Which function has the largest slope?

5 - 3tan3x = 0 trên -π< x < π.

serious [3.7K]

Answer:

x = 0.343

Step-by-step explanation:

We want to solve:

5 - 3tan(3x) = 0

such that:

-π< x < π

where π = 3.14

then:

-3.14 < x < 3.14

Let's solve the equation:

5 - 3tan(3x) = 0

-3tan(3x) = -5

tan(3x) = -5/-3 = 5/3

Now we can use the inverse tan function, Atan(x).

Remember that:

Atan( tan(x) ) = tan( Atan(x)) = x

Then if we apply that function to both sides, we get:

Atan( tan(3x)) = Atan(5/3)

3x = Atan(5/3)

x = Atan(5/3)/3 = 0.343

4 0

3 years ago

What are the values of x and y in the parallelogram?

postnew [5]

9514 1404 393

Answer:

x = 60

y = 30

Step-by-step explanation:

Adjacent angles are supplementary.

(5x -180) +x = 180

6x = 360 . . . . . . . . . . add 180, collect terms

x = 60 . . . . . . . . divide by 6

Opposite angles are congruent.

2y = 60 . . . . . . 2y = x

y = 30 . . . . . . . .divide by 2

The value of x is 60; the value of y is 30.

6 0

3 years ago

Which expression can be used to convert 22 Australian dollars to US dollars? Assume 1. 2 Australian dollars equals 1 US dollar.

kolbaska11 [484]

The correct expression to convert the 22 AUD into USD is option A.

<h2>How do you convert the Australian dollars into US dollars?</h2>

Given that the value of 1 US dollar is equal to the value of 2 Australian dollars. We can write this as given below.

1 USD = 2 AUD

1 AUD = 1/2 USD

The 22 Australian dollars can be converted as,

$22 \;\rm AUD = \dfrac {1}{2}\times 22 \;\rm USD$

Hence the correct expression to convert the 22 AUD into USD is option A.

To know more, follow the link given below.

brainly.com/question/19943359.

3 0

2 years ago

Determine the equation of the line that passes through the points of intersection of the graphs of the quadratic functions f(x)

timofeeve [1]

Answer: $x-2y-2=0$

Step-by-step explanation:

Given :

$f(x) = x^2 - 4 \\ g(x) = - 3x^2 + 2x + 8$

Point of intersection :

$f(x)=g(x)\\x^2-4=-3x^2+2x+8\\4x^2-2x-12=0\\2x^2-x-6=0\\2x^2-4x+3x-6=0\\2x(x-2)+3(x-2)=0\\(x-2)(2x+3)=0\\x=2\,,\,\frac{-3}{2}$

$x=2\,;f(2)=2^2-4=0\\x=\frac{-3}{2}\,; f\left ( \frac{3}{2} \right )=\left ( \frac{3}{2} \right )^2-4=\frac{-7}{4}=-1.75$

So, we have points $\left ( 2,0 \right )\,,\,\left ( -1.5,-1.75\ \right )$

Equation of line passing through two points $\left ( x_1,y_1 \right )\,,\,\left ( x_2,y_2 \right )$ is given by $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left ( x-x_1 \right )$

Let $\left ( x_1,y_1 \right )=\left ( 2,0 \right )\,,\,\left ( x_2,y_2 \right )=\left ( -1.5,-1.75\ \right )$

So, equation is as follows :

$y-0=\frac{-1.75-0}{-1.5-2}\left ( x-2 \right )\\y=\frac{-1.75}{-3.5}\left ( x-2 \right )\\y=\frac{1}{2}(x-2)\\2y=x-2\\x-2y-2=0$

4 0

4 years ago

At a particular restaurant, each pizza roll has 60 calories and each mini hotdog has 70 calories. A combination meal with pizza

PolarNik [594]

Answer:

There are 9 pizza rolls and 12 mini hotdogs in the meal.

Step-by-step explanation:

We are given the following in the question.

Let x be the number of pizza rolls sold and y be the number of mini hotdogs in the combination meal.

Total number of items in combination meal = 21

Thus, we can write the equation:

$x + y = 21$

Calorie in a pizza roll = 60

Calorie in a mini hotdog = 70

Total calories = 1380

Thus, we can write the equation:

$60x + 70y = 1380$

Solving the two equations, we get,

$60x + 70y - (60x+60y) = 1380 - 60(21) \\10y = 120\\\Rightarrow y = 12\\\Rightarrow x = 21-12 = 9$

Thus, there are 9 pizza rolls and 12 mini hotdogs in the meal.

4 0

3 years ago