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Kruka [31]
3 years ago
10

Cot^2x + 3cscx=-3 all real numbers solve for x

Mathematics
1 answer:
ArbitrLikvidat [17]3 years ago
6 0
\cot^2x+3\csc x=-3
\csc^2x-1+3\csc x+3=0
\csc^2x+3\csc x+2=0
(\csc x+2)(\csc x+1)=0

\csc x+2=0\iff\dfrac1{\sin x}=-2\iff\sin x=-\dfrac12
\implies x=\begin{cases}\dfrac{7\pi}6+2n\pi\\\\\dfrac{11\pi}6+2n\pi\end{cases}

\csc x+1=0\iff\dfrac1{\sin x}=-1\iff\sin x=-1
\implies x=\dfrac{3\pi}2+2n\pi

In all solutions, n is any integer.
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A woman bought some large frames for $10 each and some small frames for $5 each add a closeout sale if she bought 20 frames for
vampirchik [111]

Answer:

The quantity of large frames is 7

The quantity of small frames is 13

Step-by-step explanation:

Given as :

The price of each large frames = $ 10

The price of each small frames = $ 5

The total number of both frames bought = 20

The price for both the frames = $ 135

Now,

Let the quantity of large frames = L

And The quantity of small frames = S

So , According to question

The total number of both frames bought = 20

Or, The quantity of large frames + the quantity of small frame = 135

Or, L + S = 20         ......A

And $ 10 L + $ 5 S = $ 135                         ................B

Or, $ 10× ( L + S ) = $ 10× 20

Or, $ 10 L + $ 10 S = $ 200

(  $ 10 L + $ 10 S ) - ( $ 10 L + $ 5 S ) = $ 200 - $ 135

Or , ( $ 10 L - $ 10 L ) + ( $ 10 S - $ 5 S ) = $ 65

Or, 0 + 5 S = 65

∴  S = \frac{65}{5}

I.e S = 13

So, The quantity of small frames = S = 13

Put the Value of S in eq A

So , L + S = 20

Or, L = 20 - S

Or, L = 20 - 13

∴   L = 7

So, The quantity of large frames = L = 7

Hence The quantity of large frames is 7

And   The quantity of small frames is 13   Answer

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3 years ago
Read 2 more answers
A figure is composed of a rectangle and a right triangle. What is the area of the figure?
strojnjashka [21]

QUESTION 1

The figure is a tra-pezoid.

The area of a trapezoid is given by the formula;

A=\frac{1}{2}(Sum\:of\:parallel\:sides)\times h

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Area=\frac{1}{2}(13.2cm+8.4cm)\times 6cm

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The approximate length of the ribbon is equal to the circumference of the circular table cloth.

We can find this by using the formula for calculating the circumference of a circle.

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Type of quadrilateral:Rectangle

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The two pairs of opposite sides of a rectangle are also congruent.

QUESTION 4.

The circumference of a semi circle is calculated using the formula;

C=\pi r

where r=12.5cm is the radius of the semicircle.

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The area of the parallelogram is given by the formula;

A=bh

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We substitute the values to obtain;

23.7=3y

y=\frac{23.7}{3}

y=7.9in.

QUESTION 7

The area of a rectangle is given by the formula;

Area=l\times b

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The area of the smaller rectangle =8\times 13=104in^2

The area of the  shaded region =135-104=31in^2

5 0
3 years ago
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