Find the midpoint (1,2)(8,-9)

The correct trigonometric substitution for evaluating integral ∫√(x² + 64) dx is option B. x = 8 tan θ.

To evaluate the integral ∫√(x² + 64) dx using trigonometric substitution, use the substitution x = 8 tan θ.

Let's go through the steps to see how this substitution leads us to the solution:

1. Substitute x = 8 tan θ.

This implies dx = 8 sec² θ dθ.

2. Substitute the expression for x and dx in the integral:

∫√(x² + 64) dx becomes ∫√((8 tan θ)² + 64) * 8 sec² θ dθ.

3. Simplify the expression:

∫√(64 tan² θ + 64) * 8 sec² θ dθ = ∫√(64(sec² θ - 1)) * 8 sec² θ dθ.

4. Further simplify:

∫√(64sec² θ - 64) * 8 sec² θ dθ = ∫√(64sec² θ) * 8 sec² θ dθ.

5. Simplify the expression inside the square root:

∫8sec θ * 8 sec² θ dθ = ∫64sec³ θ dθ.

6. Integrate with respect to θ:

∫64sec³ θ dθ = 64∫sec³ θ dθ.

Now, this integral can be evaluated using standard trigonometric integral identities or integration techniques. However, it's worth noting that the original integral did not involve the variable θ, so we would eventually need to convert the result back to x by substituting x = 8 tan θ.

The correct answer is B. x = 8 tan θ.

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The sum of the inverse cosine and the inverse sine of the same ratio is; Choice B; 90°.

The sine and inverse sine functions can help find the missing angle in a right triangle; Choice C; both is correct.

Recall that; if angles A and B are complementary angles; i.e A + B = 90; then

sin A = cos B = x

On this note since sin A = x and cos B = x;

sin-¹ x = A and cos-¹ x = B

On this note, the sum of sin-¹ x and cos-¹ x = A + B = 90°.

Hence, Choice B is correct.

2. It follows from triangle geometry that the measure of acute angles of a right triangle can be determined by trigonometric ratios.

Hence, both sin and sin-¹ would allow one to find the missing angle in a right triangle. Hence, Choice C is correct.

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Work Shown for problem 1

P(pink, then violet) = P(pink)*P(violet given 1st was pink)

= (4/14)*(2/13)

= 8/182

= 4/91

------------------------------

Work Shown for problem 2

P(gray, then gray)

= P(gray)*P(gray given 1st was gray)

= (3/14)*(2/13)

= 6/182

= 3/91

-------------------------------

Work Shown for problem 3

P(not yellow, not yellow)

= P(not yellow)*P(not yellow given 1st was not yellow)

= (9/14)*(8/13)

= 72/182

= 36/91

-------------------------------

Work Shown for problem 4

P(yellow, not yellow)

= P(yellow)*P(not yellow given 1st was yellow)

= (5/14)*(9/13)

= 45/182

closer to, shorter, longer.  (T=A^1.5

just took the assigniment.

Answer:

So, their orbital periods are than Earth's orbit. The further a planet is from the sun, the its orbit is.

Step-by-step explanation:

Even though Venus is farther from the sun than mercury, Venus's surface is hotter than Mercury's because Venus has a carbon dioxide atmosphere that traps the sun's heat.

Answer:

\(0.98268\)

Step-by-step explanation:

We are given that

Mean, \(\mu=3408\)miles

Variance, \(\sigma^2=249001\)

We have to find  the probability that the mean of a sample of 36 cars would differ from the population mean by less than 198 miles.

n=36

\(P(|\bar{x}-3408}|<198)=P(3408-198<\bar{x}<198+3408)\)

=\(P(3210<\bar{x}<3606)\)

=\(P(\frac{3210-3408}{\sqrt{\frac{249001}{36}}}<\frac{\bar{x}-\mu}{\sqrt{\frac{variance}{n}}}<\frac{3606-3408}{\sqrt{\frac{249001}{36}}}\)

\(=P(-2.38<Z<2.38)\)

\(=P(Z<2.38)-P(Z<-2.38)\)

\(=0.99134-0.00866\)

=\(0.98268\)

Hence,  the probability that the mean of a sample of 36 cars would differ from the population mean by less than 198 miles=\(0.98268\)

Answer:

Line means going on upto point but line segment means limited line

Answer:

Line:No ending points.

