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3 years ago

If the endpoints of the diameter of a circle are (−8, 0) and (−12, 2), what is the standard form equation of the circle?

Mathematics

1 answer:

WITCHER [35]3 years ago

3 0

We know that

the standard form equation of the circle is
(x-h)²+(y-k)²=r²
where
(h,k)------> is the center
and
r----> is the radius

let
A------> the point (−8, 0)
B-------> the point (−12, 2)

step 1
find the distance point A and point B
d=√[(2-0)²+(-12+8)²]------> d=√20-----> d=2√5 units

the distance AB is equals to the diameter
and
the radius r=2√5/2-----> r=√5 units

step 2 find the midpoint AB
midpoint ABx=(-8-12)/2-----> -10
midpoint ABy=(2+0)/2-----> 1

the midpoint is (-10,1)
the center is equal to the midpoint
so
(h,k)------> (-10,1)

step 3
find the equation of a circle
(x-h)²+(y-k)²=r²------> (x+10)²+(y-1)²=(√5)²
(x+10)²+(y-1)²=5

the answer is
(x+10)²+(y-1)²=5

see the attached figure

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4 years ago

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Answer:

Step-by-step explanation:

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2 years ago

A demographer wants to measure life expectancy in countries 1 and 2. Let μ1 and μ2 denote the mean life expectancy in countries

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Answer:

For this case we want to test if life expectancy in country 1 is more than 10 years lower than in country 2, (alternatibe hypothesis), so then the system of hypothesis are:

Null hypothesis: $\mu_1 \leq \mu_2 -10$

Alternative hypothesis: $\mu_1 > \mu_2 -10$

Or equivalently:

Null hypothesis: $\mu_1 - \mu_2 \leq 10$

Alternative hypothesis: $\mu_1 - \mu_2 >10$

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

Solution to the problem

For this case we want to test if life expectancy in country 1 is more than 10 years lower than in country 2, (alternatibe hypothesis), so then the system of hypothesis are:

Null hypothesis: $\mu_1 \leq \mu_2 -10$

Alternative hypothesis: $\mu_1 > \mu_2 -10$

Or equivalently:

Null hypothesis: $\mu_1 - \mu_2 \leq 10$

Alternative hypothesis: $\mu_1 - \mu_2 >10$

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4 years ago

Read 2 more answers

Please answer the following questions

laila [671]

Answer:

4a) 110 square centimetres

4b) 127 square centimetres

6) 292 square centimetres

8) 800 tiles

Step-by-step explanation:

4. We need to find the area of the large rectangle and then deduct the area of the unshaded part:

a) The large rectangle has dimensions 12 cm by 15 cm. Its area is:

A = 12 * 15 = 180 square centimetres

The unshaded part has a length of 15 - (3 + 2) cm i.e. 10 cm and a width of 7 cm. Its area is:

a = 10 * 7 = 70 square centimetres

Therefore, the area of the shaded part is:

A - a = 180 - 70 = 110 square centimetres

b) The large rectangle has dimensions 13 cm by 11 cm. Its area is:

A = 13 * 11 = 143 square centimetres

The unshaded part has dimensions 8 cm by 2 cm. Its area is:

a = 8 * 2 = 16 square centimetres

Therefore, the area of the shaded part is:

A - a = 143 - 16 = 127 square centimetres

6. The background area of the space not covered by the photograph is the area of the frame minus the area of the photograph.

The frame has dimensions 24 cm by 18 cm. Therefore, its area is:

A = 24 * 18 = 432 square centimetres

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A - a = 432 - 140 = 292 square centimetres

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A = 8 * 4 = 32 square centimetres

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