Evaluate 43 – 3m for m = 6.

Let's consider a right triangle with an angle θ such that sin θ = x. By definition,  To prove the identity cos(sin^⁻¹x) = √(1 - x^2), we can use the properties of trigonometric functions and inverse trigonometric functions.

Let's consider a right triangle with an angle θ such that sin θ = x. By definition, sin^⁻¹x represents the angle whose sine is x. In the triangle, the side opposite to θ has length x, and the hypotenuse has length 1.

Using the Pythagorean theorem, we can find the length of the adjacent side, which is √(1 - x^2). This represents the cosine of the angle θ.

Therefore, we have cos(sin^⁻¹x) = √(1 - x^2), which proves the given identity.

To elaborate further, we can use the definition of sine and cosine in terms of the sides of a right triangle. The sine of an angle θ is defined as the ratio of the length of the side opposite to θ to the length of the hypotenuse. In this case, sin θ = x.

Using the Pythagorean theorem, we find that the length of the adjacent side is √(1 - x^2). This length represents the cosine of the angle θ.

Thus, we have cos(sin^⁻¹x) = √(1 - x^2), demonstrating the validity of the given identity.

Learn more about Pythagorean theorem here:

https://brainly.com/question/14930619

#SPJ11

Answer:

(0,3), graph is attached.

Step-by-step explanation:

We know that the first equation will increase 2 points in y for every 1 x, since the constant next to x is 2. We also know it's y-intercept will be 3.

As for the second equation, we know it will have no y and instead run through the y=3 line, crossing every value of x.

Graphing this, we see that these lines intersect at (0,3) so that's the solution to this system.

Hope this helped!

To find a plane containing the point (-5, 6, -6) and the line defined by parametric equations x(t) = 7 - 5t, y(t) = 3 - 6t, and z(t) = -6 - 6t, we can use the point-normal form of the equation of a plane.

The equation of a plane in point-normal form is given by Ax + By + Cz + D = 0, where (A, B, C) is the normal vector to the plane, and (x, y, z) are the coordinates of a point on the plane. We can determine the normal vector by taking the cross product of two direction vectors in the plane.

The direction vector of the line can be obtained by taking the coefficients of t in the parametric equations, which gives us (-5, -6, -6). We can choose any two non-parallel direction vectors in the plane, for example, (1, 0, 0) and (0, 1, 0). Taking the cross product of these two vectors, we get the normal vector (0, 0, -1).

Now, we can substitute the values of the point (-5, 6, -6) and the normal vector (0, 0, -1) into the point-normal form equation. This gives us 0*(-5) + 0*6 + (-1)*(-6) + D = 0, which simplifies to D = -6. Thus, the equation of the plane containing the point (-5, 6, -6) and the given line is 0*x + 0*y - z - 6 = 0, or simply -z - 6 = 0.

Learn more about point here:

https://brainly.com/question/32083389

#SPJ11

Answer:

4.9,5.0

Step-by-step explanation:

Thier is two open spaces and the decimals are decreasing by 1 tenth. So if 1 tenth is being decreased the order would be 4.9, 5.0, 5.1, 5.2, 5.3, 5.4.

Answer:

4.9, 5 , 5.1 , 5.2 , 5.3 , 5.4

Step-by-step explanation:

5.4-5.3 = 0.1

5.3-5.2 = 0.1

5.2-5.1 = 0.1

then the pattern is : adding 0.1 to the number to get the next number

5.1 - 0.1 = 5

5 - 0.1 = 4.9

The length of side RQ is 13.00 ft.

Given that a triangle RPQ, with sides RP = 8 ft, PQ = 13 ft and angle P between these sides equal to 71°, we need to find the length of side RQ which is opposite to the angle P,

To find the length of side RQ using the cosine rule, we can use the formula:

RQ² = RP² + PQ² - 2 RP PQ Cos(P)

Let's plug in the given values:

RP = 8 ft

PQ = 13 ft

angle P = 71°

Now we can calculate RQ:

RQ² = 8² + 13² - 2 × 8 × 13 × cos(71°)

Using a calculator, we can evaluate the cosine term:

RQ² = 64 + 169 - 208 × cos(71°)

RQ² ≈ 64 + 169 - 208 × 0.3072

RQ² ≈ 64 + 169 - 63.9936

RQ² ≈ 169.0064

Taking the square root of both sides:

RQ ≈ √169.0064

RQ ≈ 13.00 ft (rounded to two decimal places)

Therefore, the length of side RQ is 13.00 ft.

Learn more about cosine rule click;

https://brainly.com/question/30918098

#SPJ1

Answer:

Since

Therefore, option (A) is true.