Line segment :Two ending points.

Answer:

3/4 , 3

Step-by-step explanation:

Let one number = x

Other = 4x

Sum:

x + 4x = 15/4

5x = 15/4

x = 3/4

Thus the numbers are 3/4 , 3

Answer:

41 meters

Step-by-step explanation:

\(\frac{31}{64}\) = \(\frac{19.8}{x}\)

31x = (19.8)(64)

31x = 1267.2  Divide both sides by 31 and round

x = 41

Answer: 64 m/s at 8 seconds.

Step-by-step explanation:

Think of the given equation as a function of time for velocity.  Thus, by simply graphing the function, you find a maximum at (8, 64).

Hope it helps :)

The maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

To find the maximum area of a Norman window with a given perimeter, we can use calculus. Let's denote the radius of the semicircle as r and the height of the rectangular window as h.The perimeter of the Norman window consists of the circumference of the semicircle and the sum of all four sides of the rectangular window. Therefore, we have the equation:

πr + 2h = 9We also know that the area of the Norman window is the sum of the area of the semicircle and the area of the rectangle, given by:

A = (πr^2)/2 + rh

To find the maximum area, we need to express the area function A in terms of a single variable. We can do this by substituting r from the perimeter equation:

r = (9 - 2h)/(π)

Now we can rewrite the area function in terms of h only:

A = (π/2) * ((9 - 2h)/(π))^2 + h * (9 - 2h)/(π)

Simplifying this equation, we get:

A = (1/2)(9h - h^2/π)

To find the maximum area, we differentiate the area function with respect to h, set it equal to zero, and solve for h:

dA/dh = 9/2 - h/π = 0

Solving this equation, we find:h = 9π/2

Substituting this value of h back into the area function, we get:

A = (1/2)(9 * 9π/2 - (9π/2)^2/π) = (81π/2 - 81π/4) = 81π/4

Therefore, the maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

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The probabilities are given as follows:

3. P(rides bus|owns a car) = 1/3.

4. P(red|organic) = 3/5.

The probability of an event in an experiment is obtained as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

For item 3, the outcomes are given as follows:

Hence the probability is:

P(rides bus|owns a car) = 8/24 = 1/3.

For item 4, the outcomes are given as follows:

The error was in identifying the total outcomes, and the probability is:

P(red|organic) = 18/30 = 3/5.

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A sample of matter experiences a decrease in average kinetic energy as it continues to cool. One would anticipate that the particles will eventually come to a complete stop. The temperature at which particles should theoretically stop moving is absolute zero. Thus, option B is correct.

What theory directly contradicts concept of absolute zero?

All molecules are predicted to have zero kinetic energy and, as a result, no molecular motion at absolute zero (273.15°C). Zero is a hypothetical value (it has never been reached).

Absolute zero signifies that there is no kinetic energy involved in random motion. A substance's atoms don't move relative to one another.

Therefore, Kinetic energy because it can create heat which goes against the absolute zero. A gas molecule's kinetic energy tends to zero when the temperature reaches absolute zero.

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1. Andy's oldest daughter ate the most pizza. She ate the entire personal pizza, which is 10 inches in diameter

2. If the company offered an extra large pizza, you could find out how much of it a person ate if they cut their own piece with a central angle of M°

Andy's oldest daughter ate the most pizza. She ate the entire personal pizza, which is 10 inches in diameter. This means that she ate 100% of the pizza. Andy's wife ate 2/6 of the small pizza, which is 12 inches in diameter. This means that she ate 1/3 of the pizza. Andy's younger daughter ate 1/8 of the medium pizza, which is 14 inches in diameter.

This means that she ate 12.5% of the pizza. Andy cut himself a piece that had a central angle of 180° from the large pizza, which is 16 inches in diameter. This means that he ate 50% of the pizza.

The least amount of pizza was eaten by Andy's younger daughter. She only ate 1/8 of the medium pizza.

