Which set of polar coordinates names the same point as () -5.1 ? O A. (5, 7 4 O B. 57 5, 4 37 O c. (5, IT D. 5,

Let's denote the time it took Juan Pablo to drive from home to college as "t1" and the time it took him to drive back from college to home as "t2". We know that the average speed is equal to the total distance divided by the time taken.

The distance from home to college is the same as the distance from college to home, so we can denote it as "d".  Using the formula: Speed = Distance / Time, we can write the equations: 59.6 = d / t1     (Equation 1) 67.2 = d / t2     (Equation 2) We are also given that the total round trip took 10 hours, so we have the equation: t1 + t2 = 10     (Equation 3) To solve these equations, we can rearrange Equation 1 and Equation 2 to solve for "d" in terms of "t1" and "t2": d = 59.6 * t1     (Equation 4) d = 67.2 * t2     (Equation 5) Now, substituting Equation 4 and Equation 5 into Equation 3, we get: 59.6 * t1 + 67.2 * t2 = 10 Solving this equation will give us the values of t1 and t2. However, we need additional information to find a unique solution for t1 and t2.

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Answer:

7(m+p)

Step-by-step explanation:

We know that\(`lim_(n->∞)|a(n+1)/a(n)| = lim_(n->∞)|n3/3n| = 1`\)

The radius of convergence \(`R` is `R = 1/1 = 1`.\)

To determine the interval of convergence, we test the endpoints\(`x = -1` and `x = 1`.\)

When \(`x = -1`,\)

the series becomes \(`∑n=1+[infinity]​(−1)^nn​3n​`.\)
We can write\(`2 + x^(1/2)` as `2(1 + (1/2)x^(1/2))`. \\)

Therefore, we can start with the power series representation of\(`1 + x^(1/2)`\)and multiply by `2`. We have:

\(```1 + x^(1/2) = ∑n=0+[infinity]​[(1/2)nCnx^n/2^n]  (by the binomial series)2 + x^(1/2) = 2∑n=0+[infinity]​[(1/2)nCnx^n/2^n] = ∑n=0+[infinity]​[2(1/2)nCnx^n/2^n]```\)

The radius of convergence of\(`1 + x^(1/2)` is `R = 1`\).

Therefore, the radius of convergence of \(`2 + x^(1/2)`\) is also `R = 1`.
4. We can write \(`1 + x^(1/3)` as `(x^(1/3))/(x^(1/3)) + 1 = (x^(1/3))(1 + x^(-1/3))`.\)

Therefore, we can start with the power series representation of\(`1 + x`\)and substitute\(`x^(1/3)`\)for `x`. We have:
\(```1 + x = ∑n=0+[infinity]​[x^n]1 + x^(1/3) = ∑n=0+[infinity]​[x^(n/3)]```\)
Therefore, the power series representation of \(`1 + x^(1/3)`\) is:

\(```1 + x^(1/3) = ∑n=0+[infinity]​[x^n/3^n]```\)

The radius of convergence of \(`1 + x` is `R = 1`.\)

Therefore, the radius of convergence of \(`1 + x^(1/3)`\) is also `R = 1`. We can integrate term-by-term to obtain:

\(```∫01/2​(1 + x^(1/3)) dx= ∑n=0+[infinity]​[∫01/2​x^n/3^n dx]= ∑n=0+[infinity]​[1/(n+1)(3^n)(2^(n+1)/3 - 1/3)]```\)

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The correct logarithm form is: a. log5 125 = 3

Question is about finding the logarithm form of 5³ = 125 using the given options.

The correct logarithm form is:

a. log5 125 = 3

Here's the step-by-step explanation:

1. The exponential form is given as 5³= 125.
2. To convert it to logarithm form, you have to express it as log(base) (argument) = exponent.
3. In this case, the base is 5, the argument is 125, and the exponent is 3.
4. Therefore, the logarithm form is log5 125 = 3.

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Answer:

1. Shift down

2. Shift Up

3. More Steep

4. Less Steep

Step-by-step explanation:

Hope I helped

Answer:

3.671%

Step-by-step explanation:

\(\frac{1786}{48650}\) x 100 =3.671

Using the formula of area of a circle, about 226.08in² has been eaten

The diameter of the pizza is given as 24 inches. To calculate the area of the entire pizza, we need to use the formula for the area of a circle:

Area = π * r²

where π is approximately 3.14 and r is the radius of the circle.

