A bouncing ball reaches a height of 27 feet at its first peak, 18 feet at its second peak, and 12 feet at its third peak. Describe how a sequence can be used to determine the height of the ball when it reaches its fourth peak..

Answer:

The city residents born in 1980 are prob 93,000 :3

Step-by-step explanation:

:3

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

To find the values of Z, we can start by expressing 2 + i√3 in polar form. Let's denote it as re^(iθ), where r is the modulus and θ is the argument.

Given: 2 + i√3

To find r, we can use the modulus formula:

r = sqrt(a^2 + b^2)

= sqrt(2^2 + (√3)^2)

= sqrt(4 + 3)

= sqrt(7)

To find θ, we can use the argument formula:

θ = arctan(b/a)

= arctan(√3/2)

= π/3

So, we can express 2 + i√3 as sqrt(7)e^(iπ/3).

Now, we can find the values of Z by taking the natural logarithm (ln) of sqrt(7)e^(iπ/3) and adding 2πik, where k is an integer. This is due to the periodicity of the logarithmic function.

ln(sqrt(7)e^(iπ/3)) = ln(sqrt(7)) + i(π/3) + 2πik

Therefore, the values of Z are:

Z = ln(2 + i√3) + 2πik, where k is an integer.

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

To know more about polar form visit

https://brainly.com/question/30824428

#SPJ11

The third side of the right angle triangle is 5 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the side of the right triangle can be found using Pythagoras's theorem as follows:

c² = a² + b²

where

Therefore, using Pythagoras's theorem,

6² - (√11)² = b²

36 - 11 = b²

b² = 25

square root both sides of the equation

b = √25

b = 5 units

Therefore.

third side = 5 units.

learn more on right triangle here: https://brainly.com/question/23539229

#SPJ1

Answer:

Step-by-step explanation:

In a Harjit saves in a month $150*4= $600 Every quarter he saves (P

Answer: 3/2

Step-by-step explanation:

Given

6/10 + 9/10

Add the numerator together

= (6 + 9) / 10

Simplify by addition

= 15 / 10

Simplify to simplest form by division

= (15 ÷ 5) / (10 ÷ 5)

= 3 / 2

Hope this helps!! :)

Please let me know if you have any questions

Hello there! The answer is:

3/2 OR  1 1/2

Step-by-step explanation:

With like denominators we can add the numerators.

6 + 9 = 15.

Then that answer over the denominator which gives us 15/10. Then simplifying the answer.

That gives us: 3/2 = 1 1/2

I hope this answer helps you out. Let me know if you have any questions/concerns.

Answer:

The sample included only those people who chose to complete the survey.

Step-by-step explanation:

Answer:

if I'm not wrong it should be the second answer choice

Answer:

A

Step-by-step explanation:

did the quiz

Answer:

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

The nth term is visible in the sum:

Apply n = 10 to find the 10th term:

The matching choice is C.

Answer:

3

Step-by-step explanation:

Answer:

142

Step-by-step explanation:

An inequality that can be written in the form ax + by < c (where a and b are not both zero) is called a linear inequality in two variables.

An inequality that represents a line in a two-dimensional coordinate system is referred to as a linear inequality. The set of points that satisfies the inequality is a half-plane bounded by a line that may be dashed or solid.

In contrast to a linear equation, which represents a line, a linear inequality represents a half-plane. The points on one side of the line, rather than the points on the line, are solutions to the inequality.

The method of shading is used to graph a linear inequality in two variables. First, graph the boundary line, which is usually represented by a solid or dashed line, and then select a test point on one side of the line. Shaded regions of the half-plane containing the test point satisfy the inequality.

Learn more about linear inequality here: https://brainly.com/question/30440630

#SPJ11

The formula for the n-th term is:

aₙ = 3*(1/2)⁽ⁿ⁻¹⁾

For a geometric sequence where the first term is a₁ and the common ratio is r, the formula for the n-th term is:

aₙ = a₁*(r)⁽ⁿ⁻¹⁾

Here we know that the first term is a₁ = 3 and the common ratio is r = 1/2.

Then the formula for the n-th term of the sequence is:

aₙ = 3*(1/2)⁽ⁿ⁻¹⁾

Learn more about geometric sequences at:

https://brainly.com/question/24643676

#SPJ1

Answer:

Step-by-step explanation:

12

To find the surface area, we must define what is the surface area

In this case, we have a cube

  ⇒ which means all the sides have equal areas since all the side lengths

      are equal

That means the surface area

  ⇒ is equal to ⇒ 6 * (Area of One Side)        

        '6' comes from the # of sides on a cube

Surface Area = \(6 *\frac{1}{9} *\frac{1}{9} = \frac{6}{9 *9} =\frac{2*3}{3*3*3*3} =\) 2/27

Hoped that helped!

The expression to represent the probability that one marble is yellow and the other marble is red is P(Y and R) = \((^8C_1 \times ^5C_1)\) / \(^{25}C_2\).

Option A is the correct answer.

We have,

P(Y) represents the probability of selecting a yellow marble from the bag.

= \(^8C_1 / ^{25}C_1\)

P(Y) represents the probability of selecting a red marble from the bag.

= \(^5C_1 / ^{25}C_1\)

Now,

The probability that one marble is yellow and the other marble is red.

P(Y and R) = \(^8C_1 \times ^5C_1\) / \(^{25}C_2\)

Thus,

The expression to represent the probability that one marble is yellow and the other marble is red is:

P(Y and R) = \((^8C_1 \times ^5C_1)\) / \(^{25}C_2\)

Learn more about combination here:

https://brainly.com/question/14355408

#SPJ12

The complete question:

A bag contains eight yellow marbles, nine green marbles, three purple marbles, and five red marbles. Two marbles are chosen from the bag. What expression would give the probability that one marble is yellow and the other marble is red?

