Simplify the following functions using the Karnaugh Map method and obtain all possible minimized forms of the function. I Function 1 - Minimized SOP form (6 possible functions) F(a,b,e,d)=2m(0,1,3,4,6,7,8,9,11,12, 13, 14, 15) Function 2 - Minimized POS form (3 possible functions) F(a,b,c,d,e)=2m (4,5,8,9,12,13,18,20,21,22,25,28,30,31) Submit the following: 1. All grouped and labelled K-Maps of Function 1 2. All minimized SOP forms of Function 1 3. All grouped and labelled K-Maps of Function 2 4. All minimized POS forms of Function 2

Answer:

correct bayan HAHAHAHAHAHA

With pupils of 8 mm in diameter at night, a woman will be able to distinguish the headlights of a car facing her that are approximately 2.37 kilometers apart.

The ability to resolve or distinguish two closely spaced objects is determined by the angular resolution of the human eye. Angular resolution refers to the smallest angle between two points that can be distinguished as separate entities. In this case, we can calculate the angular resolution using the formula: angular resolution = 1.22 * (wavelength / diameter), where the wavelength of visible light is typically around 550 nm.

Given that the woman's pupils have a diameter of 8 mm, we can convert this to meters (0.008 m). Plugging in the values, we get the angular resolution = 1.22 * (550 nm / 0.008 m). Simplifying this, we find the angular resolution is approximately 0.084 radians.

To determine the distance at which the woman can distinguish the headlights of a car, we can use the formula: distance = size / angular resolution, where the size represents the physical separation between the headlights. Assuming the car's headlights are spaced 2 meters apart, we have distance = 2 m / 0.084 radians, which equals approximately 23.81 meters.

Since the question asks for the answer in kilometers, we divide the distance by 1000, giving us approximately 0.02381 kilometers, which can be rounded to 0.024 kilometers or 24 meters. Therefore, the woman will be able to distinguish the car's headlights from each other when the car is approximately 2.37 kilometers away.

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Answer:

Step-by-step explanation:

Change 2 to 2/1, then multiply the top and bottom by 4 so it has the same denomiator as the 1/4.

\(\frac{1}{4} -\frac{8}{4} =-\frac{7}{4}\)

Answer:

-1 3/4

Step-by-step explanation:

Make the denominator the same

2 = 8/4

1/4 - 8/4 = -7/4 (mixed number: -1 3/4)

The difference between the two confidence intervals is given as follows :

Width of confidence interval is directly proportional to confidence level.

This is because,  width is directly proportional to critical value (z or t), which is directly proportional to confidence level.

Now, width is inversely proportional to square root of sample size.

But if sample size is same for both levels of confidence. Then, sample size would have same effect.

Hence, the appropriate answer here is,

The 95 percent confidence interval will not be as wide as the 99 percent confidence interval.

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Answer:

\(110\)°

Step-by-step explanation:

\(A+B+C=180\)

\(48+28+C= 180\)

\(70+C=180\)

subtract \(70\) form both sides

\(C= 180\)

plz mark me brainliest. :0

Answer:

that would be

x+2x+42=180

3x+42=180

-42. -42

3x=138

______

3

x=46

Using the cosine rule, the distance the plane has flown during Jack's phone call can be calculated by taking the square root of the sum of the squares of the initial and final distances, minus twice their product, multiplied by the cosine of the angle difference.

To determine the distance the plane has flown during Jack's phone call, we can use the cosine rule in trigonometry.

The cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

Let's denote the initial distance from Jack to the plane as d1 and the final distance as d2.

We know that the altitude of the plane remains constant at 2400 meters.

According to the cosine rule:

\(d^2 = a^2 + b^2 - 2ab \times cos(C)\)

Where d is the side opposite to the angle C, and a and b are the other two sides of the triangle.

For the initial angle of elevation (70°), we have the equation:

\(d1^2 = (2400)^2 + a^2 - 2 \times 2400 \times a \timescos(70)\)

Similarly, for the final angle of elevation (50°), we have:

\(d2^2 = (2400)^2 + a^2 - 2 \times 2400 \times a \times cos(50)\)

To find the distance the plane has flown, we subtract the two equations:

\(d2^2 - d1^2 = 2 \times 2400 \times a \times (cos(70) - cos(50))\)

Now we can solve this equation to find the value of a, which represents the distance the plane has flown.

