Question Find the area enclosed by the inner loop of r = 3-6 cos 6. Round the answer to three decimal places. Provide your answer below:

Answer:

(2, -1)

(10, 15)

Step-by-step explanation:

Subtract the second equation from the first

  y = x² – 10x + 15

- (y =           2x – 5)

————————————

 0 = x² - 12x + 20

Factor

(x  - 2)(x - 10) = 0

x = {2, 10}

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

For x = 2

y = 2(2) - 5

y = -1

Solution 1

(2, -1)

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

For x = 10

y = 2(10) - 5

y = 15

Solution 2

(10, 15)

Answer:

Step-by-step explanation:

Let the amount of gas in the tank before filling was x.

We have:

let the amount of gas be x

\(\\ \sf\longmapsto x+2\dfrac{4}{7}=4\)

\(\\ \sf\longmapsto x+\dfrac{18}{7}=4\)

\(\\ \sf\longmapsto x=4-\dfrac{18}{7}\)

\(\\ \sf\longmapsto x=\dfrac{28-18}{7}\)

\(\\ \sf\longmapsto x=\dfrac{10}{7}\)

\(\\ \sf\longmapsto x=1\dfrac{3}{7}\)

Answer: No Solution

Step-by-step explanation: In picture

Answer:

169 / 14

Step-by-step explanation:

7/1 + 71/14 = 7/1 * 14/14 + 71/14

= 98/14 + 71/14

= (98 + 71) / 14

= 169 / 14

So, the answer is 169 / 14

Answer:

50 miles per hour

Step-by-step explanation:

You want to put the total amount over the hours.

Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

Answer:

uh I don't even know what this is

Answer: x = 500

Step-by-step explanation:

Use the Pythagorean Theorem

a²+b²=c²

300² + 400² = x²

90000 + 160000 = x²

250000 = x²

√250000 = √x²

500 = x

hope i explained it :)

We can solve a common base exponential equation of the form:

With the one-to-one property to get:

(a) In this case, we can take 4 as the common base, to get:

For f(x), we can use a linear equation of the form mx + b like 6x + 9, and for g(x) we can make it equal to -x² (we can use whatever equation we want because we are creating the complex exponential equation), then we get:

Since we have common bases, by means of the one-to-one property, we rewrite the above equation to get:

Simplifying and factoring:

6x + 9 + x² = x² - x²

6x + 9 + x² = 0

(x + 3)² = 0

Then, the solution to this equation is -3

(b) Similarly, taking logarithms on both side we get:

By dividing both sides by Log(4), we get:

As you can see, we got the same equation as in part (a), then the solution will be the same and it is x = -3

Answer:

T(20)  = 300

Ambient Temp = 70

Initial Temp = 375

Step-by-step explanation:

The steps to calculate the algebra at Mathpapa online has been explained

Mathpapa is an online algebra calculator that can help you solve equations, graph functions, and perform various algebraic operations. Here's a general guide on how to use Mathpapa to calculate algebra:

Go to the Mathpapa website (mathpapa.com).

Select the type of algebraic problem you want to solve from the options available on the homepage. For example, you can choose to solve an equation, graph a function, or simplify an expression.

Enter the algebraic expression or equation you want to solve in the input field. You can use the on-screen keyboard or type directly on the input field.

Once you have entered the expression or equation, click the "Solve" button to see the solution. If you are solving an equation, the solution will be displayed step-by-step.

If you want to graph a function, enter the function in the input field and click the "Graph" button. You can customize the appearance of the graph by adjusting the axis limits, adding titles and labels, and changing the line color and style.

Mathpapa also provides various tools to help you learn and practice algebra. For example, you can use the practice problems to test your skills, or watch video tutorials to learn specific algebraic concepts.

Overall, Mathpapa is a useful tool for anyone looking to improve their algebra skills or solve algebraic problems quickly and easily.

