suppose you look out the window of a skyscraper and see someone throw a tomato downward from above your window. your window is at a height of 450 feet above the ground. the tomato passes your window after 2 seconds and hits the ground 5 seconds after it was thrown. neglect air resistance, and give units in your answers.

The trigonometric ratios and the graph of the periodic function indicates that we get;

1. sin(θ) = -√(13)/7, csc(θ) = -7·√(13)/13

cos(θ) = 6/7, sec(θ) = 1 1/6

tan(θ) = -√(13)/6, cot(θ) = -6·√(13)/13

2. Vertical shift = 4

Amplitude = 3

Period = 6

Equation; y = 3·sin((π/3)·(x - 1.5)) + 4

A periodic function is one in which the values of the function are repeated at regular intervals. Trigonometric functions, such as sinusoidal functions are periodic functions.

1. sin(θ) = -√(13)/7

csc(θ) = 1/sin(θ), therefore;

csc(θ) = 1/(-√(13)/7) = -7/√(13) = -7·√(13)/13

csc(θ) = -7·√(13)/13

sin(θ) = Opposite/Hypotenuse

3·π/2 < θ < 2·π, therefore, θ is in quadrant IV

Making use of the proportional or comparative dimensions of the corresponding lengths in a unit circle, we get;

Relative length of the hypotenuse = 7 units

Relative length of the opposite side = -√(13)

The Pythagorean Theorem, indicates that the adjacent side can be found as follows;

Length of the adjacent side = √(7² - 13) = 6

cos(θ) = Adjacent/Hypotenuse

Therefore;

sec(θ) = 1/cos(θ), therefore;

sec(θ) = 1/(6/7) = 7/6 = 1 1/6

tan(θ) = sin(θ)/cos(θ)

Therefore; tan(θ) = (-√(13)/7)/(6/7) = -√(13)/6

cot(θ) = 1/tan(θ), therefore;

cot(θ) = 1/(-√(13)/6) = -6/√(13) = -6·√(13)/13

cot(θ) -6·√(13)/13

2. The vertical shift is the vertical displacement of the midline above the x-axis, which can be found as follows;

The location of the midline = (Peak value + Minimum point)/2

Therefore, the location of the midline = (7 + 1)/2 = 4

The period = 1/Frequency

The frequency = Number of cycles per second

The graph indicates that in 1 unit, the cycle completed = 1/6

Therefore; Frequency = 1/6

Period = 1/(1/6) = 6

The amplitude is the the distance from the peak to the midline, therefore;

The equation of the form of a sinusoidal function; y = A·sin(B·(x + C)) + D, indicates that we get;

A = The amplitude = 3

Period = 2·π/B, therefore;

6 = 2·π/B

B = 2·π/6 = π/3

D = The vertical shift = 4

When x = 0, y = 7 = Highest value, therefore;

sin((π/3)·(0 + C)) = sin(π/2)

π·C/3 = π/2

C/3 = 1/2

C = 3 × 1/2 = 3/2 = 1.5

The equation is therefore;

A vertical reflection of a function, f(x) is -f(x). The leading coefficient of the equation is positive, therefore, there are no vertical reflection or flip

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Option C is the correct representation of the solution of the inequality equation.

According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. Any of the symbols for inequality, including greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠).

Given the equation, [tex]\frac{x^{2} + 9x - 22 }{x + 4}[/tex] ≥ 0

factors of x² + 9x - 22 are,

x² + 11x - 2x - 22

x(x + 11) - 2(x + 11) = (x + 11)(x - 2)

[tex]\frac{(x + 11)(x - 2)}{x +4}[/tex] ≥ 0

x - 2 ≥ 0

x ≥ 2

so the line should be greater than and equal to 2.

so x + 11 ≥ 0

x ≥ -11

1/(x + 4) ≥ 0 or x + 4 < 0

x < -4

and line varies from,

-4 > x ≥ 11

graph of inequality is between -11 and -4 in which -4 is not included and -11 is included.

only the graph of option C satisfied the conditions.

Hence Option C is correct.

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The total number of brothers and sisters in the family can be represented by the equation 4x + 2.

Number of brothers and sisters mike has = x

Number of brothers and sisters Emily has = 3x

Mike = 1 brother

Emily= 1 sister

Total boys and girls are there in this family = Number of brothers and sisters mike has + Number of brothers and sisters Emily has + Mike + Emily

= x + 3x + 1 + 1

= 4x + 2

Hence, there are 4x + 2 boys and girls in the family including mike and Emily.

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We cannot determine the exact time it takes for the coffee to cool to 45°C without additional information. The value of hA/mC (heat transfer coefficient times surface area over mass times heat capacity) needs to be known to solve for Δt accurately.

The equation describing the cooling of hot coffee is given by:

dT/dt = -h * A * (T - T_room) / (mc)

where T is the temperature of the coffee, T_room is the temperature of the room, h is the heat transfer coefficient, A is the surface area of the cup, m is the mass of the coffee, and c is the heat capacity of the coffee.

We can solve for the time it takes for the coffee to cool from an initial temperature of 80°C to a final temperature of 45°C by integrating both sides of the equation over time, with the initial conditions T(0) = 80°C:

t = (mc / (h * A)) * ln((T_initial - T_room) / (T_final - T_room))

Plugging in the given values, we have:

t = (mc / (h * A)) * ln((80 - 25) / (45 - 25))

Since the units of t are in seconds, we can convert to minutes by dividing by 60:

t = (mc / (h * A)) * ln((80 - 25) / (45 - 25)) / 60

Note that the value of h * A / mc is given as ?, so we cannot determine the exact time it takes for the coffee to cool to 45°C without additional information.

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The cooling of hot coffee can be described by the following equation:

mehA(TT) where 1m is the mass of the coffee (in SI units, kg)

2. c is the heat capacity of the coffee (in SI units, J/kg C)

3. T is the temperature of the coffee (in SI units, C)

4. Tom is the temperature of the room (in SI units, °C)

5. h is the heat transfer coefficient in SI units, W/m O 6. As the surface area of the cup in SI units, m²)

7.ts time (in SI units, s)

#room temperature is 25°C and the coffee is originally at 80 C. how long will it take the coffee to cool to 45 Ct the ratio 10? Provide your answer in minutes.

In a parking lot, let x stand in for the length of the vehicles. This would be regarded as a discrete form of variable.

What exactly are discrete variables?

The procedure used to ascertain a discrete variable's value is counting. One illustration is the number of students present. how many red marbles there are in the jar. How many heads are present after the flip of three coins? students' grade level.

                         The discrete distributions most frequently used by statisticians and analysts are the multinomial, Poisson, Bernoulli, and binomial distributions. There are further instances, including the negative binomial distribution and the geometric and hypergeometric distributions.

The number of vehicles in the parking lot is a discrete numerical variable rather than a continuous one because there are only a finite number of possible values rather than an infinite number and because it must be an integer and cannot be a value between integers. In this instance, discretion is the best course of action.

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Answer:

Method 1: Calculate 40% discount on original price, then subtract discount from original price.

Amount of discount = 40% of $30

= 0.40 × $30

= $12

New price = $30 - $12 = $18

Method 2:

New price = (100% - discount percentage) of original price

= 60% of original price

= 0.60 × $30

= $18

Answer:

-18 and -27 ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Answer:

a. They are proportional

b. 11

Step-by-step explanation: They table is said to be proportional because all their ratios are the same/equal.

b. 5.5 multiplied by 2 is 11.( cross check the other values of wet dog food by multiplying the values by 2)

The solution to the equation [tex] {6}^{(4x - 3)} = - 4[/tex] is x = 0.3019.

To solve the equation [tex]{6}^{(4x - 3)} = - 4[/tex], we need to isolate the variable x. Here are the steps to solve this equation:

First, we need to take the logarithm base 6 of both sides of the equation. This will help us to isolate the exponent.

log6 [tex]{6}^{(4x - 3)}[/tex]= log6 -4

Use the logarithmic property that [tex] log(b) {b}^{x} = x[/tex] to simplify the left-hand side.

4x - 3 = log6 -4

Use a logarithmic table or calculator to find the value of the right-hand side.

4x - 3 = log6 -4

4x - 3 = -1.7924

Finally, we can isolate the variable x by adding 3 to both sides of the equation and then dividing both sides by 4.

4x = 3 - 1.7924

4x = 1.2076

x = 1.2076 ÷ 4

x = 0.3019

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The truth value of a statement can be determined by evaluating the statement in the context of the given universe of discourse.

3xVy(xy = 0): False. The statement is saying that for any x and y in the universe of discourse, the product of x and y must be zero. This is impossible in the set of real numbers.

3x (x2 = -1): False. The statement is saying that for any x in the universe of discourse, the square of x must be -1. This is impossible in the set of real numbers.

3xVy 0(xy = 1): False. The statement is saying that for any x and y in the universe of discourse, the product of x and y must be one. This is impossible in the set of real numbers.

VxSy((x + y = 2) A (2x - y = 1)): True. The statement is saying that for any x and y in the universe of discourse, the sum of x and y must be 2 and the difference between 2x and y must be 1. This is possible in the set of real numbers, so the statement is true.

Vx #03y(xy = 1): False. The statement is saying that for any x and y in the universe of discourse, the product of x and y must be one. This is impossible in the set of real numbers.

3x(x2 = 2): False. The statement is saying that for any x in the universe of discourse, the square of x must be 2. This is impossible in the set of real numbers.

