what is the slope of the line tangent to the polar curve r = 2θ2 when θ = π ?

Answer:

m+10 has the solution of 11

The collecting area of a telescope is proportional to the square of its diameter. This means that if the diameter of one telescope is two times that of another, its collecting area will be four times larger.

In mathematical terms, the collecting area of a telescope is given by the formula A = πr^2, where A is the collecting area and r is the radius of the telescope's aperture. Since the diameter of a telescope is twice its radius, we can rewrite this formula as A = π(d/2)^2, where d is the diameter of the telescope.

If the diameter of one telescope is two times that of another, then the collecting area of the larger telescope will be A = π(2d/2)^2 = 4π(d/2)^2 = 4A, where A is the collecting area of the smaller telescope.

Therefore, the collecting area of the larger telescope is four times larger than that of the smaller telescope.

Learn more about collecting area at:

https://brainly.com/question/21224118

#SPJ11

Answer: (f-g)(2)=14

Step-by-step explanation:

(f – g) (-2) means the same as subtracting f(2) and g(2). Since we are given f(x) and g(x), we can use them to solve. There are two ways to solve. One is to find f(2) and g(2), and then subtract them. Another way is to do (f-g)(x), then plug in x=2. I will show both methods.

Method 1

f(2)=3(2)²+1                                [exponent]

f(2)=3(4)+1                                  [multiply]

f(2)=12+1                                     [add]

f(2)=13

g(2)=1-(2)                                    [subtract]

g(2)=-1                  

(f-g)(2)=13-(-1)                            [subtract f(2) and g(2)]

(f-g)(2)=14

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

Method 2

(f-g)(x)=3x²+1-(1-x)                     [distribute -1]

(f-g)(x)=3x²+1-1+x                      [combine like terms]

(f-g)(x)=3x²+x

(f-g)(2)=3(2)²+2                         [plug in x=2, exponent]

(f-g)(2)=3(4)+2                           [multiply]

(f-g)(2)=12+2                             [add]

(f-g)(2)=14

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

Now, we know that (f-g)(2)=14. We confirmed this with both methods.

The indicated power of the given complex number is 614,656.Answer: 614,656.

De Moivre's theorem is one of the main tools used for determining positive integer powers of complex numbers. According to De Moivre's theorem, if z = r(cosθ + i sinθ) is a complex number, then zⁿ = rⁿ(cosnθ + i sinnθ). Hence, we can use De Moivre's theorem to determine the indicated power of the given complex number.(-3+31) is equal to 28. Therefore, the given complex number is z = 28(cosπ + i sinπ).We can write this in polar form as z = 28cisπ.To obtain the fourth power of this complex number, we can use De Moivre's theorem: z⁴ = (28cisπ)⁴= 28⁴cis(4π)= 28⁴(cos(4π) + i sin(4π))= 28⁴(1 + i(0))= 28⁴= 614, 656.Therefore, the indicated power of the given complex number is 614,656.Answer: 614,656.

To know more about DeMoivre's Theorem visit:

https://brainly.com/question/32194031

#SPJ11

The range of time values describes the entire interval over which Georgiana would be interpolating is 0 to 30 minutes.

Now, According to the question:

We know that:

Linear model regression is used to predict the relationship between 2 variables by fitting the observed data in a linear equation.

What is the domain and range of a function?

The domain of a function is the set of x values for which it is defined, whereas the range is the set of y values for which it is defined.

As in the table, the minimum time for which the distance is defined is 0 minutes while the maximum time is 30 minutes. Therefore, the range of time values describes the entire interval over which Georgiana would be interpolating is 0 to 30 minutes.

                                     Distance over time

          Time(min)                                              Distance (miles)

              0                                                                   0

              5                                                                   4

             10                                                                   9

             15                                                                   13

            30                                                                   18

Learn more about Linear Equation at:

https://brainly.com/question/11897796

#SPJ4            

Answer:

hope this helps

2x-4

Step-by-step explanation:

Answer:

14x14x14x14x14=14.5

Step-by-step explanation:

Step-by-step explanation:

hope it is helpful to you

Answer:

170 Bagels

Step-by-step explanation:

Add the amount of bagels from the first and second hour which equals to 71, then subtract that from the total which is 241 and you will get 170.

Answer:

-10/3 \(\leq\) x \(\leq\) -13/6

Step-by-step explanation

-3 \(\leq\) 3x +7 \(\leq\) 1/2

-10 \(\leq \\\) 3x \(\leq\) -13/2

-10/3 \(\leq\) x \(\leq\) -13/6

If his growth spurt continued at the same rate Andrew will grow 26/7 inches per month during that growth spurt.

