The most general antiderivative of the function is -7cosx-4secx+C on the interval (-π/2,π/2) is not defined.
Given that,
We have a function f(x)=7sinx -4secx tanx.
We have to find the most general antiderivative of the function on the interval (-π/2, π/2).
We know that,
Take the function,
f(x)=7sinx -4secx tanx.
The antiderivative is
= [tex]\int {7sinx-4secxtanx} \, dx[/tex]
= [tex]7\int{sinx} \, dx -4\int {secxtanx} \, dx[/tex]
= 7(-cosx)-4[tex]\int {sinx/cos^{2}(x) } \, dx[/tex]
Take cosx =u
-sinxdx=du
= -7cosx-4[tex]\int {-1/u^{2} } \, du[/tex]
= -7cosx-4(1/u)+C
=-7cosx-4(1/cosx)+C ( since we know u=cosx)
= -7cosx-4secx+C
Now for the interval (-π/2,π/2)
= -7(cosπ/2-cos(-π/2))-4(secπ/2-sec(-π/2))+C
= -7(0-0)-4(∞-∞)+C
=not defined
Therefore, The most general antiderivative of the function is -7cosx-4secx+C on the interval (-π/2,π/2) is not defined.
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There are 32 teams in the first round of a basketball tournament. One half of the teams that play in each round of the tournament move on to play in the next round.
a. Explain why the expression 32 x 1/2^3 represents the number of teams that play in the fourth round?
b. How many teams play in the fourth round? Show your work.
Answer:
So there are 32/4= 8 such groups. In each group, every team plays once against every other team
Step-by-step explanation:
Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs.
You need a $160,000 loan.
Option 1: a 30-year loan at an APR of 10%
Option 2: a 15-year loan at an APR of 9.5%
Find the monthly payment for each option.
The monthly payment for option 1 is $___
The monthly payment for option 2 is $___
Monthly payment option 1 = $300,000 / 166.79161 = $1,798.65 and the monthly payment option 2 = $300,000 / 130.7201 = $2,294.98.
How to calculate the monthly payment?The numbers are missing, so I looked for similar questions to fill in the blanks:
You need a $300,000 loan. Option 1: a 30-year loan at an APR of 6%. Option 2: a 15-year loan at an APR of 4.5%.
We can use the present value of an annuity formula to calculate monthly payments.
Present value = monthly payment x PV annuity factor
Monthly payment = present value / PV annuity factor
Present value = $300,000
Option 1: PV annuity factor, 0.5%, 360 periods = 166.79161
Option 2: PV annuity factor, 0.375%, 180 periods = 130.7201
Monthly payment option 1 = $300,000 / 166.79161 = $1,798.65
Monthly payment option 2 = $300,000 / 130.7201 = $2,294.98
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what's the answer? The double number line shows that Henrik has a mass of 60kg
The required solutions of percentages are below as :
100% of 60 kg = 60 kg, 20% of 60 kg = 12 kg, and 40% of 60 kg = 24 kg.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
The double number line shows that Henrik has a mass of 60kg.
According to the given question, the required solution would be as:
100% of 60 kg
⇒ (100/100) x 60
⇒ 1 x 60
⇒ 60
So, 100% of 60 kg = 60 kg
20% of 60 kg
20% is expressed as 20/100 in fractional form
⇒ (20/100) x 60
20/100 is expressed as 0.20 in decimal form
⇒ 0.20 x 60
Apply the multiplication operation, and we get
⇒ 12
So, 20% of 60 kg = 12 kg
40% of 60 kg
⇒ (40/100) x 60
⇒ 0.40 x 60
⇒ 24
So, 40% of 60 kg = 24 kg.
Thus, the required solutions are 100% of 60 kg = 60 kg, 20% of 60 kg = 12 kg, and 40% of 60 kg = 24 kg.
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The average person burns approximately 221 calories per half-hour while bicycling. If a person
does 2 hours of bicycling per day then how many calories will they burn in a week if they work
out 5 days a week?
3 Find the x-intercept of the equation x + 5y = 20. A 1 B 4 C 5 D 20
Answer:
line | Cartesian equation x + 5 y = 20 | x-intercept = 20 thus: D
Step-by-step explanation:
Solve the equation -128 = 4x for x
-124
132
-32
32
x= -32.
Step-by-step explanation:1. Write the expresion.[tex]-128 = 4x[/tex]
2. Divide both sides by 4.[tex]\frac{-128}{4} = \frac{4x}{4} \\\\-32=x\\ \\x=-32[/tex]
Select the two values of x that are roots or this equation x^2-5x+2=0
The roots of the given quadratic equation are 4.56 and 0.439.
What are the roots of an equation?The roots of an equation are the solution of that equation, since an equation consists of hidden values of the variable so to determine them by different processes and then the resultant is called roots.
As per the given quadratic equation,
x² - 5x + 2 = 0
The roots will be as,
x = [+5 ± √(5² - 4 × 1 × 2)]/(2 × 1)
x = [5 ± 4.1232]/2
x = 4.56,0.439
Hence "The roots of the given quadratic equation are 4.56 and 0.439".
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please help me on math very easy graphing! thank you!! due soon
The graph that shows the proportional relationship between the number of liters of water (y) supplied after some time (x), is shown below.
What is a Proportional Relationship?A proportional relationship can be defined as a relationship between two variables, say x and y, in such a way that the equation, y = kx, models their relationship, where k is the constant of proportionality.
Given that the faucet supplies 12 liters of water after 3 minutes, where:
y = liters of water
x = number of minutes
Constant of proportionality, k = y/x = 12/3 = 4
The equation that describes the relationship would therefore be written by substituting the value of k = 4 into y = kx:
y = 4x
Thus, the graph that shows this proportional relationship is attached below.