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Substituting the derivatives we previously found:
\(\[F_t = e^{(y/z)} \cdot 2t + x \cdot e^{(y/z)} \cdot (-1) + (-x) \cdot e^{(y/z)} \cdot \left(\frac{y}{z^2}\right.\)


\(To find \(F_t\), we'll use the chain rule. Given that \(w = x \cdot e^{(y/z)}\) with \(x = t^2\), \(y = 1 - t\), and \(z = 1 + 2t\), we can proceed as follows:\)

Step 1: Find the partial derivative of \(w\) with respect to \(x\):
\[
\(\frac{\partial w}{\partial x} = e^{(y/z)} \cdot \frac{\partial (x)}{\partial x}\]Since \(\frac{\partial (x)}{\partial x} = 1\), we have:\[\frac{\partial w}{\partial x} = e^{(y/z)}\]\)

Step 2: Find the partial derivative of \(w\) with respect to \(y\):
\[
\(\frac{\partial w}{\partial y} = x \cdot \frac{\partial}{\partial y}\left(e^{(y/z)}\right)\]Using the chain rule, we differentiate \(e^{(y/z)}\) with respect to \(y\) while treating \(z\) as a constant:\[\frac{\partial w}{\partial y} = x \cdot e^{(y/z)} \cdot \frac{\partial}{\partial y}\left(\frac{y}{z}\right)\]\[\frac{\partial w}{\partial y} = x \cdot e^{(y/z)} \cdot \left(\frac{1}{z}\right)\]\)

Step 3: Find the partial derivative of \(w\) with respect to \(z\):
\[
\(\frac{\partial w}{\partial z} = x \cdot \frac{\partial}{\partial z}\left(e^{(y/z)}\right)\]Using the chain rule, we differentiate \(e^{(y/z)}\) with respect to \(z\) while treating \(y\) as a constant:\[\frac{\partial w}{\partial z} = x \cdot e^{(y/z)} \cdot \frac{\partial}{\partial z}\left(\frac{y}{z}\right)\]\[\frac{\partial w}{\partial z} = -x \cdot e^{(y/z)} \cdot \left(\frac{y}{z^2}\right)\]\)

Step 4: Find the partial derivative of \(x\) with respect to \(t\):
\(\[\frac{\partial x}{\partial t} = 2t\]Step 5: Find the partial derivative of \(y\) with respect to \(t\):\[\frac{\partial y}{\partial t} = -1\]\\\)
Step 6: Find the partial derivative of \(z\) with respect to \(t\):
\(\[\frac{\partial z}{\partial t} = 2\]Finally, we can calculate \(F_t\) using the chain rule formula:\[F_t = \frac{\partial w}{\partial x} \cdot \frac{\partial x}{\partial t} + \frac{\partial w}{\partial y} \cdot \frac{\partial y}{\partial t} + \frac{\partial w}{\partial z} \cdot \frac{\partial z}{\partial t}\]Substituting the derivatives we previously found:\[F_t = e^{(y/z)} \cdot 2t + x \cdot e^{(y/z)} \cdot (-1) + (-x) \cdot e^{(y/z)} \cdot \left(\frac{y}{z^2}\right.\)

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\(\qquad \qquad\huge \underline{\boxed{\sf Answer}}\)

Let's find the slope of line, considering the two points (2 , 1) and (8 , 9)

\( \qquad \sf  \dashrightarrow \: \dfrac{9 - 1}{8 - 2} \)

\( \qquad \sf  \dashrightarrow \: \dfrac{8}{6} \)

\( \qquad \sf  \dashrightarrow \: \dfrac{4}{3} \)

So, the required choice is A. 4/3

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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Answer:

4^5/ 4^-9

Step-by-step explanation:

the third one

The riddle mentioned in the question is about a farmer who is traveling along with a sack of rye, a goose, and a mischievous dog.

He comes to a river that he must cross from east to west, and there is a boat available to do so.  Therefore, the farmer takes the goose back to the east side and leaves it there. He then takes the sack of rye across the river, drops it off with the dog, and goes back to the east side to pick up the goose. In this manner, all of the farmer's possessions can be safely transported across the river without any of them being lost to the dog or the goose.This riddle is a classic example of a type of logical puzzle known as a "transport problem."

The goal of a transport problem is to determine how to transport one or more objects from one location to another while satisfying certain constraints, such as the size of the transport vehicle or the safety of the objects being transported.

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Answer:

One point perspective

Step-by-step explanation:

So there will always be a middle point line. A one point perspective image is only going to meet at one point on that line. A two point perspective is going to meet at two points on that line.

Let me show you some examples:

Below you will see an example of a one point and then a two point perspective. Then you will also see an image of me showing you how the image you have given is in one point perspective.

The approximate air pressure at the center of a hurricane is 910 millibars.

