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3 years ago

Solve for x: sinx-cosx=√2

1 answer:

6 0

sinx - cosx =sqrt(2)
Taking square on both sides:
(sinx - cosx)^2 =sqrt(2)^2
sin^2(x) -2cos(x)sin(x) + cos^2(x) = 2
Rearranging the equation:
sin^2(x)+cos^2(x) -2cos(x)sin(x)=2
As,
sin^2(x)+cos^2(x) = 1
So,
1-2sinxcosx=2
1-1-2sinxcosx=2-1
-2sinxcosx = 1
Using Trignometric identities:
-2(0.5(sin(x+x)+sin(x-x))=1
-sin2x+sin0=1
As,
sin 0 = 0
So,
sin2x+0 = -1
sin2x = -1
2x=-90 degrees + t360
Dividing by 2 on both sides:
x=-45 degrees + t180
or 2x=270 degrees +t360
x= 135 degrees + t180 where t is integer

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Jackson used the process of completing the square to solve the equation 2x2−12x=−6.

Nikolay [14]

Answer:

$x=3-\sqrt{6},x=3+\sqrt{6}$

Step-by-step explanation:

we are given equation as

$2x^2-12x=-6$

Since, we have to solve it by using complete square

so, firstly we will complete square

and then we can solve for x

step-1:

Factor 2 from both sides

$2(x^2-6x)=-3\times 2$

step-2:

Simplify it

$x^2-6x=-3$

step-3:

Add both sides 3^2

$x^2-6x+3^2=-3+3^2$

now, we can complete square

$(x-3)^2=6$

step-4:

Take sqrt both sides

$(x-3)=-\sqrt{6},(x-3)=\sqrt{6}$

step-5:

Add both sides by 3

we get

$x=3-\sqrt{6},x=3+\sqrt{6}$

3 0

3 years ago

Erica can paint her room 5 hours .If she had her friend Rachel help her , they can paint the room together in 3 hours .How long

LUCKY_DIMON [66]

Answer:

7 hours 30min

Step-by-step explanation:

Step one :

Given data

We are told that Erica can paint 1 room in 5hours

Her work rate is 1/5 room per hour

And also with the assistance of her friend they can paint 1 room in 3 hours

Hence their combined work rate is 1/3 room per hour

Step two

The combined work expression is

1/A+1/B=1/T

Where A=Erica's work rate

B=Rachael's work rate

T=combined work

1/5+1/B=1/3

1/B=1/3-1/5

1/B=5-3/15

1/B=2/15

B=15/2

B=7.5 hours

It will take Rachel 7 hours 30min to paint the room

4 0

3 years ago

Help me pleaseeeeeee

iogann1982 [59]

You start by finding two points on the line. In this case, (-4,1) and (-2,2) will do.

To get from (-4,1) to (-2,2), you need to go “up 1, right 2” which gives you a slope of m = 1/2

Next you need the b-value, which comes from the y-intercept of (0,3). The b-value is 3.

Putting the slope and b-value into y=mx+b, you have y = 1/2 x + 3.

4 0

3 years ago

Solve the absolute value equation. 12 + 2x[ = [x - 6]

Tom [10]

Answer:

x=−18

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

12+2x=x−6

12+2x=x+−6

2x+12=x−6

Step 2: Subtract x from both sides.

2x+12−x=x−6−x

x+12=−6

Step 3: Subtract 12 from both sides.

x+12−12=−6−12

x=−18

6 0

3 years ago

PLEASE ANSWER ASAPPPPPP! What is the quotient of 6 and -1/2.

const2013 [10]

Answer:

-12

Step-by-step explanation:

6 ÷ -1/2

Copy dot flip

6 * -2/1

-12

3 0

3 years ago