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3 years ago

Find the equation for the circle with center (-1, - 4) and passing through (-5,5).

Mathematics

1 answer:

jenyasd209 [6]3 years ago

4 0

Answer:

$(x+1)^2+(y+4)^2=97$

Step-by-step explanation:

Hi there!

Equation of a circle centered at (h,k):

$(x-h)^2+(y-k)^2=r^2$ where r is the radius

1) Plug in the center

$(x-(-1))^2+(y-(-4))^2=r^2\\(x+1)^2+(y+4)^2=r^2$

2) Plug in the given point and solve for r²

$(x+1)^2+(y+4)^2=r^2$

Plug in (-5,5)

$(-5+1)^2+(5+4)^2=r^2\\(-4)^2+(9)^2=r^2\\16+81=r^2\\r^2=97$

3) Plug r² back into the equation

$(x+1)^2+(y+4)^2=r^2\\(x+1)^2+(y+4)^2=97$

I hope this helps!

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Train A arrives at central station on the hour and every 12 minutes. Train B arrives o the hour and every 15 minutes. When do bo

lana [24]

Answer:

Every 30 hours

Step-by-step explanation:

Train A arrives at central station on the hour and every 12 minutes, you mean with that on every 72 minutes

Train B arrives at central station on the hour and every 15 minutes, you mean with that on every 75 minutes

In accordance with the given, the smallest number containing numbers 72 and 75 is 1800 minutes.

When we convert this number of minutes in hours we get:

1800 / 60 = 30 hours

God with you!!!

7 0

2 years ago

Applications 24. A rocket is launched into the air. Its height in feet, after x seconds, is given by the equation The starting h

SVEN [57.7K]

The given function is

$h(x)=-16x^2+300x+20$

According to this function, the starting height of the rocket is 20 feet because that's the initial condition of the problem stated by the independent term.

Additionally, we find the maximum height by calculating the vertex of the function V(h,k).

$h=-\frac{b}{2a}$

Where a = -16 and b = 300.

$\begin{gathered} h=-\frac{300}{2(-16)}=\frac{300}{32}=\frac{150}{16}=\frac{75}{8} \\ h=9.375 \end{gathered}$

Then, we find k by evaluating the function

$\begin{gathered} k=-16(9.375)^2+300(9.375)+20 \\ k=-1406.25+2812.5+20=1426.25 \end{gathered}$

Hence, the maximum height is 1426.25 feet.

At last, to know the time need to hit the ground, we just use h=9.375 and we multiply it by 2

$t=2\cdot9.375=18.75$

Hence, the rocket hits the ground after 18.75 seconds.

6 0

10 months ago

It took six people four days to build a wall.

Sever21 [200]

Answer:

a=5 days, 3 hours

b= 3 people

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2 years ago

Use a calculator to solve for theta in the given interval

Allushta [10]

Answer:

d. $1.82\: or\:4.46$

Step-by-step explanation:

The given trigonometric equation is;

$\sec \theta=-4.0545$

Recall that;

$\cos \theta=\frac{1}{\sec \theta}$

$\implies \cos \theta=\frac{1}{-4.0545}$

$\implies \cos \theta=-0.2466$

The cosine function is negative in the second and third quadrant.

$\theta=\pi-\cos^{-1}(0.2466)\: or\:\pi+\cos^{-1}(0.2466)$

$\theta=1.82\: or\:4.46$

4 0

2 years ago

Determine the coordinates of the intersection of the diagonals of square ABCD with verticals A(-4,6), B(5,6) C(4,-2), and D(-5,-

timama [110]

Given:

Vertices of a square are A(-4,6), B(5,6) C(4,-2), and D(-5,-2).

To find:

The intersection of the diagonals of square ABCD.

Solution:

We know that diagonals of a square always bisect each other. It means intersection of the diagonals of square is the midpoint of diagonals.

In the square ABCD, AC and BD are two diagonals. So, intersection of the diagonals is the midpoint of both AC and BD.

We can find midpoint of either AC or BD because both will result the same.

Midpoint of A(-4,6) and C(4,-2) is

$Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$Midpoint=\left(\dfrac{-4+4}{2},\dfrac{6+(-2)}{2}\right)$

$Midpoint=\left(\dfrac{0}{2},\dfrac{6-2}{2}\right)$

$Midpoint=\left(\dfrac{0}{2},\dfrac{4}{2}\right)$

$Midpoint=\left(0,2\right)$

Therefore, the intersection of the diagonals of square ABCD is (0,2).

4 0

2 years ago