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aleksandrvk [35]

3 years ago

11

Which equations are correct?

1 answer:

torisob [31]3 years ago

4 0

Answer:

All of them are correct equations.

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(csc x - 1) (csc x + 1)

victus00 [196]

<h2>Explanation:</h2>

Here we have the following expression:

$(csc x - 1) (csc x + 1)$

So we need to extend this. Remember that the difference of squares tells us:

$(a-b)(a+b)=a^2-b^2$

So here:

$a=cscx \\ \\ b=1$

Thus:

$(csc x - 1) (csc x + 1)=csc^2x-1 \\ \\ \\ But: \\ \\ cscx=\frac{1}{sinx} \\ \\ \\ Then: \\ \\ csc^2x-1=\frac{1}{sin^2x}-1=\frac{1-sin^2x}{sin^2x}=\frac{cos^2x}{sin^2x}=cot^2x \\ \\ \\ Finally: \\ \\ \boxed{(csc x - 1) (csc x + 1)=cot^2x}$

4 0

3 years ago

The mass of carbon is 1.995 x 10^-23 grams per atom and the mass of hydrogen is

Goshia [24]

Answer:

Carbon

Step-by-step explanation:

When the power of 10 is negative, the less the exponent the bigger the number

3 0

3 years ago

Read 2 more answers

Given that f(x) = √(ax + 1) , with x ≥ -1/a and a > 0

padilas [110]

Answer:

$\displaystyle 7$

Step-by-step explanation:

first thing I assume by f~¹ you meant $f^{-1}$ however

we want to find <u>a²</u><u>+</u><u>3</u><u>x</u><u>-</u><u>3</u><u> </u>for the given condition. with the composite function condition we can do so

<u>Finding</u><u> the</u><u> </u><u>inverse</u><u> of</u><u> </u><u>f(</u><u>x)</u><u>:</u>

$\displaystyle f(x) = \sqrt{ax + 1}$

substitute y for f(x):

$\displaystyle y= \sqrt{ax + 1}$

interchange:

$\displaystyle x= \sqrt{ay + 1}$

square both sides:

$\displaystyle ay + 1 = {x}^{2}$

cancel 1 from both sides:

$\displaystyle ay = {x}^{2} - 1$

divide both sides by a:

$\displaystyle y = \frac{{x}^{2} - 1 }{a}$

substitute f^-1 for y:

$\displaystyle f ^{ - 1} (x) = \frac{{x}^{2} - 1 }{a}$

<u>finding</u><u> the</u><u> </u><u>inverse</u><u> of</u><u> </u><u>g(</u><u>x)</u><u>:</u>

$\displaystyle g(x) = \frac{x + 1}{x}$

substitute y for g(x)

$\displaystyle y= \frac{x + 1}{x}$

interchange:

$\displaystyle \frac{y + 1}{y} =x$

cross multiplication

$\displaystyle y + 1= xy$

cancel 1 from both sides

$\displaystyle y - xy= - 1$

factor out y:

$\displaystyle y(1 - x)= - 1$

divide both sides by 1-x:

$\displaystyle y= - \frac{1}{ 1 - x}$

substitute g^-1 for y:

$\displaystyle g ^{ - 1} (x)= - \frac{1}{ 1 - x}$

remember that

$\displaystyle (f \circ g)x = f(g(x))$

therefore we obtain:

$\rm \displaystyle (f ^{ - 1} \circ g ^{ - 1} ) (3) = \frac{{ \bigg(- \dfrac{1}{1 - 3} } \bigg)^{2} - 1 }{a}$

since (f~¹•g~¹)(3)=-⅜ thus substitute:

$\rm \displaystyle \frac{{ \bigg(- \dfrac{1}{1 - 3} } \bigg)^{2} - 1 }{a} = - \frac{3}{8}$

simplify parentheses:

$\rm \displaystyle \frac{{ \bigg( \dfrac{1}{2} } \bigg)^{2} - 1 }{a} = - \frac{3}{8}$

simplify square:

$\rm \displaystyle \frac{{ \dfrac{1}{4} } - 1 }{a} = - \frac{3}{8}$

simplify substraction:

$\rm \displaystyle \frac{ - \dfrac{3}{4} }{ a}= - \frac{3}{8}$

simplify complex fraction:

$\rm \displaystyle - \dfrac{3}{4a} = - \frac{3}{8}$

get rid of - sign:

$\rm \displaystyle \dfrac{3}{4a} = \frac{3}{8}$

divide both sides by 3:

$\rm \displaystyle \dfrac{1}{4a} = \frac{1}{8}$

cross multiplication:

$\rm \displaystyle 4a= 8$

divide both sides by 4:

$\rm \displaystyle \boxed{ a= 2}$

as we want to find <u>a²</u><u>+</u><u>3</u><u>a</u><u>-</u><u>3</u><u> </u>substitute the got value of a:

$\displaystyle {2}^{2} + 3.2 - 3$

simplify square:

$\displaystyle 4 + 3.2 - 3$

simplify multiplication:

$\displaystyle 4 +6 - 3$

simplify addition:

$\displaystyle 10 - 3$

simplify substraction:

$\displaystyle 7$

and we are done!

7 0

3 years ago

Find the solution of the system of the equations 7x+14y=35 -2x-2y=-8

grandymaker [24]

Answer:

(x,y)=(309/7,-317/14) If you ever get stuck on similar problems I recommend using the photomath app.

Step-by-step explanation:

4 0

3 years ago

Four friends are going to share the responsibility of babysitting 3 children for 7 hours. How much time will each friend spend b

Effectus [21]

Answer:

1.75 hours :)

Step-by-step explanation:

8 0

3 years ago