Find an equation of the circle that satisfies the given conditions. Endpoints of a diameter are P(-1, 1) and Q(5,9)

Answers

Answer 1

Answer: The equation of a circle:
$(x-h)^2+(y-k)^2=r^2$
(h,k) - the coordinates of the centre
r - the radius

The midpoint of the diameter is the centre of a circle.
The coordinates of the midpoint:
$((x_1+x_2)/(2), (y_1+y_2)/(2))$
(x₁,y₁), (x₂,y₂) - the coordinates of endpoints

$P(-1,1) \nx_1=-1 \n y_1=1 \n \n Q(5,9) \n x_2=5 \n y_2=9 \n \n(x_1+x_2)/(2)=(-1+5)/(2)=(4)/(2)=2 \n (y_1+y_2)/(2)=(1+9)/(2)=(10)/(2)=5$

The centre of the circle is (2,5).

The radius is the distance between an endpoint of the diameter and the centre.
The formula for distance:
$d=√((x_2-x_1)^2+(y_2-y_1)^2)$

$(-1,1) \n x_1=-1 \n y_1=1 \n \n (2,5) \n x_2=2 \n y_2=5 \n \n d=√((2-(-1))^2+(5-1)^2)=√(3^2+4^2)=√(9+16)=√(25)=5$

The radius is 5.

$(x-2)^2+(y-5)^2=5^2 \n\boxed{(x-2)^2+(y-5)^2=25}$

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Complete the equations of the system in slope-intercept form. Use a decimal for the slope if necessary.Line 1
x y
0 3
1 5

Line 2
x y
–1 1
–2 –1

Answers

$y=2x+3$

$y=-2x+3$

A closet contains 5 shirts, 8 skirts, and 3 pairs of shoes. How many possible outfit combinations are there?

Answers

actually the answer is 120, apex:)

Answer:

120 combos

Step-by-step explanation:

VOTE ME FOR BRAINILEST.

Select the correct answer.Mary deposited $350 in a bank account that promises 2.8 percent interest compounded continuously. Approximately how many years will it take to reach a balance of $500?

A.
1.43 years

B.
2.80 years

C.
5.55 years

D.
12.77 years

Answers

Answer:

2.80 years

Step-by-step explanation:

beacause it is simple that it will take option B . You

don't have to worry .

What is the problem of this solving?!

Answers

This question can be solved primarily by L'Hospital Rule and the Product Rule.

$y= \lim_(x \to 0) (x^2cos(x)-sin^2(x))/(x^4)$

I) Product Rule and L'Hospital Rule:

$y= \lim_(x \to 0) ([2xcos(x)-x^2sin(x)]-2sin(x)cos(x))/(4x^3)$

II) Product Rule and L'Hospital Rule:

$y= \lim_(x \to 0) ([-2xsin(x)+2cos(x)]-[2xsin(x)+x^2cos(x)]-[2cos^2(x)-2sin^2(x)])/(12x^2) \n y= \lim_(x \to 0) (2cos(x)-4xsin(x)-x^2cos(x)-2cos^2(x)+2sin^2(x))/(12x^2)$

III) Product Rule and L'Hospital Rule:

$]y= \alpha + \beta \n \n \alpha =\lim_(x \to 0) (-2sin(x)-[4sin(x)+4xcos(x)]-[2xcos(x)-x^2sin(x)])/(24x) \n \beta = \lim_(x \to 0) (4sin(x)cos(x)+4sin(x)cos(x))/(24x) \n \n y = \lim_(x \to 0) (-6sin(x)-4xcos(x)-2xcos(x)+x^2sin(x)+8sin(x)cos(x))/(24x)$

IV) Product Rule and L'Hospital Rule:

$y = \phi + \varphi \n \n \phi = \lim_(x \to 0) (-6cos(x)-[-4xsin(x)+4cos(x)]-[2cos(x)-2xsin(x)])/(24x) \n \varphi = \lim_(x \to 0) ([2xsin(x)+x^2cos(x)]+[8cos^2(x)-8sin(x)])/(24x)$

V) Using the Definition of Limit:

$y= (-6*1-4*1-2*1+8*1^2)/(24) \n y= (-4)/(24) \n \boxed {y= (-1)/(6) }$

Evaluate the algebraic expression a + b - c when a = 3, b = 5 and c = 7.

Answers

3 + 5 - 7 = 1
1, Hope this helps!

I told you, you can ask me
a+b-c
3+5-7
=1

A teacher buys pizza for her class. There are 5 pizzas, each with 8 slices. If she has 25 students, how many slices of pizza does each student get?Group of answer choices

Answers

There are 40 slices pratap and 25 kids. 40/25 is 1.6 meaning each student can only get one slice because not everybody could get two

I don’t even knowwww

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