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3 years ago

Given that sin x equals to a over b then what is tan x

Mathematics

2 answers:

yawa3891 [41]3 years ago

8 0

Answer:

Hey there!

Sine is equal to opposite/hypotenuse

Tangent is equal to opposite/adjacent

opposite=a

hypotenuse=b

adjacent=c

Thus, tangent x= a/c.

Hope this helps :)

djverab [1.8K]3 years ago

7 0

Answer:

tan x = a/sqrt(b^2 - a^2)

Step-by-step explanation:

sin x = a/b = opp/hyp

tan x = opp/adj

adj^2 + opp^2 = hyp^2

adj^2 + a^2 = b^2

adj = sqrt(b^2 - a^2)

tan x = a/sqrt(b^2 - a^2)

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Find an equation for the nth term of the arithmetic sequence.

amm1812

Answer:

$a_n=-301 +37(n-1)$

Step-by-step explanation:

arithmetic sequence formula: $a_n=a +(n-1)d$

where $a$ is the first term and $d$ is the common difference

Given:

$a_{10}=32$

⇒ $a +(10-1)d=32$

⇒ $a+9d=32$

Given:

$a_{12}=106$

⇒ $a +(12-1)d=106$

⇒ $a+11d=106$

Rearrange the first equation to make $a$ the subject:

a = 32 - 9d

Now substitute into the second equation and solve for $d$

(32 - 9d) + 11d = 106

⇒ 32 + 2d = 106

⇒ 2d = 106 - 32 = 74

⇒ d = 74 ÷ 2 = 37

Substitute found value of $d$ into the first equation and solve for $a$ :

a + (9 x 37) = 32

a + 333 = 32

a = 32 - 333 = -301

Therefore, the equation is: $a_n=-301 +37(n-1)$

4 0

2 years ago

Find the equation of an exponential function in the form y = ab^x, given the points (0, 3) and (2, 108/25). Please simplify your

lilavasa [31]

We have the equation:

$y=a\cdot b^x$

We know two points and we will use them to calculate the parameters a and b.

The point (0,3) will let us know a, as b^0=1.

$\begin{gathered} y=a\cdot b^x \\ 3=a\cdot b^0=a \\ a=3 \end{gathered}$

Now, we use the point (2, 108/25) to calcualte b:

$\begin{gathered} y=3\cdot b^x \\ \frac{108}{25}=3\cdot b^2 \\ 3\cdot b^2=\frac{108}{25} \\ b^2=\frac{108}{25\cdot3}=\frac{108}{3}\cdot\frac{1}{25}=\frac{36}{25} \\ b=\sqrt[]{\frac{36}{25}} \\ b=\frac{\sqrt[]{36}}{\sqrt[]{25}} \\ b=\frac{6}{5} \end{gathered}$

Then, we can write the equation as: