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nevsk [136]
3 years ago
13

Which is the focus of a parabola with equation y2 = 4x?

Mathematics
1 answer:
statuscvo [17]3 years ago
6 0

Answer:

(1, 0)

Step-by-step explanation:

Please write this as y^2 = 4x; the " ^ " indicates exponentiation.

The appropriate equation for a horizontal parabola that opens to the right is

y^2 = 4px

Here, we are told that  y^2 = 4x; this tells us that 4p = 4, and so p = 1.  

Again, this parabola is a horizontal one and it opens to the right.  p = 1 is the distance of the focus from the vertex, and in this case p = 1.  Thus, the focus is at (1, 0) (situated on the x-axis).

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Matt and Anna Killian are frequent fliers on​ Fast-n-Go Airlines. They often fly between two cities that are a distance of 1980
Ymorist [56]

Answer:

y (plane speed) 400 miles/hr

x (wind speed)  40 miles/hr

Step-by-step explanation:

going into the wind make the plane flew 5,5 hours to get 1980 miles, implies the real travel speed was

1980 / 5,5 = 360 miles/hours, and at the same time is the result of:  

speed plane (y)  in direction A to B  plus wind speed (x) in direction B to A. Notice opposites direction speed, so we have:

y + (-x) = 360          (1)

The return fly  took 4,5 hours so 1980/4,5 = 440 miles/ hours as the result

Y + x = 440             (2)

We have a two equation with two variables system, It could be solved for any of the procedures. We will use the substitution method.

From equation      (1)        y + (-x) = 360         y  - x = 360      y = 360 + x    (1)

In the second equation    

y + x = 440         then we replace y for its value as function of x

(360 + x ) + x = 440

Solving for x        360 + 2x = 440      or    2x = 440 – 360        

 x   (440 - 360)/2

 x = 40 miles/hr

 X (wind speed ) = 40 miles/hr

And replacing the value of x in eq. (1)        y = 360 + 40 = 400

Y (plane speed) = 400 miles /hr

3 0
3 years ago
3. Michel invests $850 at 7%/a simple interest. How long will he
Kipish [7]

~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&\$200\\ P=\textit{original amount deposited}\dotfill & \$850\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years \end{cases} \\\\\\ 200=850(0.07)t\implies \cfrac{200}{850(0.07)}=t\implies \stackrel{\textit{about 3 years, 4 months and 10 days}}{3.36\approx t}

5 0
2 years ago
A city has a population of 250,000 people. Suppose that each year the population grows by 6%. What will the population be after
irinina [24]

Answer:

503,049

Step-by-step explanation:

250,000 × 1.06^12 is the formula.

You take the percentage which is 6% and you add 1 to it.

So, you get 1.06

Then you take the 1.06 and raise it to the number of years which is 12.

1.06^12

Then you multiply that number to the base number which is 250,000 and get 503,049.

Hope this helps!

5 0
3 years ago
−2t−5&lt;9<br><br> Hiiiiiiii<br><br> Huuuu
Brilliant_brown [7]

Answer:

t > -7

Step-by-step explanation:

To solve for t, first add 5 to both sides:

-2t - 5 < 9

-2t < 14

Divide each side by -2, and flip the inequality because we are dividing by a negative number:

-2t < 14

t > -7

So, the solution is t > -7

4 0
2 years ago
Read 2 more answers
Solve using substitution<br> y=3x-5<br> 2x+5y=-42
Paul [167]

Answer:

Solution point is (-1,-9)

Step-by-step explanation:

Put the value of y in the first equation into the second equation.

  • 2x + 5(3x - 5) = - 42            Remove the brackets on the left
  • 2x + 15x - 25 = - 42            Combine like terms on the left
  • 17x - 25 = - 42                     Add 25 to both sides
  • 17x - 25 + 25 = - 42 + 25    Do the addition
  • 17x = - 17                              Divide by 17
  • 17x/17 = -17/17                      Do the division
  • x = - 1    

=======

Solve for y

  • y = 3x - 6
  • x = -1
  • y = 3(-1) - 6
  • y = -3 - 6
  • y = - 9
6 0
3 years ago
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