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3 years ago

Write the first six terms of the arithmetic sequence The first term

Mathematics

1 answer:

Gelneren [198K]3 years ago

7 0

Answer: 3, 10, 17, 24, 31, 38, 45

Step-by-step explanation:

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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

Which one i greater 2/8 or 1/2 ?

ryzh [129]

$\frac{2}{8}=\frac{1}{4}\\
\frac{1}{2}=\frac{2}{4}\\\\
\frac{2}{4}>\frac{1}{4} \Rightarrow\frac{1}{2}>\frac{2}{8}$

5 0

3 years ago

For any two nonzero integers, the product and quotient have the same sign. True or False

victus00 [196]

That's true. If the integers both have the same sign, then their product and quotient are both positive. If signs are different, then product and quotient are both negative.

5 0

3 years ago

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One plane leaves an hour after another plane. The first plane travels at 400mph. How fast must the second plane travel to catch

Dovator [93]

Answer:

200 mph

Step-by-step explanation:

Ⓗⓘ ⓣⓗⓔⓡⓔ

Plane a: 400mph

Plane b: x mph

2x=400

x=200

(っ◔◡◔)っ ♥ Hope this helped! Have a great day! :) ♥

BTW, brainliest would be greatly appreciated, I only need one more before I advance, thanks!

Also, I may have done something wrong, please tell me if it's incorrect!

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3 years ago

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A prism has a length of 6 feet, height of 2 feet, and width of 5 feet.A prism has a length of 6 feet, height of 2 feet, and widt

Akimi4 [234]

Answer:

Step-by-step explanation

6x2x5= 60

7 0

3 years ago