Vx3y(x2 = y): False. The statement is saying that for any x and y in the universe of discourse, the square of x must be equal to y. This is impossible in the set of real numbers.

Vx3y (x = y): True. The statement is saying that for any x and y in the universe of discourse, x must be equal to y. This is possible in the set of real numbers, so the statement is true.

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Answer:

So, the difference of the rates at which the pools are being filled is 1/18 inch per minute.

Step-by-step explanation:

We can find the rate of filling of each pool by dividing the inches filled per hour by the number of minutes it takes to fill them.

Rate of Pool A = 4 inches / 12 minutes = 1/3 inch per minute

Rate of Pool B = 7 inches / 18 minutes = 7/18 inch per minute

The difference in the rates of filling the two pools is:

(7/18) - (1/3) = (7/18) - (6/18) = 1/18 inch per minute.

So, the difference of the rates at which the pools are being filled is 1/18 inch per minute.

a four-story office building has interior columns spaced 30 ft apart in two perpendicular directions

Determine the service live load for a first floor interior column direction

following ASCE-7  guidelines

Area = 20 * 25 = 500 ft^2 which is > 400 ft^2

Nominal live load on every floor = 80 psf

Hence the reduced service live load ( L )

L = Lo [ 0.25 + 15 / √AI ]  ------ ( 1 )

Lo = unreduced load

AT = Tributary area = 500 * number of floors = 2000 ft^2

AI ( influence area ) = AT * number of floors = 2000 * 4 = 8000 ft^2

Lo = 1.6 * 80 psf * 2000 ft^2 = 256 kips

Input values into equation 1 above

L = 106 kips

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At the end of the week, the flower is 96.5 inches tall.

Answer.

Tha answer will be 6x/5 as a fraction

Step-by-step explanation:

As a decimal it is 1.2 cause

6/5=1 1/5= 1.2

Answer:

6/5x

Step-by-step explanation:

To find the equivalent expression, you need to simplify the expression (4/5x + 1) + (2/5x - 1) by combining like terms.

Starting with the first pair of terms:

(4/5x + 1) + (2/5x - 1)

= (4/5x) + (2/5x) + 1 - 1

= (6/5x) + 0

= 6/5x.

So, the equivalent expression for (4/5x + 1) + (2/5x - 1) is 6/5x.

The problem's matrix representation of linear regression is written as =ε = [ε1 ε2 ε3]'.

A variable's value can be predicted using linear regression analysis depending on the value of some other variable.

Y = Xβ + ε,  where Y is indeed the n x 1 vector of a dependent variable, can be used to describe the linear regression issue as a matrix (Yi),

With n = 3 (observations), k = 2 (independent variables), and a matrix representation of a issue, the following can be written:

Y = Xβ + ε

Y = [0.3 0.8 -0.3]

X = [1 1 1; 1 2 0.1]

β = [β0 β1]'

ε = [ε1 ε2 ε3]'

Thus, the problem's matrix form is written as =ε = [ε1 ε2 ε3]'.

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All the reasoning of the statement is given below.

CA ≅ CB, by the congruent triangles.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Given:

CD bisects AB at D.

CD⊥AB

To prove: CA ≅ CB:

Statement 2:

AD ≅ BD

Reason 2:

Definition of segment bisector.

Statement 3:

CD ⊥ AB

Reason 3:

Given.

Statement 6:

CD ≅ CD.

Reason 6:

Reflexive property of congruence.

Statement 7:

ΔCAB ≅ ΔCBD

Reason 7:

Congruent by the criterion SAS.

Therefore, CA ≅ CB.

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The volume of the solid obtained by rotating the region in the first quadrant can be found using the method of cylindrical shells.  

The volume of the solid is obtained by rotating the region in the first quadrant bounded by the curves y = tan(x), y = 3, and x = 0 about the line y = 3.

The formula for the volume is:

where a is the value of x such that y = tan(x) intersects y = 3, and y = tan(x) is the equation of the upper boundary of the region being rotated. To find a, we need to solve the equation tan(x) = 3 for x. The exact value of a can then be plugged into the integral.

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For two fair 6-sided diced that are rolled, the expected value of maximum (E(m)) is 3.5 and variance of maximum (Var(m)) is 2.91.