Finally, we calculate the square root of \(a^2\) to find the distance in meters.

It's important to note that the angle of elevation assumes a straight-line path for the plane's movement and does not account for any changes in altitude or course adjustments that might occur during the phone call.

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Step-by-step explanation:

6/√3×√3/√3=6√3\√3

because √3×√3=3 hope you are not confused pls follow

Answer:

2√3

Step-by-step explanation:

because yes

You should pay approximately $10,117.09 initially to secure the annuity and receive annual payments of $1500 over the 9-year period.

To find the cost of the annuity, we need to calculate the present value of the future payments. The present value represents the current worth of future cash flows, taking into account the interest earned or charged over time. In this case, we'll calculate the present value of the $1500 payments using compound interest.

The formula to calculate the present value of an annuity is:

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

Where:

PV is the present value of the annuity (the amount you should pay initially)

PMT is the payment amount received annually ($1500 in this case)

r is the interest rate per period (6.28% or 0.0628)

n is the total number of periods (9 years)

Let's substitute the values into the formula:

PV = $1500 × [1 - (1 + 0.0628)⁻⁹] / 0.0628

Calculating this expression:

PV = $1500 × [1 - 1.0628⁻⁹] / 0.0628

PV = $1500 × [1 - 0.575255] / 0.0628

PV = $1500 × 0.424745 / 0.0628

PV ≈ $10117.09

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Answer:

35*7=$245

Step-by-step explanation:

The statement is true. If f is continuous on [0, ∞) and the improper integral ∫₀^∞ f(x) dx is convergent, then the integral ∫₀^∞ f(f(x)) dx is also convergent.

To understand why the statement is true, we can use the concept of substitution in integrals. Let u = f(x). If we substitute u for f(x), then the differential du becomes f'(x) dx. Since f is continuous on [0, ∞), f' is also continuous on [0, ∞).

Now, consider the integral ∫₀^∞ f(f(x)) dx. Using the substitution u = f(x), we can rewrite the integral as ∫₀^∞ f(u) (1/f'(x)) du. Since f'(x) is continuous and non-zero on [0, ∞), 1/f'(x) is also continuous on [0, ∞).

Since ∫₀^∞ f(u) (1/f'(x)) du is the product of two continuous functions, and the integral ∫₀^∞ f(x) dx is convergent, it follows that ∫₀^∞ f(f(x)) dx is also convergent. Therefore, the statement is true.

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Answer:

4,050 ft^3

Step-by-step explanation:

Separate the figure into a cube and a square pyramid.

Volume of the cube (a^3):

15 x 15 x 15 = 3,375

3,375 ft^3

Volume of the square pyramid (lwh/3):

15 x 15 x 9/3 = 675

675 ft^3

Add the volumes of both figures:

675 ft^3 + 3,375 ft^3 = 4,050

The volume of the whole figure is 4,050 cubic feet.

Hope this helps!

In given triangle ABC the length if BC is 7.1 .

What is trigonometric functions?

A subfield of mathematics called trigonometry is concerned with the study of triangles. It is frequently referred to as "trig" casually. In trigonometry, mathematicians look at how triangles' sides and angles relate to one another.

Here in given triangle contains 90°, So it is right triangle.

Now using tangent function then

=> tan B = \(\frac{opposite}{adjacent}\) then

=> tan 38° = \(\frac{AC}{BC}\)

=> BC = tan 38° × AC

=> BC = tan 38° × 9.1

=> BC = 7.1

Hence the length of the side BC is 7.1.

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The length of BC in the triangle ABC is 7.109.

Trigonometry is a branch of mathematics concerned with the study of triangles. It is commonly referred to as "trig" in a casual manner. Trigonometry examines how the sides and angles of triangles relate to one another.

Because the given triangle contains 90°, it is a right triangle.

Now, using the tangent function,

The tangent function is one of trigonometry's six primary functions.

Tan A = Opposite Side/Adjacent Side is the Tangent Formula. In terms of sine and cosine, tangent may be represented as: Tan A = Sin

then,

= tan B = opposite side / adjacent side

= tan 38° = AC/BC

= BC = 38° tan x AC

= BC = tan 38° × 9.1

= BC = 7.109

As a result, the length of the side BC is 7.109.

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a)  False - The consequent (2 + 2 = 5) does not hold true when the condition (1 + 1 = 2) is satisfied.

b)  False - Neither the condition (1 + 1 = 3) nor the consequent (2 + 2 = 4) is true.

c)  False - The consequent (2 + 2 = 5) does not follow when the condition (1 + 1 = 3) is met.

d)  True - Since the condition (monkeys can fly) is false, the statement (1 + 1 = 3) holds true due to the structure of the conditional statement.

In the given conditional statements, we need to determine whether each statement is true or false based on the provided conditions.

a) If 1 + 1 = 2, then 2 + 2 = 5. This statement is false because the initial condition (1 + 1 = 2) is true, but the consequent (2 + 2 = 5) is false. In mathematics, if the condition is true, the consequent should also be true, but in this case, it is not.

b) If 1 + 1 = 3, then 2 + 2 = 4. This statement is false because both the condition (1 + 1 = 3) and the consequent (2 + 2 = 4) are false. The initial condition is not satisfied, so the statement cannot be true.

c) If 1 + 1 = 3, then 2 + 2 = 5. This statement is false for the same reason as statement a) - the initial condition is true, but the consequent is false.

d) If monkeys can fly, then 1 + 1 = 3. This statement is true because it follows the structure of a conditional statement where the condition (monkeys can fly) is false, and therefore the statement is always true.

In summary, statement a), b), and c) are false, while statement d) is true.

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Answer: 50pi or about 157

Step-by-step explanation: Find the distance between the two points using the Pythagorean theorem, and since that is the radius double it to get the diameter, then multiply that by pi to get the answer. Hope this helps!

Answer:

Circumference ~ 157

Step-by-step explanation:

Use the distance formula to find the radius. The radius is 25. Plug 25 into the formula 2(pi)r to get 50pi or about 157.

Answer:

y=1152

Step-by-step explanation:

18 x 64 hope I was helpfull

Answer:

Below

Step-by-step explanation:

To complete the square, the leading x^2 coefficient needs to be = 1 , so factor out a 3 to get

y = 3 ( x^2 + 5/3x )   +3                (I assumed it was a + sign between the terms)

 Then take 1/2 of the 5/3   ( 5/6 )  , square it  (25/36) , add it to the parentheses.... then subtract the amount you added (3 * 25/36) by doing this.....  to have this :

y = 3 ( x^2 + 5/3 x + 25/36)  -   3 * 25/36   +3      then simplify to

y = 3 ( x + 5/6)^2  + 11/12               Done.

The statement "System analysts define an object's attributes during the systems design process" is true because  defining object attributes is an essential part of the systems design process to ensure that the system meets the desired functional requirements.

In systems design, objects are used to represent real-world entities that are relevant to the system being developed. These objects have attributes that describe their characteristics or properties, which are used to identify and manipulate them within the system. System analysts define these attributes during the systems design process to ensure that the system meets the desired functional requirements.

For example, in a library system, a book object may have attributes such as title, author, publisher, and ISBN. Defining these attributes helps ensure that the system can properly manage and retrieve books as needed. Object-oriented design is a popular approach to systems design that relies heavily on defining objects and their attributes.

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Answer:

5

Step-by-step explanation:

im not sure

Answer:

-27 °C

Step-by-step explanation:

-15 -12 = -27

The value of F(x) = V² + 11, F(5) = V² + 11, F'(5) = 10V and F''(5) = 10(dV/dx).

Given Function:F(x) = V² + 11(a) F(5) = V² + 11We can find the value of F(5) by simply substituting the value of x = 5 in the given function F(x)So, F(5) = V² + 11(b) F'(5) = 2V (Differentiation of F(x) w.r.t x)Differentiation of F(x) w.r.t x is given by:F'(x) = 2V(dV/dx)Now, we know that F'(5) = 2V(5) = 10V (As F'(x) = 2V)Therefore, F'(5) = 10V(c) F''(5) = 2(dV/dx)Differentiation of F'(x) w.r.t x is given by:F''(x) = 2(dV/dx)(d²V/dx²)Now, we know that F''(x) = 2(dV/dx)So, F''(5) = 2(dV/dx)(5) = 10(dV/dx) (As F''(5) = 2(dV/dx))Therefore, F''(5) = 10(dV/dx)So, the final answers are as follows:(a) F(5) = V² + 11(b) F'(5) = 10V(c) F''(5) = 10(dV/dx)

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\(\frac{3}{5}\) is the score of Jonathan.

