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1 year ago

Find the quotient. Simplify your answer.

Mathematics

1 answer:

brilliants [131]1 year ago

8 0

Let's see

$\\ \rm\Rrightarrow \dfrac{s+1}{s^2+1}\div \dfrac{s^2}{6s^2}$

$\\ \rm\Rrightarrow \dfrac{s+1}{s(s+1)}\div\dfrac{1}{5s^2}$

$\\ \rm\Rrightarrow \dfrac{1}{s}\times{5s^2}$

$\\ \rm\Rrightarrow \dfrac{5s^2}{s}$

$\\ \rm\Rrightarrow 5s$

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(2x² - 5x-3)/ (x-3) DIvide the polynomials

Anika [276]

Answer:

2x + 1

Step-by-step explanation:

$\frac{(2x² - 5x-3)}{(x - 3)}$

Factor out 2x² - 5x-3

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

divide x - 3 by x - 3

=> 2x + 1

Or another step

Step by Step Solution

STEP

Equation at the end of step 1

STEP

2x² - 5x - 3/ x - 3

Trying to factor by splitting the middle term

2.1 Factoring 2x² - 5x - 3

The first term is, 2x² its coefficient is 2 .

The middle term is, -5x its coefficient is -5 .

The last term, "the constant", is -3

Step-1 : Multiply the coefficient of the first term by the constant 2 • -3 = -6

Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is -5 .

-6 + 1 = -5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 1

2x² - 6x + 1x - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

2x • (x-3)

Add up the last 2 terms, pulling out common factors :

1 • (x-3)

Step-5 : Add up the four terms of step 4 :

(2x+1) • (x-3)

Which is the desired factorization

Canceling Out :

2.2 Cancel out (x-3) which appears on both sides of the fraction line.

Final result :

2x + 1

6 0

2 years ago

Prove whether the following are identities 2tanh 1/2x / 1−tanh^2 1/2 x = sinh x

Tanzania [10]

Recall that

$\cosh^2(x) - \sinh^2(x) = 1$

Dividing both sides by cosh²(x) gives

$1 - \tanh^2(x) = \mathrm{sech}^2(x)$

Also, recall the identity

$\sinh(2x) = 2\sinh(x)\cosh(x)$

Then

$\dfrac{2\tanh\left(\frac x2\right)}{1 - \tanh^2\left(\frac x2\right)} = \dfrac{2\tanh\left(\frac x2\right)}{\mathrm{sech}^2\left(\frac x2\right)} \\\\ \dfrac{2\tanh\left(\frac x2\right)}{1 - \tanh^2\left(\frac x2\right)} = 2\tanh\left(\dfrac x2\right)\cosh^2\left(\dfrac x2\right) \\\\ \dfrac{2\tanh\left(\frac x2\right)}{1 - \tanh^2\left(\frac x2\right)} = 2\sinh\left(\dfrac x2\right)\cosh\left(\dfrac x2\right) \\\\\dfrac{2\tanh\left(\frac x2\right)}{1 - \tanh^2\left(\frac x2\right)} = \sinh(x)$

4 0

3 years ago

In the equation Y = 8x+ 5 the name for y are

VLD [36.1K]

Answer:

The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis.

Step-by-step explanation:

4 0

3 years ago

Find the value of x in the triangle

Fofino [41]

Answer:

x=63

Step-by-step explanation:

55+62+x=180

117+x=180

180-117=63

x=63

4 0

3 years ago

A map is drawn to scale such that 1 inch equals 100 miles. To mark a distance of 500 miles, the length on the map must be_____ i

Degger [83]

Answer:

5 inches

Step-by-step explanation:

its simple

1in-100m

500m= 100m x 5

so multiply five to the other side

1in x 5=5 in

5in-500m

7 0

2 years ago

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