Step-by-step explanation:

Determining the slope

Given the points

Finding the slope between the points (-8, 1) and (0, 3)

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(\left(x_1,\:y_1\right)=\left(-8,\:1\right),\:\left(x_2,\:y_2\right)=\left(0,\:3\right)\)

\(m=\frac{3-1}{0-\left(-8\right)}\)

\(m=\frac{1}{4}\)

Thus, the slope is 1/4.

Determining the y-intercept

We know that the value of y-intercept can be computed by setting the value x= 0 and determining the corresponding value of y.

From the table, it is clear that

at x=0, y = 3

Thus, the y-intercept is (0, 3)

Since

Therefore, option (A) is true.

Answer:

320/4=8   8 tens /4 tens =2

Step-by-step explanation:

Answer:

the answer is 80/10=8 tens/ 1 ten

Step-by-step explanation:

The inverse of the secant function is the arcsecant function, also known as the inverse secant or the arccosecant.

The secant function is defined as the reciprocal of the cosine function, while the arcsecant function is defined as the inverse of the secant function.

The arcsecant function takes a value as its argument and returns an angle whose secant is equal to the input value. In other words, it answers the question "What angle has a secant equal to x?"

The domain of the arcsecant function is limited to values greater than or equal to 1 and less than or equal to -1. The range of the function is typically limited to values between 0 and pi or between -pi/2 and pi/2, depending on the convention used.

The notation for the arcsecant function is usually "arcsec(x)" or "asec(x)". It is an important mathematical function in trigonometry, and is used in many applications, including physics, engineering, and computer graphics.

To learn more about click trigonometry on,

https://brainly.com/question/1447063

#SPJ4

The Ferris wheel spins steadily at an angle of 4 radians per minute. 2v/80.24 radians per minute is the constant angular speed at which the Ferris wheel turns.

Using the formula: one can determine the Ferris wheel's diameter.

C = 2πr

where r denotes the Ferris wheel's diameter. If we substitute r = 38 feet, we obtain:

C = 2π(38) ≈ 238.76 feet

The Ferris wheel completes one rotation every eight minutes, so the calculation for angular speed is:

ω = θ/t

where t is the time it takes for one rotation to be completed and is the angle in radians at which the Ferris wheel rotates. The angle is equivalent to two radians, or one full rotation, so we have:

Radians per minute Equals 2/8 = 4

As a result, the Ferris wheel spins at a steady rate of /4 radians per minute.

b. The Ferris wheel's circumference can be calculated using the same method as C = 2πr

C = 2π(32) ≈ 201.06 feet

t = sqrt(2πr^2)/v = sqrt(2π(32)^2)/v ≈ 80.24/v

ω = θ/t = 2π/(80.24/v) = 2πv/80.24 radians per minute.

Because of this, the Ferris wheel spins at a constant rate of 2 v/80.24 radians per minute.

Learn more about speed here:

https://brainly.com/question/28224010

#SPJ4

Answer:

Its equal 3

Step-by-step explanation:

because x+3 = 3 because x is 0 so that means that 0+3=3 so y is 3 trust me

Answer:

let y =3

then y= x+3

3= x+3

3-3 =x

x =0 at x = 0 the value of y = 3

let x = -3

y = x +3

y = -3+3

y= o

In order to calculate the length of the third side, let's use the law of cosines:

Now, let's calculate angle A using law of sines:

Since the sum of internal angles in any triangle is equal to 180°, we have:

Therefore the answer is option A:

A = 44.9°, C = 30.4°, b = 11.41 m

Answer: C

Step-by-step explanation:

The value of the function at x = 0 represents the cost of a drink and 1 ounce of yogurt. The correct answer would be an option (C).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation is given in the question, as follows:

y = 0.50x + 2.25   .....(i)

It can model the total cost of Maddie's purchases, the frozen yogurt x is priced by the ounce.

Substitute the value of x = 0 in equation (i), and we get

y = 0.50(0) + 2.25

y = 2.25

So, the value of the function at x = 0 represents the cost of a drink and 1 ounce of yogurt.

Thus, the correct answer would be option (C).

Learn more about the equation here:

brainly.com/question/10413253

#SPJ2

Answer:

Around $988.40

Step-by-step explanation:

For a single alveolus requires the surface area of 0.133 square meters for gas exchange.

In this question, we have been given each human lung contains about 300 million alveoli with a summed total surface area for gas exchange of 40 square meters.

we need to find  the approximate surface area of a single alveolus.

By unitary method the required surface area would be,

A = 40/300

A = 10/75

A = 0.133 square meters

Therefore, the approximate surface area of a single alveolus = 0.133 square meters

Learn more about unitary method here:

https://brainly.com/question/22056199

#SPJ4

Answer:

why did this get taking down?