Percentage, which may also be referred to as percent, is a fraction of a number out of 100%. Percentage means "per 100" and denotes a piece of a total amount.

To calculate the percentage , Use the percentage formula:

\(X * \frac{Percentage}{100} = Y\)

According to the question:

Sarah scored on the spelling test  = \(\frac{8}{10}\)

Jonathan scored  = 75%

By formulating both the values;

\(\frac{8}{10} * \frac{75}{100}\)

= \(\frac{3}{5}\)

Therefore , \(\frac{3}{5}\) is the score of Jonathan.

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Answer:

2x

Step-by-step explanation:

an even number is a number EXACTLY divisible by 2

therefore if x is an even number the next is X times 2 which is 2x

Answer:

x+2

Step-by-step explanation:

Main Answer:The points on the given curve where the tangent line is horizontal are (8, 0), (-8, π), (8, 2π), (-8, 3π), and so on and the Vertical tangent  are (0, π/2), (0, 3π/2), (0, 5π/2),so on.

Supporting Question and Answer:

How do we find points on a curve where the tangent line is horizontal or vertical?

To find points on a curve where the tangent line is horizontal or vertical, we need to determine the values of θ (or any parameter) that correspond to those points. This can be done by analyzing the derivatives of the curve equation and identifying the conditions under which the derivative is zero or undefined. Horizontal tangent lines occur when the derivative with respect to θ is zero, while vertical tangent lines occur when the derivative with respect to r is undefined or infinite.

Body of the Solution:To find the points on the curve r = 8 cos θ where the tangent line is horizontal or vertical, we need to determine the values of θ that correspond to those points.

  Differentiating r = 8 cos θ with respect to θ, we get:

dr/dθ = -8 sin θ

Setting dr/dθ = 0, we have:

-8 sin θ = 0

Since sin θ = 0 when θ is an integer multiple of π, the values of θ that give a horizontal tangent line are: θ = 0, π, 2π, 3π, ...

For each value of θ, we can find the corresponding value of r by substituting it back into the equation r = 8 cos θ.

   Differentiating r = 8 cos θ with respect to r, we get:

dθ/dr = -1 / (8 sin θ)

For a vertical tangent line, sin θ must be equal to zero, which occurs when θ is an integer multiple of π.

Therefore, the values of θ that give a vertical tangent line are: θ = π/2, 3π/2, 5π/2, ...

Again, for each value of θ, we can find the corresponding value of r by substituting it into the equation r = 8 cos θ.

Combining the values of θ and their corresponding values of r, we have: Horizontal tangent: (8, 0), (-8, π), (8, 2π), (-8, 3π), ... Vertical tangent: (0, π/2), (0, 3π/2), (0, 5π/2), ...

Final Answer:Thus, the points on the given curve where the tangent line is horizontal are (8, 0), (-8, π), (8, 2π), (-8, 3π), and so on, while the points where the tangent line is vertical are (0, π/2), (0, 3π/2), (0, 5π/2), and so on.

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The points on the given curve where the tangent line is horizontal are (8, 0), (-8, π), (8, 2π), (-8, 3π), and so on and the Vertical tangent  are (0, π/2), (0, 3π/2), (0, 5π/2),so on.

To find points on a curve where the tangent line is horizontal or vertical, we need to determine the values of θ (or any parameter) that correspond to those points. This can be done by analyzing the derivatives of the curve equation and identifying the conditions under which the derivative is zero or undefined. Horizontal tangent lines occur when the derivative with respect to θ is zero, while vertical tangent lines occur when the derivative with respect to r is undefined or infinite.

To find the points on the curve r = 8 cos θ where the tangent line is horizontal or vertical, we need to determine the values of θ that correspond to those points.

Horizontal tangent line: A horizontal tangent line occurs when the derivative of r with respect to θ is equal to zero.

 Differentiating r = 8 cos θ with respect to θ, we get:

dr/dθ = -8 sin θ

Setting dr/dθ = 0, we have:

-8 sin θ = 0

Since sin θ = 0 when θ is an integer multiple of π, the values of θ that give a horizontal tangent line are: θ = 0, π, 2π, 3π, ...

