The solution of the differential equation is given by r = 5tan(t + c) where c is the constant of integration, determined by the initial condition (x, 5).
The given differential equation is dr sec21dt tant 1. This is a first order linear differential equation which can be solved using an integrating factor. The integrating factor is given by e^(integral(sec^2(t)dt)). The solution of the equation is given by
[tex]r = (integral(sec^2(t))) + c[/tex]
where c is the constant of integration
Let y = sec(2x)
dy/dt = 2tan(2x)sec(2x)
Now, substituting the given point, we get
5 = sec(2x)
⇒ 2x = arccosec(5)
⇒ x = arccosec(5)/2
Now, substituting this in the equation of the differentiable curve, we get
[tex]\int\limits^a_b {x} \, dx dy/dt = 2tan(arccosec(5))sec(arccosec(5))[/tex]
Hence, the solution of the differential equation passing through the given point is y = sec(2x) = sec(arccosec(5))
or r = sec(arccosec(5))
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A circular field has a diameter of 60 m. So Andi ran around the area 3 times. Then the distance traveled by Andi is .... meters.
Answer:
565.2 m------------------------------
One full circle is:
C = πdC = 3.14*60 m = 188.4 mThree times the same distance:
188.4 m * 3 = 565.2 mAnswer:
Distance travelled = 565.2 m
Step-by-step explanation:
Formula of circumference,
→ C = 2πr = π × d
The circumference of circle is,
→ π × d
→ (22/7) × 60
→ 1320/7
→ 188.4
Distance traveled after 3 rounds,
→ C × 3
→ 188.4 × 3
→ 565.2 m
Hence, Andi covered 565.2 m.
Question 2 of 9
Use the scale to help you solve the equation and find the value of x. Enter the
value of x below.
Y
x+2=7
X =______
Answer: 5
Step-by-step explanation:
x=7-2
x=5
Answer:
x=5
Step-by-step explanation:
5+2=7 or 7-2=5
Enola wants to invest $8,600.00 in a savings account that pays 5.1% simple interest.
How many years will it take for this investment to triple in value?
Round your answer to the nearest tenth of a year.
years for this investment to triple in value.
It will take _____ years for this investment to triple in value.
Step-by-step explanation:
To find the number of years it will take for Enola's investment to triple in value, we can use the formula for simple interest:
I = P * r * t
where I is the total interest earned, P is the principal (the initial amount invested), r is the interest rate, and t is the number of years.
Since the investment will triple in value, the total interest earned will be equal to two times the initial investment, or 2 * $8,600.00 = $17,200.00. Substituting these values into the formula and solving for t, we get:
$17,200.00 = $8,600.00 * 5.1% * t
t = $17,200.00 / ($8,600.00 * 5.1%) = 3.28 years
Rounding this value to the nearest tenth of a year, we get t = 3.3 years. Therefore, it will take approximately 3.3 years for Enola's investment to triple in value.
Of the 24 fast-food businesses on Valley Mills Drive, the number that have a drive-up window, outside seating, or a pay telephone is summarized as follows:
18 have a drive-up window.
17 have outside seating.
8 have pay telephones.
12 have a drive-up window and outside seating.
6 have outside seating and a pay telephone.
5 have a drive-up window and a pay telephone.
4 have all three.
Find the number of businesses that have the following.
(a) a drive-up window and no outside seating
(b) a drive-up window and outside seating, but no pay telephone
(c) no pay telephone
(d) only a drive-up window
(e) outside seating or a pay telephone
By using a Venn diagram, we can conclude that:
a. 10 businesses have a drive-up window and no outside seating
b. 4 Businesses have a drive-up window and outside seating, but no pay telephone
c. 20 businesses have no pay telephone
d. 9 businesses have only a drive-up window
e. 8 businesses have outside seating or a pay telephone
A Venn diagram is a diagram consisting of overlapping circles to illustrate the logical relationship between two or more sets of items.
In the question, there are 3 sets of criteria that describe the condition of the fast-food businesses in Valley Mills Drive: whether or not there is a drive-up window, outside seating, or a pay telephone.
Let d denotes the number of businesses that have the three criteria.
If a denotes the number of businesses that have drive-up window and outside seating only, then:
drive-up window and outside seating = a + d
12 = a + 4
a = 8
If b denotes the number of businesses that have outside seating and a pay telephone only, then:
outside seating and a pay telephone = b + d
6 = b + 4
b = 2
If c denotes the number of businesses that have drive-up window and a pay telephone only, then:
drive-up window and a pay telephone = c + d
5 = c + 4
c = 1
If x denotes the number of businesses that have drive-up window only, then:
have a drive-up window = a + c + d + x
18 = 4 + 1 + 4 + x
18 = 9 + x
x = 9
If y denotes the number of businesses that have outside seating only, then:
have outside seating = a + b + d + y
17 = 4 + 2 + 4 + y
17 = 10 + y
y = 7
If z denotes the number of businesses that have pay telephone only, then:
Have pay telephone = b + c + d + z
8 = 2 + 1 + 4 + z
8 = 7 + z
z = 1
Then we can draw a Venn diagram to illustrate those numbers to get a better illustration in answering the questions.
a. a drive-up window and no outside seating = c + x = 1 + 9 = 10
b. a drive-up window and outside seating, but no pay telephone = a = 4
c. no pay telephone = x + y + a = 9 + 7 + 4 = 20
d. only a drive-up window = x = 9
e. outside seating or a pay telephone = y + z = 7 + 1 = 8
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2. JOY leather, a manufacturer of leather Products, makes three types of belts A, B and C which are processed on three machines M1, M2 and M3. Belt A requires 2 hours on machine (M1) and 3 hours on machine (M2) and 2 hours on machine (M3). Belt B requires 3 hours on machine (M1), 2 hours on machine (M2) and 2 hour on machine (M3) and Belt C requires 5 hours on machine (M2) and 4 hours on machine (M3). There are 8 hours of time per day available on machine M1, 10 hours of time per day available on machine M2 and 15 hours of time per day available on machine M3. The profit gained from belt A is birr 3.00 per unit, from Belt B is birr 5.00 per unit, from belt C is birr 4.00 per unit. What should be the daily production of each type of belt so that the profit is maximum?
a) Formulate the problem as LPM
b) Solve the LPM using simplex algorithm.
c) Interpret the shadow prices
The number of belts produced must be positive: X1, X2, X3 >= 0
The shadow price of a constraint can be understand as the change in the objective function value for a unit change in the right-hand side (RHS) value of the constraint, with all other variables held constant.
What are constraints?A constraint is a condition of an optimization problem that should be satisfied the condition.
Here we can formulate this problem as a linear programming model (LPM):
Consider X1 be the number of belt A produced per day
Let X2 be the number of belt B produced per day
Let X3 be the number of belt C produced per day
The objective function is to maximize the profit, that is;
3X1 + 5X2 + 4X3.
The constraints are as follows:
The time spent on machine M1 must be less than or equal to 8 hours per day then;
2X1 + 3X2 <= 8
The time spent on machine M2 must be less than or equal to 10 hours per day then;
3X1 + 2X2 + 5X3 <= 10
The time spent on machine M3 must be less than or equal to 15 hours per day then we have
2X1 + 2X2 + 4X3 <= 15
Thus number of belts produced must be positive:
X1, X2, X3 >= 0
To solve this LPM using the simplex algorithm, you can follow these steps:
w In standard form, the objective function is to minimize the cost, and all constraints are in the form of "less than or equal to" a certain value.
The pivot row is the row that corresponds to the smallest positive ratio between the right-hand side (RHS) value and the corresponding pivot column element the constraint 2X1 + 3X2 ≤ 8.
Now Interpret the shadow prices.
The shadow price of a constraint can be understand as the change in the objective function value for a unit change in the right-hand side (RHS) value of the constraint, with all other variables held constant.
