If PQRS is a rectangle,
find the measure of ZQPT.
P
(16x - 17)
(10x + 1)°
T
R
S

A solution of the first order IVP consisting of this differential equation is   y = [tex]\frac{1}{x^2-5}[/tex] and the domain of y considered as a function over the reals is (-∞, -√5) ∪ (-√5, +√5) ∪ (√5, ∞).

We have to find the domain of y considered as a function over the reals.

The differential equation is  y' + 2x[tex]y^2[/tex] = 0

The solution of the given differential equation is y = 1/([tex]x^2[/tex] + c)......(1)

The given initial value; y(-3) = 1/4

Replace the initial value in the first-order DE solution provided. To obtain the equation for y, locate the constant c and then re-substitute 'c'.

Now put x = -3 and y(-3) = 1/4 in equation 1

[tex]\frac{1}{4}=\frac{1}{(-3)^2+c}[/tex]

[tex]\frac{1}{4}=\frac{1}{9+c}[/tex]

9+c = 4

Subtract 9 on both side, we get

c = -5

Now substitute the value of c again in equation 1

y = [tex]\frac{1}{x^2-5}[/tex]

To find the domain of y we can write it as

y = [tex]\frac{1}{(x)^2-(\sqrt{5})^2}[/tex]

Now the simplified form is

y = [tex]\frac{1}{(x-\sqrt{5})(x+\sqrt{5})}[/tex]

Now the domain of y over R is

(-∞, -√5) ∪ (-√5, +√5) ∪ (√5, ∞).

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The complete question is:

y = 1/([tex]x^2[/tex] + c) is a one parameter family of solutions of the first order DE y' + 2x[tex]y^2[/tex] = 0. Find a solution of the first order IVP consisting of this differential equation and the given initial condition.

y(-3) = 1/4

Find the domain of y considered as a function over the reals. (Enter your answer using interval notation.)

Answer:

Option 3. Look at my screenshot so you can see the circled one

Step-by-step explanation:

The reasoning behind this is slope is rise over run (rise/run)
Graph 3 goes down 3 so -3 and runs 1 over so (-3/1)
This is simplified as -3.

I hope this helps you out :D

The average salary for college graduates is 53% higher than that of high school graduates.

Mathematically, percentage increase can be calculated by using this mathematical expression:

Percentage increase = [Final value - Initial value]/Initial value × 100

Substituting the given parameters into the percentage increase formula, we have the following;

Percentage increase = [62,047 - 40,626]/40,626 × 100

Percentage increase = 21,421/40,626 × 100

Percentage increase = 0.527 × 100

Percentage increase = 52.7 ≈ 53%.

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Answer:

v^2+4v+4

Step-by-step explanation:

To do this we have to know that (2+v)^2 is the same as (2+v) (2+v)

Next, use the distributive property and add like variables to get the final answer of v2+4v+4

I hope this was able to help you out :D

The speed of the bicycle is 381 meters per minutes

we know that,

revolutions per minute = speed in meters per minute / circumference in meters.

Diameter = 32 inches

Circumference of the wheel = 2πr

r = Diameter/2 = 32/2 = 16

Circumference = 2 × π × 16

=  100.5714 inches

Approximately = 100 inches

we know that,

1 inch = 0.0254 meter

100 inches = x

x = 100 × 0.0254 meters

x = 2.54 meters

Hence:

Revolutions per minute = Speed in meters per minute / circumference in meters.

Speed = Revolutions per minute × circumference in meters.

Speed = 150 RPM × 2.54 meters

Speed = 381  meters per minutes

so, the speed of the bicycle is 381 meters per minutes.

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The equation will be 4(x + 2) = 40. Then the value of the variable 'x' will be 8.

The sum of all the sides of the square or the product of the four and the edge length of the square is known as the perimeter of the square. For a square with a side length of a unit, we get:

Perimeter of the square = 4a unit

The perimeter of the square is 40 cm. And the sides length of the square is (x + 2) cm. Then the perimeter of the square is given as,

4(x + 2) = 40

Simplify the equation, then we have

4(x + 2) = 40

(x + 2) = 10

x = 10 - 2

x = 8

The equation will be 4(x + 2) = 40. Then the value of the variable 'x' will be 8.

