What is the formula for the area of this triangle?

From the polar coordinates, the integrate value of f(x,y), f( x,y) = 2xy ; x,y ≥ 0, x² + y² = 25 over D using polar coordinates is equals to the \( \frac{625}{4}\). The sketch of D is in attached figure.

The equation of a circumference in rectangular coordinates and origin as centre is x² +y² =R² , where R is the radius of the circumference. In polar coordinates, x² + y² = ρ, ρ is the polar radius. We have function f( x,y) = 2xy ; x,y ≥ 0, x² + y² = 25. It is an equation of a circle with radius 5 centered at the origin, however, since x and y must both be greater than or equal to 0, the region D is restricted to the portion of the circle in the first quadrant. So, the sketch of D is present in attached figure.

Now, we convert the cylindrical coordinates, r will span from 0 to 5 and θ will span from 0 to π/2. The integrand, f(x,y) = 2xy then f(r, θ) = 2(r sin(θ))(r cos(θ)) = 2r²sin(θ)cos(θ) = r²sin(2θ) and the double integral is \(\int_{0}^{\frac{π}{2}}\int_{0}^{5} r³sin(2θ)drdθ\)

\(= \int_{0}^{\frac{π}{2}}[\frac{ r⁴}{4}sin(2θ)]_{0}^{5}dθ\)

\(= \int_{0}^{\frac{π}{2}}[\frac{5⁴}{4}sin(2θ)]dθ\)

\(= \frac{5⁴}{4}[\frac{ -cos(2θ)}{2}]_{0}^{\frac{π}{2}}\)

\(= -\frac{5⁴}{8}[ cos(π) - cos(0°)]\)

\(= - \frac{5⁴}{8}[ -1 - 1 ]\)

\(= \frac{625}{4}\)

Hence, required value is \( \frac{625}{4}\).

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Answer:3.141598

Step-by-step explanation: that is all I can remember on the top of my head

We have: SM = TM ( because M is the midpoint )

So: x + 12 = 8x - 2

=> x - 8x = -2 - 12

=> -7x = -14

=> x = (-14) / (-7) = 2

Answer: x = 2

Ok done. Thank to me :>

The geometric cumulative distribution function should be used.

The geometric cumulative distribution is a discrete likelihood conveyance where the random variable demonstrates the quantity of the Bernoulli trial expected to get the primary achievement. A Bernoulli trial is an experiment that can have just two potential results, ie., achievement or disappointment. All in all, in a mathematical dispersion, a Bernoulli trial is rehashed until a triumph is gotten and afterward halted. Here we are interested in the first success in the three chances, which is completely specified with the distribution function of a geometric distribution, and because the question asked for the probability of having a hand with five cards in the same suit in one of the first three hands. Hence the correct option is the cumulative distribution function.

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Step-by-step explanation:

\( - 24 \div 4 = - 6\)

\( - 24 \div 4 = \\ \frac{ - 24}{4} \\ = \frac{ - 12}{2} \\ = /frac{-6}{1}

Answer:

-6

-6/1 or 6/-1

Step-by-step explanation:

-24/4 is equal to -6 which is the same as -6/1 or 6/-1

Answer:

-4/5

Step-by-step explanation:

Just simply use your knowledge to eliminate the d

The measurement of the angles are 95°, 120°, and 145°.

Let the smallest angle = x

Second angle = x + 25

Third angle = x + 25 + 25 = x + 50

x + x + 25 + x + 50 = 360

3x + 75 = 360

3x = 360 - 75

3x = 285

x = 285/3

x = 95°

Second angle = 95 + 25 = 120°

Third angle = 95 + 50 = 145°

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Answer:

4. rise

match the following definition with the correct term:

the vertical distance between two points on a line

1. run

2. rate of run

3. slope

4. rise

Answer:

  9/4

Step-by-step explanation:

You want to know the value required to complete the square in the equation 1 = x² -3x.

Your picture shows the required value: (-3/2)² = 9/4.

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The probability that a girl will win two weeks in a row is 24%.

Probability tells how many times something will happen or be present.

The probability of a girl winning in a given week is 17/35 since there are 17 girls and 35 students total. Assuming each week's selection is independent of previous selections, the probability of a girl winning two weeks in a row is (17/35) x (17/35) = 289/1225.

Rounding this to the nearest percent gives a probability of 24%.

Therefore, the probability is 24%.

