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3 years ago

Which of the following equations will produce the graph shown below?

Mathematics

2 answers:

a_sh-v [17]3 years ago

8 0

Answer:

Option (B) is correct.

$\frac{x^2}{20}+\frac{y^2}{20}=1$ equation will produce the graph shown.

Step-by-step explanation:

Given a graph showing circle .

We have to determine the equation that will produce the graph shown.

Consider the given graph.

It shows a circle with radius 4.5

The general equation of circle is represented by $x^2+y^2=r^2$

Since option (A) represents the equation of hyperbola.

Option (C) represents the equation of circle with radius 4, but the given graph has radius grater than 4 .

Option (D) can be rewritten as by dividing by 6,

$x^2+y^2=\frac{144}{6}=24$ which is a equation of circle with radius 4.9 (approx)

Thus, only Option (B) works for the given graph.

$\frac{x^2}{20}+\frac{y^2}{20}=1$

Multiply , by 20 , we get,

$x^2+y^2=20$ also, $\sqrt{20}=4.47(approx)$

Thus, Option (B) is correct.

$\frac{x^2}{20}+\frac{y^2}{20}=1$

natta225 [31]3 years ago

5 0

Answer: B

Step-by-step explanation:

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Is anyone able to figure this out, I can't do this

katrin [286]

Answer:

C. √2 - 1

Step-by-step explanation:

If we draw a square from the center of the large circle to the center of one of the small circles, we can see that the sides of the square are equal to the radius of the small circle (see attached diagram)

Let r = the radius of the small circle

Using Pythagoras' Theorem $a^2+b^2=c^2$

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

to find the diagonal of the square:

$\implies r^2 + r^2 = c^2$

$\implies 2r^2 = c^2$

$\implies c=\sqrt{2r^2}$

So the diagonal of the square = $\sqrt{2r^2}$

We are told that the radius of the large circle is 1:

⇒ Diagonal of square + r = 1

$\implies \sqrt{2r^2}+r=1$

$\implies \sqrt{2r^2}=1-r$

$\implies 2r^2=(1-r)^2$

$\implies 2r^2=1-2r+r^2$

$\implies r^2+2r-1=0$

Using the quadratic formula to calculate r:

$\implies r=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$\implies r=\dfrac{-2\pm\sqrt{2^2-4(1)(-1)}}{2(1)}$

$\implies r=\dfrac{-2\pm\sqrt{8}}{2}$

$\implies r=-1\pm\sqrt{2}$

As distance is positive, $r=-1+\sqrt{2}=\sqrt{2}-1$ only

5 0

2 years ago

Read 2 more answers

Use cavalieri's principle to a circular pillar candle is 2.8 inches wide & 6 inches tall. find the volume of the candle.

wolverine [178]

The candle has the shape of a cylinder with height H=6 in, and radius of the circular base R= (2.8)/2 =1.4 (in).

The volume of the cylinder is Area(base)*height =

$\pi R^{2} *H=3.14* (1.4)^{2}*6= 37$ (in cubed)

According to Cavalieri's principle, the volume of the candle is equal to the volume of the cylinder we described.

Answer: 37 in cubed

5 0

3 years ago

Question 3 (1 point)

sertanlavr [38]

Answer:

d: 15 units squared

Step-by-step explanation:

The area of a triangle is $\frac{b*h}{2}$ :