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The complete question is given below.

Solve it to find the value of x. Also, find the actual length of each square perimeter of the square is 40 cm and side length is (x + 2).

The angle whose supplement is 30 degrees greater than 4 times the supplement is 30°

Two angles are called supplementary when their measures add up to 180 degrees.

For example:- 120° and 60°, 110° and 70°, 140° and 40°, 90° and 90°, 20° and 160°, 135° and 45° are some example of supplementary angles.

Given that, an angle whose supplement is 30 degrees greater than 4 times the supplement.

Let the angle asked be x,

Therefore, the supplement of x, will be = 180°-x

According to the question, Its supplement is 30 degrees greater than 4 times the supplement.

Therefore, establishing the equation,

So, for solving for x, we have,

180°-x = 30°+4x

4x+x = 180°- 30°

5x = 150°

5x/5 = 150°/5

x = 30°

As, we considered the angle asked be x,

Hence, the angle whose supplement is 30 degrees greater than 4 times the supplement is 30°

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Answer:

I believe it's BC

Step-by-step explanation:

I can't really give an explanation but I've done this before and struggled but learned it, hope I'm right

Answer:

So, there are 5,280 feet in a mile, so you will want to find out how many times 5, 280 will go into 23,760. To do this, you will divide.

23,760/5,280 = 4.5

There are 4.5 or 4 1/2 miles in 23,760 feet!

Step-by-step explanation:

Hope it helps! =D

The equation that matches the hanger diagram is 2x=5

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

The hanger diagram added as an attachment

From the diagram, we hav

Left = x + x

Right = 1 + 1 + 1 + 1 + 1

This gives

Left = 2x

Right = 5

So, we have

2x = 5

hence, the equation is 2x = 5

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Answer:

490 adults at the museum!

hope that helps :)

mark brainly please.

Answer:hie

hie

Step-by-step explanation:hie

This problem is designed to minimize the cost of feeding students in the dorms while providing a minimum of 1800 calories. The objective function is to minimize the cost of the diet, which is calculated by multiplying the pounds of each food by its cost and adding them together. The constraints of the problem are that A must be greater than or equal to 0, B must be greater than or equal to 2, and C must be less than or equal to 0.75.

1. 2.25A + 2B + 3C

2. A >= 0

3. B >= 2

4. C <= 0.75

The objective of this problem is to minimize the cost of feeding students in the dorms, while the diet must contain a minimum of 1800 calories. To achieve this, three decision variables were defined: A, B, and C, which represent the pounds of food A, B, and C respectively. The objective function is to minimize the cost of the diet, which is calculated by multiplying the pounds of each food by its cost, and adding them together. There are three constraints in the problem: A must be greater than or equal to 0, B must be greater than or equal to 2, and C must be less than or equal to 0.75. These constraints ensure that the diet contains the desired amount of each food and that the total calories meet the minimum requirements.

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Answer:  -1 7/20

Step-by-step explanation:

hope this helps

Answer:

$10,224.30

Step-by-step explanation:

Answer:

c (72)

Step-by-step explanation:

since there are four wheels to every bike, you just have to multiply the number of bikes to the amount of wheels per bike. given this, 18 * 4=72.

The surface area of the container is 62 square inches.

The correct option is D.

In three-dimensional space,

a prism is a polyhedron where two ends are similar.

Given:

A student draws the net below to show the dimensions of a container that is shaped like a right rectangular prism.

We have H = 2 inches

L = 5 inches

W = 3 inches

Surface area of the rectangular prism,

A = 2(W×L + H×L + H×W)

A = 2(3×5+2×5+2×3)

A = 2(15+10+6)

A = 2(31)

A = 62 square inches

Therefore, the surface area is 62 square inches.

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The solution of the equation x/6 + 2 = 15 will be 78 by using the property of subtraction and multiplication of equality.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The equation is given below.

x/6 + 2 = 15

Subtract 2 on both sides. Then we have

x / 6 + 2 - 2 = 15 - 2

x / 6 = 13

Multiply the equation by 6, then we have

x/6 × 6 = 6 × 13

x = 78

The solution of the equation x/6 + 2 = 15 will be 78 by using the property of subtraction and multiplication of equality.

