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3 years ago

Tanx-cotx=0 solve in radians

1 answer:

6 0

tan x + 1 / tan x = 2

tan^2 x + 1 = 2 tan x

tan^2 x - 2 tan x + 1 = 0

( tan x - 1 )^2 = 0

tan x = 1

x = π/4 , 5π/4

You might be interested in

Solve xy-6=k for x Please help me out

dedylja [7]

Answer:

$\times = \frac{k + 6}{y}$

Step-by-step explanation:

$xy - 6 = k \\ xy = k + 6 \\ x = \frac{k + 6}{y}$

4 0

3 years ago

Complete the square and write in standard form. Show all work.What would be the conic section:CircleEllipseHyperbolaParabola

mote1985 [20]

ANSWER

This is an ellipse. The equation is:

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

EXPLANATION

We have to complete the square for each variable. To do so, we have to take the first two terms and compare them with the perfect binomial squared formula,

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

For x we have to take 16x² and -32x. Since the coefficient of x is not 1, first, we have to factor out the coefficient 16,

$16x^2-32x=16(x^2-2x)$

Now, the first term of the expanded binomial would be x and the second term -2x. Thus, the binomial is,

$(x-1)^2=x^2-2x+1$

To maintain the equation, we have to subtract 1,

$16(x^2-2x+1-1)=16((x-1)^2-1)=16(x-1)^2-16$

Now, we replace (16x² - 32x) from the given equation by this equivalent expression,

$16(x-1)^2-16+9y^2+72y+16=0$

The next step is to do the same for y. We have the terms 9y² + 72y. Again, since the coefficient of y² is not 1, we factor out the coefficient 9,

$9y^2+72y=9(y^2+8y)$

Following the same reasoning as before, we have that the perfect binomial squared is,

$(y+4)^2=y^2+8y+16$

Remember to subtract the independent term to maintain the equation,

$9(y^2+8y)=9(y^2+8y+16-16)=9((y+4)^2-16)=9(y+4)^2-144$

And now, as we did for x, replace the two terms (9y² + 72y) with this equivalent expression in the equation,

$16(x-1)^2-16+9(y+4)^2-144+16=0$

Add like terms,

$\begin{gathered} 16(x-1)^2+9(y+4)^2+(-16-144+16)=0 \\ 16(x-1)^2+9(y+4)^2-144=0 \end{gathered}$

Add 144 to both sides,

$\begin{gathered} 16(x-1)^2+9(y+4)^2-144+144=0+144 \\ 16(x-1)^2+9(y+4)^2=144 \end{gathered}$

As we can see, this is the equation of an ellipse. Its standard form is,

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$

So the next step is to divide both sides by 144 and also write the coefficients as fractions in the denominator,

$\begin{gathered} \frac{16(x-1)^2}{144}+\frac{9(y+4)^2}{144}=\frac{144}{144} \\ \\ \frac{(x-1)^2}{\frac{144}{16}}+\frac{(y+4)^2}{\frac{144}{9}}=1 \end{gathered}$

Finally, we have to write the denominators as perfect squares, so we identify the values of a and b. 144 is 12², 16 is 4² and 9 is 3²,

$\frac{(x-1)^2}{(\frac{12}{4})^2}+\frac{(y+4)^2}{(\frac{12}{3})^2}=1$

Note that we can simplify a and b,

$\frac{12}{4}=3\text{ and }\frac{12}{3}=4$

Hence, the equation of the ellipse is,

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

3 0

1 year ago

The price of a pizza plus 12% delivery charge comes to a total cost of $17.92. What was the price of the pizza?

Leya [2.2K]

Answer:

i believe the answer is 14.93 dollars.

Step-by-step explanation:

3 0

2 years ago

Please help! Correct answer only, please! Consider the following information matrices for the price of clothing at a clothing st

ololo11 [35]

Answer: b) Large blue t-shirt & Medium RC jeans

Step-by-step explanation:

The subscript numbers attached to the matrix letter represents the:

ROW, COLUMN

$A=\left[\begin{array}{ccc}a_{1,1}&a_{1, 2}&a_{1, 3}\\a_{2,1}&a_{2, 2}&a_{2, 3}\\a_{3,1}&a_{3, 2}&a_{3, 3}\end{array}\right] \qquad B=\left[\begin{array}{ccc}a_{1,1}&b_{1, 2}&b_{1, 3}\\b_{2,1}&b_{2, 2}&b_{2, 3}\\b_{3,1}&b_{3, 2}&b_{3, 3}\end{array}\right]\\$

A₁,₃ = 1st row, 3rd column

1st row is Blue, 3rd column is Large

B₃,₂ = 3rd row, 2nd column

3rd row is RC jeans, 2nd column is Medium

A₁,₃ + B₃,₂ = Large blue t-shirt & Medium RC jeans

8 0

3 years ago

How do you write this number using words? 47

jasenka [17]

Answer is fourty seven

4 0

3 years ago