It can help to understand the value of the constraints in the LPM and how they contribute to the optimal solution.
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A store manager purchased a total of 15 pens and markers. Each pen cost $3.50, and each marker cost $1.75. If the manager spent a total of $38.50, how many pens did the store manager purchase?
The store manager purchases 7 pens which can be determined by the concept of equations.
What are equations?According to question store manager purchased a total of 15 pens and markers. So, let us assume the total number of pens =x and the total number of markers = y
The above statement gives us the equation as follows:
x + y=15
The statement each pen cost $3.50, and each marker cost $1.75 and the manager spent a total of $38.50 gives us the equation as follows:
3.50x +1.75 y=38.50
By solving both the equation on multiplying first eq by 3.50 gives
3.50x+3.50y=52.5
Subtracting the above two equations gives
1.75y=14
y=8
Putting value of y in first equation gives x=7
As we had assumed that the total number of pens = x
Hence, the total number of pens =7
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suppose the relative risk of an outcome given exposure versus non-exposure is unity. determine the percent increased risk rounded to the nearest hundredth of a percent.
The percentage of higher risk is unaffected by exposure as relative risk in unity.
In order to determine the strength of the relationship between exposures (treatments or risk factors) and outcomes, relative risk is employed in the statistical analysis of data from ecological, cohort, medical, and intervention studies. For instance, in a study looking at how the drug apixaban affected the occurrence of thromboembolism, 8.8% of patients receiving a placebo developed the condition, whereas only 1.7% of patients receiving the medication did. This means that the relative risk is.19 (1.7/8.8), meaning that patients receiving apixaban had 19% the disease risk of patients receiving a placebo. [4] In this instance, apixaban lowers the probability of disease, making it a protective rather than a risk factor.
Values of relative risk can be understood as long as the relationship between the exposure and the result is assumed to be causal.
RR = 1 denotes that the outcome is unaffected by exposure.
When the risk of the outcome is less than 1, this is referred to as a "protective factor."
RR > 1 indicates that the exposure, a "risk factor," has an effect on the outcome's risk.
Therefore, the percentage of higher risk is unaffected by exposure as relative risk in unity.
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The profit, p(x), that Rivka’s Delivery Service makes from delivering packages between local businesses is P(x), where x is the number of $0.10 price increases for each delivery. Use the graph below to answer the question.
2.5 price hikes are often required to optimize profit.
How do you calculate the cost per unit?
To get the unit price of an item, we divide the price of a specific number of units by the number of units. If 12 ounces of soup cost $2.40, for instance, divide $2.40 by 12 ounces to get the unit price of soup, which is $0.20 per ounce.
x = the number of price hikes
y = Earnings
Additionally from the query, we have
starts at (0, 50)
expands to (2.5, 81.25)
Reduce through (6.531, 0)
It follows that
the most is (2.5, 81.25)
Remember that
x = the number of price hikes
Thus, we have
x = 2.5
Hence, the number of price increases is 2.5
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Anna has 7,209 cans of soup that need to be boxed. If she puts 9 cans of soup in 1 box, how many boxes will she need.
Answer:
Anna needs 801 boxes.
Step-by-step explanation:
You need to know how many groups of 9 are in 7209.
Use division to find this answer.
7209 ÷ 9 = 801
Anna needs 801 boxes.
Which equation represents the line that passes through points (0, 6) and (2, 0)?
O y=-x+2
O y=-x+6
X+
Oy=-3x+2
O y=-3x+6
Find the volumes of the solid generated by revolving the regions bounded by the graphs of the graphs of the equations about the given lines:
y=5x2y=0x=3
a) on the y-axis.
b) on the x-axis.
c) on the line y = 45.
d) on the line x = 3.
Volume of solid generated by revolving the region bounded by the graph is 3817.53 unit
What do you mean by volume of revolution?A volume is created while a plane figure rotating about an axis or around any straight line situated on the same plane.