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Work Shown:

A = P*(1+r*t)

A = 5000*(1+0.12*30/12)

A = 6500

The amount $6500 is what you pay back

Divided over 30 months gives 6500/30 = 216.67 dollars per month.

Side note: The value t is in years, so 30 months = 30/12 years.

The height in meters is 19.75 meters

The rocket hit the ground after 8.06 sec

The maximum height in seconds is 81 meters

we would have to use 0.5 as the value for t in the formula

h(t) = -5t² + 40t + 1

h(0.5) = -5(0.5)² + 40(0.5) + 1

= -1.25 + 20 +1

= 19.75

To find when the rocket hit the ground, we need to find when the height of the rocket is equal to 0. So we will set h(t) = 0 and solve for t:

-5t² + 40t + 1 = 0

by using Quadratic equation formula we get t = (-b ± √(b²-4ac))/2a

we solve this using the calculator

so t1 = (40 + 40.6)/10 = 80.6/10 = 8.06 sec

Since the time of the rocket hit the ground should be positive, so the rocket hit the ground after 8.06 seconds after launch.

To find the rocket's maximum height, we need to find the vertex of the parabola. The vertex of the parabola can be found by using the formula x = -b/2a,

where x is time and a, b, c are from equation.

so, x = -b/2a

= -40/2*-5

= -40/ -10

= 4 sec

and by using the above formula of x, we get the

h(4) = -5(4)² + 40(4) + 1

= -80 + 160 + 1

= 81 meters

Therefore, the rocket's maximum height is 81 meters.

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These points (-1,-8), (0,-6), (1,-4), and (2,-2) are the set of ordered pairs made up of points on the graph of the function y = 2x – 6.

What is the linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The linear function is given below.

y = 2x – 6

The points (-1,-8), (0,-6), (1,-4), and (2,-2) lies on the equation.

As when the put the given points in the equation , than it satisfies the given condition.

Hence, these points (-1,-8), (0,-6), (1,-4), and (2,-2) are the set of ordered pairs made up of points on the graph of the function y = 2x – 6.

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a) The probability of a student living within walking distance of campus is 0.1521.

To find the probability of a student living within walking distance of the campus, we can use the formula for conditional probability:

P(A and B) = P(A) * P(B|A).

For this situation, An is "living within walking distance to campus" and B is "living with parents."

Thus, P(A and B) = (0.23)(0.67) + (0.06)(0.33) = 0.1521.

Hence, the probability of a student living within walking distance of campus is 0.1521.

b)  The probability given a student living within walking distance of campus they experience with their parents is 0.67.

To find the probability given a student day to day routines within walking distance to campus they experience with their parents, we can use the formula for conditional probability:

P(A|B) = P(A and B)/P(B).

In this situation, A is "living with parents" and B is "living within walking distance to campus."

Thus, P(A|B) = P(A and B)/P(B) = (0.23)(0.67)/0.1521 = 0.67.

Subsequently, the probability gave a student living within walking distance of campus experience with their parents is 0.67.

c) Living with parents and living within walking distance are independent events.

To decide whether living with parents and living within walking distance are independent events, we can analyze P(A|B) with P(A).

On the off chance that P(A|B) = P(A), the events are independent. For this situation, P(A|B) = 0.67 and P(A) = 0.67, so living with parents and living within walking distance are independent events.

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a) 0.04550 has four significant figures.

b) 5.0003 has four significant figures.

c) 1.000 x [tex]10^5[/tex] has four significant figures.

d) 0.00002 has one significant figure.

e) 1.01 x [tex]10^{-2}[/tex] has three significant figures.

f) 7 has one significant figure.

Significant figures are the digits in a number that are known with certainty, including one uncertain digit. In general, any non-zero digit is considered a significant figure, and zeros between non-zero digits are also significant figures.

Leading zeros before the first non-zero digit and trailing zeros after the last non-zero digit are not considered significant figures.

For example, in the given number 5.006, there is four significant number,

since all zeros between integers are always significant.

