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3 years ago

Find cot theta if csc theta= the square root of 5/2 and tan theta>0

1 answer:

3 0

Since $\cot^2\theta+1=\csc^2\theta$ , you have

$\cot^2\theta=\left(\dfrac{\sqrt5}2\right)^2-1=\dfrac14$
$\cot\theta=\pm\sqrt{\dfrac14}=\pm\dfrac12$

Since $\tan\theta>0$ , and $\cot\theta=\dfrac1{\tan\theta}$ , you know that $\cot\theta$ is also positive, which means

$\cot\theta=\dfrac12$

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The system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the ge

Leno4ka [110]

Answer:

Infinite number of solutions.

Step-by-step explanation:

We are given system of equations

$5x+4y+5z=-1$

$x+y+2z=1$

$2x+y-z=-3$

Firs we find determinant of system of equations

Let a matrix A= $\left[\begin{array}{ccc}5&4&5\\1&1&2\\2&1&-1\end{array}\right]$ and B= $\left[\begin{array}{ccc}-1\\1\\-3\end{array}\right]$

$\mid A\mid=\begin{vmatrix}5&4&5\\1&1&2\\2&1&-1\end{vmatrix}$

$\mid A\mid=5(-1-2)-4(-1-4)+5(1-2)=-15+20-5=0$

Determinant of given system of equation is zero therefore, the general solution of system of equation is many solution or no solution.

We are finding rank of matrix

Apply $R_1\rightarrow R_1-4R_2$ and $R_3\rightarrow R_3-2R_2$

$\left[\begin{array}{ccc}1&0&1\\1&1&2\\0&-1&-3\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\1\\-5\end{array}\right]$

Apply $R_2\rightarrow R_2-R_1$

$\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&-1&-3\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\6\\-5\end{array}\right]$

Apply $R_3\rightarrow R_3+R_2$

$\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&0&-2\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\6\\1\end{array}\right]$

Apply $R_3\rightarrow- \frac{1}{2}$ and $R_2\rightarrow R_2-R_3$

$\left[\begin{array}{ccc}1&0&1\\0&1&0\\0&0&1\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]$

Apply $R_1\rightarrow R_1-R_3$

$\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$ : $\left[\begin{array}{ccc}-\frac{9}{2}\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]$

Rank of matrix A and B are equal.Therefore, matrix A has infinite number of solutions.

Therefore, rank of matrix is equal to rank of B.

4 0

3 years ago

Which is the correct answers? (more than one)

viktelen [127]

B True because both graphs approaches x=0 but never touches it

E True if you just graph it out you can see that graph of g is going down and the graph of x is going up

A false because neither of the equations have a y intercept they have asymptote of x=0

C false because it is also a reflection across the x axis

D incorrect is because they both have domain {0<x<♾}

Hope this helped!

6 0

3 years ago

Find the equation for the line that passes through (-7,5) that has a slope of 2

Setler79 [48]

Point slope formula y-y1=x(x-x1)

7 0

3 years ago

Read 2 more answers

A house is 46.0 ft long and 50 ft wide, and has 8.0-ft-high ceilings. what is the volume of the interior of the house in cubic m

I am Lyosha [343]

Volume of house = 46*50*8=18400 ft^3
Each foot equals 0.3048 m. (exactly).
Therefore 1 ft^3 = 0.3048^3 m^3
Therefore volume of the interior of the house
= 18400 ft^3 * .3048^3 m^3/ft^3
=18400*.3048^3 m^3
=521.0299772928 m^3
=521 m^3 (nearest m^3) ................(a)
or, in cubic centimeters
=521 m^3 * (100cm/m)^3
=521.0299772928 * 100^3 cm^3
=521029977.2928 cm^3
=521029977 cm^3 (nearest cm^3) .........(b)

Answer: see (a) and (b).

4 0

3 years ago

Compute the permutation.

Anon25 [30]

So you have 8 digits (number available) to form 3 digit numbers (number selected).

Using the formula $^{a} P_{c}$ where a is the number of available digits, P is the permutation function and c is the number of digits to be selected.

The number of three digit numbers that can be formed = $^{8} P_{3}$
= 336

 O R

By using the formula $Permutation = \frac{a ! }{( a - c) !}$ where a is the number of available digits and c is the number of digits to be selected.

⇒ $Permutation = \frac{8 ! }{( 8 - 3) !}$

⇒ $Permutation = \frac{40, 320 }{120}$

⇒ Permutation = 336

8 0

3 years ago