How to calculate volume of solid generated by revolving the region?We apply definite integration to calculate the required volume.
we are given the equation y = 5x² and y =0, x= 3
volume is calculated by using the formula, V = ∫π y² dx
V = ∫₀³π (5x²) ² dx
On the y-axis x = 0 so upper limit x = 3 and lower limit x= 0
V= π × 25/5 [x⁵] ³₀
V = 15.71 [3⁵- 0]
hence, the volume of solid = 3817.53 unit
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Hi, I need help with this. Thank you.
1. The solution to the quadratic equation, x² - 14x + 49 = 40, is x = 13.32 and x = 0.68
2. The solution to the quadratic equation, x² - x = 12, is x = -3 and x = 4
3. i. The factors of 2x² - 15x - 8 = 0 are (2x +1) and (x - 8)
ii. The x-intercepts of 2x² - 15x - 8 = 0 are x = -1/2 and x = 8
Solving Quadratic equationsFrom the question, we are to solve the given quadratic equation by completing the square.
The given equation is
x² - 14x + 49 = 40
Solving the equation
x² - 14x + 49 = 40
x² - 14x = 40 - 49
x² - 14x = -9
Multiply the coefficient of x by 1/2 square and add to both sides
x² - 14x + (-7)² = -9 + (-7)²
(x - 7)² = -9 + 49
(x - 7)² = 40
x - 7 = ±√40
x = 7 ± √40
x = 7 ± 6.32
x = 7 + 6.32 OR 7 - 6.32
x = 13.32 OR 0.68
Solving x² - x = 12 by factoring
x² - x = 12
x² - x - 12 = 0
x² -4x + 3x - 12 = 0
x(x - 4) + 3(x - 4) = 0
(x + 3)(x - 4) = 0
x + 3 = 0 OR x - 4 = 0
x = -3 OR x = 4
Determining the factors of 2x² - 15x - 8 = 0
2x² - 15x - 8 = 0
2x² - 16x + x - 8 = 0
2x(x - 8) + 1(x - 8) = 0
(2x + 1)(x - 8) = 0
The factors are (2x +1) and (x - 8)
Determining the x-intercepts
(2x + 1)(x - 8) = 0
2x + 1 = 0 and x - 8 = 0
2x = -1 and x = 8
x = -1/2 and x = 8
Hence, the x-intercepts are -1/2 and 8
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Cindy is a travel agent. She receives a 9% commission based on the value of the trips she books. Today she spent eight hours arranging a $9,300 cruise for a newlywed couple. 19. How much commission did she earn? 20. What was her mean hourly pay for the work she did?
Cindy was able to make $837 in commission thanks to her commission rate, which equates to $104.62 per hour.
What is the explanation?Cindy is a travel agent. She receives a 9% commission based on the value of the trips she books. Today she spent eight hours arranging a $9,300 cruise for a newlywed couple
The commission that Cindy received can be determined by:
= Commission % x Price of booked trip
= 9% x 9,300
= $837
Consequently, the following is her hourly wage:
= Commission received / Hours worked
= 837 / 8
= $104.62
The bottom line is that made $104.62 per hour plus $837 in commission.
Cindy was able to make $837 in commission thanks to her commission rate, which equates to $104.62 per hour.
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Look at the diagram
Complete the following sentences.
Angle e= Angle , as they are alternate angles.
Angle f= Angle , as they are alternate angles.
Angles a, b and c add up to °, as they are on a straight line.
Therefore, angles e, f and b also add up to
Answer:
Angle e = Angle a, as they are alternate angles.
Angle f = Angle c, as they are alternate angles.
Angles a, b, and c add up to 180°, as they are on a straight line.
Therefore, angles e, f and b also add up to 180°.
