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3 years ago

What is the equation of a circle with a center located at (-3, 4) and a diameter of 14?

Mathematics

1 answer:

AnnZ [28]3 years ago

7 0

Answer: (x + 3)^2 + (y - 4)^2 = 49

Step-by-step explanation:

The equation of a circle given the center and radius: (x - h)^2 + (y - k)^2 = r^2

Given: center (-3,4) ; h = -3 and k = 4

diameter = 14

To find the radius: divide the diameter by 2 = 14/2 = 7 = r

Center: (-3,4) and radius: 7

Equation of a circle: (x - h)^2 + (y - k) ^2 = r^2

Substitute h = -3, k = 4, r = 7

(x - (-3))^2 + (y - 4)^2 = 7^2

Answer:

Equation of the circle: (x + 3)^2 + (y - 4)^2 = 49

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Answer:

The minimum total distance the employee may have driven before getting stuck in traffic is 8.3 miles

Step-by-step explanation:

* Lets explain how to solve the problem

- The rule of the distance between to points $(x_{1},y_{1})$

and $(x_{2},y_{2})$ i s $d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

- So at first we will find the distance between the three points

∵ A = (-3 , 1) , B = (3 , 3) , C = (3 , -1)

- By using the rule of distance

∴ $AB=\sqrt{(3--3)^{2}+(3-1)^{2}}=\sqrt{36+4}=\sqrt{40}=6.325$

∴ $BC=\sqrt{(3-3)^{2}+(-1-3)^{2}}=\sqrt{0+16}=4$

∴ $AC=\sqrt{(3--3)^{2}+(-1-1)^{2}}=\sqrt{36+4}=\sqrt{40}=6.325$

∵ Each unit coordinate plane represents 1 mile

∵ AB = 6.3 units

∴ The distance between branches A and B = 6.325 miles

∵ BC = 4 units

∴ The distance between branches B and C = 4 miles

∵ AC = 6.3 units

∴ The distance between branches A and C = 6.325 miles

- A bank employee drives from Branch A to Branch B and then

drives halfway to Branch C before getting stuck in traffic

∵ The distance from branch A to branch B is 6.325 miles

∵ The distance from branch B to branch C is 4 miles

∵ The half way from branch B to branch C = 1/2 × 4 = 2 miles

∴ The distance the employee may have driven before getting

stuck in traffic = 6.325 + 2 = 8.325 miles

∴ The minimum total distance the employee may have driven

before getting stuck in traffic is 8.3 miles

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