2. If the company offered an extra large pizza, you could find out how much of it a person ate if they cut their own piece with a central angle of M° by using the following formula:

Percentage of pizza eaten = (M° / 360°) * 100%

For example, if a person cut themselves a piece of an extra large pizza with a central angle of 180°, they would have eaten 50% of the pizza.

Percentage of pizza eaten = (180° / 360°) * 100% = 50%

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Answer:

option 1

Step-by-step explanation:

The ordered pair that solves the system of equation is (0, 0).

To solve this system, we can substitute the first equation into the second equation to eliminate y:

x = 2x

Solving for x, we get x = 0.

Substituting x = 0 into the first equation, we get y = 0.

Therefore, the ordered pair that solves the system is (0, 0).

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Step-by-step explanation:

I just answered this ...

the first thing we notice : the quadrilateral has 2 pairs of equally long sides with 2 angles being openly 90°.

so, we are dealing with a rectangle here.

we know that one pair of the sides (NK = LM) are 24 cm long.

and we know that KL:LM = 3:4.

that means that the pair KL = MN are the shorter sides of the rectangle. and their length is according to the ratio 3/4 of NK=LM.

3/4 × 24 = 18 cm

the area of that rectangle is therefore

18 × 24 = 432 cm²

The function with the steepest slope is \(y = 7x - 3\).

The correct answer is C.

The linear function with the steepest slope is the one with the highest absolute value for the coefficient of x.

Let's compare the coefficients of x in each of the given functions:

\(y = -8x + 5\)

Slope: -8

\(y - 9 = -2(x + 1)\)

Simplifying, we get \(y - 9 = -2x - 2\)

Rearranging, we have \(y = -2x + 7\)

Slope: -2

\(y = 7x - 3\)

Slope: 7

\(y + 2 = 6(x + 10)\)

Simplifying, we get \(y + 2 = 6x + 60\)

Rearranging, we have \(y = 6x + 58\)

Slope: 6

Therefore, the steepest slope is the \(y = 7x - 3\).

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Answer:

∠ BDA = 55° , ∠ BCA = 70°

Step-by-step explanation:

∠ BOA = 360° - 250° = 110° ( angles round a point )

The central angle is twice the angle on the circle, subtended on the same arc

∠ BDA = \(\frac{1}{2}\) ∠ BOA = \(\frac{1}{2}\) × 110° = 55°

OBCA is a tangent kite

Opposite angles sum to 180° , then

∠ BCA = 180° - ∠ BOA = 180° - 110° = 70°

Answer:

11-96

Step-by-step explanation:

The money required for Simon to buy two more plants is 11.96

What is Average?

The average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.

Given data ,

Number of plants Simon bought = 3 plants

Total amount of plants = 17.94

Amount for one plant = Total amount of plants / Number of plants bought

So , Amount for one plant = 17.94 / 3

                                           = 5.98

Therefore , Amount of cost for Simon to buy two more plants = Amount of one plant x 5.98

= 5.98 x 2

= 11.96

Hence , The money required for Simon to buy two more plants is 11.96

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The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

I got -6 + 2i

Step-by-step explanation:

(3-5i)(-2+4i)

So we would multiply the following:

3*-2 = -6

3*4i =12i

-5i*-2 = 10i

-5i * 4i = -20i

Therefore the expression would be

- 6 + 12i + 10i - 20i

we then would add and subtract the variables, which would be

-6 + 2i

I hope this helps! Have a nice day!

The total cost of the pita bread and hummus dips will be $305.00.

To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:

Cost of pita bread:

Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates

Cost of each crate = $15.00

Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00

Cost of hummus dips:

Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes

Cost of each box = $20.00

Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00

Therefore, the expressions Toula can use to determine the costs are:

Cost of pita bread = 3 crates × $15.00/crate

Cost of hummus dips = 13 boxes × $20.00/box

The total cost will be the sum of the costs of pita bread and hummus dips:

Total cost = Cost of pita bread + Cost of hummus dips

Total cost = $45.00 + $260.00

Total cost = $305.00

Therefore, the total cost of the pita bread and hummus dips will be $305.00.