Given that the diameter is 24 inches, the radius (r) would be half of the diameter, which is 12 inches.

Let's calculate the area of the entire pizza first:

Area = 3.14 * 12²

Area = 3.14 * 144

Area ≈ 452.16 square inches

Now, if half of the pizza is consumed, we need to calculate the area of half of the pizza. To do that, we divide the area of the entire pizza by 2:

Area of half of the pizza = 452.16 / 2

Area of half of the pizza ≈ 226.08 square inches

Therefore, if half of the pizza is consumed, approximately 226.08 square inches of pizza would be eaten.

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The mean of the sample from number of patients treated at Dr. Frank's dentist office each day for ten days is 8.2

Given data:

13, 9, 7, 8, 2, 4, 22, 12, 5, 0.

Mean of the sample = Total number of patients treated / number of days

= (13 + 9 + 7 + 8 + 2 + 4 + 22 + 12 + 5 + 0) / 10

= 82/10

= 8.2

Therefore, the mean of the sample is 8.2

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In the line of symetry for this parabola is x = -1.

The maxima or minima of the parabola is \(-\frac{21}{4}\)

Estimate the gradient of the curve at x = 4 is 5.

The equation of the tangent of the point (4, 1) is 5x² - y² - 40x + 2y + 89 = 0.

The gradient of the curve at the point (-1, 1) is -1.

The steps are as follows:

The function of parabola y = x² - 3x - 3

(i) In the line of symetry for this parabola.

Symetry of the parabola:

x =  \(-\frac{b}{2a}\)    → for y = ax² + bx + c

x =  \(-\frac{-3}{-3}\)

x = -1

(ii) The maxima or minima of the parabola.

The maximum or minimum parabola can be found when the derivative is 0

y = x² - 3x - 3

y' = 2x - 3

0 = 2x - 3

2x = 3

x =  \(\frac{3}{2}\)

The maxima or minima of the parabola

y = x² - 3x - 3

  = ( \(\frac{3}{2}\) )² - 3 (  \(\frac{3}{2}\) ) - 3

  =  \(\frac{9}{4}\)  -   \(\frac{9}{2}\)  - 3

  =   \(\frac{9}{4}\)  -  \(\frac{18}{4}\)  -  \(\frac{12}{4}\)

  = \(-\frac{21}{4}\)

(iii) Estimate the gradient of the curve at x = 4

y = x² - 3x - 3

y' = 2x - 3

y' = m = 2(4) - 3

          = 8 - 3

          = 5

y = x² - 3x - 3

y = 4² - 3(4) - 3

  = 16 - 12 - 3

  = 1

(iv) The equation of the tangent of the point (4, 1)

(y - b)² = m (x - a)²

(y - 1)² = 5 (x - 4)²

y² - 2y + 1 = 5 (x² - 8x + 16)

y² - 2y + 1 = 5x² - 40x + 90

5x² - y² - 40x + 2y + 90 - 1 = 0

5x² - y² - 40x + 2y + 89 = 0

(v) The gradient of the curve at the point (-1, 1)

y = x² - 3x - 3

y' = 2x - 3

y' = m = 2(1) - 3

          = 2 - 3

          = -1

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The correct value of the inequality as solves is x > 14 , and the error made by the student was that he directly divided the RHS by 7.

To simplify the equation we will multiply 7 on both the sides.

Then we will get the result as 7x > 98

Thus, we can say that the new inequality will be x > 14 ,

Hence , the mistake made by the student was that he didn't divided both the sides by 7 but only one side.

So a result, he obtained the incorrect result x>2.

Inequality is a concept in mathematics and uses symbols such as > , < , <= , >= etc.

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Answer:

:-f(x)=x²-2x-24

Step-by-step explanation:

according to the rules of polynomial

f(-4) is the same thing as (x+4)

f(6) is the same thing as (x-6)

how?

x+4=0; x=-4

x-6=0; x=6

(x+4)(x-6)

x²-6x+4x-24

x²-2x-24

:-f(x)=x²-2x-24

award me

Answer: B

Step-by-step explanation:

First you have to do what’s in parentheses so you do 7-3, which is 4. Then you do 4 - 2 = 2. Hope this helped!

Answer:

a. r = d/t, 145(rate) = 145(distance)/1(time)

b. The second train is travelling faster

The first train has a rate of 145 mph the second has a rate of 150 mph since r = 300 miles/2 hours = 150

Therefore the second train has a rate of 150 mph while the first train has rate of 145 mph

The correct option is a) -0.15.

