Given r = 1 – 3 sin 0, find the following. Find the area of the inner loop of the given polar curve rounded to 4 decimal places.

Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.

Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.

First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.

Next, we can find the vertex using the formula:

Vertex = (-b/2a, f(-b/2a))

where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:

Vertex = (-b/2a, f(-b/2a))

= (-6/(2*-1), f(6/(2*-1)))

= (3, -14)

So the vertex of the parabola is at the point (3,-14).

Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.

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The real solutions of the polynomial equation x⁴ = 16 are x = ±2.To find the real or imaginary solutions of the polynomial equation x⁴ = 16, we can start by rewriting it as x⁴ - 16 = 0.

We can then factor the equation as a difference of squares: (x²)² - 4² = 0. Now, we have a quadratic equation in the form a² - b² = 0, which can be factored using the difference of squares formula: (x² - 4)(x² + 4) = 0. From this equation, we get two possible cases: Case 1: x² - 4 = 0. Solving for x, we have: x² = 4; x = ±2. Case 2: x² + 4 = 0.  

This equation has no real solutions because the square of a real number is always positive. Therefore, the real solutions of the polynomial equation x⁴ = 16 are x = ±2.

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The mass of the medium can is approximately 728.33g and the mass of the large can is approximately 1233.33g.

In mathematics, mass usually refers to the amount of matter in an object, often measured in kilograms or grams. In some contexts, mass can also refer to the total sum of a set of quantities or values, or the distribution of a set of values around a central value, such as the mean or median.

Assuming that the cans are made of the same material, we can use the relationship between surface area, height, and mass to find the masses of the other two sizes.

Let M be the mass of the small can, and let m be the mass of the medium can. Then we have:

M/24 = m/46 (since the two cans are similar and have the same shape)

=> m = (46/24)M

Similarly, let M be the mass of the small can, and let L be the mass of the large can. Then we have:

M/24 = L/78 (since the two cans are similar and have the same shape)

=> L = (78/24)M

Using the given mass of the small can (380g), we can find the masses of the other two sizes:

m = (46/24)M = (46/24)*380 = 728.33g (rounded to 2 decimal places)

L = (78/24)M = (78/24)*380 = 1233.33g (rounded to 2 decimal places)

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Using expression 2² * 3, Tony can pack 12 DVDs in each box.

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations that represents a value or a quantity. Expressions can be written using various mathematical symbols such as addition, subtraction, multiplication, division, exponents, and parentheses.

Now,

To find the greatest number of DVDs Tony can pack in each box, we need to find the greatest common divisor (GCD) of the three numbers: 12, 24, and 30.

Now,

12 = 2² * 3

24 = 2³ * 3

30 = 2 * 3 * 5

Then, we can find the GCD by multiplying the common factors raised to their lowest powers:

GCD = 2² * 3 = 12

Therefore, Tony can pack 12 DVDs in each box. He would need 1 box for the comedy DVDs, 2 boxes for the animated DVDs, and 2.5 boxes for the musical DVDs (which could be rounded up to 3 boxes).

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Answer:

2.3

Step-by-step explanation:

We are to determine the opposite length given an angle of 30 degrees and an adjacent side of 4

we would make use of tan 30

tan 30 = opposite / adjacent

0.5774 = opposite / 4

opposite = 0.5774 x 4 = 2.3

(1, -4)

You could just count the units

Answer:

-6p-1/7

Step-by-step explanation:

Answer: 64 cm

Step-by-step explanation:

V = 384 cm ; 6 cubes

(6)(side^3)/6 = 384/6 (divide both sides by 6)

s^3 = 384/6

s^3 = 64

v = 1 = 64

s = 3sq root of 64

s = 4 cm

now, we're looking at the 4 squares that's gonna be unpainted

A = 4^2 = 16

= 4 (16)

A = 64 cm is the area of the unpainted surface

sorry for the late answer i hope this helps

good luckseu



One cup can hold (A), you will need a total of 205.37 paper cups (B), and a total of 5 packages (C).

Let's calculate the volume of the cone:

V=1/3πhr²

V= 1.04 x 11 x 4 ^2 (diameter / 2 radius)

V= 1.04 x 11  x 16 = 184.30 cubic centimeters

Total of lemonade: 37850 cubic centimeters (10 gallons x 3785 cubic centimeters per gallon)

37850 / 184.30 = 205.37 cups

205.37 / 50 cups = 4.1 packages

However, as you need to buy complete packages, this can be rounded to 5 packages.

