Use Pythagorean Theorem and/or Quotient theorem to find the remaining five trigonometric functions, given that tan θ = 4/3 and θ in quadrant II.

Answer:

on seconded I will come back and edit my answer

The implicit solution to the given differential equation Dx/dt = 4x² + (9t/√(6²+x²)) / (4tx) using the method for solving homogeneous equations is F(t,x) = C, where C is an arbitrary constant.

To solve the given differential equation, we can separate the variables and integrate both sides. Rearranging the equation, we have:

(4tx) Dx = (4x² + (9t/√(6²+x²))) dt. Next, we integrate both sides. Integrating the left side with respect to x and the right side with respect to t, we get:

∫(4tx) Dx = ∫(4x² + (9t/√(6²+x²))) dt. Integrating both sides will result in a function F(t,x) on the left side and the integral on the right side. Since we are looking for an implicit solution in the form F(t,x) = C, we can write the equation as:

F(t,x) = C. cccThis represents the general solution to the given differential equation, where C is an arbitrary constant. The specific form of the function F(t,x) will depend on the integration process and the initial conditions, if provided.

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Answer: 60.84mm

Step-by-step explanation:

The area of Triangle is:

A = 1/2 * base * height

7.8mm * 3mm = 23.4mm

23.4mm * 1/2
= 11.7mm

Now, find the area of the rectangle:

A = Base * Height

9.3mm * 7.8mm = 72.54mm

Now subtract the area of the triangle from the area of the rectangle

72.54mm - 11.7mm = 60.84mm

Answer:

6 pounds

Step-by-step explanation:

Answer:

beat your meat??? also you are bad!!!!

Step-by-step explanation:

Answer:i think the anwser is 6

Step-by-step explanation:

The area of the surface defined by z = xy and x2 + y2 ≤ 22 would be, Area = ∬ sqrt(1 + r^2) * r dr dθ, with limits 0 ≤ r ≤ sqrt(2) and 0 ≤ θ ≤ 2π.Evaluate the integral to get the area of the surface.

To find the area of the surface defined by z = xy and x^2 + y^2 ≤ 2, we need to use a double integral over the region bounded by the inequality x^2 + y^2 ≤ 2.

First, we should rewrite the inequality in polar coordinates: x^2 + y^2 ≤ 2 becomes r^2 ≤ 2, where r is the radial distance and θ is the angle. This means 0 ≤ r ≤ sqrt(2) and 0 ≤ θ ≤ 2π.

Next, we find the Jacobian for the polar coordinates, which is |J(r,θ)| = r.

Now, we need to compute the magnitude of the gradient of z = xy in terms of polar coordinates. The gradient of z is given by the partial derivatives:

∂z/∂x = y and ∂z/∂y = x

In polar coordinates, x = r*cos(θ) and y = r*sin(θ). So, we have:

∂z/∂r = cos(θ)*∂z/∂x + sin(θ)*∂z/∂y = r*cos^2(θ) + r*sin^2(θ) = r

Now, we use the double integral to find the surface area:

Area = ∬ sqrt(1 + (∂z/∂r)^2) * |J(r,θ)| dr dθ

Area = ∬ sqrt(1 + r^2) * r dr dθ, with limits 0 ≤ r ≤ sqrt(2) and 0 ≤ θ ≤ 2π.

Evaluate the integral to get the area of the surface.

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Answer:

Adding 12 to the circle area is equal to the square area.

Or

s2 = 12 + A

Where

s = side of square

A = area of circle

So

s2 = 12 + 36

s2 = 48

Solve this for s to get the side length

Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

The number of ball bearings that can be made based on the volume will be 10 ball bearings.

It should be noted that the volume based on the information given will be:

V = 4/3πr³

= 4/3 × 3.14 × 0.5³

= 0.524

From the information, it takes 5.24 cubic centimeters of molten steel to have a diameter of 1 centimeter.

Therefore, the number of ball bearings will be:

= 5.24/.0524

= 10

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The step 1 will process with beginning, mapping, and optimising. The step 2 will includes matrices calculation, creating control chart and analysis.

The steps to be followed for step 1 are as follows-

Begin with value identification which is the creation of word document. Map the value stream to remove redundant activites followed by waste elimination. Then work on to improve the efficiency by using templates, headers, using keyboard shortcuts and enabling autosave.

