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Ksenya-84 [330]
3 years ago
11

Find the standard form of the equation of the circle with endpoints of a diameter at the points (3,8) and (-7,2)

Mathematics
1 answer:
poizon [28]3 years ago
8 0

(x+2)^{2}+(y-5)^{2}= 34

The equation of a circle in standard form is

(x-a)^{2}+(y-b)^{2}=r^{2}

where (a , b) are the coordinates of the centre and r is the radius

The centre is at the midpoint of the endpoints and the radius is the distance from the centre to either of the 2 endpoints

Using the midpoint formula

midpoint = [\frac{1}{2}(xx_{1}+x_{2}, \frac{1}{2}(y_{1}+y_{2}

where (x_{1},y_{1}=(3,8) and (x_{2},y_{2}=(-7,2)

centre = (\frac{1}{2}(3-7),\frac{1}{2}(8+2)) = (-2,5)

Calculate r using the distance formula

r = √(x_{2}-x_{1})²+(y_{2}-y_{1})²)

= √((3+2)²+(8-5)²) = √(25+9) = √34 ⇒ r² =(√34)² = 34

equation of circle is : (x+2)²+(y-5)² = 34


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The sum of the first and third of three consecutive even integers is 136. find the three even integers.
tatyana61 [14]
Based on your problem, you only have one given. So, you can't make an equation for this because there are not limits to the equation. The only thing that you know is that the three numbers are consecutive even integers. My way of solution for this is trial-and-error. However, it's really quite easy. 

For example: 42 + 46 = 88. I have to increase the numbers more to reach 136. Suppose: 82 + 86 = 168. That exceeded 136. So, it must be between 46 and 82. Suppose again: 66 + 70 = 136. Therefore, the sequence of the consecutive even integers are 66, 68, and 70. 

5 0
3 years ago
PLEASE HELP 30 POINTS AND BRANILEST
LUCKY_DIMON [66]

Answer:

Go through the explanation you should be able to solve them

Step-by-step explanation:

How do you know a difference of two square;

Let's consider the example below;

x^2 - 9 = ( x+ 3)( x-3); this is a difference of two square because 9 is a perfect square.

Let's consider another example,

2x^2 - 18

If we divide through by 2 we have:

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Let's take another example;

x^6 - 64

The above expression is the same as;

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Let's take another example

a^5 - y^6 ; a^5 - (y ^3)^2

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Lastly let's consider

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3 0
3 years ago
How do I solve for the variable? 3(x-14) + 1= -4x + 5
bearhunter [10]

Answer:

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6 0
3 years ago
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In a study of variation in systolic blood pressure upon application of leaches, it is found that the standard deviation of the 2
kondor19780726 [428]

Answer:

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with 21 degrees of freedom

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Step-by-step explanation:

use the expression I attached in the image to find

[(n - 1) *S^2  ]/    σ ^2

where S = the standard deviation calculated from the sample of n  trials.

sigma is the population standard deviation.

[(22 - 1) *(3.9)^2  ]/    (3.4) ^2  =  21 * 15.21 / 11.56  =  27.6306

all we have to do now is to  make sure this number is in the  90 % confidence

interval.      remember this has 21 degrees of freedom,  look at the chi-squared chart.

11.5913  <   27.6306    <  32.67905

where 11.5913  is the lower bound of the chart

and  32.67905 is the upper bound

6 0
3 years ago
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gogolik [260]
3.26d+9.75d-2.65 =13.01d−2.65



4 0
3 years ago
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