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Answer: I lie between 6 and 7.

Step-by-step explanation:

If the number multiplied by itself  gets the product 42.25  then if I find the square root of the number 42.25, I will get the number.  

So find the square root of 42.25

\(\sqrt{42.25}\)   = 6.5

This means  the number will lie between 6 and 7.

Let's call the number we are trying to find "x". According to the given information, when x is multiplied by itself (x^2), the product is 42.25.

Therefore, we can write the equation: \(x^2 = 42.25\) To find the value of x, we need to take the square root of both sides of the equation: \(√(x^2) =\)\(√42.25 |x| = 6.5\) (taking the positive square root as we are looking for the absolute value of x) Now, we know that x lies between -6.5 and 6.5 (exclusive) because it is the absolute value of x.

However, since -6.5 and 6.5 are not integers, we need to round them to the nearest integers. Rounding -6.5 to the nearest integer gives -7, while rounding 6.5 gives 7. Therefore, the number x lies between -7 and 7 (exclusive) and corresponds to the interval (-7, 7).

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The surge tank is a vital component of a system in which the flow rate fluctuates significantly. The flow rate entering the tank varies significantly, causing the fluid level in the tank to fluctuate as a result of the compressibility of the liquid. The surge tank is utilized to reduce pressure variations generated by a rapidly fluctspace uating pump flow rate. To determine the matrices A,B,C, and D using state-space notation, here are the steps:State representation is given by:dx/dt = Ax + Bu; y = Cx + DuWhere: x represents the state variablesA represents the state matrixB represents the input matrixC represents the output matrixD represents the direct transmission matrixThe equation can be written asA = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0Thus, the matrices A,B,C and D assuming that the level deviations are the state variables: h'₁ and h'₂. The input variable is q'ᵢ, and the output variable is the flow rate deviation, q'₂ are given by A = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0.Hence, the required matrices are A = [ -1/R₁ 0; 1/R₁ -1/R₂], B = [1/A₁; 0], C = [0 1/R₂], and D = 0 using state-space notation for the given system of equations for two liquid surge tanks.

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It will take 2 days for the car to cover the route.

To determine how many days it will take a car to cover a route of length M kilometers, we need to use the given formula:

Distance = Rate × Time

where distance is M kilometers, and rate is N kilometers per day.

We want to find the time in days.

Therefore, rearranging the formula, we have: Time = Distance / Rate

Substituting the given values, we get: Time = M / N

Therefore, the function days(n, m) that returns the number of days to cover the route can be defined as follows: def days(n, m):    return m / n

Now, let's use this function to calculate the number of days it will take for a car that covers a distance of 700 kilometers per day to cover a route of length 750 kilometers:

days(700, 750) = 1.0714...

Since the number of days should be a whole number, we need to round up the result to the nearest integer using the ceil function from the math module: import mathdef days(n, m):    return math.ceil(m / n)

Now, we can calculate the number of days it will take for a car that covers a distance of 700 kilometers per day to cover a route of length 750 kilometers as follows: days(700, 750) = 2

Therefore, it will take 2 days for the car to cover the route.

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B. 10.5 pounds. To calculate the total pounds of coffee beans, we convert the given ounces to pounds and then add them together. Ms. Martin bought 96 ounces of decaf coffee beans, which is 96/16 = 6 pounds.

She also bought 72 ounces of green coffee beans, which is 72/16 = 4.5 pounds. Adding both amounts, we get 6 + 4.5 = 10.5 pounds. To solve this problem, we need to convert the given ounces to pounds and then add them together. There are 16 ounces in 1 pound, so we divide the given number of ounces by 16 to convert them to pounds.Ms. Martin bought 96 ounces of decaf coffee beans, so we divide 96 by 16 to get 6 pounds. Similarly, she bought 72 ounces of green coffee beans, which is equivalent to 72/16 = 4.5 pounds. Now, we add the pounds of decaf coffee beans (6 pounds) to the pounds of green coffee beans (4.5 pounds). The total is 6 + 4.5 = 10.5 pounds. Therefore, Ms. Martin bought a total of 10.5 pounds of coffee beans.