To proceed to step 2 and check if the process could benefit from other tools, consider these three actions: 1. Calculating the metrices that includes variation and process capability. 2. Formulate the control chart for process. 3. Analyse the metrices and control chart via the SPC method.

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Answer:

Step-by-step explanation:

for (i = 0; i < dataPoints.size(); ++i) {

     if (dataPoints.at(i) > maxVal) {

        dataPoints.at(i) = dataPoints.at(i) - 4;

     }

  }

Answer:

see explanation

Step-by-step explanation:

x = 65° ( vertically opposite angles )

y = 71° ( alternate angles )

The sum of the 3 angles in a triangle = 180° , then

x + y + z = 180° , that is

65° + 71° + z = 180°

136° + z = 180° ( subtract 136° from both sides )

z = 44°

So x = 65°, y = 71° , z = 44°

750 bikes would be sold for $350

Let x represent the number of bikes sold per month and y represent the price.

550 bikes are sold at a price of $250, this can be represented by (550, 250). Also, 750 bikes is sold at a price of $150, hence it is represented by (750, 150)

A linear function is represented by:

y = mx + b

m is the slope, b is the y intercept.

Therefore the function is:

\(y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-250=\frac{150-250}{750-550} (x-550)\\\\y=\frac{1}{2}x-25\)

The number of bikes sold for $350 is:

350 = (1/2)x - 25

x = 750

Therefore 750 bikes would be sold for $350

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Answer:

I believe the answer is A

Step-by-step explanation:

three times x can be equal to, but never greater than -6

Answer:

A. 3x ≤ -6

Step-by-step explanation:

the sentence ‘3x is at most -6

means that the most 3x is allowed to be is -6

it can be -6 or any number less than -6

So, the phrase 3x is at most -6

’ means ‘

3x ≤ -6

Answer:

59

Step-by-step explanation:

all triangles add up to 180 degrees.

add 87+34=121

do 180-121=59 because you want to find the value of x

to check your work add up all of the degrees together and when you get 180 you will be correct!

Answer:

x=59

Step-by-step explanation:

87+x+34=180 because its a straight line

121+x=180

x=59

Answer:

72.9

Step-by-step explanation:

1) Line X and Z is the opposite, line X, Y is the adjacent

2) With this, we can use tangent to calculate the size of the angle

3) We need to inverse tan to find the angle, so on your calculator type:

tan^-1 (13/4)

= 72.89

1 decimal place = 72.9

The size of angle XYZ is 72.9

a. ln(7x) can be expanded as ln(7) + ln(x). b. ln(x + 3) remains as it is, since it cannot be simplified further. c. ln(x^8) can be expanded as 8ln(x). d. 15,000ln(xy^4) can be expanded as ln(x) + 4ln(y) + ln(15,000).

a. To expand the logarithmic expression ln(7x), we can use the property of the natural logarithm that states ln(ab) = ln(a) + ln(b).

Therefore, ln(7x) can be expanded as ln(7) + ln(x).

b. Similarly, the logarithmic expression ln(x + 3) can be expanded using the property ln(ab) = ln(a) + ln(b).

Hence, ln(x + 3) remains as it is since we cannot simplify it further.

c. Expanding the logarithmic expression ln(x^8) can be done using the property ln(a^b) = b * ln(a).

Thus, ln(x^8) becomes 8 * ln(x).

d. Expanding the logarithmic expression 15,000ln(xy^4) can be done by applying the property ln(ab) = ln(a) + ln(b).

Therefore, 15,000ln(xy^4) can be expanded as 15,000[ln(x) + ln(y^4)].

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Answer:

\(8\sqrt{3}\) \(\text{in.}\)

Step-by-step explanation:

60 · 60 · 60

60³ = 180

Diameter - 8

3 sides, diameter 8 = answer.

Answer:

D) \(4\sqrt{3}\)

Step-by-step explanation:

\(x = \sqrt{8^{2} - 4^{2} } = \sqrt{48}= \sqrt{4*16}= 4\sqrt{3}\)

Note that the function takes the trapezoid's area as input and returns as output the length of the other base is A(x)/7-5=x.

Recall that the function for the trapezoid area is:

A(x)=(B+b)*h/2

where

B and b are the bases and

h is the height.