Given,

The mean sustained wind velocity equation, v = 6.3 × √(1013 - p)

p is the air pressure in millibars

The mean sustained wind velocity - 64 meters per second.

We have to find the approximate air pressure.

Here,

The equation for wind velocity ;

v = 6.3 × √(1013 - p)

v is given 64

Then substitute;

64 = 6.3 × √1013 - p

64/6.3 = √1013 - p

10.16 = √1013 - p

Square both sides

(10.16)² = (√1013 - p)²

We get,

103.23 = 1013 - p

p = 1013 - 103.33 = 909.67 ≈ 910 millibars

That is,

The approximate air pressure at the center of a hurricane is 910 millibars.

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Answer:

D

Step-by-step explanation:

Answer:

D. the distance between A and C

Step-by-step explanation:

|-2| = 2

its the distance between -2 and 0

Two lines are parallel if their slopes are equal. The slopes of UV and WX can be found using the following formulas:

```

Slope of UV = (5 - 1)/(8 - (-8)) = 4/16 = 1/4

Slope of WX = (y - 0)/(4 - (-4)) = y/8

```

Since UV and WX are parallel, their slopes must be equal. Therefore, we have the following equation:

```

y/8 = 1/4

```

Solving for y, we get y = 2.

Therefore, the value of y such that UV ∥ WX is 2.

Answer:

D 57

Step-by-step explanation:

The value of X

Therefore, From the above equations, we can see that sin(x) is odd, and cos(x) is even. To summarize:
sin(-x) = -sin(x) (odd function), cos(-x) = cos(x) (even function)

To understand the even-odd properties of sinusoidal functions, let's first recall that an even function satisfies f(-x) = f(x) and an odd function satisfies f(-x) = -f(x).
Now, consider the sinusoidal functions f(x) = sin(x) and g(x) = cos(x). We can use the addition and subtraction formulas for sine and cosine to determine their even-odd properties.
The addition and subtraction formulas are as follows:
1. sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
2. cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
Let a = x and b = -x. Then, we get:
1. sin(x - x) = sin(x)cos(-x) + cos(x)sin(-x)
2. cos(x - x) = cos(x)cos(-x) - sin(x)sin(-x)
Since sin(-x) = -sin(x) and cos(-x) = cos(x), we can simplify:
1. sin(0) = sin(x)cos(x) - cos(x)sin(x) => 0 = 0
2. cos(0) = cos(x)cos(x) + sin(x)sin(x) => 1 = cos^2(x) + sin^2(x)

Therefore, From the above equations, we can see that sin(x) is odd, and cos(x) is even. To summarize:
sin(-x) = -sin(x) (odd function), cos(-x) = cos(x) (even function)

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Saturn's distance is 9.5 farther from the Sun than the earth.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Earth's distance from the sun = 1.496 x \(10^8\) km

Saturn's distance from the sun = 1.4246 x \(10^9\) km

Divide Saturn's distance by Earth's distance.

= 1.4246 x \(10^9\) / 1.496 x \(10^8\)

= 9.5

We see that,

Saturn's distance from the sun x 0.95 = Earth's distance from the sun.

Thus,

Saturn's distance is 0.95 farther from the sun.

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The probability that if a random person is chosen from the group of lawyers, the person will be a liar is 38/45, or 0.84.

As a fraction: The probability is given as 38/45, which means that out of 45 people chosen randomly from the group of lawyers, 38 of them are expected to be liars.

As a decimal: To express the probability as a decimal, we divide the numerator (38) by the denominator (45):

38 ÷ 45 ≈ 0.8444444444444444

Rounded to two decimal places, this would be approximately 0.84.

As a percentage: To express the probability as a percentage, we multiply the decimal form by 100:

0.8444444444444444 * 100 ≈ 84.44%

Rounded to two decimal places, this would also be approximately 84.44%.

So, the probability that if a random person is chosen from the group of lawyers, the person will be a liar can be expressed as 38/45 as a fraction, approximately 0.84 as a decimal, or approximately 84.44% as a percentage.

This can be expressed as a fraction, decimal, or percentage, whichever is more helpful.

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Answer:

knew Orleans

Step-by-step explanation: i think i'm not really sure

Based on the table, Phoenix has the highest temperature in January. Therefore, the correct option is option C among all the given options.

The physical concept of temperature indicates in numerical form how hot or cold something is. A thermometer is used to determine temperature. Thermometers are calibrated using a variety of temperature scales, which historically defined distinct reference points including thermometric substances.