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To determine the required sample size for a political poll with a 4% margin of error and a 97.5% confidence level, a formula can be used. For this scenario, the sample size required would be approximately 862 respondents.

To calculate the sample size needed for a political poll with a 4% margin of error and a 97.5% confidence level, the following formula can be used:

n = (Z^2 * p * (1-p)) / E^2

Where:

n is the sample size

Z is the Z-score associated with the desired confidence level (in this case, it is 2.24)

p is the expected proportion of support for the candidate (this value is typically unknown, so a conservative estimate of 0.5 is often used to get the maximum sample size)

E is the margin of error

Plugging in the values for this scenario, we get:

n = (2.24^2 * 0.5 * (1-0.5)) / 0.04^2

n ≈ 862

Therefore, the required sample size for this political poll is approximately 862 respondents. This sample size would provide a margin of error of 4% at a 97.5% confidence level, meaning that there is a 97.5% chance that the true proportion of support for the candidate lies within the range of the survey results plus or minus the margin of error.

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The value of side length w is 13.75 .

Given right angled triangle,

Perpendicular = w

Hypotenuse = 17

Angle of triangle = 54°

So,

According to the trigonometric ratios,

tanФ = p/b

cosФ = b/h

sinФ = p/h

By using sinФ,

sinФ = p/h

sin 54° =  w/ 17

0.809 = w/17

w = 13.75 .

Thus after correction w will be 13.75

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Work Shown:

\(\sqrt{a} + \sqrt{b} = x\\\\\sqrt{36} + \sqrt{25} = x\\\\6+5 = x\\\\11 = x\\\\x = 11\)

The required value in (36,25,x) is an O'Hara triple, of x is 11.

Three positive integers a, b, and x form an O'Hara triple (a,b,x) if and only if √a+√b=x. For example, (1,4,3) is an O'Hara triple because √1+√4=3. If (36,25,x) is an O'Hara triple,  To determine the value of x.

In mathematics, it deals with numbers of operations according to the statements.

From example,
(1,4,3) is an O'Hara triple because √1+√4=3, in the example sum of the square roots of the first two numbers is equal to the third number. so the value of x in  (36,25,x)  can be determined in the same manner.

Following the example,
√36+√25=x
6 + 5 = x
x = 11

Thus, the required value in (36,25,x) is an O'Hara triple, of x is 11.

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Expressions can be represented as equations or inequalities

(a) The hiker's backpack weighs 15 lb.

(b) the hiker can add additional 19.5 pounds

The inequality that represents the additional weight is:

The hiker can add additional 19.5 pounds

(a) Long hike

The hiker's weight is given as:

, the recommended weight (x) of the backpack is calculated as:

The hiker's backpack weighs 15 lb.

So now what weare supposed to do is

Subtract 15 from both sides

(b) Day hike

The hiker's weight is given as:

The hiker is embarking on a day hike (i.e. short hike), the recommended weight (x) is calculated as:

The hiker's backpack weighs 7.5 lb.

So, the additional weight the hiker can add is represented as:

Subtract 7.5 from both sides

Hence, the hiker can add additional 19.5 pounds

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Researchers engage in experimentation to exercise maximum control over the factors they are interested in studying.

Generally, experimenter trials are used to control the study's variables. The experimental approach entails changing one variable to see if it affects another variable. This approach uses controlled exploration methods and arbitrary subject selection to test a thesis.

For illustration, experimenters might be interested in changing how colorful visual patterns may affect our perception. They might also consider whether specific actions can enhance memory. Multitudinous behavioral issues are the subject of trials, some of which include cognition, emotion, memory, perception, and sensation.

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Answer:

It is arithmetic, the common difference is 5

Step-by-step explanation:

What an arithmetic sequence has to have is a common difference meaning you are adding or subtracting the same number each time, in this case you are adding 5 every time so it is arithmetic

Answer:

8

Step-by-step explanation: this is easy lol

By using the Cauchy-Riemann equations on a real-valued function, it can be proven that the function f(z) is constant in the domain D. This is important for understanding analytic functions in complex analysis.

To prove that if f(z) is real-valued for all z in D, then f(z) must be constant throughout D, let a function f be analytic everywhere in a domain D. We know that a real-valued function is said to be a function whose values lie on the real line. In the case of the complex plane, a function whose values lie on the real line is real-valued.

