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denpristay [2]
3 years ago
15

If Tanø =a/b Find the value of sinø+cosø/sinø-cosø

Mathematics
1 answer:
inysia [295]3 years ago
4 0

Answer:

\frac{b+a}{b-a}

Step-by-step explanation:

Tan θ = \frac{perpendicular}{base} = \frac{b}{a}

So, Perpendicular = b, base = a

<em><u>Finding hypotenuse by Pythagorean Theorem:</u></em>

c^2 = a^2+b^2

=> So, <u><em>hypotenuse = c</em></u>

Sin θ = \frac{perpendicular}{hypotenuse}= \frac{b}{c}

Cos θ = \frac{base}{hypotenuse}= \frac{a}{c}

So, <u><em>Now finding </em></u>\frac{sin\theta+cos\theta}{sin\theta-cos\theta}

=> \frac{b}{c} + \frac{a}{c} ÷ \frac{b}{c} - \frac{a}{c}

=> \frac{b+a}{c} ÷ \frac{b-a}{c}

=> \frac{b+a}{c} * \frac{c}{b-a}

=> \frac{b+a}{b-a}

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Given f(x) = 2x² + 4 and g(x) = 3x – 1 ……<br> What is (fg)(x)? <br><br> Show your work.
Lelu [443]

Answer:

(fg)(x) = 6x³ - 2x² + 12x - 4

Step-by-step explanation:

( f g ) ( x ) = f ( x ) * g ( x )

f(x) = 2x² + 4

g(x) = 3x – 1

( f g ) ( x ) = (2x² + 4) (3x – 1)

               = 6x³ - 2x² + 12x - 4

6 0
3 years ago
Which statement is true regarding the functions on the
Leto [7]

Answer:

f(-3) = g(-3)

Step-by-step explanation:

Remember points on the graph get their location from the x-axis (horizontal) and y-axis (vertical).

In function notation, "f(x)" means when "x" is the value in the brackets, what the value of "y" will be.

First option for example: f(-3) = g(4)

<em>Value of "y" for f(x) when x = -3:</em>

On the blue line, when x = -3, y = -4.

<em>Value of "y" for g(x) when x = 4:</em>

On the red line, when x = 4, y = -3.

<u>Therefore</u>:

f(-3) = g(4)

-4 = -3          <= This is false.

In the third option: f(-3) = g(-3)

<em>On f(x) blue, when x = -3: </em>y = -4

<em>On g(x) red, when x = -3: </em>y = -4

<u>Therefore</u>:

f(-3) = g(-3)

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4 0
3 years ago
Using​ 45-in. fabric, Regan needs 2 and one fourth yd for a​ dress, one fourth yd of contrasting fabric for the band at the​ bot
Arte-miy333 [17]

Answer:

7\dfrac14$ yards

Step-by-step explanation:

Regan needs the following:

2\dfrac{1}{4} yards for a​ dress

\dfrac{1}{4}$ yards of contrasting fabric for the band at the bottom$\\4\dfrac{3}{4}$ yards for a coordinating jacket.

Total Length of fabric needed

= 2\dfrac{1}{4}+\dfrac{1}{4}+4\dfrac{3}{4}\\=2+4+\dfrac{1}{4}+\dfrac{3}{4}+\dfrac{1}{4}\\=6+1+\dfrac{1}{4}\\=7\dfrac{1}{4}$ yards

The number of yards of 45-in. fabric needed is 7\dfrac14$ yards.

4 0
3 years ago
Read 2 more answers
Write the expression in terms of sin x and cos x only. sin(2x)+cos(3x)
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5 0
3 years ago
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A cat keeps eating to gain weight while a dog keeps doing exercise.Later, the cat's weight increases by 20% and the dog's weight
lesya [120]

Answer:

Step-by-step explanation:

We will call the dog's original weight d and the cat's c.  according to the problem 1.2c=.9d

1.2c is the cat's weight increased by 20% and .9d is the dog's weight decreased by 10%  Now we just solve this with algebra for the dog's original weight.

1.2c=.9d

(1.2/.9)c = d

(4/3)c = d

Now, this tells us that the dog's original weight was 4/3 of the cat's.or  about 33.33% larger

It kinda looks like the question is then asking what the cat's current weight is  in comparison to the dog's original.  If that's the case we need just one more step.  We want the dog's original weight and the cat's current weight in terms of the same variable.  Well, we have that.  

Current cat = 1.2c or 6/5, since we have the other in fractional form.

original dog = (4/3)c  

Now, what do we multiply the first to get to the second?  Well, we need common denominators.  15 is the lcm of 3 and 5, so we'll use that.

6/5 = 18/15 and 4/3 = 20/15

Nowwe want to know what we have to multiply 18 by to get to 20.  some algebra will find that.

18x=20

x = 20/18

x = 10/9

that's about 1.11, so the dog's original weight is about 11% higher than the cat's current weight.  

Hopefully that's the answer it wanted, if not or if there is something you didn't understand let me know.

7 0
3 years ago
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