To calculate someone's age, you would subtract their birth year from the current year. For example, if someone was born in 1995 and it is now 2020, their age would be calculated as 2020 - 1995 = 25 years old.

If you have a birthdate, you can use a date calculator to find the exact age in years, months and days.

It's also important to note that, if the person's birthday hasn't occurred yet in the current year, you would subtract the birth year from the current year minus one.

We can start by converting the mixed number 4 1/3 to an improper fraction by multiplying the whole number by the denominator and adding the numerator: 4 x 3 + 1 / 3 = 13/3

To find out how much Andrew grew per month, we need to divide the total growth by the number of months.

13/3 inches / 3 1/2 months = (13/3) / (7/2) = (13/3) x (2/7) = 26/7 inches/month.

So, Andrew grew 26/7 inches per month during that growth spurt.

To know more about improper fraction visit: https://brainly.com/question/21449807

#SPJ4

With a total pay last week of $4720 and a 2.5% commission on sales, she made 275 in sales.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.

Here,

The money earned by sales=2.5%*600

=$15

Let the total sales be x,

600+15x=4720

15x=4720-600

15x=4120

x=274.67

x=275 sales

Her last week sales was 275 as her total salary last week was $4720 and she receives 2.5% commission on sales.

To know more about percent,

https://brainly.com/question/1987628

#SPJ4

Answer:

14m + 5

Step-by-step explanation:

Answer:

14m+5

Step-by-step explanation

combining like terms when you add

11m + 3m

and

1 + 4

(a) The mass of the lamina is 1/4 (9 ln(2 + √3) - 3√3 - 2).

(b) The center of mass of the lamina is (x, y) = (1/5 (9 ln(2 + √3) - 2√3 - 1), 1/5 (3 ln(2 + √3) - √3)).

(a) Mass of the Lamina:

The mass of the lamina is given by the double integral of the density function over the region D. That is,

M = ∬D p(x,y) dA,

where dA is the differential area element in the xy-plane. In our case, D is the triangular region with vertices (0,0), (2,1), and (a,a). To calculate the mass, we need to evaluate the double integral over this region. However, since the region is a triangle, it is easier to evaluate the integral using polar coordinates.

Converting the integral to polar coordinates, we get

M = \(\int _ 0^{\pi/4}\) (r cosθ + r sinθ - r² cos²θ - r² sin²θ) r dr dθ

Simplifying this expression, we get

M = \(\int _ 0^{\pi/4}\)  (r cosθ + r sinθ - r²) r dr dθ

M =\(\int _ 0^{\pi/4}\)  [1/4 (9 sec⁴θ - 6 sec²θ + 2)] dθ

M = 1/4 (9 ln(2 + √3) - 3√3 - 2)

(b) Center of Mass of the Lamina:

The center of mass of the lamina is the point (x, y) given by

x = (1/M) ∬D x p(x,y) dA,

y = (1/M) ∬D y p(x,y) dA,

where M is the mass of the lamina. To evaluate these integrals, we need to convert them to polar coordinates.

Using polar coordinates, we get

x = r cosθ,

y = r sinθ,

dA = r dr dθ.

Therefore,

x = (1/M) \(\int _ 0^{\pi/4}\)  (r² cosθ + r³ sinθ - r⁴ cos²θ - r⁴ sin²θ) r dr dθ

x = (1/M) \(\int _ 0^{\pi/4}\)  [1/5 (27 sec^6θ - 30 sec⁴θ + 15 sec²θ - 2)] dθ

x = 1/5 (9 ln(2 + √3) - 2√3 - 1)

Similarly,

y = (1/M) \(\int _ 0^{\pi/4}\) (r² sinθ + r³ cosθ - r⁴ cosθ sinθ - r⁴ sinθ²) r dr dθ

y = (1/M) \(\int _ 0^{\pi/4}\)[1/5 (3 sec⁴θ - 3 sec²θ + 2)] dθ

y = 1/5 (3 ln(2 + √3) - √3)

To know more about density function here

https://brainly.com/question/30689274

#SPJ4

Answer:

The mean is 4 if im correct.

Answer:

4

Step-by-step explanation:

-4+4+6+-7+7+10+7+9=32

32/8=4

Answer:

7

1. -6

5 5 5

2. -35a b c

3

5.2t

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

Let's solve your equation step-by-step.

10x−27=2x+29

Step 1: Subtract 2x from both sides.

10x−27−2x=2x+29−2x

8x−27=29

Step 2: Add 27 to both sides.

8x−27+27=29+27

8x=56

Step 3: Divide both sides by 8.