The weakest correlation relationship between two variables is given by -0.15.

With the aid of correlation, the strength of the relationship between two variables can be determined. We can tell from this study whether there is no correlation, weak correlation, or a strong correlation between the two variables.

Two different types of correlation exist:

The correlation value (r) always lies between -1 and 1.

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The complete question is -

Which of the following is the weakest correlation relationship between two variables?

a) -0.15

b) 0.27

c) -0.70

d) 0.55

Answer:

19.6349540849

Step-by-step explanation:

π × 2.5^2 = 19.6349540849

The basic arithmetic operations are:

Addition (+): The operation of finding the total of two or more numbers.

Subtraction (-): The operation of finding the difference between two numbers.

Multiplication (*): The operation of finding the product of two or more numbers.

Division (/): The operation of finding the quotient of two numbers, where the numerator is divided by the denominator.

Exponentiation (^ or **): The operation of finding the result of raising a number to a power.

These basic arithmetic operations form the foundation of many mathematical and scientific concepts, and are used in a wide variety of applications. In addition, they are the building blocks for more advanced

mathematical operations, such as logarithms, derivatives, and integrals.

Linear equations are mathematical expressions that describe a linear relationship between two variables. In a linear equation, the highest power of the variables is 1, and the coefficients and variables are related in a straightforward manner.

A linear equation in one variable (such as y = 2x + 1) describes a straight line when plotted on a graph. In two variables, a linear equation describes a plane in three-dimensional space.

Linear equations have the form:

y = mx + b

where x and y are variables, m is the slope of the line, and b is the y-intercept, the point at which the line crosses the y-axis.

Linear equations are used in many fields, including economics, physics, and engineering, to model and analyze relationships between variables.

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Answer: n=8

Step-by-step explanation:

1. Subtract 4.4n on both sides:

2n-10=6

2. Add 10 on both sides:

2n=16

3. Divide both sides by 2:

n=8

Have a nice day :D

The depth of the water in the cone-shaped tank is increasing at a rate of approximately 1.385 meters per second.

To determine the rate at which the depth of the water is changing, we can use related rates. Let's denote the depth of the water as h(t), where t represents time. We are given that dh/dt (the rate of change of h with respect to time) is 12 m/sec, and we want to find dh/dt when h = 18 meters.

To solve this problem, we can use the volume formula for a cone, which is V = (1/3)πr^2h, where r is the base radius and h is the depth of the water. We can differentiate this equation with respect to time t, keeping in mind that r is a constant (since the base radius does not change).

By differentiating the volume formula with respect to t, we get dV/dt = (1/3)πr^2(dh/dt). Now we can substitute the given values: dV/dt = 12 m/sec, r = 26 meters, and h = 18 meters.

Solving for dh/dt, we have (1/3)π(26^2) (dh/dt) = 12 m/sec. Rearranging this equation and solving for dh/dt, we find that dh/dt is approximately 1.385 meters per second. Therefore, the depth of the water in the tank is increasing at a rate of about 1.385 meters per second.

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Arithmetic operations consists primarily of operations such as addition, subtraction, multiplication, and division. So the option A is correct.

The process of adding things together is known as addition. The '+' sign represents the addition process. It entails combining two or more numbers into a single expression.

The difference between two numbers is calculated using the subtraction operation. The '-' sign represents subtraction. It is nearly identical to addition, but it is the conjugate of the second term.

Multiplication is also referred to as repeated addition. It is indicated by " or '*'. It can also be combined with two or more values to produce a single value.

Division is the inverse of multiplication and is usually denoted by ". It is made up of two terms, dividend and divisor, and the dividend is divided by the divisor to yield a single term value.

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The magnitude of the average velocity vector is approximately 3.651 m/s.

To find the magnitude of the average velocity vector, we need to calculate the displacement and divide it by the time taken.

Representation:

Initial position: D1 = (50 m North, 10 m East)

Final position: D2 = (5 m North, 35 m East)

Time taken: t = 15 seconds

Equations:

Displacement vector (ΔD) = D2 - D1

Average velocity vector (\(V_{avg}\)) = ΔD / t

Algebra work:

ΔD = D2 - D1

   = (5 m North, 35 m East) - (50 m North, 10 m East)

   = (-45 m North, 25 m East)

|ΔD| = √((-45)^2 + 25^2)  [Magnitude of the displacement vector]

\(V_{avg}\) = ΔD / t

       = (-45 m North, 25 m East) / 15 s

       = (-3 m/s North, 5/3 m/s East)

|\(V_{avg}\)| = √((-3)^2 + (5/3)^2)  [Magnitude of the average velocity vector]

Symbolic answer:

The magnitude of the average velocity vector is approximately 3.651 m/s.

