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Brilliant_brown [7]

2 years ago

8

Which expression is equivalent to StartRoot StartFraction 25 x Superscript 9 Baseline y Superscript 3 Baseline Over 64 x Supersc

ript 6 Baseline y Superscript 11 Baseline EndFraction EndRoot? Assume x Greater-than 0 and y > 0.

2 answers:

MAVERICK [17]2 years ago

5 0

Answer:

$\displaystyle \frac{5x}{8y^{4}}\sqrt{x}$

Step-by-step explanation:

<u>Simplfy in Algebra </u>

We have the following expression

$\displaystyle E=\sqrt{\frac{25x^9y^3}{64x^6y^{11}}}$

Simplifying like factors in the denominator and numerator

$\displaystyle E=\sqrt{\frac{25x^3}{64y^{8}}}$

All the factors are perfect squares except $x^3$ , thus we rewrite:

$\displaystyle E=\sqrt{\frac{25xx^2}{64y^{8}}}$

Taking the square root of all the perfect square factors:

$\boxed{\displaystyle E=\frac{5x}{8y^{4}}\sqrt{x}}$

blagie [28]2 years ago

4 0

Answer:

D On edge.

Step-by-step explanation:

Its Very Simple i Took it just now :D

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Function f is a linear function with an initial value of 17 and a rate of change of –3. Some values for the linear function g ar

tia_tia [17]

Answer:

g(x) exceed f(x) by $10$ when $x=5$

Step-by-step explanation:

step 1

Find the equation of function f(x)

we know that

The initial value is the y-intercept of the linear function (value of y when the value of x is equal to zero)

so

$b=17$

The rate of change is equal to the slope

so

$m=-3$

therefore

$f(x)=-3x+17$

step 2

Find the equation of function g(x)

Let

$A(0,-8),B(2,0)$

Find the slope

$m=(0+8)/(2-0)=4$

$b=-8$ ----> point A

therefore

$g(x)=4x-8$

step 3

Find the value of f(x) and g(x) for $x=5$

$f(5)=-3(5)+17=2$

$g(5)=4(5)-8=12$

Find the difference

$g(5)-f(5)=12-2=10$

3 0

1 year ago

Randy presses RAND on his calculator twice to obtain two random numbers between 0 and 1. Let $p$ be the probability that these t

anygoal [31]

Answer:

$\frac{\pi}{4}$

Step-by-step explanation:

Lets call x,y the numbers we obtain from the calculator. x and y are independent random variables of uniform[0,1] distribution.

Lets note that, since both x and y are between 0 and 1, then 1 is the biggest side of the triangle.

Lets first make a geometric interpretation. If the triangle were to be rectangle, then the side of lenght 1 should be its hypotenuse, and therefore x and y should satisfy this property:

x²+y² = 1

Remember that in this case we are supposing the triangle to be rectangle. But the exercise asks us to obtain an obtuse triangle. For that we will need to increase the angle obtained by the sides of lenght x and y. We can do that by 'expanding' the triangle, but if we do that preserving the values of x and y, then the side of lenght 1 should increase its lenght, which we dont want to. Thus, if we expand the triangle then we should also reduce the value of x and/or y so that the side of lenght 1 could preserve its lenght. With this intuition we could deduce that

x²+y² < 1

Now lets do a more mathematical approach. According to the Cosine theorem, a triangle of three sides of lenght a,b,c satisfies

a² = b²+c² - 2bc* cos(α), where α is the angle between the sides of lenght b and c.

Aplying this formula to our triangle, we have that

$1^2 = x^2 + y^2 - 2bc* cos(\alpha)$ , where $\alpha$ is the angle between the sides of lenght x and y.

Since the triangle is obtuse, then $\pi/2 < \alpha < \pi$ , and for those values $cos(\alpha)$ is negative , hence we also obtain

1 > x² + y²

Thus, we need to calculate P(x²+y² <1). This probability can be calculated throught integration. We need to use polar coordinates.

(x, y) = (r*cosФ,r*senФ)

Where r is between 0 and 1, and Ф is between 0 and $\pi /2$ (that way, the numbers are positive).

The jacobian matrix has determinant r, therefore,

${\int\int}\limits_{x^2+y^2 < 1} \, dxdy = \int\limits^1_0\int\limits^{\frac{\pi}{2}}_0 {r} \, d\phi dr = \frac{\pi}{2} * \int\limits^1_0 {r} \, dr = \frac{\pi}{2} * (\frac{r^2}{2} |^1_0) = \frac{\pi}{4}$

As a conclusion, the probability of obtaining an obtuse triangle is $\frac{\pi}{4}$ .

6 0

1 year ago

Read 2 more answers

A sailboat is sitting at rest near its dock. A rope attached to the bow of the boat is drawn in over a pulley that stands on a p

irina [24]

Answer:

The boat is approaching the dock at rate of 2.14 ft/s

Step-by-step explanation:

The situation given in the question can be modeled as a triangle, please refer to the attached diagram.

A rope attached to the bow of the boat is drawn in over a pulley that stands on a post on the end of the dock that is 5 feet higher than the bow that means x = 5 ft.

The length of rope from bow to pulley is 13 feet that means y = 13 ft.

We know that Pythagorean theorem is given by

$x^{2} + y^{2} = z^{2}$

Differentiating the above equation with respect to time yields,

$2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 2z\frac{dz}{dt}$

$x\frac{dx}{dt} + y\frac{dy}{dt} = z\frac{dz}{dt}$

dx/dt = 0 since dock height doesn't change

$y\frac{dy}{dt} = z\frac{dz}{dt}$

$\frac{dy}{dt} = \frac{z}{y} \frac{dz}{dt}$

The rope is being pulled in at a rate of 2 feet per second that is dz/dt = 2 ft/s

First we need to find z

z² = (5)² + (13)²

z² = 194

z = √194

z = 13.93 ft

So,

$\frac{dy}{dt} = \frac{z}{y} \frac{dz}{dt}$

$\frac{dy}{dt} = \frac{13.93}{13}(2)$

$\frac{dy}{dt} = 2.14$ $ft/s$

Therefore, the boat is approaching the dock at rate of 2.14 ft/s

8 0

1 year ago

Frank wants to build a garden with the dimensions below.

dexar [7]

Given:
Length = x + x + 3 = 2x + 3
Width = 2 + x

Area = length * width
91 ft² = (2x + 3) (2+x)
91 = 4x + 2x² + 6 + 3x
0 = 2x² + 7x + 6 - 91
0 = 2x² + 7x - 85

(2x + 17) ( x - 5)

x = -17/2 or x = 5

Let x = 5 ;

length = 2x + 3 = 2(5) + 3 = 13
width = 2 + x = 2 + 5 = 7

Area = 13 x 7 = 91

Perimeter = 2(length + width)
Perimeter = 2(13 + 7)
Perimeter = 2(20)
Perimeter = 20 feet of fencing

7 0

1 year ago

Read 2 more answers

A 2-column table has 4 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1. The second column is label

tangare [24]

Answer:

5

Step-by-step explanation:

take 0.5 divided by 5 and it gives you your next number on the chart:)

9 0

1 year ago

Read 2 more answers