(88 -2x)

This is the equation for a downward-opening parabola with zeros at x=0 and x=44. The vertex is located halfway between those zeros, at x = 22.

The dimensions of the largest garden are 22 ft parallel to the road and 44 ft perpendicular to the road.

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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