8x/8=56/8

x=7

Answer:

hypotenuse = 4.24

Step-by-step explanation:

sin θ = opposite / hypotenuse

sin 45 = 3\(\sqrt{2}\)/ hypotenuse

0.707 = 3\(\sqrt{2}\)/ hypotenuse

hypotenuse = 4.24

Answer:

Step-by-step explanation:

Answer:

wait do we solve it or is there answer choices??

Answer:

1/5

Step-by-step explanation:

1/7 * x = 1/35    multiply both sides by 7

x = 7/35 = 1/5

Using the Pigeonhole Principle, it can be shown that in a set of n positive integers, none exceeding 2n, there is at least one integer that divides another integer.

We can prove this statement by contradiction using the Pigeonhole Principle.

Suppose we have a set of n positive integers, none of which exceed 2n, and assume that no integer in the set divides another integer.

Consider the prime factorization of each integer in the set. Since each integer is at most 2n, the largest prime factor in the prime factorization of any integer is at most 2n.

Now, let's consider the possible prime factors of the integers in the set. There are only n possible prime factors, namely 2, 3, 5, ..., and 2n (the largest prime factor).

By the Pigeonhole Principle, if we have n+1 distinct integers, and we distribute them into n pigeonholes (corresponding to the n possible prime factors), at least two integers must share the same pigeonhole (prime factor).

This means that there exist two integers in the set with the same prime factor. Let's call these integers a and b, where a ≠ b. Since they have the same prime factor, one integer must divide the other.

This contradicts our initial assumption that no integer in the set divides another integer.

Therefore, our assumption must be false, and there must be at least one integer in the set that divides another integer.

To know more about integer,

https://brainly.com/question/29808939

#SPJ11

Answer:

x = -1/3 or x = 6

Step-by-step explanation:

For this equation, you should use the FOIL method or the BOX method. Break it apart to solve it easier. Sites like mathpapa or symbolab can help break these down for you.

The rate at which the distance is changing is calculated to be 14.42 miles per hour.

Consider the east direction to be denoted by x and the north direction to be denoted by y, therefore;

dx / dt = 12 mph

dy / dt = 8 mph
x is equal to 4 miles

Consider the distance between them to be s

Time taken by you to travel 4 miles = distance / speed

Time taken by you to travel 4 miles = 4/12 hour

Distance traveled by the friend in that time = speed × time

Distance traveled by the friend in that time = 8 × (4/12) = 2.67 miles

Now we use the Pythagorean theorem,

x^2 + y^2 + s^2 ...... (1)

Substitute, x = 4 miles and y = 2.67 miles

s^2 = 16 + 7.1289 = 23.1289

s = 4.81

Now differentiate equation 1 with respect to t as follows;

2x (dx/dt) + 2y (dy/dt) = 2s (ds/dt)

2(4) (12) + 2(2.67) (8) = 2 (4.81) (ds/dt)

96 + 42.72 = 9.62 (ds/dt)

138.72 = 9.62 (ds/dt)

ds/dt = 138.72/9.62 = 14.42 miles per hour

Thus the distance is changing at the rate of 14.42 miles per hour.

To learn more about distance; click here:

https://brainly.com/question/13049940

#SPJ4

Answer:

4/6 and 8/12 and 16/24

Step-by-step explanation:

well because it is math and math works like this basically all of theese are equal to 2/3

Answer:

44%

Step-by-step explanation:

Answer:

44%

Hope this helps

The cube roots of 117 441 in rectangular form are: a. 3.00 +4.002, b. –4.96 +0.604, c. -1.96 + 1.964, d. - 124.10 + 11.95, e. 3.00 4.00, f. 4.68 - 1.764, g. 1.96 4.602, and h. 75.00+ 100.00.

To find the nth roots of a complex number, the exact values are given in rectangular form, while the approximate values are given in polar form.

To calculate the exact values of the cube roots, we use the principle of nth roots. This principle states that, for a complex number (a + bi), its nth roots are given by (a + bi)^(1/n) = r^(1/n) (cos(θ + 2πk/n) + i sin(θ + 2πk/n)), where r = √(a² + b²) and θ = arctan(b/a).

By applying this principle, we can obtain the exact values of the cube roots, which are the 8 answers above, rounded to the nearest hundredth.

To know more about rectangular form click on below link:

https://brainly.com/question/29550350#

#SPJ11

Answer:

The team is measuring at 364 ft below the surface

Step-by-step explanation:

Here, we want to get the depth at which the pressure was measured at

to get this, we will have to use the equation that relates the pressure to the depth

From the question, we have this as;

P = 13 + 8/13(d)

From the question, P is 237

Substituting this into the equation, we have

237 = 13 + 8/13(d)

237-13 = 8/13(d)

224 = 8/13(d)

8d = 13 * 224

d = (13 * 224)/8

d = 364 ft