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Complementary angles always are 90 degrees when added to each other, so:

x = angle 1

x + 89.8 = angle 2

x + x + 89.8 = 90

2x = 90 - 89.8

2x = 0.2

x = 0.1

angle 1 = 0.1 degrees

angle 2 = 0.1 + 89.8 = 89.9 degrees

if you want to check, just sum one to the other and see if they equal 90, like this: 89.9 + 0.1 = 90

The solution to the initial value problem y'' + 2y' + 2y = 0, with initial conditions y(0) = a and y'(0) = b (where a and b are constants), is given by y(t) = e^(-t) * (a * cos(sqrt(3)t) + (b - a sqrt(3)) * sin(sqrt(3)t)), where e is the base of the natural logarithm.

To solve the given initial value problem, we assume a solution of the form y(t) = e^(rt). Substituting this into the differential equation, we obtain the characteristic equation r^2 + 2r + 2 = 0. Solving this quadratic equation, we find two complex roots: r = -1 + i√3 and r = -1 - i√3.

Using Euler's formula, we can express these complex roots in exponential form: r1 = -1 + i√3 = -1 + √3i = 2e^(iπ/3) and r2 = -1 - i√3 = -1 - √3i = 2e^(-iπ/3).

The general solution of the differential equation is given by y(t) = c1e^(r1t) + c2e^(r2t), where c1 and c2 are constants. Since the roots are complex conjugates, we can rewrite the solution using Euler's formula: y(t) = e^(-t) * (c1e^(i√3t) + c2e^(-i√3t)).

To determine the constants c1 and c2, we use the initial conditions. Taking the derivative of y(t), we find y'(t) = -e^(-t) * (c1√3e^(i√3t) + c2√3e^(-i√3t)).

Applying the initial conditions y(0) = a and y'(0) = b, we get c1 + c2 = a and c1√3 - c2√3 = b.

Solving these equations simultaneously, we find c1 = (a + b√3) / (2√3) and c2 = (a - b√3) / (2√3).

Therefore, the solution to the initial value problem is y(t) = e^(-t) * ((a + b√3) / (2√3) * e^(i√3t) + (a - b√3) / (2√3) * e^(-i√3t)).

Simplifying the expression using Euler's formula, we obtain y(t) = e^(-t) * (a * cos(sqrt(3)t) + (b - a sqrt(3)) * sin(sqrt(3)t)).

The solution to the given initial value problem y'' + 2y' + 2y = 0, with initial conditions y(0) = a and y'(0) = b, is y(t) = e^(-t) * (a * cos(sqrt(3)t) + (b - a sqrt(3)) * sin(sqrt(3)t)). This solution represents the behavior of the system on the interval t ≥ 0.

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Answer:

It's B.

Step-by-step explanation:

Answer:

[see below]

Step-by-step explanation:

\(3x-y=5\\\\3x-3x-y=5-3x\\\\-y=5-3x\\\\\frac{-y=-5+3x}{-1} \\\\y=-5+3x\\\\\boxed{y=3x-5}\)

Hope this helps.

The greatest possible number of different types of this caterpillar that could exist is 120.

If we assume that the order of the parts does not matter and that all caterpillars with the same color arrangement are considered identical, we can use combinations to find the number of different types of caterpillars that could exist.

First, we need to choose 2 out of the 5 parts to be green, which can be done in 5 choose 2 ways:

5 choose 2 = (5!)/(2!(5-2)!) = 10

For each green-yellow arrangement there are;

3! ways to permute the yellow parts and

2! ways to permute the green parts.

Therefore, the total number of different types of caterpillars is:

10 × 3! × 2! = 10 × 6 × 2 = 120

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The sum of two Toeplitz matrices is a Toeplitz matrix, but the product of two Toeplitz matrices may not be a Toeplitz matrix.

The sum of two Toeplitz matrices is indeed a Toeplitz matrix. A Toeplitz matrix is a matrix in which each descending diagonal from left to right is constant. When you add two Toeplitz matrices, each corresponding element from the two matrices is added together. Since the constant values on the descending diagonals remain the same, the sum of the two Toeplitz matrices will also have constant values on the descending diagonals. Therefore, the sum of two Toeplitz matrices is still a Toeplitz matrix.

On the other hand, the product of two Toeplitz matrices may not necessarily be a Toeplitz matrix. The product of two matrices is obtained by multiplying each element from the first matrix with the corresponding element from the second matrix and summing the results. In general, this operation may change the structure of the matrix, including the constant values on the descending diagonals. Therefore, the product of two Toeplitz matrices may not exhibit the constant values on the descending diagonals, and hence, it may not be a Toeplitz matrix.