For each value of θ, we can find the corresponding value of r by substituting it back into the equation r = 8 cos θ.

Vertical tangent line: A vertical tangent line occurs when the derivative of θ with respect to r is undefined or infinite.

  Differentiating r = 8 cos θ with respect to r, we get:

dθ/dr = -1 / (8 sin θ)

For a vertical tangent line, sin θ must be equal to zero, which occurs when θ is an integer multiple of π.

Therefore, the values of θ that give a vertical tangent line are: θ = π/2, 3π/2, 5π/2, ...

Again, for each value of θ, we can find the corresponding value of r by substituting it into the equation r = 8 cos θ.

Combining the values of θ and their corresponding values of r, we have: Horizontal tangent: (8, 0), (-8, π), (8, 2π), (-8, 3π), ... Vertical tangent: (0, π/2), (0, 3π/2), (0, 5π/2), ...

Thus, the points on the given curve where the tangent line is horizontal are (8, 0), (-8, π), (8, 2π), (-8, 3π), and so on, while the points where the tangent line is vertical are (0, π/2), (0, 3π/2), (0, 5π/2), and so on.

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Answer:

You multiply each term inside the parentheses by -1 in order to subtract each term, since subtraction is the additive inverse.

Step-by-step explanation:

Subtraction is the additive inverse. We multiply each term in parentheses by -1  in order to open the parentheses and start adding the resulting terms.

Answer:

3

Step-by-step explanation:

3-9=-6 but absolute is 6

The value of integration ∫ 26/[(x - 1)(x² + 25)] is:

 - ln(x² + 25)/2] - arctan(x/5)/5 + ln(|x - 1|) + C

We need to find the value of integration ∫ 26/[(x - 1)(x² + 25)] dx

∫ 26/[(x - 1)(x² + 25)] dx

= 26  ∫ 1 / [(x - 1)(x² + 25)] dx          ............(1)

Now we solve the integration  ∫ 1 / [(x - 1)(x² + 25)] dx

After partial fraction decomposition we get,

∫ 1 / [(x - 1)(x² + 25)] dx

=  ∫ [(1 / 26(x - 1)) - ((x + 1)/ 26(x² + 25))] dx

Applying linearity we get,

=  ∫ 1 / 26(x - 1) dx -  ∫ (x + 1)/ 26(x² + 25) dx

=  (1/26) ∫ 1/(x - 1) dx -  (1/26) ∫(x + 1)/ (x² + 25) dx

= [ln(x−1)/26] - [ln(x² + 25)/52] - [arctan(x/5)/130]

Substitute this value in (1) we get,

26  ∫ 1 / [(x - 1)(x² + 25)] dx

= - ln(x² + 25)/2] - arctan(x/5)/5 + ln(|x - 1|) + C

where C is the constant of integration

Therefore,   ∫ 26/[(x - 1)(x² + 25)] = - ln(x² + 25)/2] - arctan(x/5)/5 + ln(|x - 1|) + C

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The complete question is:

Evaluate the integral.

(remember to use absolute values where appropriate. use c for the constant of integration.)

∫ 26/[(x - 1)(x² + 25)] dx

Answer:

\(Area_{kite}=736m^2\)

Step-by-step explanation:

There are a few methods to find the area of this figure:

1. kite area formula

2. 2 triangles (one top, one bottom)

3. 2 triangles (one left, one right)

4. 4 separate right triangles.

Recall the formula for area of a kite:  \(Area_{kite}=\frac{1}{2} d_{1}d_{2}\) where d1 and d2 are the lengths of the diagonals of the kite ("diagonals" are segments that connect non-adjacent vertices -- in a quadrilateral, vertices that are across from each other).

If you've forgotten why that is the formula for the area of a kite, observe the attached diagram: note that the kite (shaded in) is half of the area of the rectangle that surrounds the kite (visualize the 4 smaller rectangles, and observe that the shaded portion is half of each, and thus the area of the kite is half the area of the large rectangle).

The area of a rectangle is \(Area_{rectangle}=bh\), sometimes written as \(Area_{rectangle}=bh\), where w is the width, and h is the height of the rectangle.

