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3 years ago

Find the 12th term of thsi sequence 5 12 19

Mathematics

1 answer:

enyata [817]3 years ago

4 0

It's adding 7 each time. So...

5, 12, 19, 26, 33, 40, 47, 54, 61, 68, 75, and

82

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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

1 is 25% of what number

lbvjy [14]

Answer:

25x4=100%

1x4=4

4 0

2 years ago

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Find f(2) if f(x)=2x+1

Finger [1]

$f(x) =2 x+1 \\\\ \text{If x = 2,}\\\\f(2) = 2(2) +1 = 4+1 = 5$

8 0

2 years ago

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Gina looks at the architectural plan of a four-walled room in which the walls meet each other at right angles. The length of one

masha68 [24]

If the shape of the room is a square, then the square root of the sum of the squares of the the two adjacent sides will give the diagonal.

i.e.

$\sqrt{17^2+17^2} = \sqrt{2(17^2)} \\ \\ = \sqrt{2(289)} = \sqrt{578} =24.04$

Since the square root of the sum of the squares of the the two adjacent sides is 24.04 and not 18.79, therefore, the shape of the room is not a square.

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3 years ago

A circle has a radius that measures 9 centimeters what is the area of the circle to the nearest tenth use pie 3.14

Tanzania [10]

Step-by-step explanation:

Given

radius (r) = 9 cm

Area of the circle (A) 

= πr²

= 3.14 * 9²

= 3.14 * 81

= 254.34 cm²

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3 years ago