Use algebraic rules of equations to predict the solution type to the system of equations
The solution type to the system is one solution or consistent system
How to predict the solution type to the system?From the question, we have the following parameters that can be used in our computation:
f(x) = [x + y = 4
[y = 2x - 1
Substitute y = 2x - 1 in the equation x + y= 4
So, we have the following representation
x + 2x - 1 = 4
Evaluate the like terms
3x = 5
So, we have
x = 5/3
Substitute x = 5/3 in y = 2x - 1
So, we have the following representation
y = 2 * 5/3 - 1
Evaluate
y = 2.33
Because x and y have real values
Then, the solution type is a consistent system
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Sunil drove 63.9823 km to visit his grandmother. When he reached his grandmother's house he noticed that the car had used up 3.31 litre of petrol. How many km can the car go in 1 litre?
The km per liter based on the information that Sunil can drive is 19.33 km.
How to illustrate the expression?An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, Sunil drove 63.9823 km to visit his grandmother. When he reached his grandmother's house he noticed that the car had used up 3.31 litre of petrol.
Therefore, the km per liter will be:
= 63.9823 / 3.31
= 19.33 km per liters
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given the function that indicates the time it takes to double an investment compounded continiuosly at 6.35% then solve for t
10.9 years long will it take for $1000 to double at a 6.35% annual interest rate that is compounded every month.
Given that,
We have to find how long will it take for $1000 to double at a 6.35% annual interest rate that is compounded every month.
We know that,
P = $1000
r = 6.35% = 0.635
n=12
A = $2000
A = P(1+r/n[tex])^{nt}[/tex]
2000 = 1000(1+0.635/12[tex])^{12t}[/tex]
2= (1+0.635/12[tex])^{12t}[/tex]
log2= log(1+0.635/12[tex])^{12t}[/tex]
log2= 12t×log(1+0.635/12)
t=log2/12×log(1+0.635/12)
t≈10.9 years.
Therefore, 10.9 years long will it take for $1000 to double at a 6.35% annual interest rate that is compounded every month.
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What is f(2) for the function f(x)=6x+8?
Answer: 20
Step-by-step explanation:
x = 2
6(2)+8 = 20
Answer: 20
Step-by-step explanation:
f(2)= 6(2)+8
=20
plug in x with 2
48 es un número irracional
no 48 es un numero irracional
¿Qué es un número irracional?Cualquier número real que no se puede escribir como el cociente de dos números enteros, p/q, donde p y q son ambos números enteros, se denomina número irracional. Por ejemplo, la raíz cuadrada de 2 no se puede expresar como un número entero o una fracción.
Explicación detallada:
48 se puede expresar como [tex]\frac{48}{1}[/tex] aquí se puede ver que la forma p/q está presente. Entonces es un número racional.
no 48 es un numero irracional.
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48 is not an irrational number
What is an irrational number?Any real number that cannot be written as the quotient of two integers, p/q, where p and q are both integers, is called an irrational number. For example, the square root of 2 cannot be expressed as a whole number or a fraction.
Calculation:48 can be expressed as [tex]\frac{48}{1}[/tex] here you can see that the p/q form is present. So it is a rational number.
48 is not an irrational number.
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Hello I have to find the perimeter.
Answer:
10/3 mile
Step-by-step explanation:
perimeter = 4 × side
perimeter = 4 × 5/6 mile
perimeter = 20/6 mile
perimeter = 10/3 mile
My question is what is the answer to this question when
7p+5 when p=12
Answer:89
Step-by-step explanation:math
Answer:89
Step-by-step explanation:7p+5
This means 7 *p+5
Where we see the p we put in 12
We get 7*12+5=89
Find the slope from the line of best fit y = 5 - 3x.
Answer:
slope = -3
Step-by-step explanation:
⭐ What is the equation of a line in slope intercept form?
[tex]y = mx+b[/tex]m is the slope. It is always multiplied with the variable (x)b is the y-intercept. It is always the term without a variableThe given line of best fit is written in slope-intercept form. All we have to do is identify which term is the slope.
[tex]y = -3x + 5[/tex]
-3 is the coefficient of x. Therefore, -3 is the slope.
What’s the difference between solving a whole number and a fraction?
There’s these two methods I saw but not sure when I should use them when I do stumble on a problem.
