What is the value of x in the system of equations below?

Sholpan [36]

1) We have that the equation is $x^2=20y$ , hence y=x^2/20. The standard equation of such an equation is y= $\frac{1}{4p} x^2$ . Hence, p=5 in this case. The focus is at (0,5) and the directrix is at y=-5 (a tip is that the directrix is always "opposite" the focus point of a parabola; if the directrix is at x=-7 for example, the focus is at (7,0)).
2) Similarly, we have that the equation is $x=3y^2 \\ \frac{1}{4p} =3$ . Thus, p=1/12. In this case, the parabola opens along the x-axis and the focus is at (1/12, 0). Also, the directrix is at x=-1/12. Hence the correct answer is B.
3) We are given that the parabola has a p of 9. Also, the focus lies along the y-axis, hence the parabola is opening along the y-axis. Finally, the focus is on the positive half, so the parabola is opening upwards. The equation for this case is y= $y=\frac{1}{4p} x^2= \frac{1}{36 } x^2$ .
4) Similarly as above. The directrix is superfluous, we only need the p-value. THe same comments about the parabola apply and if we substitute p=8 in the formula: $y= \frac{1}{4p} x^2$ we get y= $\frac{1}{32} x^2$ .
5) This is somewhat different, even though we do not need the directrix again. The focus lies on the x-axis, thus the parabola opens in this direction. The focus lies on the positive part of the axis, thus the parabola opens to the right. We also are given p=7. Hence, the equation we need is of the form $x= \frac{1}{4p} y^2$ . Substituting p=7, we get $x= \frac{1}{28} y^2$ .
6) The equation of a prabola with a vertex at (0,0) is of the form y=-ax^2. The minus sign is needed since the parabola is downwards. Since we are given anothe point, we can calculate a. We have to take y=-74 and x=14 feet (since left to right is 28, we need to take half). $-a= \frac{y}{x^2} = \frac{-74}{14^2} =-0.378$ . Thus a=0.378. Hence the correct expressions is y=-0.378* $x^2$

7 0

3 years ago

Read 2 more answers

Agent Bond is standing on a bridge, 13.5 m above the road below, and his pursuers are getting too close for comfort. He spots a

Scrat [10]

Answer:

Step-by-step explanation:

Eek! Let's give this a go. Things we know:

acceleration of Bond in free fall is -9.8 m/s/s

velocity of the truck is 25 m/s

displacement Bond will travel when he jumps is -10 m

What we are looking for is the time it will take him to hit the top of the truck, knowing that the truck can travel from one pole to the next in 1 second.

Our displacement equation is

Δx = v₀t + 1/2at²

Filling in we have

$-10=25t+\frac{1}{2}(-9.8)t^2$

Simplifying we get

$-10=25t-4.9t^2$

This is a quadratic that needs to be solved however you personally solve quadratics. When you do that, you find that the times it will take Bond to drop that displacement is either -.37 seconds or 5.47 seconds. Many things in physics can be negative, like velocity and acceleration, but time NEVER will be. So it takes Bond 5.5 seconds to drop to the roof of the moving truck. That means that he needs to jump when the truck is between the 5th and the 6th poles away from him.

Good luck with this!

Cheers!

6 0

3 years ago

Which are not lengths of a right triangle?

zubka84 [21]

It’s D Have Ah Good Day

8 0

3 years ago

Evaluate the following

fgiga [73]

12C5 = 792 5P4 = 120

6 0

3 years ago

Find the value of x that makes lines u and v parallel

gogolik [260]

Answer:

x = 4 for Lines U and V to be parallel

<u>Skills needed: HS Geo, Angle Theorems, Equations</u>

Step-by-step explanation:

1) We see that there are two angle measures given to us. There is an angle marked with the measure of $130$ °, and the other is marked with ( $33x-2$ )°.

First of all, these two angles are categorized alternate interior angles. They are on alternate sides of the transversal, and are within the two lines (not on the outer side of the lines). I will add an image for reference regarding this idea.
If 2 lines are parallel, alternate interior angles are congruent. This means that: $33x-2=130$

2) Solving this equation is fairly straightforward.

$33x-2+2=130+2$ (add 2 to both sides in order to get the $33x$ by itself.
$33x\div33=132\div33$ (to get $x$ by itself)
132 divided by 33 is 4, and 33x divided by 33 is x, so $x=4$

--------------------------------------------------------------------------------------------------------------Hope you understood, have a great day.

7 0

2 years ago