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3 years ago

Write the equation in standard form of a circle with center (-3,6), tangent to the y-axis.

Mathematics

1 answer:

Romashka-Z-Leto [24]3 years ago

8 0

Answer:

$(x+3)^2+(y-6)^2=9$

Step-by-step explanation:

The equation of a circle in standard form is written as

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

where

(a, b) are the coordinates of the center

r is the radius of the circle

In this problem, the circle is centered at (-3,6), so we have

a = -3

b = 6

Also, we know that the circle is tangent to the y-axis, and the x-coordinate of its center is 3: this means that the horizontal distance between the point of the circle tangent to the y-axis and the centre of the circle is 3, therefore the radius of the circle is 3.

So, the equation of this circle is:

$(x-(-3))^2+(y-6)^2=3^2$

$(x+3)^2+(y-6)^2=9$

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Find the roots of h(t) = (139kt)^2 − 69t + 80

Sonbull [250]

Answer:

The positive value of $k$ will result in exactly one real root is approximately 0.028.

Step-by-step explanation:

Let $h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80$ , roots are those values of $t$ so that $h(t) = 0$ . That is:

$19321\cdot k^{2}\cdot t^{2}-69\cdot t + 80=0$ (1)

Roots are determined analytically by the Quadratic Formula:

$t = \frac{69\pm \sqrt{4761-6182720\cdot k^{2} }}{38642}$

$t = \frac{69}{38642} \pm \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$

The smaller root is $t = \frac{69}{38642} - \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$ , and the larger root is $t = \frac{69}{38642} + \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$ .

$h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80$ has one real root when $\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} = 0$ . Then, we solve the discriminant for $k$ :

$\frac{80\cdot k^{2}}{19321} = \frac{4761}{1493204164}$

$k \approx \pm 0.028$

The positive value of $k$ will result in exactly one real root is approximately 0.028.

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2 years ago

Need help on this please

Ket [755]

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3 years ago

Fraction of the shape shaded on these two shapes??

xxTIMURxx [149]

The one of the left isn't too tricky, in the bottom left of it you have 1/2 of 1/4 of the shape, and on the bottom right you have 1/4 of 1/4. Imagine the whole shape was cut up like that bottom right bit into 16 triangles, then you would have three of them shaded (see my diagram).

The one on the right seems like guesswork to me, so I'm sorry if I'm wrong. It look like you just have to use your eyes to work out how much of the bottom half of the shape is shaded: looks like 1/16 to me (i.e. you can draw four of those along and four down, again, see my diagram.) So plus the top half, which is 8/16, you get 9/16.

Answers: left picture: 3/16.
right picture: 9/16.

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3 years ago