Units check:

The units for displacement are in meters (m) and time in seconds (s). The average velocity is therefore in meters per second (m/s), which confirms the units are consistent with the calculation.

Therefore, the magnitude of the average velocity vector is approximately 3.651 m/s.

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The rate of climb required in feet per minute is 490.

The Ground Speed = 140 Knots

The ground speed in minutes = 140/60

                                                   = 2.33 knots

Required speed is in feets per minutes so mulitply the knots with 210

Required Rate =  210 X 2.33

                         = 489.93

                         ≈ 490.

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In linear equation , 13 April  is day was the flower 16. 5 centimeters tall.

What are a definition and an example of a linear equation?

Rate of change = 17.4 - 15/16 - 8

                        = 2.4/3

                         = 0.3 cm/day

Difference between 16.5 cm and 15 cm = 16.5 - 15  = 1.5 cm

Number of days required to grow from 15 cm to 16.5 cm = 1.5/0.3 = 5 days

Date on which the flower was 16.5 cm tall = 8th April + 5 = 13 April

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Answer:

12$ tip together is will be 92$

Step-by-step explanation:

Step-by-step explanation:

The answer will be-+ 11376

Answer:

√{5688×5688×4}=√{5688²×2²)==±11376

Answer:

64 square centimeters

Step-by-step explanation:

The surface are of a pyramid is found by finding the sum of the area of the four sides and the base.

Finding the triangular face:

Area of triangle = \(\frac{1}{2} b h\) = \(\frac{1}{2}*4*6 = 12\)

12 * 4 (4 sides) = 48 square cm

Finding the Base = \(w * l = 4 * 4 = 16\)

Finally, we add it together. 48 + 16 = 64

Answer:

The value of x is 12

Step-by-step explanation:

4x3=12

7x3=21

Therefore 12/21

To explain further:

If you divide 12 by 3 you get 4

If you divide 21 by 3 you get 7

Therefore resulting to 4/7

(I found out that the number three goes in both numbers to begin with)

Is this clearer?

Answer:

The required inequality is:

\(\mathbf{x >60\: and\: x<135}\)

Step-by-step explanation:

Minimum Money students should bring = $60

Maximum Money students should bring= $135

We need to write compound inequality  that  represents the amounts of money a student can bring.

Compound inequalities are combination of two inequalities combined with "and" , and "or"

And is used, when both inequalities should be true.

Or is used when one of the inequality should be true.

In our case we would use and because we need  both inequalities to be true.

The required inequality is:

\(\mathbf{x >60\: and\: x<135}\)

Answer: √20

Step-by-step explanation:

4.47213595 (the 5 repeats)

Answer:

12 feet

Step-by-step explanation:

just convert 4 yards into feet

Answer:

6.25 or 6 1/4

Step-by-step explanation:

first divide 5/4

then multiply 25/4

simplify 6.25

The clearinghouse and research middle on servant management is now called c. The Greenleaf Center for Servant Leadership.

The middle turned into named after Robert K. Greenleaf, who first brought the idea of servant leadership in his essay "The Servant as Leader" published in 1970. The Greenleaf Center for Servant Leadership serves as a worldwide useful resource for promoting the knowledge and exercise of servant leadership.

It conducts studies, provides educational applications, and gives a platform for individuals and businesses to study and interact with servant management ideas. The middle's recognition is on nurturing moral and compassionate management that prioritizes the nicely-being and growth of individuals and the groups they serve. Through its initiatives, the Greenleaf Center pursuits to inspire and empower leaders to create a superb and impactful exchange by embracing the servant management philosophy.

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The clearinghouse and research center on servant leadership is called The Greenleaf Center for Servant Leadership.

The clearinghouse and research center on servant leadership is called The Greenleaf Center for Servant Leadership. It is a nonprofit organization that was founded in 1964 by Robert K. Greenleaf. The center is dedicated to promoting the principles of servant leadership, which emphasizes serving others and putting their needs first.

The Greenleaf Center conducts research, provides resources and training, and serves as a hub for individuals and organizations interested in servant leadership.

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