When baking cookies, each cookie should be placed about 2 inches from one another to allow room to expand. if one cookie has a radius of 1 inch and a center at c(1, –1), find the center and equation of the cookie immediately to the right. (assume that each cookie is uniform with a radius of 1 inch and that 1 inch = 1 unit on a coordinate plane.)

Center: (1, 3)

Equation: (x - 1)² + (y - 3)² = 1

Explanation:

1) The initial distance between the centers of two adjacent cookies must be equal to the separation indicated (2 inches) plus the radius of each cookie, which is 2 × 1 in.

So, the separation of the centers is 2 in + 2 × 1 in = 2in + 2 in = 4 in.

2) Then the coordinates of the center the cookie to the right of the given cookie are (1, -1 + 4) = (1, 3).

3) The equation of the circle of radius r and center (a,b) is:

(x - a)² + (y - b)² = r²

So, using a = 1, b = 3, and r = 1, you get:

(x - 1)² + (y - 3)² = 1

m a t h w a y. c o m

step-by-step explanation:

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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