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3 years ago

Given sin theta=1/3 and 0 < theta< π/2; find tan 2 theta.

Mathematics

1 answer:

mote1985 [20]3 years ago

6 0

Answer:

tan2θ = 4√2/7

Step-by-step explanation:

Given sin theta=1/3 and 0 < theta< π/+

Required

tan 2 theta

tan2 theta = 2tanθ/1-tan²θ

Get tan θ

sinθ = opp/hyp

adj = √3²-1²²

adj = √9-1

adj = √8

tanθ = opp/adj = 1/2√2

tan2 theta = 2(1/2√2/1-(1/2√2)²

tan2θ = 1/√2/1-1/8

tan2θ = 1/√2/7/8

tan2θ = 8/7√2

Rationalize

tan2θ = 8√2/14

tan2θ = 4√2/7

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Answer:

A 12

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Step-by-step explanation:

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3 years ago

Jenna and Becca were both selling cookies door to door. Jenna sold 8 boxes of cookies for every 3 boxes of cookies Becca sold. C

LenaWriter [7]

Answer:
Jenna sold 280 boxes, Becca sold 105 boxes.

Step-by-step explanation:
For every 3 boxes B sold, J sold 8 boxes and ended with a total of 385 boxes sold.
3b+8j=385
From how the question is asked, we can assume that each round of sales would equal 11 total sales. (3b+8j=11)
Knowing the sales take place in intervals of 11, we can solve the problem by doing 385/11.
385/11=35
Finally, with 35 rounds of sales happening and knowing Jenna sells 8 while Becca sells 3 at each one, all that's left to do is multiply.
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1 year ago

Write a rule in function notation for each situation:

algol [13]

Answer:

1. $\bold{S=f(P) = 0.07P}$

2. x = 16

3. Part 1: P is the independent variable and S is the dependent variable.

Part 2: x is the independent variable and y is the dependent variable.

Step-by-step explanation:

1. To write the function notation for:

Sales tax is 7% of the total price.

Let the total price be $P$ .

And sales tax be $S$ .

As per the given statement:

$S = 7\% \ of\ P\\\Rightarrow S =\dfrac{7}{100}P\\\Rightarrow S=0.07P$

Writing it in the function notation:

$\bold{S=f(P) = 0.07P}$

2. To find the value of x such that $f(x) = 14$ and

$f(x) = \dfrac{1}4x + 10$

Putting the value of $f(x) = 14$

$14 = \dfrac{1}4x + 10\\\Rightarrow \dfrac{1}4x =14-10\\\Rightarrow \dfrac{1}4x =4\\\Rightarrow x =4\times 4\\\Rightarrow \bold{x =16}$

3. To find the dependent and independent variable.

Independent variables are those whose value is not dependent on the other variable's values.

Dependent variables are dependent on the value of other variables.

In question 1:

$\bold{S=f(P) = 0.07P}$

P is the independent variable.

S is the dependent variable.

In question 2:

If we write it as follows:

$y=f(x) = \dfrac{1}4x + 10$

x is the independent variable and y is the dependent variable.

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4 years ago

Bill has fruit trees on his farm, and 42 of them are apple trees. If apple trees represent 35% of all his fruit trees, how many

azamat

Answer:

Step-by-step explanation:

t(35/100)=42

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t=120

So there is a total of 120 fruit trees.

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