Mathematics, 03.07.2021 16:10 amar82

Does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?

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Answer from: heids17043

Given equation of the Circle is ,

$\sf\implies x^2 + y^2 = 25$

And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,

$\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2$

Here we can say that ,

• Radius = 5 units

• Centre = (0,0)

Finding distance between the two points :-

$\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }$

Here we can see that the distance of point from centre is less than the radius.

Hence the point lies within the circle .

Answer from: bryan1528489

inside the circle

Step-by-step explanation:

we want to verify whether (-4,2) lies inside or outside or on the circle to do so recall that,

if $\displaystyle (x-h)^2+(y-k)^2r^2$ then the given point lies outside the circleif $\displaystyle (x-h)^2+(y-k)^2$ then the given point lies inside the circleif $\displaystyle (x-h)^2+(y-k)^2=r^2$ then the given point lies on the circle

step-1: define h,k and r

the equation of circle given by

$\displaystyle {(x - h)}^{2} + (y - k) ^2= {r}^{2}$

therefore from the question we obtain:

$\displaystyle h= 0$ $\displaystyle k= 0$ ${r}^{2} = 25$

step-2: verify

In this case we can consider the second formula

the given points (-4,2) means that x is -4 and y is 2 and we have already figured out h,k and r² therefore just substitute the value of x,y,h,k and r² to the second formula

$\displaystyle {( - 4 - 0)}^{2} + (2 - 0 {)}^{2} \stackrel {?}{ < } 25$

simplify parentheses:

$\displaystyle {( - 4 )}^{2} + (2 {)}^{2} \stackrel {?}{ < } 25$

simplify square:

$\displaystyle 16 + 4\stackrel {?}{ < } 25$

simplify addition:

$\displaystyle 20\stackrel { \checkmark}{ < } 25$

hence,

the point (-4, 2) lies inside the circle

Answer from: Quest

chase is right because he already been to the swings and he know how far it will be to get there

step-by-step explanation:

Answer from: Quest

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

The graph below shows the value of a $100 deposited into three different accounts over a period of 2

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