Ask question

Ask question

All categories

Artyom0805 [142]

3 years ago

7

Can you help me with this problem: Elena and Jada both read at a constant rate, but Elena reads more slowly. For every 4 pages t

hat Elena read, Jada can read 5. Complete the table. (Look at photo for the table.)

1 answer:

Paraphin [41]3 years ago

7 0

4 pages Elena = 5 pages Jada

To figure out how many pages Jada reads if Elena reads 1, divide 5 by 4: 1.25. This means that for every 1 page Elena reads, Jada reads 1.25 pages.

So if Elena reads 9 pages, multiply 1.25 by 9: 11.25 pages that Jada reads.

For S pages read by Elena, this is a variable, so I’m assuming it means for every S pages, Jada reads 1.25S

You might be interested in

Rewrite the following integral in spherical coordinates.

lora16 [44]

In cylindrical coordinates, we have $r^2=x^2+y^2$ , so that

$z = \pm \sqrt{2-r^2} = \pm \sqrt{2-x^2-y^2}$

correspond to the upper and lower halves of a sphere with radius $\sqrt2$ . In spherical coordinates, this sphere is $\rho=\sqrt2$ .

$1 \le r \le \sqrt2$ means our region is between two cylinders with radius 1 and $\sqrt2$ . In spherical coordinates, the inner cylinder has equation

$x^2+y^2 = 1 \implies \rho^2\cos^2(\theta) \sin^2(\phi) + \rho^2\sin^2(\theta) \sin^2(\phi) = \rho^2 \sin^2(\phi) = 1 \\\\ \implies \rho^2 = \csc^2(\phi) \\\\ \implies \rho = \csc(\phi)$

This cylinder meets the sphere when

$x^2 + y^2 + z^2 = 1 + z^2 = 2 \implies z^2 = 1 \\\\ \implies \rho^2 \cos^2(\phi) = 1 \\\\ \implies \rho^2 = \sec^2(\phi) \\\\ \implies \rho = \sec(\phi)$

which occurs at

$\csc(\phi) = \sec(\phi) \implies \tan(\phi) = 1 \implies \phi = \dfrac\pi4+n\pi$

where $n\in\Bbb Z$ . Then $\frac\pi4\le\phi\le\frac{3\pi}4$ .

The volume element transforms to

$dx\,dy\,dz = r\,dr\,d\theta\,dz = \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi$

Putting everything together, we have

$\displaystyle \int_0^{2\pi} \int_1^{\sqrt2} \int_{-\sqrt{2-r^2}}^{\sqrt{2-r^2}} r \, dz \, dr \, d\theta = \boxed{\int_0^{2\pi} \int_{\pi/4}^{3\pi/4} \int_{\csc(\phi)}^{\sqrt2} \rho^2 \sin(\phi) \, d\rho \, d\phi \, d\theta} = \frac{4\pi}3$

4 0

2 years ago

Slove algebraically<br><br>3x - 4y = -24<br>x +4y=8<br>

Vanyuwa [196]

Solve algebrically 3x - 4y = -24 and x + 4y = 8 is x = -4 and y = 3

<u>Solution:</u>

We have been given two equations which are as follows:

3x - 4y = -24 ----- eqn 1

x + 4y = 8 -------- eqn 2

We have been asked to solve the equations which means we have to find the value of ‘x’ and ‘y’.

We rearrange eqn 2 as follows:

x + 4y = 8

x = 8 - 4y ------eqn 3

Now we substitute eqn 3 in eqn 1 as follows:

3(8 - 4y) -4y = -24

24 - 12y - 4y = -24

-16y = -48

y = 3

Substitute "y" value in eqn 3. Therefore the value of ‘x’ becomes:

x = 8 - 4(3)

x = 8 - 12 = -4

Hence on solving both the given equations we get the value of x and y as -4 and 3 respectively.

5 0

3 years ago

Write x2 - 8x - 3 in vertex form.

crimeas [40]

Vertex form:

y = a(x - h)² + k

I have not learned this stuff yet, but by using online calculators, I can determine that the vertex form is:

Y = (x - 4)² - 19

I believe so :/

6 0

3 years ago

What is 3X +7 equals five

NNADVOKAT [17]

$3x + 7 = 5$

$3x = 5 - 7$

$3x = - 2$

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

5 0

3 years ago

For which positive integer values of $k$ does $kx^2+20x+k=0$ have rational solutions? Express your answers separated by commas a

Musya8 [376]

Answer:

-10,10

Step-by-step explanation:

The given quadratic equation is

$k {x}^{2} + 20x + k = 0$

The discriminant of this equation is given by;

$D = {b}^{2} - 4ac$

where a=k, b=20, c=k

For rational solutions, the discriminant must be zero.

${20}^{2} - 4 \times k \times k = 0$

Simplify to get:

$400 - 4 {k}^{2} = 0$

This implies that:

$400 = 4 {k}^{2}$

$100 = {k}^{2}$

Take square root to get:

$k = \pm\sqrt{100}$

$k = \pm10$

$k = - 10 \: or \: k = 10$

3 0

3 years ago