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3 years ago

Divide 260 in to the ratio of 1:3

Mathematics

2 answers:

FinnZ [79.3K]3 years ago

7 0

1 : 3 → 1 + 3 = 4

260 : 4 = 65

1 · 65 = 65
3 · 65 = 195

Answer: 65 and 195

Andreyy893 years ago

7 0

65 and 195 would be your answer

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A parabola can be drawn given a focus of (5, -3) and a directrix of y=1. Write the equation of the parabola in any form.

Anna71 [15]

Answer:

(x²-10x+33)/(-8) = y

Step-by-step explanation:

The distance between any point on a parabola from both its focus and directrix are the same.

Let's say we have a point (x,y) on the parabola. We can then say that using the distance formula,

$\sqrt{(x-5)^2+(y-(-3))^2}$ is the distance between (x,y) and the focus. Similarly, the distance between (x,y) and the directrix is |y-1| (I use absolute value here because distance is always positive). We can find this equation by taking the shortest distance from the point to the line. Because the closest point to the line will be the same x value as the point itself, the distance is simply the distance between the y value of the point and the y value of the directrix.

Equating the two equations given, we have

$\sqrt{(x-5)^2+(y-(-3))^2} = |y-1|$

square both sides to get

(x-5)²+(y+3)²=(y-1)²

expand the y components

(x-5)² + y²+6y+9 = y²-2y+1

subtract y²+6y+9 from both sides

(x-5)² = -8y - 8

expand the x components

x²-10x+25 = -8y - 8

add 8 to both sides to isolate the -8y

x²-10x+33 = -8y

divide both sides by -8 to isolate y

(x²-10x+33)/(-8) = y

6 0

2 years ago

Factor 26r3s + 52r5 – 39r2s4.

algol [13]

Answer:

13r²(2rs + 4r³ - 3s⁴)

Step-by-step explanation:

In equation 26r³s + 52r⁵ - 39r²s⁴;

The GCF of 26, 52, and 39 = 13

The GCF of r³, r⁵ and r² = r²

The GCF of s, (no "s"), and s⁴ = no "s" (Since one of the number doesn't have "s")

Now we can factor out 13r² from all three expressions;

26r³s + 52r⁵ - 39r²s⁴

=> 13r²(2rs) + 13r²(4r³) - 13r²(3s⁴)

To factor it all together;

13r²(2rs + 4r³ - 3s⁴)

Hope this helps!

7 0

3 years ago

Solve the simultaneous equation 4x-y=9 2x-3y= -23

MrMuchimi

Answer:

x = 5

y = 11

Step-by-step explanation:

y = 4x - 9

2x -3(4x - 9) = -23

2x - 12x + 27 = -23

-10x = -23 -27

-10x = -50

minus cancels out

x = 5

y = 4(5) -9

y = 20 - 9

y = 11

4 0

3 years ago

You gave your little sister a good push on a swing and it made an arc of 12 ft. On the third swing it made an arc of 8.67 ft. Ho

jonny [76]

10.2 ft Ans.

We solve this using geometric series.

A1 = 12 ft
A2 = ?
A3 = 8.67ft
Now, for geomteric progression,

$\frac{A1}{A2} = \frac{A2}{A3} 

$

$\frac{12}{A2} = \frac{A2}{8.67}$

$A2 * A2 = (A2)^{2} = \sqrt{12 * 8.67 }$

A2 = 10.2 ft

6 0

3 years ago

Open Ended Alexandra is working on a float for a parade She is making a sphere out of paper mache She knows the circumference of

iogann1982 [59]

Answer:

r=C2

Step-by-step explanation:

C=2r is the equation to find circumference

She needs to work backwards in this case, so:

r=C2

r=The circumference she knows x 2 x 3.14(or 3.14159265359)

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<h3>I would recommend writing/typing all of this(Especially if you need to show you work)!</h3>

I hope this helped!

7 0

3 years ago