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3 years ago

Which of the following is the quotient of the rational expression shown below

Mathematics

1 answer:

tatyana61 [14]3 years ago

3 0

Answer:

Step-by-step explanation:

None of the expressions on the numerators/ denominators factor

To divide the 2 rational expressions

leave the first fraction

Change division to multiplication

Turn the second fraction upside down, that is

$\frac{2x}{4x+3}$ × $\frac{2x}{x-1}$

Multiply the values on the numerators/ denominators, that is

$\frac{2x(2x)}{(4x+3)(x-1)}$

= $\frac{4x^2}{4x^2-x-3}$ → B

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As you are walking down a path, you see a sign telling the path has a 2% grade (ie., a rise of 2 metres for a horizontal change

Leni [432]

Answer:

Option (A)

Step-by-step explanation:

It has been given in this question that sign telling path has a 2% grade.

2% grade means a rise of 2 meters for a horizontal change of 100 m (As given in the figure attached).

All the trigonometric ratios for the angle θ between the path and the horizontal are,

Sinθ = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

Cosθ = $\frac{\text{Adjacent side}}{\text{Hypotenuse}}$

tanθ = $\frac{\text{Opposite side}}{\text{Adjacent side}}$

Since measures of the opposite side and adjacent sides are given

Therefore, tangent ratio will be applied to get the measure of the angle,

tanθ = $\frac{2}{100}$

θ = $\text{tan}^{-1}(\frac{2}{100})$

Option (A) will be the answer.

5 0

3 years ago

If -4 is a root of the equation x^2+px-4=0 and the equation x^2+px+q=0 has equal roots, find the value of p and q

zubka84 [21]

Answer:

p = 3, q = 2.5

Step-by-step explanation:

Given that x = - 4 is a root of the equation, then

(- 4)² - 4p - 4 = 0, that is

16 - 4p - 4 = 0

12 - 4p = 0 ( subtract 12 from both sides )

- 4p = - 12 ( divide both sides by - 4 )

p = 3

Also given that the equation x² + px + q = 0 has equal roots

Thus the value of the discriminant b² - 4ac = 0

Here a = 1, b = p and c = q, thus

p² - 4q = 0 ← substitute p = 3 from above into the equation

9 - 4q = 0 ( subtract 9 from both sides )

- 4q = - 9 ( divide both sides by - 4 )

q = 2.5

8 0

4 years ago

Find a number in the closed interval [1/2,3/2] such that the sum of the number and its reciprocal is

sattari [20]

Let's assume that number as x

so,

the sum of the number and its reciprocal is

$S(x)=x+\frac{1}{x}$

Firstly, we will find derivative

$S'(x)=1-\frac{1}{x^2}$

now, we can set it to 0

and then we can solve for x

$S'(x)=1-\frac{1}{x^2}=0$

$x=-1,x=1$

Since, only x=1 lies on [1/2,3/2]

so, we will consider only x=1

now, we can plug end values and x=1 into S

At x=1/2:

we can plug x=1/2

$S(\frac{1}{2})=\frac{1}{2} +\frac{1}{\frac{1}{2}}$

$S(\frac{1}{2})=\frac{1}{2} +2$

$S(\frac{1}{2})=\frac{5}{2}$

At x=1:

we can plug x=1

$S(1)=1 +\frac{1}{1}$

$S(1)=1 +1$

$S(1)=2$

At x=3/2:

we can plug x=3/2

$S(\frac{3}{2})=\frac{3}{2} +\frac{1}{\frac{3}{2}}$

$S(\frac{3}{2})=\frac{3}{2} +\frac{2}{3}$

$S(\frac{3}{2})=\frac{13}{6}$

(a)

Smallest value:

The smallest value among them

$S(1)=2$

So, a number is 1..........Answer

(b)

Largest value:

The largest value among them

$S(\frac{1}{2})=\frac{5}{2}$

So, a number is $\frac{1}{2}$ ........Answer

6 0

4 years ago

Saved<br> Find all solutions of 5−4 secx = −3 on the interval [0, 2π).

taurus [48]

Uterlly useless considering 11-34 is 3

8 0

4 years ago

Read 2 more answers

Consider the data. 2,2,2,3,5,6,8,30

miv72 [106K]

The mean of the data plot is 7.25.
The mean of the data plot without the outlier is 4.333333333.

So the mean decreased by 2.916666666.

6 0

4 years ago