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3 years ago

What value of b with cause the system to have an infinite number of solutions?

Mathematics

1 answer:

Rom4ik [11]3 years ago

5 0

Step-by-step explanation:

-3x+3x-(b÷2)=-3

0-(b÷2)=-3

-(b÷2)=-3

b=-2×-3=+6

=> b=6

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The planets move around the sun in elliptical orbits with the sun at one focus. The point in the orbit at which the planet is cl

gladu [14]

Consider the attached ellipse. Let the sun be at the right focus. Then perihelion is at right vertex on the x-axis and aphelion is at the left vertex on the x-axis.

The distances:

from perihelion to the sun in terms of ellipse is a-c;
from aphelion to the sun in terms of ellipse is a+c.

Then

$\left\{\begin{array}{l}a-c=741,000,000\\a+c=817,000,000\end{array}\right.$

Add these two equations:

$2a=1,558,000,000 \\ \\a=779,000,000$

and subtract first equation from the second:

$2c=76,000,000 \\ \\c=38,000,000.$

Note that $b=\sqrt{a^2-c^2},$ thus

$b=\sqrt{779,000,000^2-38,000,000^2}=\sqrt{605,397,000,000,000,000}.$

The equation for the planet's orbit is

$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\Rightarrow \dfrac{x^2}{606,841,000,000,000,000}+\dfrac{y^2}{605,397,000,000,000,000}=1.$

7 0

3 years ago

A property map is drawn at a scale of 1:1000. Calculate the corresponding actual distance if the distance between two points on

zvonat [6]

Answer:10 m

Step-by-step explanation:

Given

Scaling ratio 1:1000

i.e. one unit in map is equal to 1000 unit in actual distance

therefore if the distance between two points is 1 cm in map then

it is 1000 cm in reality

8 0

3 years ago

If one-sixth of a number plus one-third returns two-thirds of that number What is the number

Solnce55 [7]

Answer:

$x= \frac{2}{3}$

Step-by-step explanation:

Let the number be x

Given

$\frac{1}{6}x + \frac{1}{3} = \frac{2}{3}x$

Required

Find x

$\frac{1}{6}x + \frac{1}{3} = \frac{2}{3}x$

Collect Like Terms

$\frac{1}{6}x - \frac{2}{3}x = - \frac{1}{3}$

Take LCM

$\frac{1 - 4}{6}x = \frac{-1}{3}$

$\frac{- 3}{6}x = \frac{-1}{3}$

Multiply both sides by 6

$6 * \frac{- 3}{6}x = \frac{-1}{3} * 6$

$-3x= -2$

Divide both sides by -3

$\frac{-3x}{-3}= \frac{-2}{-3}$

$x= \frac{2}{3}$

Hence, the number is $\frac{2}{3}$

7 0

3 years ago

Can anyone help me with dis

dolphi86 [110]

Answer:

Slope is 2.

Step-by-step explanation:

So to find slope, we need to take the change in the y value, and the change in the x value, and then divide them. This may be confusing, so here is just 3 formulas in 3 seperate steps that we use to find it:

Step 1 - $x_2-x_1=change_.in_.x$