The most popular scales are the Kelvin scale (K), which is mostly used for scientific purposes, the Celsius scale (°F), as well as the Celsius scale, which has the unit symbol °C. Based on the table, Phoenix has the highest temperature in January.

Therefore, the correct option is option C.

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Answer:

\(ax^5+ by^5=241\)

Step-by-step explanation:

Given:

We can re-write the left sides of the given equations as follows:

\(ax^2+ by^2=(ax+by)(x+y)-xy(a+b)\)

\(ax^3+ by^3=(ax^2+by^2)(x+y)-xy(ax+by)\)

\(ax^4+ by^4=(ax^3+by^3)(x+y)-xy(ax^2+by^2)\)

Therefore, following this pattern:

\(ax^5+ by^5=(ax^4+by^4)(x+y)-xy(ax^3+by^3)\)

Use the given values and the expanded expressions to create 2 equations to help find the values of (x+y) and xy:

Equation 1

\(ax^3+ by^3=(ax^2+by^2)(x+y)-xy(ax+by)\)

\(\implies 25=11(x+y)-xy(1)\)

\(\implies 25=11(x+y)-xy\)

Equation 2

\(ax^4+ by^4=(ax^3+by^3)(x+y)-xy(ax^2+by^2)\)

\(\implies 83=25(x+y)-xy(11)\)

\(\implies 83=25(x+y)-11xy\)

Multiply Equation 1 by 11:

\(\implies 275=121(x+y)-11xy\)

Then subtract Equation 2 from this to eliminate 11xy and find the value of (x+y):

\(\implies 192=96(x+y)\)

\(\implies (x+y)=2\)

Multiply Equation 1 by 25:

\(\implies 625=275(x+y)-25xy\)

Multiply Equation 2 by 11:

\(\implies 913=275(x+y)-121xy\)

Subtract the 2nd from the 1st to eliminate 275(x+y) and find the value of xy:

\(\implies 288=-96xy\)

\(\implies xy=-3\)

Therefore, we now have:

Substitute these into the equation for ax⁵ + by⁵ and solve:

\(\implies ax^5+ by^5=(ax^4+by^4)(x+y)-xy(ax^3+by^3)\)

\(\implies ax^5+ by^5=(83)(2)-(-3)(25)\)

\(\implies ax^5+ by^5=166+75\)

\(\implies ax^5+ by^5=241\)

Answer: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. (Non-adjacent interior angles may also be referred to as remote interior angles.)

Step-by-step explanation:  ???

The probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even is 5/52

probability is an occurence of a particular events. This particular problem can be solved using permutations and combinations.

Given that, if each coded item in a catalog begins with 4 distinct letters followed by 4 distinct nonzero digits

Like the 4 distinct letters be A,B,C,D

4 distinct nonzero digits are 2,3,4,5

The probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even is approximately equals to the 10/104 = 5/52

Here the probability is an occurence of a particular events. This particular problem can be solved using permutations and combinations and the probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even is approximately equals to 5/52

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Therefore, in either partial derivatives, we have u = 0 or v = 0.

The given information implies that two vectors u and v satisfy:

u * v = 0, where * denotes the dot product between vectors.

u X v = 0, where X denotes the cross product between vectors.

From the first equation, we know that the angle between u and v is either 90 degrees or 270 degrees. That is, u and v are orthogonal (perpendicular) to each other.

From the second equation, we know that the magnitude of the cross product u X v is equal to the product of the magnitudes of u and v multiplied by the sine of the angle between them. Since u and v are orthogonal, the angle between them is either 90 degrees or 270 degrees, which means that the sine of the angle is either 1 or -1. Therefore, we have:

|u X v| = |u| * |v| * sin(θ)

= 0

Since the magnitudes of u and v are non-negative, it follows that sin(θ) must be zero. This can only happen if the angle between u and v is either 0 degrees (i.e., u and v are parallel) or 180 degrees (i.e., u and v are anti-parallel).

In the case where u and v are parallel, we have:

u * v = |u| * |v| * cos(θ)

= |u|²

= 0

This implies that |u| = 0, which means that u = 0.

In the case where u and v are anti-parallel, we have:

u * v = |u| * |v| * cos(θ)

= -|u|²

= 0

This again implies that |u| = 0, which means that u = 0.

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