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3 years ago

Cos x= 3/4, s in quadrant 1

Mathematics

1 answer:

just olya [345]3 years ago

7 0

Answer: x = 41.4°

Step-by-step explanation:

We want to solve:

Cos(x) = 3/4

Such that this is on quadrant 1.

(if x is in degrees, the possible values of x will be: 0° ≤ x ≤ 90°)

To solve this we need to remember the inverse functions.

If we have two functions f(x) and g(x), these functions are inverses if:

f( g(x) ) = x

g( f(x) ) = x

Then the inverse of the cosine function (this function is "arcos(x)") is such that:

Arcos( cos(x) ) = x

Then in our equation:

Cos(x) = 3/4

We can apply the inverse function to both sides to get:

Arcos(Cos(x)) = Arcos(3/4)

x = Arcos(3/4)

(To find the Arcos function in your calculator, you need to use the button "inv" and then the "cos" button, and remember to have your calculator in deg mode)

x = Arcos(3/4) = 41.4°

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it takes ten tickles for an octopus to laugh

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3 years ago

50 points + brainlest if you answer correctly

Mumz [18]

Answer:

5 is the value which makes the equation true .

Step-by-step explanation:

In this question we have provided an equation that is 9 ( 3x - 16 ) + 15 = 6x - 24 . And we are asked to write the steps to solve the equation with explanation  and to find the value of X .

Solution : -

$\longmapsto \quad \: 9(3x - 16) + 15 = 6x - 24$

Step 1 : Solving parenthesis on left side using distributive property which means multiplying 9 with 3x as well as -16 :

$\longmapsto \quad \:27x - \bold{144 }+ \bold{15 }= 6x - 24$

Step 2 : Solving like terms on left side that are -144 and 15 :

$\longmapsto \quad \:27x -129 = 6x - 24$

Step 3 : Adding 129 on both sides :

$\longmapsto \quad \:27x - \cancel{129} - \cancel{129} = 6x \bold{ - 24 } + \bold{129}$

Now on cancelling -129 with 129 on left side and solving the terms that are -24 and 129 on right side , We get :

$\longmapsto \quad \:27x = 6x + 105$

Step 4 : Subtracting with 6x on both sides :

$\longmapsto \quad \: \bold{27x} - \bold{6x} = \cancel{6x} +105 - \cancel{ 6x}$

On calculating further, We get :

$\longmapsto \quad \:21x = 105$

Step 5 : Now we are Dividing with 21 on both sides so that we can isolate the variable that is x :

$\longmapsto \quad \: \dfrac{ \cancel{21}x}{ \cancel{21}} = \dfrac{105}{ 21}$

Now , by cancelling 21 with 21 on left side , We get :

$\longmapsto \quad \:x = \cancel{\dfrac{105}{21}}$

Step 6 : Now our final step is to simplify the value of x that is 105/21 . We know that 21 × 5 is equal to 105 . So :

$\longmapsto \quad \: \purple{\underline{\boxed{\frak{ x = 5 }}}}$

Henceforth , value of x is 5

Verifying : -

Now we are verifying our answer by substituting value of x in the given equation . So ,

9 ( 3x - 16 ) + 15 = 6x - 24

9 [ 3 ( 5 ) - 16 ] + 15 = 6 ( 5 ) - 24

9 ( 15 - 16 ) + 15 = 30 - 24

9 ( -1 ) + 15 = 6

-9 + 15 = 6

6 = 6

L.H.S = R.H.S

Hence , Verified .

Therefore, our value for x is correct that means it'll makes the equation true .

<h2>#Keep Learning</h2>

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