All categories

2 years ago

What is the simplified form of 3 over x squared all over 1 over x-cubed ? (1 point)

Mathematics

1 answer:

aliya0001 [1]2 years ago

8 0

The answer is 3x. C is correct

You might be interested in

(5a^2+6a+2)-(7a^2-7a-5)

krok68 [10]

For this case we must simplify the following expression: $(5a^ 2 + 6a + 2) - (7a^ 2-7a-5) =$

We eliminate the parentheses taking into account that:

$- * + = -\\- * - = +$

So:

$5a ^ 2 + 6a + 2-7a ^ 2 + 7a + 5 =$

We add similar terms taking into account that:

Equal signs are added and the same sign is placed.

Different signs are subtracted and the major sign is placed.

$5a ^ 2-7a^2 + 6a + 7a +2 +5 =\\-2a ^ 2 + 13a + 7$

Answer:

$-2a ^ 2 + 13a + 7$

8 0

3 years ago

Cheryl paid $37.20 for 12 gallons of ice cream for a school picnic. How much would 1 quart of ice cream cost?

Stells [14]

First, you need to get to one gallon, which is 37.20 divided by 12. (3.1)
Divide that number by four, which is: 0.775, or 0.78 rounded up to the nearest hundredth.
Hope that helped.

7 0

3 years ago

Read 2 more answers

Mary wants to buy one large pizza, one medium pizza, and three drinks. The drinks cost $p$ dollars each, the medium pizza costs

Korolek [52]

Answer:

$30-8p$

Step-by-step explanation:

Let p represent cost of each drink.

We have been given that the medium pizza costs two times as much as one drink, so the cost of medium pizza would be $2p$ .

We are also told that the large pizza costs three times as much as one drink, so the cost of la pizza would be $3p$ .

We have been given that Mary wants to buy one large pizza, one medium pizza, and three drinks.

Since the cost of one drink is p, so cost of 3 three drinks would be $3p$ .

The total cost of one large pizza, one medium pizza, and three drinks would be $2p+3p+3p=8p$

Mary started with $30, so amount left after all of her purchases would be 30 minus total cost of all purchases.

$30-8p$

Therefore, Mary will have $30-8p$ dollars left after making all of her purchases.

4 0

3 years ago

Find the critical points of the function f(x, y) = 8y2x − 8yx2 + 9xy. Determine whether they are local minima, local maxima, or

NARA [144]

Answer:

Saddle point: $(0,0)$

Local minimum: $(\frac{3}{8}, -\frac{3}{8})$

Local maxima: $(0,-\frac{9}{8})$ , $(\frac{9}{8},0)$

Step-by-step explanation:

The function is:

$f(x,y) = 8\cdot y^{2}\cdot x -8\cdot y\cdot x^{2} + 9\cdot x \cdot y$

The partial derivatives of the function are included below:

$\frac{\partial f}{\partial x} = 8\cdot y^{2}-16\cdot y\cdot x+9\cdot y$

$\frac{\partial f}{\partial x} = y \cdot (8\cdot y -16\cdot x + 9)$

$\frac{\partial f}{\partial y} = 16\cdot y \cdot x - 8 \cdot x^{2} + 9\cdot x$

$\frac{\partial f}{\partial y} = x \cdot (16\cdot y - 8\cdot x + 9)$

Local minima, local maxima and saddle points are determined by equalizing both partial derivatives to zero.

$y \cdot (8\cdot y -16\cdot x + 9) = 0$

$x \cdot (16\cdot y - 8\cdot x + 9) = 0$

It is quite evident that one point is (0,0). Another point is found by solving the following system of linear equations:

$\left \{ {{-16\cdot x + 8\cdot y=-9} \atop {-8\cdot x + 16\cdot y=-9}} \right.$

The solution of the system is (3/8, -3/8).

Let assume that y = 0, the nonlinear system is reduced to a sole expression:

$x\cdot (-8\cdot x + 9) = 0$

Another solution is (9/8,0).

Now, let consider that x = 0, the nonlinear system is now reduced to this:

$y\cdot (8\cdot y+9) = 0$

Another solution is (0, -9/8).

The next step is to determine whether point is a local maximum, a local minimum or a saddle point. The second derivative test:

$H = \frac{\partial^{2} f}{\partial x^{2}} \cdot \frac{\partial^{2} f}{\partial y^{2}} - \frac{\partial^{2} f}{\partial x \partial y}$

The second derivatives of the function are:

$\frac{\partial^{2} f}{\partial x^{2}} = 0$

$\frac{\partial^{2} f}{\partial y^{2}} = 0$

$\frac{\partial^{2} f}{\partial x \partial y} = 16\cdot y -16\cdot x + 9$

Then, the expression is simplified to this and each point is tested:

$H = -16\cdot y +16\cdot x -9$

S1: (0,0)

$H = -9$ (Saddle Point)

S2: (3/8,-3/8)

$H = 3$ (Local maximum or minimum)

S3: (9/8, 0)

$H = 9$ (Local maximum or minimum)

S4: (0, - 9/8)

$H = 9$ (Local maximum or minimum)

Unfortunately, the second derivative test associated with the function does offer an effective method to distinguish between local maximum and local minimums. A more direct approach is used to make a fair classification:

S2: (3/8,-3/8)

$f(\frac{3}{8} ,-\frac{3}{8} ) = - \frac{27}{64}$ (Local minimum)