The Cauchy-Riemann equations, which define the necessary conditions for a function f(z) to be analytic in a domain, say that the imaginary component of f(z) is determined by its real component.

To be more precise, if f(z) is real-valued for all z in D, then we can say that:u(x, y) = f(z),v(x, y) = 0

By definition, the Cauchy-Riemann equations can be stated as:

∂u/∂x = ∂v/∂y∂u/∂y = -∂v/∂x

Taking the first equation, we get:

∂u/∂x = ∂v/∂y => ∂v/∂y = 0

Since v is equal to 0 for all values of x and y, the above equation reduces to ∂u/∂x = 0, which implies u is constant with respect to x.

Similarly, taking the second equation, we get:

∂u/∂y = -∂v/∂x => ∂u/∂y = 0

Since u is equal to a constant for all values of x and y, the above equation reduces to ∂v/∂y = 0, which implies v is constant with respect to y. Since u and v are both constant with respect to their respective variables, u + iv = f(z) is a constant with respect to z throughout the domain D. Thus, we have proved that if f(z) is real-valued for all z in D, then f(z) must be constant throughout D.

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Answer:

Input x 0 1 2

Output y -1 2 5

Step-by-step explanation:

just plug in all the answers for x and solve the equation. like this:

y=3*0-1=

y=0-1=

y= -1

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

y=3*1-1=

y=3-1=

y=2

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

y=3*2-1=

y=6-1=

y=5

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

all the results match with the table

hope I helped God bless you

A file that contains 154 megabytes occupies 22% of the available space.

We can calculate the percent of the space by using the following formula:

The percent of the space = used space / storage space × 100%

A CD-Rom holds 700 megabytes of data.

A file containing 154 megabytes occupies the space.

The percent of the space = used space / storage space × 100%

The percent of the space = 154 / 700 × 100%

The percent of the space = 0.22 × 100%

Apply the multiplication operation, and we get

The percent of the space = 22%

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Answer:

Step-by-step explanation:

A function is a relation in which each input has only one output

so a relation cannot have more than one output

Answer:

each input (x-value) only has one output (y-value)

Step-by-step explanation:

you can use the vertical line test; pretend to draw vertical lines and if there are two point on the graph where the vertical line touches, it cannot be considered function.

The number of patients that Dr. Howard sees this year is 1472.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.

From the information Illustrated, Dr. Howard saw 920 patients last year and this year, the number of patients he saw was 60% higher.

Dr. Howard saw 60% more patients this year than he did last year, so the number of patients he saw this year was 1 + 0.60 = 1.60 times the number he saw last year.

It should be noted that based on the information given, this will be solved thus:

= 920 × (1 + 60%)

= 920 × 1.6

= 1472

Therefore, based on the calculation, Dr. Howard saw 1,472 patients this year.

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Answer:

The dude above me lied its only -6

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

12÷3/4=12/1×4/3

=16

Answer:

16

Step-by-step explanation:Factor the numerator and denominator and cancel the common factors. and divide 12/(3/4)

The value of cups of water in milliliter can be calculated by simply divide the volume by 236.6 so 150 milliliters can be 0.634 US cups.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

Divide the millilitre volume by the cup size to convert 150 mL to cups: The formula to convert 150 mL to cups is [cups] = 150 / cup size. Following are the outcomes as a result:

Cups to 150 mL =

Please take note that these 150mL to cups conversion figures have been adjusted to five decimals. If you're unsure which cup unit you have, you can find further details on our main page.

In any event, you must first determine the size of your cup before applying the formula or using our converter, which can change any volume, to convert 150mL to cups.

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Answer:

h = 10 bc 4.7 x 10 = 47

f = 36 bc 6 x 36 = 216

g = 3.5 bc 3.5 + 1.6 = 5.1

unlock number equation = f - g x h or 36 - 3.5 x 10

unlock number: 1

Answer:

Unlock number: 1

Step-by-step explanation:

6f = 216

6f/6 = 216/6

f = 36

1.6 + g = 5.1

5.1 - 1.6 = 3.5

g = 3.5

4.7h = 47

4.7h/4.7 = 47/4.7

h = 10

f - g x h

36 - 3.5 x 10

36 - 35

1

Answer:

11.50x + 65.50 = 146

He must sell 7 earbud cases to meet his goal.

Step-by-step explanation:

11.50x + 65.50 = 146

11.50x = 146 - 65.50

x = 80.50/11.50

x = 7