1 method: start by multiply the numerator towards the whole number and once u do then divide the numerator and denominator separately.
2 method: start by giving the whole number a 1 of the denominator and find the lCD of the fraction and start finishing the problem from either adding or subtracting.
Answer:
hey
Step-by-step explanation:
Determine the surface area of the cylinder. (Use π = 3.14)
net of a cylinder where radius of base is labeled 5 inches and a rectangle with a height labeled 4 inches
157 in2
219.8 in2
282.6 in2
314 in2
Answer:
282.6in^2
Step-by-step explanation:
Surface area of a cylinder = 2πrh+2πr^2
plugging in r=5 and h=4 gives
2π20+2π25
40π+50π = 90π
90*3.14=282.6in^2
Select all of the following equations that are true when 3.27 is used. Use number sense to help.
□ ÷ 1,000 = 0.0327
□ ÷ 102 = 0.327
□ ÷ 1 = 3.27
□ ÷ 10 = 0.327
□ ÷ 100 = 3.27
Answer:
The following equations are true when 3.27 is used:
÷ 1,000 = 0.0327
÷ 10 = 0.327
÷ 100 = 3.27
Note that the equations ÷ 102 and ÷ 1 are not true when 3.27 is used. The equation ÷ 102 is not true because 102 is not a multiple of 1,000, so dividing 3.27 by 102 will not result in a value that is close to 0. The equation ÷ 1 is not true because it is simply stating that 3.27 divided by 1 is equal to 3.27, which is true but not very interesting or useful.
Solve for x (9x-16) (3x+11) (7x-5)
9x²-16x(3x+11)(7x-5)
9x²-48x²-176x(7x-5)
9x²-48x²-1232x²+880
-1271x²+880
A. (f•g)(x)
B. (f•g)(-3)
f(x) = x^2+3x-2
g(x)= x-2
Answer: A. x^3 +x^2-8x+4 B. 10
Step-by-step explanation: (f•g)(x) is the same as f(x) • g(x)
A. (x^2+3x-2) • (x-2) = (x^3+3x^2-2x) -(2x^2+6x-4) -> x^3 +x^2-8x+4
B. plug in -3 for x -> (-3)^3 + (-3)^2 -8(-3) + 4 -> 10
Does the graph represent a proportional relationship?
graph with a line from 0 comma 0 and going through 10 comma 2
No, it is not proportional because the line does not go through (0, 0).
No, it is not proportional because the graph is curved.
Yes, it is proportional because it is a line that goes through (0, 0).
Yes, it is proportional because the x-axis and y-axis are numbered correctly.
pls help
Answer:
Yes, it is proportional because it is a line that goes through (0, 0).
Step-by-step explanation:
Answer:
Yes, it is proportional because it is a line that goes through (0, 0).
Step-by-step explanation:
G(x) = 4x - 5, find g(3)
Answer:
7
Step-by-step explanation:
g(3)=4(3)-5
g(3)=12-5
g(3)=7
Answer:
g(3) = 7
Step-by-step explanation:
Given function:
[tex]g(x)=4x-5[/tex]
To find g(x3) substitute x = 3 into the function:
[tex]\begin{aligned}x=3 \implies g(3)&=4(3)-5\\&=12-5\\&=7\end{aligned}[/tex]
Therefore:
g(3) = 76 minus radical 2 over 4 simplified
The response will be -10 if the stated statement is accurate.
What radicals are most prevalent?This same square root and cubed root are the two radicals we see most frequently. Since the square root is so often employed, it is customary to presume that any radical written without the need for an index is a square root. The figure above constitutes a radical taken as a whole.
What does a math radical mean?An phrase that has a root, often a square or cube root, is referred to as a radical. A radical is made up of three main parts, namely: It expresses the degree of radicand multiplication. If the root symbol's numeric component is absent, it is assumed as 2 (square root). The symbol √ means “root of”.
Briefing:= 6 - 4²
= 6 - 16
= - 10
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The correct questions are-
6 - 4²