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2 years ago

Solve for x in sin xtan x + tan x – 2sin x + cos x = 0 for 0 ≤ x ≤2π rads.

Mathematics

1 answer:

konstantin123 [22]2 years ago

3 0

The value of x = 4.71, 0.41, or 5.89 radian value

Specification:

sinxtanx + tanx -2sinx + cosx = 0

tanx = sinx / cosx

sinx (sinx / cosx) + sinx / cosx -2sinx + cosx = Multiply 0

cosx to remove the fraction

sin ^ 2 (x) + sinx -2sinxcosx + cos ^ 2 (x) = 0

sin ^ 2 (x) + cos ^ Replace with 1. 2 (x) = 1

sinx -2sinxcosx + 1 = 0

sinx (1-2cosx) = -1

1-2cosx = -1 / sinx

-2cosx = -1 / sinx -1

2cosx = 1 / sinx + 1

cosx = 1 / 2sinx + 1/2

sqr (1-sin ^ 2 (x)) = 1 / 2sinx + 1/2

Squared on both sides

1-sin ^ 2 (x) = 1 / 4sin ^ 2 (x) + 1 / 2sinx + 1/4

4sin ^ 2 (x) Multiply

4sin ^ 2 (x) -4sin ^ 4 (x) = 1 + 2sinx + sin ^ 2 (X)

4sin ^ 4 (x) -3sin ^ 2 (x) + 2sinx +1 = 0

y = sinx

4y ^ 4 -3y ^ 2 + 2y + 1 = 0

sinx = y = -1 or -0.3478

x = 270, 180-22.61 or -22.61 degrees

x = 270, 157.39 or 337 .39 degrees

x = 3pi / 2, 0.13pi or 1.87pi radians

x = 4.71, 0.41 Or 5.89 radians

For more information about trigonometry, visit brainly.com/question/24349828

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The following estimated regression equation was developed for a model involving two independent variables.

Alik [6]

Answer:

(a): y increases on average by 8.63/unit of x1 in the first equation and increases on average by 9.01/unit of x1 in the second

(b): Yes

Step-by-step explanation:

Given

$\wedge y = 40.7 + 8.63x_1 +2.71x_1$

$\wedge y = 42.0 + 9.01x_1$

Solving (a): An interpretation of x1 coefficient

We have the coefficients of x1 to be 8.63 and 9.01

Literally, the coefficient represents the average change of y-variable per unit increase of the dependent variable

Since the coefficients of x1 in both equations are positive, then that represents an increment on the y variable.

So, the interpretation is:

y increases on average by 8.63/unit of x1 in the first equation and increases on average by 9.01/unit of x1 in the second

Solving (b): Multicollinearity

This could be the cause because x1 and x2 are related and as a result, x2 could take a part of the coefficient of x2

7 0

3 years ago

The figure is made up of a cylinder and a hemisphere. To the nearest whole number, what is the approximate volume of this figure

Novosadov [1.4K]

Hello!

The figure is made up of a cylinder and a hemisphere. To the nearest whole number, what is the approximate volume of this figure?

Use 3.14 to approximate π .

Enter your answer in the box. in.³

Data: (Cylinder)

h (height) = 7 in

r (radius) = 2.5 in (The diameter is 5 being twice the radius)

Adopting: $\pi \approx 3.14$

V (volume) = ?

Solving: (Cylinder volume)

$V = \pi *r^2*h$

$V = 3.14 *2.5^2*7$

$V = 3.14*6.25*7$

$V = 137.375 \to \boxed{V_{cylinder} \approx 137.38\:in^3}$

Note: Now, let's find the volume of a hemisphere.

Data: (hemisphere volume)

V (volume) = ?

r (radius) = 2.5 in (The diameter is 5 being twice the radius)

Adopting: $\pi \approx 3.14$

If: We know that the volume of a sphere is $V = 4* \pi * \dfrac{r^3}{3}$ , but we have a hemisphere, so the formula will be half the volume of the hemisphere $V = \dfrac{1}{2}* 4* \pi * \dfrac{r^3}{3} \to \boxed{V = 2* \pi * \dfrac{r^3}{3}}$

Formula: (Volume of the hemisphere)

$V = 2* \pi * \dfrac{r^3}{3}$

Solving:

$V = 2* \pi * \dfrac{r^3}{3}$

$V = 2*3.14 * \dfrac{2.5^3}{3}$

$V = 2*3.14 * \dfrac{15.625}{3}$

$V = \dfrac{98.125}{3}$

$\boxed{ V_{hemisphere} \approx 32.70\:in^3}$

Now, to find the total volume of the figure, add the values: (cylinder volume + hemisphere volume)

Volume of the figure = cylinder volume + hemisphere volume

Volume of the figure = 137.38 in³ + 32.70 in³

$Volume\:of\:the\:figure =170.08 \to \boxed{\boxed{\boxed{Volume\:of\:the\:figure = 170\:in^3}}}\end{array}}\qquad\quad\checkmark$

_______________________

I Hope this helps, greetings ... Dexteright02! =)

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3 years ago

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Find the value of the cosine

galina1969 [7]

Answer:

I believe the answer is c

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2 years ago

Which expression gives the measure of XYZ?

Mkey [24]

Answer:

1/2( 110+42)

Step-by-step explanation:

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<<XYZ = 1/2( 42+110)

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3 years ago

On Tuesday, Hayley only has 15 cups of flour and 9 eggs, but she has more than enough butter and sugar. Which system of linear i

BabaBlast [244]

Missing part of the question

Hayley bakes zucchini bread and banana bread. Some ingredients Hayley uses for each type of bread are shown in the tables

Zucchini Bread

2 eggs 2 cups of flour 1.5 cups of sugar 0.5 stick of butter

Banana Bread

1 egg 3 cups of flour 2 cups of sugar 0.25 stick of butter

Answer:

$2z + b \le 9$

$2z + 3b \le 15$

Step-by-step explanation:

Given

$Flour = 15$

$Egg =9$

Since there are enough of other ingredients, we will only consider the amount of eggs and cups of flour.

So, we have:

Zucchini Bread

$Egg = 2$

$Flour = 2$

Banana Bread

$Egg = 1$

$Flour = 3$

For the eggs

The ratio of eggs to use in the Zucchini bread to Banana bread is:

$Egg = 2$ (z) : $Egg = 1$ (b)

This gives:

$2z + 1b$

The total number of eggs cannot exceed 9.

So, the inequality is:

$2z + 1b \le 9$

$2z + b \le 9$

For the flours

The ratio of flours to use in the Zucchini bread to Banana bread is:

$Flour = 2$ (z) : $Flour = 3$ (b)

This gives:

$2z + 3b$

The total cups of flours cannot exceed 15.

So, the inequality is:

$2z + 3b \le 15$

Hence:

The system of inequalities is:

$2z + b \le 9$

$2z + 3b \le 15$

7 0

3 years ago