Answer:

$ 7.29

Step-by-step explanation:

bill = $40.50

tip = 18%

tip amount = tip% of bill

=18/100 * $40.50

=729/100

=$ 7.29

Answer:

7.29 DOLLARS IS THE ANSWER

The expression 2^7 times 19 can be simplified by first evaluating the exponential term, 2^7, which is equal to 128. Therefore:2^7 times 19 = 128 * 19We can then evaluate the product of 128 and 19 using multiplication. When we do that, we get:2^7 times 19 = 2432Therefore, the choice that is equivalent to the expression 2^7 times 19 is 2432

(a) The slope is 6.

(b)the rate of change is 6 hundred pounds per inch of rain.

(c)When 0 inches of rain fall, 4 hundred pounds of tomatoes are harvested.

(a) The slope of the line defined by the equation is the coefficient of x, which is 6.

(b) The rate of change of the function represents how the quantity of tomatoes harvested changes with respect to the amount of rain. In this case, the rate of change is 6 hundred pounds per inch of rain.

(c) Evaluating f(0) means substituting x = 0 into the function. Therefore, we have:

f(0) = 6(0) + 4 = 0 + 4 = 4

The interpretation for f(0) is: When 0 inches of rain fall, 4 hundred pounds of tomatoes are harvested.

To learn more about slope visit:

brainly.com/question/3605446

#SPJ11

Answer:

480 g of cereal ...........

The probability that client D will be able to live to be 59 years old is 0.4.

Youe information is incomplete. Therefore, an overview of probability will be given.

Let's assume that there is an entire population of 50 people and the number of those that lives to 59 years is 20.

Therefore, the probability that can be deduced of those that live to 59 years will be:

= 20/50 × 100

= 2/5 × 100.

= 40%

= 0.4

In conclusion, the probability is 0.4.

Learn more about probability on:

https://brainly.com/question/24756209

Answer:

parrellograms

Step-by-step explanation:

Answer:

blurr...

Step-by-step explanation:

Answer:

D. 68+(6x+4)=180

x = 18

Step-by-step explanation:

"Supplementary angles" are angles that add up to 180°

So we add the twi angles 68+(6x+4) and that equals to 180°.

68 + 6x + 4 = 180

add 68 and 4

72 + 6x = 180

subtract 72.

6x = 108

divide by 6.

x = 18

Answer:

A=-1, B=2

Step-by-step explanation:

2a + 3b=4 equation 1

a-b=-3 equation 2

a=-3+b isolate a in equation 2

2(-3+b) + 3b=4. Substitute value of a in equation 2 (-3+b) into a value of  equ 1

-6+2b+3b=4

5b=10

b=2

solve for a:

a-b=-3

a-(2)=-3

a-2=-3

a=-1

The Laplace equation is defined as Au=0. The aim is to solve analytically Laplace's equation in the square [0, 1]²2 with boundary conditions u(x,0) = 0 = u(0, y), u(x, 1) = u(1, y) = 1.

Let's consider the Laplace equation as followsAu = ∂²u/∂x² + ∂²u/∂y²= 0Given boundary conditions areu(x, 0) = 0u(0, y) = 0u(x, 1) = u(1, y) = 1The solution of the Laplace equation is as followsu(x,y) = X(x).Y(y)Let's find the boundary conditionsu(x, 0) = 0

Let's substitute the value of Y(0) in the solution to get X(x).Y(0) = 0, which implies Y(0) = 0Similarly, u(0, y) = 0 => X(0).Y(y) = 0 => X(0) = 0Now, let's find the remaining boundary conditionsu(x, 1) = 1X(x).Y(1) = 1 => Y(1) = 1/X(x)u(1, y) = 1 => X(1).Y(y) = 1 => X(1) = 1/Y(y)Now, let's put the values of X(0) and X(1) in the below equationX(0) = 0, X(1) = 1/Y(y)X(x) = x

Now, let's put the values of Y(0) and Y(1) in the below equationY(0) = 0, Y(1) = 1/X(x)Y(y) = sin(n.π.y) /sinh(n.π)Therefore, the solution of Laplace's equation u(x, y) is as follows;u(x,y) = Σ(n=1 to ∞)sin(n.π.y).sinh(n.π.x) /sinh(n.π)Answer:Therefore, the solution of Laplace's equation u(x, y) is u(x,y) = Σ(n=1 to ∞)sin(n.π.y).sinh(n.π.x) /sinh(n.π).

To know more about Laplace equation visit

https://brainly.com/question/31583797

#SPJ11

The linear function in this problem is given as follows:

y = -1/4x + 5.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

What differentiates a linear function from the other functions is the variable x has an exponent of 1.

2x + 7 = 12 is not a function, as it does not have the y variable, it is an equation.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Answer:10 square units

Step-by-step explanation:

To find the area use the formula: l*h or count the amount of squares in the rectangle

Answer:

-true

-false

-true

-true

Answer:

true ,false,true,false

Step-by-step explanation:

60 for a family of five that means 12x5