A. P(Y and R) = \(^8C_1 ~^5P_1 ~^{25}P_2\)

B. P(Y and R) = \(^8C_1 ~^5P_2 ~^{25}P_2\)

C. P(Y and R) = \(^8C_1 ~^5P_2 ~^{25}P_2\)

D. P(Y and R) = \(^8C_3 ~^5P_1 ~^{25}P_2\)

Answer:

Both x and y-coordinate are negative.

Answer:

(-4(x-2))/((x+2)|(x-4)|)

Step-by-step explanation:

You were so close. I stared at your problem for a

long time when you first posted it. I used a graphing utility to experiment. Your denominator was perfect for getting the vertical asymptotes in the right place. The y-intercept worked. The x-intercept was exactly right. I couldn't get the far right piece of the curve to reflect down in the fourth quadrant.

Hours later...suddenly BAM! ABSOLUTE VALUE pops into my head.

I always thought the numerator should be negative, so that middle portion of the curve that looks like a cubic would start "up to the left" and end "down to the right" But those left and right curves should be like mirror images of each other sort of. So I tried the absolute value and it worked! Good luck with your work. Hope this helps a little.

A person pays $1 to play a certain game by rolling a single die once. if a 1 or 2 comes up, the person wins nothing. if, however, the player rolls a 3, 4, 5, or 6 he or she wins the difference between the number rolled and $1, this means that the game is not fair, based on the expected value

We can see that the expected value of the game can be found by multiplying each payout by its probability of occurring and then summing up the results:Expected value = (0.2)($1) + (0.2)($1) + (0.2)($2) + (0.2)($3) + (0.2)($4) + (0.2)($0) + (0.2)($0)Expected value = $0.40 Since the expected value of the game is positive, it means that, over the long run, players are expected to make money on average. This means that the game is not fair.

See more about expected value at: https://brainly.com/question/14723169

#SPJ11

Therefore, the control represented by the decimal value 15 is the one with all four bits set to 1.

In digital electronics, binary digits (bits) are used to represent numbers and control various devices. Each bit can have a value of either 0 or 1, and by combining multiple bits, we can represent larger numbers or control signals. The decimal system, which we are most familiar with, uses 10 digits (0-9) to represent numbers. In contrast, the binary system uses only 2 digits (0 and 1) to represent numbers or controls. To convert a decimal number to binary, we repeatedly divide the number by 2 and keep track of the remainders. The binary representation of a number is the sequence of remainders read in reverse order.

The decimal value 15 can be represented as a control with four binary digits (bits), as follows:

1 1 1 1

Each bit represents a power of 2, from right to left: 2^0, 2^1, 2^2, 2^3. Adding up the powers of 2 where there is a 1 in the binary representation gives us the decimal value.

So, in this case, we have:

1x2^0 + 1x2^1 + 1x2^2 + 1x2^3 = 1 + 2 + 4 + 8 = 15

To know more about decimal value,

https://brainly.com/question/31494892

#SPJ11

We can only add or substract likely terms.

a) In this case we have a mass unit (pounds) and a length unit (feet), so we can not add them together. They are not like terms.

b) In this case we have both lemons, so we can do the operation:

c) In this case, the birds and seconds are not the same units so the terms are not like terms.

Answer:

a) Not like terms

b) 2 lemons

c) Not like terms

Answer:

A line segment has two endpoints. It contains these endpoints and all the points of the line between them. A segment is named by its two endpoints. A ray is a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray.

Step-by-step explanation:

Answer:

Option D

Sine and cosine are same for complementary angles.

The differential d y is  \(d y = ( 1 / 5 ) e^ ( x / 5 )dx\)  and when the values of x and dx are 0 and 0. 05 then the d y is equal to 0.01.

we have to find the differential of d y and Evaluate d y when the given values  of x and dx are 0 and 0. 05,

a) the differential d y,

\(y = e^(x/5)\)

differentiating the above equation with dx we get:

\(d y/dx = (1 / 5 ) e ^ ( x / 5 )\)

\(d y = ( 1 / 5 ) e^ ( x / 5 )dx\)

Therefore, the differential of d y is \(d y = ( 1 / 5 ) e^ ( x / 5 )dx\)

b) To evaluate d y for x = 0 and dx = 0.05, we substitute these values into the differential expression we found in part (a):

\(d y = ( 1 / 5 ) e^( x / 5 )dx\)

\(d y = ( 1 / 5 ) e^(0 / 5 )( 0.05 )\)

= (1/5) ( 1) (0.05)

= 0.01

Therefore, when x = 0 and dx = 0.05, d y is equal to 0.01.

To learn more about the differential equation:

https://brainly.com/question/28099315

#SPJ4

We already know that the solution is (9, -3/5), let's show that

Let's plug our solution into the equation

The second equation is true!

\(2=x^2-10x\\\\\implies x^2 -10x =2\\\\\implies x^2 -2\cdot 5 x +5^2 -5^2 = 2\\\\\implies x^2 -2\cdot 5x +5^2 = 2+5^2 \\\\\implies (x-5)^2 = 27\\\\\implies x-5 = \pm\sqrt {27}\\\\\implies x = \pm\sqrt{27} +5=\pm3\sqrt{3}+5\\\\\text{Hence,}~ x = 5+3\sqrt 3~\text{or}~ x = 5-3\sqrt 3\)

The maximum power of the variable present in the equation is equal to the degree of the polynomial. The variable in this case is x, and the term 4x2 has x to its maximum power of 2.

To learn more about variable refer to:

https://brainly.com/question/28248724

#SPJ1