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2 years ago

Work out 4/5 - 1/3 -

Mathematics

1 answer:

Andru [333]2 years ago

5 0

Answer:

7/15

Step-by-step explanation:

find L.C.M of 5 and 3 then work out

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Find , , and if and terminates in quadrant .

ioda

sin2x =12/13

cos2x = 5/13

tan2x = 12/5

STEP - BY - STEP EXPLANATION

What to find?

• sin2x

• cos2x

• tan2x

Given:

tanx = 2/3 = opposite / adjacent

We need to first make a sketch of the given problem.

Let h be the hypotenuse.

We need to find sinx and cos x, but to find sinx and cosx, first determine the value of h.

Using the Pythagoras theorem;

hypotenuse² = opposite² + adjacent²

h² = 2² + 3²

h² = 4 + 9

h² =13

Take the square root of both-side of the equation.

h =√13

This implies that hypotenuse = √13

We can now proceed to find the values of ainx and cosx.

Using the trigonometric ratio;

$\sin x=\frac{opposite}{\text{hypotenuse}}=\frac{2}{\sqrt[]{13}}$ $\cos x=\frac{adjacent}{\text{hypotenuse}}=\frac{3}{\sqrt[]{13}}$

And we know that tanx =2/3

From the trigonometric identity;

sin 2x = 2sinxcosx

Substitute the value of sinx , cosx and then simplify.

$\sin 2x=2(\frac{2}{\sqrt[]{13}})(\frac{3}{\sqrt[]{13}})$ $=\frac{12}{13}$

Hence, sin2x = 12/13

cos2x = cos²x - sin²x

Substitute the value of cosx, sinx and simplify.

$\begin{gathered} \cos 2x=(\frac{3}{\sqrt[]{13}})^2-(\frac{2}{\sqrt[]{13}})^2 \\ \\ =\frac{9}{13}-\frac{4}{13} \\ =\frac{5}{13} \end{gathered}$

Hence, cos2x = 5/13

tan2x = 2tanx / 1- tan²x

$\tan 2x=\frac{2\tan x}{1-\tan ^2x}$ $=\frac{2(\frac{2}{3})}{1-(\frac{2}{3})^2}$ $=\frac{\frac{4}{3}}{1-\frac{4}{9}}$ $=\frac{\frac{4}{3}}{\frac{9-4}{9}}$ $=\frac{\frac{4}{3}}{\frac{5}{9}}$ $=\frac{4}{3}\times\frac{9}{5}=\frac{4}{1}\times\frac{3}{5}=\frac{12}{5}$

$\tan 2x=\frac{\sin 2x}{\cos 2x}=\frac{\frac{12}{13}}{\frac{5}{13}}=\frac{12}{5}$

Hence, tan2x = 12/5

Therefore,

sin2x =12/13

cos2x = 5/13

tan2x = 12/5

3 0

1 year ago

Please help?<br>:):):):)

Citrus2011 [14]

Answer:

6.48%

Step-by-step explanation:

t - c = b

t = 31.93

c = 29.99

b = 31.93 - 29.99

b = 6.48%

4 0

3 years ago

A dragon likes to eat red peppers and green peppers because they help him breathe fire. If the dragon eats 2 red peppers, he can

N76 [4]

it's 45

Step-by-step explanation:

Okay, so if 2 peppers is 25 meters long, you just divide 25 by 2 to get how many peppers the dragon breathes as 1 pepper. So then you get 12.5, And if you do that with the green peppers, you get 1.5. So, the dragon ate 3 green peppers, so it's 12.5 x 3 , aka. 12.5+12.5+12.5. That's 37.5, and if you do 1.5x5 for the green peppers, it's 7.5, And now you add 37.5+7.5, and you get 45.

4 0

2 years ago

A vehicle purchased for $20700 depreciates at a constant rate of 5% . Determine the approximate value of the vehicle 10 years af

SVEN [57.7K]

Answer:

I believe it is 12,393.86

5 0

3 years ago

1. What is express the same relationship between two quantities.

Phantasy [73]

I do not know I will tell u but I think it is 65?

8 0

2 years ago