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2 years ago

(3) Find the value of x.

Mathematics

1 answer:

jek_recluse [69]2 years ago

3 0

Answer:

x=4

Step-by-step explanation:

since triangles are proportional by 2:1, then:

16/2=3x-4

8=3x-4

3x=12

x=4

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Given cosα = −3/5, 180 < α < 270, and sinβ = 12/13, 90 < β < 180

torisob [31]

I got

$- \frac{6 3}{65}$

What we know

cos a=-3/5.

sin b=12/13

Angle A interval are between 180 and 270 or third quadrant

Angle B quadrant is between 90 and 180 or second quadrant.

What we need to find

Cos(b)

Cos(a)

What we are going to apply

Sum and Difference Formulas

Basics Sine and Cosines Identies.

1. Let write out the cos(a-b) formula.

$\cos(a - b) = \cos(a) \cos(b) + \sin(a) \sin(b)$

2. Use the interval it gave us.

According to the given, Angle B must between in second quadrant.

Since sin is opposite/hypotenuse and we are given a sin b=12/13. We. are going to set up an equation using the pythagorean theorem.

${12}^{2} + {y}^{2} = {13}^{2}$

$144 + {y}^{2} = 169$

$25 = {y}^{2}$

$y = 5$

so our adjacent side is 5.

Cosine is adjacent/hypotenuse so our cos b=5/13.

Using the interval it gave us, Angle a must be in the third quadrant. Since cos is adjacent/hypotenuse and we are given cos a=-3/5. We are going to set up an equation using pythagorean theorem,

$( - 3) {}^{2} + {x}^{2} = {5}^{2}$

$9 + {x}^{2} = 25$

${x}^{2} = 16$

$x = 4$

so our opposite side is 4. sin =Opposite/Hypotenuse so our sin a =4/5.Sin is negative in the third quadrant so

sin a =-4/5.

Now use cosine difference formula

$- \frac{3}{5} \times \frac{5}{13} + - \frac {4}{5} \times \frac{12}{13}$

$- \frac{15}{65} + ( - \frac{48}{65} )$

$- \frac{63}{65}$

Hope this helps

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2 years ago

Share £60 in the ratio 1:4

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Answer:

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Step-by-step explanation:

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2 years ago

How many ways can 3 students be chosen from a class of 20 to represent their class at a banquet?

boyakko [2]

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3 years ago

Read 2 more answers

Fill in the missing term in the equation

Y_Kistochka [10]

Answer:

Step-by-step explanation:

Let's simplify the LHS so it can be equated to the RHS.

$\frac{x}{x^{2} -4x+4} - \frac{x}{x^{2} -3x+2}$

$\frac{x}{(x-2)^{2} } - \frac{x}{(x-1)(x-2)}$

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$\frac{x^{2} -x-x^{2}+2x }{(x-2)^{2}(x-1)}$

$\frac{x}{(x-2)^{2}(x-1)}$

Hence, the missing term in the numerator of the answer is <u>x</u>

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1 year ago

What’s the answer please?

seropon [69]

3 miles, because if you think of it like a box, a box has to have 4 sides, you know that there are 2 sets of sides, a set that will be the size of the length and a set that will be the size of the width, so you multiply the width by 2 then multiply the length by 2 and add them

1*2 = 2
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3 years ago