All categories

3 years ago

Find the point on the parabola y^2 = 8x at which the ordinate is double the abscissa.

Mathematics

1 answer:

aliya0001 [1]3 years ago

3 0

Answer:

Step-by-step explanation:

Let's make a complex of functions

y^2 = 8x

y = 2x

Now let's solve it

(2x)^2 = 8x

4x^2 - 8x = 0

4x(x - 2) = 0

x = 0, 2

y = 0, 4

So the answer is (2, 4)

Hope you like it, study well

You might be interested in

Hello! Please help me with this question. I’ll mark brainly! Thank you :)

Anettt [7]

Answer:

$\Huge\boxed{\$ 12.12}$

Step-by-step explanation:

In order to find how much credit is left after 92 minutes, we need to

1. Figure out the equation that describes this graph (since we don't know the y-intercept)

2. Find the credit remaining after 92 minutes using the equation formed.

<h2>Figuring out the equation of this graph:</h2>

First things first is to figure out the slope of this graph. Since this is a linear function, the slope will remain constant, and we can note something about slope here.

The slope of a line will be it's change in x divided by its change in y, often referred to with a formula.

$\frac{\Delta y}{\Delta x}$

Since we know two points on this graph, we can find the changes in the x and y then divide for the slope.

Since minutes used is the x, and credit left is the y, we have two points.

(41, 19.26) and (68, 15.48).

The change in y is -3.78, as $19.26-15.48=3.87$ , and we decreased, so -3.78.
The change in x is 27 as $68-41=27$ , and we increased.

The slope will then be $\frac{-3.78}{27}$ which comes out to be -0.14.

Now that we know the slope, that means our equation will look something like $y = -0.14x+b$ - however, we still have b to solve for!

To solve for it, we can substitute one of our points in - let's do (41, 19.26) - to the equation and solve for b.

$19.26 =-0.14 \cdot 41 +b$
$19.26 = -5.74+ b$
$b = 19.26+5.74$
$b = 25$

Now that we know that b = 25, we can plug it into our equation, <u><em>making the final equation that represents this scenario</em></u>

$y = -0.14x+25$

<h2>Solving for 92 minutes</h2>

Now that we know the equation to our graph, we can substitute in 92 minutes as the x value to find our y value (credit left).

$y = -0.14 \cdot 92 + 25$
$y = -12.88+25$
$y =12.12$

Therefore, after 92 minutes, the amount of credit left is $12.12

Hope this helped!

3 0

3 years ago

Find the area of the surface. the part of the hyperbolic paraboloid z = y2 − x2 that lies between the cylinders x2 + y2 = 4 and

Nadusha1986 [10]

Call the surface $S$ ; then the area of $S$ is given by the surface integral

$\displaystyle\iint_S\mathrm d\mathbf S$

Parameterize the surface by

$\mathbf r(u,v)=\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=u^2\cos^2v-u^2\sin^2v=u^2\cos2v\end{cases}$

with $2\le u\le4$ and $0\le v\le2\pi$ . The surface element is given by

$\mathrm d\mathbf S=\|\mathbf r_u\times\mathbf r_v\|\,\mathrm du\,\mathrm dv$
$\mathrm d\mathbf S=u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv$

So the area is

$\displaystyle\iint_S\mathrm d\mathbf S=\int_{v=0}^{v=2\pi}\int_{u=2}^{u=4}u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv$
$=\displaystyle2\pi\int_{w=17}^{w=65}\sqrt w\,\frac{\mathrm dw}8$

where $w=1+4u^2\implies\mathrm dw=8u\,\mathrm du$

$=\displaystyle\frac\pi4\frac23w^{3/2}\bigg|_{w=17}^{w=65}$
$=\dfrac\pi6\left(65^{3/2}-17^{3/2}\right)\approx237.69$

8 0

3 years ago

11. Which is a solution of<br> b +7 >-2<br> A. b <-9<br> B. b> -9 C. b>-9

kap26 [50]

Answer:

C. b>-9

Step-by-step explanation:

subtract 7 from both sides.

8 0

2 years ago

The population of blackbirds in a park is counted every year.

user100 [1]

Answer:

the original population was 425

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Berto has $12 to put gas in his car. If gas costs $3.75 per gallon, which ordered pair on the graph of the line relating number

Nikolay [14]

<span>number of gallons of gas, x
</span><span>total cost of the gas, y
</span>
3.75x <= 12
x <= 3.2

<span>The greatest amount of gas Berto can buy is 3.2 gallons</span>

5 0

3 years ago

Read 2 more answers

Find the point on the parabola y^2 = 8x at which the ordinate is double the abscissa.​

Find the point on the parabola y^2 = 8x at which the ordinate is double the abscissa.