In the diagram, notice that the width and height are each just the diagonals of the kite.  So, the Area of the kite is half of the area of that surrounding rectangle ... the rectangle with sides the lengths of the kite's diagonals.Hence, \(Area_{kite}=\frac{1}{2} d_{1}d_{2}\)

For our situation, each of the diagonals is already broken up into two parts from the intersection of the diagonals.  To find the full length of the diagonal, add each part together:

For the horizontal diagonal (which I'll call d1): \(d_{1}=40m+6m=46m\)

For the vertical diagonal (which I'll call d2): \(d_{2}=16m+16m=32m\)

Substituting back into the formula for the area of a kite:

\(Area_{kite}=\frac{1}{2} d_{1}d_{2}\\Area_{kite}=\frac{1}{2} (46m)(32m)\\Area_{kite}=736m^2\)

If one doesn't remember the formula for the area of a kite, and can't remember how to build it, the given shape could be visualized as 2 separate triangles, the given shape could be visualized as 2 separate triangles (one on top; one on bottom).

Visualizing it in this way produces two congruent triangles.  Since the upper and lower triangles are congruent, they have the same area, and thus the area of the kite is double the area of the upper triangle.

Recall the formula for area of a triangle:  \(Area_{triangle}=\frac{1}{2} bh\) where b is the base of a triangle, and h is the height of the triangle (length of a perpendicular line segment between a point on the line containing the base, and the non-colinear vertex).  Since all kites have diagonals that are perpendicular to each other (as already indicated in the diagram), the height is already given (16m).

The base of the upper triangle, is the sum of the two segments that compose it:  \(b=40m+6m=46m\)

Finding the Area of the upper triangle\(Area_{\text{upper }triangle}=\frac{1}{2} (46m)(16m) = 368m^2\)

Finding the Area of the kite

\(Area_{kite}=2*(368m^2)\)

\(Area_{kite}=736m^2\)

The given shape could be visualized as 2 separate triangles (one on the left; one on the right).  Each triangle has its own area, and the sum of both triangle areas is the area of the kite.

Note:  In this visualization, the two triangles are not congruent, so it is not possible to  double one of their areas to find the area of the kite.

The base of the left triangle is the vertical line segment the is the vertical diagonal of the kite.  We'll need to add together the two segments that compose it:  \(b=16m+16m=32m\).  This is also the base of the triangle on the right.

Finding the Area of left and right triangles

\(Area_{\text{left }triangle}=\frac{1}{2} (32m)(40m) = 640m^2\)

The base of the right triangle is the same length as the left triangle: \(Area_{\text{right }triangle}=\frac{1}{2} (32m)(6m) = 96m^2\)

Finding the Area of the kite

\(Area_{kite}=(640m^2)+(96m^2)\)

\(Area_{kite}=736m^2\)

If you don't happen to see those composite triangles from option 2 or 3 when you're working this out on a particular problem, the given shape could be visualized as 4 separate right triangles, and we're still given enough information in this problem to solve it this way.

Calculating the area of the 4 right triangles

\(Area_{\text{upper left }triangle}=\frac{1}{2} (40m)(16m) = 320m^2\)

\(Area_{\text{upper right }triangle}=\frac{1}{2} (6m)(16m) = 48m^2\)

\(Area_{\text{lower left }triangle}=\frac{1}{2} (40m)(16m) = 320m^2\)

\(Area_{\text{lower right }triangle}=\frac{1}{2} (6m)(16m) = 48m^2\)

Calculating the area of the kite

\(Area_{kite}=(320m^2)+(48m^2)+(320m^2)+(48m^2)\)

\(Area_{kite}=736m^2\)

The cartesian form of planes perpendicular to the z-axis have in spherical coordinates is z = r cosФ.

Spherical coordinates, also known as spherical coordinates, are a type of curvilinear coordinate system that is useful for defining locations on a sphere or spheroid.

The conversion of cartesian coordinate to spherical coordinate will be

x = r cosθ sinФ

y = r sinθ sinФ

z = r cosФ

The cartesian form of planes perpendicular to the z-axis have in spherical coordinates is z = r cosФ.

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Answer:1/2

Step-by-step explanation:

3/4+(-1/2)-(-1/4)

3/4-1/2+1/4

1-1/2=1/2