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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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I need help finding x
BigorU [14]

Answer:

The answer to your question is      x = \sqrt{50}    or x = 5\sqrt{2}

Step-by-step explanation:

To solve this problem use the Pythagorean theorem because two right triangles are formed.

                    c² = a² + b²

c = 10

a = x

b = x     Because in a square all the sides measure the same.

                    10² = x² + x²

- Simplify

                    100 = 2x²

                    x² = 100/2

                   x² = 50

                    x = \sqrt{50}    or x = 5\sqrt{2}

         

3 0
3 years ago
Triangle ABC has vertices at A(2,3),B(-4,-3) and C(2,-3) find the coordinates of each point of concurrency.
dem82 [27]

Answer:

Circumcenter =(-1,0)

Orthocenter =(2,-3)

Step-by-step explanation:  

Given : Points A = (2,3), B = (-4,-3), C = (2,-3)  

Formula used :  

→Mid point of two points- (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

→Slope of two points - \frac{y_2-y_1}{x_2-x_1})

→Perpendicular of a line = \frac{-1}{slope of line})

Circumcenter- The point where the perpendicular bisectors of a triangle meets.

Orthocenter-The intersecting point for all the altitudes of the triangle.

To find out the circumcenter we have to solve any two bisector equations.

We solve for line AB and AC

So, mid point of AB =(\frac{2-4}{2},\frac{3-3}{2})=(-1,0)

Slope of AB =\frac{-3-3}{-4-2}=1

Slope of the bisector is the negative reciprocal of the given slope.  

So, the slope of the perpendicular bisector = -1  

Equation of AB with slope -1 and the coordinates (-1,0) is,  

(y – 0) = -1(x – (-1))  

y+x=-1………………(1)  

Similarly, for AC  

Mid point of AC = (\frac{2+2}{2},\frac{3-3}{2})=(2,0)

Slope of AC = \frac{-3-3}{2-2}=\frac{-6}{0}  

Slope of the bisector is the negative reciprocal of the given slope.  

So, the slope of the perpendicular bisector = 0  

Equation of AC with slope 0 and the coordinates (2,0) is,  

(y – 0) = 0(x – 2)  

y=0 ………………(2)  

By solving equation (1) and (2),  

put y=0 in equation (1)

y+x=-1

0+x=-1

⇒x=-1  

So the circumcenter(P)= (-1,0)

To find the orthocenter we solve the intersections of altitudes.

We solve for line AB and BC

So, mid point of AB =(\frac{2-4}{2},\frac{3-3}{2})=(-1,0)

Slope of AB =\frac{-3-3}{-4-2}=1

Slope of the bisector is the negative reciprocal of the given slope.  

So, the slope of CF = -1  

Equation of AB with slope -1 and the coordinates (-1,0) gives equation CF  

(y – 0) = -1(x – (-1))  

y+x=-1………………(3)  

Similarly, mid point of BC =(\frac{-4+2}{2},\frac{-3-3}{2})=(-1,-3)

Slope of AB =\frac{-3+3}{-4-2}=0

Slope of the bisector is the negative reciprocal of the given slope.  

So, the slope of AD = 0

Equation of AB with slope 0 and the coordinates (-1,-3) gives equation AD

(y-(-3)) = 0(x – (-1))  

y+3=0

y=-3………………(4)  

Solve equation (3) and (4),

Put y=-3 in equation (3)

y+x=-1

-3+x=-1

x=2

Therefore, orthocenter(O)= (2,-3)


7 0
3 years ago
Leonardo da Vinci drew a portrait of a young woman. The portrait is shaped like a rectangle. It is 13.5 inches long and 10 inche
ivann1987 [24]
Let
x---------------> long side rectangle------------> 13.5 in
y---------------> wide side rectangle------------> 10 in
d--------------> <span>length of a diagonal
</span>
we know <span>applying the Pythagorean theorem
</span>d²=x²+y²-----------> d²=13.5²+10²-> d²=282.25
d=√282.25=16.80 in

the answer is 16.8 in
3 0
3 years ago
Helpp me pleasee ╹◡╹
anyanavicka [17]

Answer:

55 for 1 min

110 for 2 min

165 for 3 min

4 0
2 years ago
Read 2 more answers
Standard deviation of 300, 785, 670, 187, 760, 724
White raven [17]
STEP 1

Mean = \frac{300+785+670+187+760+724}{6} = \frac{3426}{6}=571

STEP 2

Subtract the mean from each data value then square the answer
300-571=-271 ⇒ (-271)^{2} =73441
785-571=214 ⇒ (214)^{2}=45796
670-571=99 ⇒ (99)^{2}=9801
187-571=-384 ⇒ (-384)^{2} =147456
760-571=189 ⇒ 189^{2}=35721
724-571=153 ⇒ 153^{2} =23409

STEP 3

Add the squared answers in STEP 2 then find the mean

\frac{73441+45796+9801+147456+35721+23409}{6}= \frac{335624}{6}=55937.3

STEP 4

Square root the answer in STEP 3
\sqrt{55937.3} =236.5

Standard deviation is 236.5
 
7 0
3 years ago
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