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Answer:

im pretty sure its 2

Step-by-step explanation:

Answer:

2 3/4

Step-by-step explanation:

Adding a negative integer to the current temperature would result in a decrease in temperature, which is consistent with Kin's prediction of a drop in temperature.

Temperature can be treated as a quantitative measure of the hotness or coldness of an object or a substance.

It is often represented using numerical values on a temperature scale, such as Celsius or Fahrenheit.

Temperature can be used in various mathematical calculations, such as in thermodynamics and statistical mechanics.

In the context of the previous problem, adding a negative integer would represent a decrease in temperature.

This is because a negative integer represents a value less than zero, and in the context of temperature, a negative value indicates a temperature that is lower than the reference point (usually taken as 0 degrees Celsius or 32 degrees Fahrenheit).

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T = 50 + (-10), which denotes the addition of a negative integer of minus 10 to the original temperature to produce the new, lower temperature.

An integer is first and foremost a whole number that can be positive, negative, or zero.

A decrease in temperature now denotes a decline in temperature.

This implies that, for instance, if the temperature is 50 °C, a drop of 10 °C would require subtracting 10 from 50 to determine the current temperature.

Currently, the temperature would be;

T = 50 – 10

In order to demonstrate that it is obtained by adding a negative integer:

Another way to express this as;

T = 50 + (-10)

Because minus multiplied by plus yields negative according to the mathematical multiplication signs.

Since, T = 50 + (-10), which denotes the addition of a negative integer of minus 10 to the original temperature to produce the new, lower temperature.

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Rest of the given question is,

A drop in temperature means the temperature will decrease. That decrease is represented by a negative integer, which should be added to the previous temperature.

The value of the probability given as P(V|M) is expressed as; A) 251/723

Two-way frequency tables are defined as a visual representation of the possible relationships that exists between two sets of categorical data.

Now, we are told that;

M = farmer lives in the Midwest.

V = farmer grows vegetables

We want to find P(V|M). This means the probability that the farmer lives in the Midwest and grows vegetables.

From the given frequency table, we can see that;

The number that lives in the midwest and grows vegetables = 251.

Meanwhile, the number that grows vegetables in total is 723.

Thus;

The value of P(V|M) is;

P(V|M) = 251/723

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Answer:

---------------------------

There are two triangular faces with base of 16 cm and height of 15 cm and three rectangular faces.

Find the sum of areas of all five faces:

Answer:

Step-by-step explanation:

The fraction of the larger square has not been shaded is 2/3. Therefore, option D is the correct answer.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

In the given figure, two rhombus are shaded.

Completely, the given square is divided into 6 rhombus.

Fraction to represent the shaded area = 2/6

Fraction to represent the not shaded area = 1-2/6

= 4/6

= 2/3

Therefore, option D is the correct answer.

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Part A: The system of equations represented by the graph: y = 3x - 5 and 2x + 4y = 8.

Part B: The solution of the system of equations : (2, 1).

Determining the significance of the variables employed in a system of equations entails solving the set of equations.

A specific system of equations may have a variety of solutions,

Let's examine three approaches to solving a set of equations, presuming that they are linear equations with two variables.

From the graph shown.

The blue line shows the equation: 2x + 4y = 8

At x =0, y= 2

At y =0, x = 4

Red line shows the equation: y = 3x - 5

At x = 0, y = -5.

Part B: solution to the system of equations.

From the graph, where two lines intersect is the solution of the system of equations.

That is point (2,1).

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Answer:

(3h+y)*(3h-y)

Step-by-step explanation:

We are given the following expression:

We want to find the LCD for:

9h²-y² and 3h + y.

3h+y is already in it's most simplified way.

9h²-y² , according to the notable product of (a²-b²) = (a-b)*(a+b), can be factored as:

(3h-y)*(3h+y).

The factors of each polynomial is:

3h + y and (3h-y)*(3h+y)

The LCD uses all unique factors(If a factor is present in more than one polynomial, it only appears once).

So the LCD is:

(3h+y)*(3h-y)

Which is option B.