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3 years ago

What is the value of tan?

Mathematics

1 answer:

olga_2 [115]3 years ago

7 0

Answer: B. $\frac{4}{3}$ .

Step-by-step explanation:

In a right triangle, the ratios of its sides are called trigonometric ratios.
The three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).

We have given , $\sin\theta=\dfrac{4}{5}\text{ and }\dfrac{\pi}{2}$ .

Then, $\cos\theta =\sqrt{1-\sin^2\theta}\ [\because\ \sin^2A+\cos^2A=1]$

Put value of $\sin\theta$ , we get

$\Rightarrow\ \cos\theta=\sqrt{1-(\frac{4}{5})^2}$

$\Rightarrow=\sqrt{1-\frac{16}{25}}=\sqrt{\frac{25-16}{25}}=\sqrt{\frac{9}{25}}=\frac{3}{5}$

Now , as we know , $\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac{\frac{4}{5}}{\frac{3}{5}}=\frac{4}{3}$

Hence, the correct option is B. $\frac{4}{3}$ .

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Please help! .........

stira [4]

Answer:

1) When x is 1, y is 4, and vice versa

2) When x is -6, y is 42, and when x is 7, y is 114

3) When x is -2, y is 2, and when x is 8, y is 42

Step-by-step explanation:

$y=x^2-6x+9$

$y+x=5$ which can be rearranged as $y=5-x$ .

Substituting this lone y into the first equation, you get:

$5-x=x^2-6x+9$

Move everything to one side:

$x^2-5x+4=0$

Factor:

$(x-4)(x-1)=0$

$x=1, 4$

$y=4, 1$

$y-30=12x$ which can be rearranged as $y=12x+30$ .

$y=x^2+11x-12$

Let's use elimination this time and subtract the first equation from the second:

$0=x^2-x-42$

Factor:

$(x-7)(x+6)=0$

$x=-6, 7$

$y= -42, 114$

$y=x^2-2x+6$

$y=4x+10$

Let's set the two equations equal to each other through substitution:

$x^2-2x-6=4x+10$

Move everything to one side:

$x^2-6x-16=0$

Factor:

$(x-8)(x+2)=0$

$x=-2, 8$

$y= 2, 42$

Hope this helps!

6 0

3 years ago

The use of mathematical methods to study the spread of contagious diseases goes back at least to some work by Daniel Bernoulli i

harina [27]

Answer:

$y(t) = y_o e^{\beta t}$

$x(t) = x_o e^{\frac{-\alpha y_o }{\beta }[e^{-\beta t} - 1] }$

$\lim_{t \to \infty} x(t) = x_oe^{\frac{-\alpha y_o}{\beta } }$

Step-by-step explanation:

From the question we are told that

$\frac{dy}{y} = -\beta dt$

Now integrating both sides

$ln y = \beta t + c$

Now taking the exponent of both sides

$y(t) = e^{\beta t + c}$

=> $y(t) = e^{\beta t} e^c$

Let $e^c = C$

$y(t) = C e^{\beta t}$

Now from the question we are told that

$y(0) = y_o$

Hence

$y(0) = y_o = Ce^{\beta * 0}$

=> $y_o = C$

$y(t) = y_o e^{\beta t}$

From the question we are told that

$\frac{dx}{dt} = -\alpha xy$

substituting for y

$\frac{dx}{dt} = - \alpha x(y_o e^{-\beta t })$

=> $\frac{dx}{x} = -\alpha y_oe^{-\beta t} dt$

Now integrating both sides

$lnx = \alpha \frac{y_o}{\beta } e^{-\beta t} + c$

Now taking the exponent of both sides

$x(t) = e^{\alpha \frac{y_o}{\beta } e^{-\beta t} + c}$

=> $x(t) = e^{\alpha \frac{y_o}{\beta } e^{-\beta t} } e^c$

Let $e^c = A$

=> $x(t) =K e^{\alpha \frac{y_o}{\beta } e^{-\beta t} }$

Now from the question we are told that

$x(0) = x_o$

$x(0)=x_o =K e^{\alpha \frac{y_o}{\beta } e^{-\beta * 0} }$

=> $x_o = K e^{\frac {\alpha y_o }{\beta } }$

divide both side by $(K * x_o)$

=> $K = x_o e^{\frac {\alpha y_o }{\beta } }$

$x(t) =x_o e^{\frac {-\alpha y_o }{\beta } } * e^{\alpha \frac{y_o}{\beta } e^{-\beta t} }$

=> $x(t)= x_o e^{\frac{-\alpha * y_o }{\beta} + \frac{\alpha y_o}{\beta } e^{-\beta t} }$

=> $x(t) = x_o e^{\frac{\alpha y_o }{\beta }[e^{-\beta t} - 1] }$

Generally as t tends to infinity , $e^{- \beta t}$ tends to zero

$\lim_{t \to \infty} x(t) = x_oe^{\frac{-\alpha y_o}{\beta } }$

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3 years ago

Suppose the population of a certain city is 5893 thousand. It is expected to decrease to 5218 thousand in 50 years. Find the per

leonid [27]

Answer:

% Decrease = 11.45%

Step-by-step explanation:

Original Population = 5893

Expected Population = 5218

% Decrease = Original Population - Expected Population / Original population

% Decrease = (5893 - 5218 ) / 5893

% Decrease = 675/5893

% Decrease = 0.11454268

% Decrease = 11.454268%

% Decrease = 11.45% approximately.

6 0

3 years ago

15. What might explain the concern female students expressed in the beginning of this lesson about the problem of assigning prac

yanalaym [24]

Answer:

Interestingly, the likelihood of a randomly chosen student being a female is 0.58 at this school.

Step-by-step explanation:

This school features more female students than male students. Consequently, if resources are allocated equally (because it has been found that both female and male male students are similarly likely to be involved), the number of female students involved in after-school athletics programs is greater than the number of male students and could clarify the facilities issues.

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3 years ago

To find the area of a triangle, you can use the expression b × h ÷ 2, where b is the base of the triangle and h is its height. W

Zolol [24]

Answer:

Step-by-step explanation:

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3 years ago