By system of substitution solve y= -3x-5 y=4

The area of the sector formed by the 110 degree central angle is 50 units squared. What is the circumference of the circle

Mama L [17]

Answer:

The circumference of the circle is $C=45.346 \:units$ .

Step-by-step explanation:

A sector is the part of a circle enclosed by two radii of a circle and their intercepted arc. A pie-shaped part of a circle.

The area of a circle is given by $A_{circle}=\pi r^2$

The formula used to calculate the area of a sector of a circle is:

$A_{sector}=\frac{central \:angle}{360} \cdot {Area \:of \:whole \:circle}\\\\A_{sector}=\frac{\theta}{360} \cdot \pi r^2$

The circumference of a circle is the distance around the outside of the circle and its given by

$C=2\pi r$

We know the central angle $\theta$ = 110º and the area of the sector 50 units squared.

First, we use the formula to calculate the area of a sector to find the radius.

$50=\frac{110}{360} \cdot \pi r^2\\\\\frac{110}{360}\pi r^2=50\\\\\frac{11\pi }{36}r^2=50\\\\11\pi r^2=1800\\\\r^2=\frac{1800}{11\pi }\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\r=\sqrt{\frac{1800}{11\pi }},\:r=-\sqrt{\frac{1800}{11\pi }}$

The radius can't be negative. Therefore,

$r=\sqrt{\frac{1800}{11\pi }}\approx 7.217 \:units$

Next, we apply the formula for the circumference of a circle.

$C=2\pi (7.217)=45.346 \:units$

7 0

2 years ago

Find 2 consecutive odd integers sum of who's square is 290 pls send fast

ELEN [110]

Answer:

<h3>Hence required integers are 11 and 13</h3>

Let x an odd positive integer

Then, according to question

x^2 +(x+2)^2=290

2x^2 +4x−286=0

x^2 +2x−143=0

x ^2+13x−11x−143=0

(x+13)(x−11)=0

x=11 as x is positive

Hence required integers are 11 and 13

Step-by-step explanation:

Hope it is helpful....

7 0

2 years ago

let f(x)=2x^2+7x-4/x^3-1 what is the domain,range,roots,end behavior and intersect the y-axis of f(X)

victus00 [196]

Here's the factorization of the equation
f(x) = [ (x+4)(2x-1) ] / [ (x-1)(x^2+x+1) ]

Domain
The domain of a function is the set of input or argument values for which the function is real and defined.
- function domain : x < 1 or x > 1

Range
Resulting f(x) values: all Real Numbers

Roots
x = 1/2 & -4

Axis interception points
x-axis: (1/2, 0) , (-4, 0)
(y-axis): (0, 4)

Asymptotes
Vertical: x = 1
Horizontal: y = 0

3 0

2 years ago

????? Anyone that can help giving 10 points

katen-ka-za [31]

Step-by-step explanation:

we know that perimeter of triangle is equals to side + side + side

but we can see that the particular triangle is having all the sides equal so it is seen to be equal lateral triangle and formula of equilateral triangle is 3 × sides.....

So,We will take sides common.....

Perimeter of equilateral triangle= 3×Side

3×4.6 cmsq.

13.8cmsq. Answer

6 0

2 years ago

Sam drove 754 miles in 13 hours, at the same rate how many miles would he drive in 9 hours

VARVARA [1.3K]

Divide 754 by 13 and you get 58
Now multiply by 9 and you get 522 miles.

8 0

3 years ago

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