To find the expected value of the maximum of two dice rolls, we need to find the sum of the products of each maximum value and its probability of occurring.The maximum value of each combination of two dice rolls can range from 2 to 6, with the following probabilities:

Maximum of 2: 1/36

Maximum of 3: 2/36

Maximum of 4: 3/36

Maximum of 5: 4/36

Maximum of 6: 5/36

So the expected value (E(m)) can be calculated as:

E(m) = (2 × 1/36) + (3 × 2/36) + (4 × 3/36) + (5 × 4/36) + (6 × 5/36)

E(m) = 3.5

To find the variance of the maximum (Var(m)), we need to use the formula for variance of a discrete random variable:

Var(m) = E((m - E(m))²)

Var(m) = E((m - 3.5)²)

Var(m) = (2 - 3.5)² × 1/36 + (3 - 3.5)² × 2/36 + (4 - 3.5)² × 3/36 + (5 - 3.5)² × 4/36 + (6 - 3.5)² × 5/36

Var(m) = 2.91

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A graph of the inequality 3x - 2y > 4 is shown in the image attached below.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

In this exercise, we would use an online graphing calculator to plot the given inequality 3x - 2y > 4 as shown on the graph attached below. Based on the graph (see attachment), we can logically deduce that the solution to the given inequality is the shaded region.

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Answer:

6,6.5

Step-by-step explanation:

Answer:

100x+900−900=112x

Step-by-step explanation:

100x+900−900=112x+504−900

The amount of money he will have after paying these bills each month is $2002.

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,

The health insurance plan he selected has an average monthly premium of $297 .

The average monthly cost of his electric bill is $281.

The phone/internet/cable package he wants costs an average of $220 each month.

The monthly salary is $2800.

Now,

Total cost.

= 297 + 281 + 220

= 798

Now,

The amount remaining.

= 2800 - 798

= $2002

Thus,

The amount of money he will have is $2002.

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dy/dx = (y-3)(y+3) is the autonomous differential equation that satisfies all of the given properties.

The autonomous differential equation that satisfies all of the given properties is dy/dx = (y-3)(y+3). This equation has two equilibrium solutions at y = 0 and y = 3, and is positive for -inf < y < 0, and negative for 0 < y < 3, and positive for 3 < y < inf.

To demonstrate this, let's consider the equation at y=-3. Since y=-3 is less than 0, the equation can be simplified to dy/dx = 6. Since 6 is positive, y' is also positive, meaning that y is increasing. Similarly, if y=3, dy/dx = 0 which is neither positive nor negative, so y remains constant. Finally, for y>3, dy/dx = -6, which is negative, so y is decreasing.

Therefore, dy/dx = (y-3)(y+3) is the autonomous differential equation that satisfies all of the given properties.

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The force acting on the adult and the student, both stuck to the wall, is determined by their weight and the centripetal force acting on them.  This means that the net force acting on both of them must be equal to zero.

The quadratic equation in LaTeX:

$ax^2 + bx + c = 0$

The weight of an object is proportional to its mass, and the centripetal force acting on an object is proportional to its mass and the square of its velocity.

Therefore, the ratio of the force acting on the adult to the force acting on the student will be equal to the square of the ratio of their masses and the square of the ratio of their velocities.

Let the mass of the student be 'm' and the mass of the adult be '2m'. Then, the ratio of the forces acting on them will be (2m) / m * (v_adult / v_student)^2, where 'v' represents velocity.

Since the ride remains stationary against the wall for both the student and the adult, this means that the net force acting on both of them must be equal to zero, i.e. their weight must be balanced by the centripetal force acting on them.

Thus, (2m) / m * (v_adult / v_student)^2 = 1.

This equation shows that the mass of the rider does not determine if the ride will remain stationary against the wall while rotating. The ride's velocity and the distribution of mass on the ride will determine whether it remains stationary or not, not the mass of the rider.

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Perimeter of a triangle is the sum of the lengths of it's sides.

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

Perimeter of a straight sided figure is the total length of it's boundary.

A triangle has three sides.

Length of the boundary of the triangle is the sum of the lengths of it's sides.

If the length of sides of a triangle are a, b and c,

Perimeter = a + b + c

If the triangle is equilateral,

Perimeter = 3a, since all the sides are equal.

Hence the perimeter of the triangle is the sum of the length of the boundary of it.

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At this point, the vector "intvector" will contain all of the integers read from input minus five.

int x = 0;

vector<int> intvector;

while (x != 0)

{

   cin >> x;

   intvector.push_back(x - 5);

}

First, we create a variable to store the integer from input, "x", and a vector to store the integers minus five, "intvector". Then, we create a while loop that runs until the value of "x" is equal to zero. Inside the loop, we read an integer from input and store the value in "x". Then, we subtract five from "x" and add the resulting value to the vector "intvector". This loop will run until the value of "x" is equal to zero.  At this point, the vector "intvector" will contain all of the integers read from input minus five.

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The variable y varies directly with x and the equation is y = 1.6x

From the question, we have the following parameters that can be used in our computation:

x y

4 6.4

7. 11.2

10 16

13. 20.8

From the table above, we can see that;

The y values is 1.6 multiplied by the x values

This implies that the equation is a direct variation

So, we have the equation to be

y = 1.6x

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