Thus, given a height of 14 and one base length of 5 with the length of its other base

With the given data: h=14 B and b =5 and x (it may vary which one is bigger)

So that function becomes:

A(x)=(5+x) * 14/2

A(x)=(5+x)*7

So if you want the inverse function, you have to operate to find x:

A(x)/7=5+x

A(x)/7-5=x

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SOLUTION

Consider the given coordinates

Since the angle given is negative, we move in the clockwise direction

Henece

Moving in the clockwise direction, the angle 315 falls in the first quadrant.

Then, -3 will be to move to the third quadrant,

hence the right option will be

Answer:

680

Step-by-step explanation:

. hope this helpsssssssssssss

The volume of the largest rectangular box in the first octant with three faces in the coordinate planes, and one vertex in the plane is V = xyz, where x, y, and z are the lengths of the sides of the rectangular box.

To find the largest volume, we need to maximize x, y, and z. Since we have three faces in the coordinate planes, one vertex will be at the origin (0, 0, 0). The other two vertices will lie on the coordinate axes.

Let's assume the vertex on the x-axis is (x, 0, 0), and the vertex on the y-axis is (0, y, 0). The third vertex on the z-axis will be (0, 0, z). Since the box is in the first octant, all the coordinates must be positive.

To maximize the volume, we need to find the maximum values for x, y, and z within the constraints. The maximum values occur when the box touches the coordinate planes. Therefore, the maximum values are x = y = z.

Substituting these values into the volume formula, we get V = xyz = x³. Therefore, the volume of the largest rectangular box is V = x³.

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What is the maximum volume of a rectangular box situated in the first octant, with three of its faces lying on the coordinate planes, and one of its vertices located in the plane?

Answer:

c

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

T = temperature

-52 < T < 108

Temperatures fall between the values of -52 and 108.  D is the number line that shows this.

Answer:

B

Step-by-step explanation:

Here, we want to calculate the square root of -√- (75)

That will be

-√(25)(-3)

= -5 √(-3)

√(-3) is same as 3i

So we have the root as;

-5i√3

The length of the rectangle is approximately 41.34 inches.

Let's assume the width of the rectangle is represented by the variable w. According to the given information, the length of the rectangle is four less than twice the width, which can be expressed as 2w - 4.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 128 inches. Since a rectangle has two pairs of equal sides, we can set up the equation:

2w + 2(2w - 4) = 128.

Simplifying the equation, we get:

2w + 4w - 8 = 128,

6w - 8 = 128,

6w = 136,

w = 22.67.

So, the width of the rectangle is approximately 22.67 inches. To find the length, we can substitute this value back into the expression 2w - 4:

2(22.67) - 4 = 41.34.

Therefore, the length of the rectangle is approximately 41.34 inches.

In summary, the length of the rectangle is approximately 41.34 inches. This is determined by setting up a system of equations based on the given information: the perimeter of the rectangle being 128 inches and the length being four less than twice the width.

By solving the system of equations, we find that the width is approximately 22.67 inches, and substituting this value back, we obtain the length of approximately 41.34 inches.

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Amir’s gas tank had 1L of gas in it. Then he drove to his cousin’s house and back and had 1/3 L left.  Amir used a total of 1/3L gas in each direction

From the question, we have the following parameters that can be used in our computation:

Initial amount = 1L

Remaining amount = 1/3L

The amount of gas he used in each direction is calculated as

Amount used in each direction =(Initial amount - Remaining amount)/2

Substitute the known values in the above equation, so, we have the following representation

Amount used in each direction =(1L - 1/3L)/2

Evaluate

Amount used in each direction =1/3L

Hence, the amount is 1/3L

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Here is the complete question:

Amir’s gas tank had 1L of gas in it. Then he drove to his cousin’s house and back and had 1/3 L left. How much gas did he use in each direction?

Answer: 5 more!

Step-by-step explanation:

Due to the lack of numbers your could do about 4 - 5 more security numbers!

Answer:

I think 81

Step-by-step explanation:

I'm not too sure since 9 x 9 is 81 but im not sureeee

Answer:

y = 3

Step-by-step explanation:

Answer : 2..A perfect square is an integer which is the square of another integer n , that is, n2 . (Since a negative times a negative is positive, a perfect square is always positive.

...

9514 1404 393

Answer:

  a = (s +t)/(m +r)

Step-by-step explanation:

Add t, then divide by the coefficient of 'a'.

  \(a(m+r)-t=s \qquad\text{given}\\\\a(m+r)=s+t \qquad\text{add $t$}\\\\\boxed{a=\dfrac{s+t}{m+r}} \qquad\text{divide by $m+r$}\)