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Yes, it is possible to offer a discount to customers who order two dozen cookies.

What is Discount ?

The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.

1 dozen=12 pieces

Yes, it's possible to offer a reduction to guests who order two dozen eyefuls. Depending on the capacity of the company, offering a reduction could help to increase the number of orders and potentially increase the company's capacity. still, it's important to consider the cost of offering a reduction and the implicit increase in profit that could be generated from the fresh orders.

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Yes, it is possible to offer a discount to customers who order two dozen cookies.

What is Discount ?

The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.

1 dozen=12 pieces

Yes, it's possible to offer a reduction to guests who order two dozen eyefuls. Depending on the capacity of the company, offering a reduction could help to increase the number of orders and potentially increase the company's capacity. still, it's important to cocost nsider the of offering a reduction and the implicit increase in profit that could be generated from the fresh orders.

So ,Yes it is possible to offer a discount to customers who order two dozen cookies.

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Analyze the diagram of the trapezoid gives BA = 10.5 units

A trapezoid (also known as a trapezium) is a four-sided geometric shape that has two parallel sides (the bases) and two non-parallel sides (the legs). The bases of a trapezoid can have different lengths, but the legs must be congruent and parallel to each other.

Let's analyze the diagram below and complete the instructions:

Since CB / CA = DE / DF

where CB = 6, DE = 4, EF = 7

We can say:

DF = DE + EF = 4 + 7 = 11

CA = CB + BA = 6 + BA

CB / CA = DE / DF

6/(6 + BA) = 4/11

6 × 11 = 4(6 + BA)

66 = 24 + 4BA

24 + 4BA = 66

4BA = 66 - 24

4BA = 42

BA = 42/4

BA = 10.5 units

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Answer: 602.88 square feet

Equation for surface area of cylinder:

A = 2πrh+2πr^2

r = 6, because radius is half of the diameter

h = 10

A = 2(3.14)(6)(10) + 2(3.14)(6)^2

A = 376.8 + 226.08

A = 602.88 square feet

The general form of exponential formula is y = a * b^x, the  population of the city in 2018 6.058454 million.(c) the population of the city be 8 million19.38548963 years.

In this problem, a = 5.21 million and b = 1 + 2.86%/100 = 1.0286.

In 2012, the population was 5.89 million.

In 2018, the population will be 5.89 * 1.0286 ^ (2018 - 2012) = 5.89 * 1.0286 ^ 6 = 6.058454 million.

To find when the population will be 9 million, your equation becomes:

9 = 5.21 * 1.0286 ^ x divide both sides of this formula by 5.21 to get:

9/5.21 = 1.0286 ^ x take the log of both sides of the equation to get:

log(9/5.21) = log(1.0286^x) since log(1.0286^x) = x * log(1.0286), the equation becomes:

log(9/5.21) = x * log(1.0286)

Divide both sides of this equation by log(1.0286) to get:

log(9/5.21) / log(1.0286) = x

Solve for x to get:

x = 19.38548963.

Confirm by replace x in the original equation to get:

9 = 5.21 * 1.0286 ^ 19.38548963 becomes 9 = 9.

This confirms the value of x is good.

The population will grow to 9 million in 19.38548963 years.

To find when the population will double, the equation becomes:

2 = 1 * 1.0286 ^ x

Simplify to get:

2 = 1.0286 ^ x

Take the log of both sides of this equation to get:

log(2) = log(1.0286 ^ x)

Since log(1.0286 ^ x) = x * log(1.0286), this equation becomes:

log(2) = x * log(1.0286)

solve for x to get:

x = log(2) / log(1.0286) = 24.5808602.

to confirm this is true, replace x in the original equation to get:

2 = 1.0286 ^ 24.5808602 which becomes 2 = 2.

This confirms the value of x is true.

The population will double in 24.5808602 years.

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[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{19})\hspace{10em} \stackrel{slope}{m} ~=~ 7 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{19}=\stackrel{m}{ 7}(x-\stackrel{x_1}{2}) \\\\\\ y-19=7x-14\implies {\Large \begin{array}{llll} y=7x+5 \end{array}}[/tex]