In summary, the sum of two Toeplitz matrices is a Toeplitz matrix, but the product of two Toeplitz matrices may not be a Toeplitz matrix.

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A unit of measurement equal to one thousand meters is called a kilometer.

The prefix "kilo" means one thousand, so a kilometer is a unit of length in the metric system that is equal to 1000 meters. Kilometers are commonly used to measure longer distances, such as the distance between cities or countries, or the length of a marathon race. In contrast, smaller distances may be measured in meters, centimeters, or millimeters, which are all smaller units of length in the metric system.

a metric measurement of length that is equal to 1,760 yards or 5,280 feet. A thousandth of a liter is the same as a metric unit of capacity. a length measurement in meters that is one-thousandth of a meter. a time interval that is frequently used and equates to 60 seconds and 1/60 of an hour.

The complete question is:-

What word goes with a unit of measurement equal to one thousand meters?

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Answer:   Q= -0.6 or -2/3

Step-by-step explanation:

Answer:

radius = 7.5 cm

Step-by-step explanation:

OM is the perpendicular bisector of AB, thus

∠ OMB = 90° and MB = 6 cm with OB being the radius of the circle

Using Pythagoras' identity in right triangle OMB

OB² = MB² + OM² = 6² + 4.5² = 36 + 20.25 = 56.25 ( square root both sides )

OB = \(\sqrt{56.25}\) = 7.5

The radius = OB = 7.5 cm

Answer:

\(\boxed{r = 7.5\ cm}\)

Step-by-step explanation:

If M is the midpoint so AM = BM = AB/2 = 12 / 2 = 6 cm

Let's Consider a ΔOMB which would be a right angled triangle. So, We can use Pythagorean theorem to find the radius of the circle:

\(c^2 = a^2+b^2\)

Where c is hypotenuse (radius) , a is base ( MB = 6 cm ) , b is the perpendicular (OM = 4.5 cm)

\(r^2 = 6^2+4.5^2\\r^2 = 36+20.25\\r^2 = 56.25\)

Taking sqrt on both sides

r ≈ 7.5 cm

The answer is that the Matrix equal to [3 2 -5 9] is A

The given matrix is [3 2 -5 9].

Let's denote this matrix as A.

In this question, find what matrix is equal to A.

A is already given in the question and

therefore it is the matrix that is equal to itself.

Thus, the matrix equal to [3 2 -5 9] is itself, which is denoted as A.

Therefore, the answer is that the matrix equal to [3 2 -5 9] is A.

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Explanation

We are given a triangle

and then asked to determine the value of x

To do so, we know that the total angles in a triangle are 180 degrees

Thus

The value of x is 41 degrees

Answer:

number 1 gvbrturcdc5dcdcdex6he46y4

Step-by-step explanation:

9 cm cm cm cm cm cm cm cm cm cm cm cm cm

Answer:

\(x = \sqrt{11}\)

Step-by-step explanation:

\(a^{2} +b^{2} =c^{2} \\\\\sqrt{6} ^{2} +\sqrt{5} ^{2} =c^{2} \\\\6 + 5 = c^{2} \\\\11 = c^{2} \\\\\sqrt{11} = c\)

The cost of one lily is 5 and cost of one ivy is 12.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. Every mathematical equation begins with L.H.S = R.H.S.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

given:

Perry store perry spent $132 on 12 daylilies and 6 post of ivy .

chelsea spent $159 on 3 daylilies and 12 pots of ivy.

let the number of daylilies sold be x.

let the number of ivy sold be y.

So, the equation is

12x+ 6y = 132

2x + y = 22......(1)

3x + 12y = 159

x + 4y = 53....(2)

Now solving (1) and (2)

x= 5

y= 12

hence, cost of one lily is 5 and cost of one ivy is 12.

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Answer:

9

Step-by-step explanation:

√x+5-2=0

√x+3=0

√x= -3

x=9   [(-3)*(-3) = 9]

Answer:

i got 12.56

Step-by-step explanation:

hope this helped :P

Answer:

12.56

Step-by-step explanation:

2*2*π= 4π. You use 3.14 for π. Then you multiply 2*2*3.14, which is 12.56 inches^2