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Determine a series of transformations that would map figure G onto Figure H
The series of transformation that would map the quadrilateral in figure G to the quadrilateral in figure H are;
A reflection about the y-axisA translation of three units leftWhat is a transformation in geometry?A geometric transformation involves either a change in location, size, or orientation or a combination of changes of a geometric figure.
The possible polygon with vertices in the question obtained from a similar question online and drawn using MS Excel is attached;
The vertices of the polygon are;
The coordinates of the vertices of Figure G; (-2, 7), (-6, 3), (-1, 5), (-1, 1)
The coordinates of the corresponding vertices of Figure H; (5, 7), (9, 3), (4, 5), (4, 1)
The y-values of figure G and figure H are the same, while the x-values changes both value and sign.
The coordinates of the point (x, y), following a reflection about the y-axis is the point (-x, y)
Therefore, the possible transformation that maps figure G unto figure H includes a reflection across the y-axis;
The coordinates of the vertices of figure G following a reflection about the y-axis are;
Image of figure G following a reflection about the y-axis; (2, 7), (6, 3), (1, 5), and (1, 1)
The transformation that maps the image produced by the reflection and figure H are;
Transformation (5 - 3, 7 - 7) = (3, 0)
(9 - 6, 3 - 3) = (3, 0)
(4 - 1, 5 - 5) = (3, 0)
(4 - 1, 1 - 1) = (3, 0)
The transformation that maps the image of figure G to figure H is therefore T₍₃, ₀₎, which is a translation of 3 units to the right.
The series of transformation that maps figure G to figure H are therefore;
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A rectangular carton is 80*60*40 i) how many packet of soaps can each of 10*5*4 cm can be kept insidethe carton? ii) by how many centimeters should the height of the carton be increased to keep 1200 packets of soaps
Answer:
i) 960 , ii) 10 cm
Step-by-step explanation:
V of rectangular carton = 80 · 60 · 40 = 192 000
V of a packet of soap = 10 · 5 · 4 = 200
192 000 / 200
1920/2
960
ii)
960 : 1200 = 192 000 : x
x = 192 000 · 1200 / 960
x = 192 000 · 120 / 96
x = 240 000
80 · 60 · x = 240 000
4800 · x = 240 000
x = 240 000/4800
x = 2400/48
x = 200/4
x = 50
50 - 40 = 10
Answer:
i) 960 packets of soap
ii) 10 cm
Step-by-step explanation:
volume of cuboid = l*w*h
volume of carton = 80*60*40 = 192000 cm³
i)
volume of a packet of soap = 10*5*4 = 200 cm³
192000/200 = 960 packets of soaps
ii)
I am assuming the height is 40 cm
volume of carton/volume of a packet of soap = number of soap
x = volume of carton
x/200 = 1200
x = 1200*200 = 240000 cm³
80*60*h = 240000
4800h = 240000
h = 240000/4800 = 50 cm
50cm (desired height) - 40cm (current height) = 10cm
Identify each as a function or not a function.
A school hockey team was given a budget at the start of
the year. The team used 60% of the money for uniforms,
10% for equipment, and 30% for travel. Which circle
graph shows this information?
The circle which shows the distribution of the money has been attached.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
In our daily life, we always see circular objects for example our bike wheel.
As per the given,
The team used 60% of the money for uniforms,10% for equipment, and 30% for travel.
60% of the area of the circle is used for uniforms.
10% of the area of the circle is used for equipment.
30% of the area of the circle is used for travel.
Hence "The attached circle depicts how the funds were distributed.".
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What is the distance between the points (6.2, -4) and
(4.5, -4)
Answer:1.7
Step-by-step explanation:
A quadratic function has an "a" value of (2) and a vertex at (5,-18) How many solution does the function have, and what are they?
The function bas solution (s), which is x=__ and x=___ (Write NA tar the second box at there is only one solution)
The function has 2 solutions which is x = 2 and x = 8.
What is a quadratic function?
A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two.
Solution:
Given :
a = 2 , vertex = (5, -18)
f(x) = a(x-h)² + K
f(x) = 2(x - 5)² - 18
f(x) = 2(x² -10x + 25) -18
f(x) = 2x² - 20x +50 - 18
f(x) = x² - 10x +16
∴ x² -10x + 16 = 0
x² - 8x - 2x + 16 = 0
x(x-8) -2(x-8) = 0
(x-2) = 0 and (x-8) = 0
∴ x = 2 and x = 8
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The quadratic function has 2 solutions which is x = 2 and x = 8.
What is a quadratic function?A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. A polynomial of degree two in one or more variables in mathematics is known as a quadratic polynomial. Any polynomial function that is defined by a quadratic polynomial is said to be quadratic.
The terms "quadratic polynomial" and "quadratic function" were almost interchangeable before the 20th century because it was difficult to tell a polynomial from its corresponding polynomial function. This is still true in many elementary courses where "quadratic" is frequently used to refer to both terms.
Solution:
Given :
a = 2 , vertex = (5, -18)
f(x) = a(x-h)² + K
f(x) = 2(x - 5)² - 18
f(x) = 2(x² -10x + 25) -18
f(x) = 2x² - 20x +50 - 18
f(x) = x² - 10x +16
∴ x² -10x + 16 = 0
x² - 8x - 2x + 16 = 0
x(x-8) -2(x-8) = 0
(x-2) = 0 and (x-8) = 0
∴ x = 2 and x = 8
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A large container holds 4.7 gallon of water. Use the following information to convert this amount of water to liters.1 gallon =4 quarts 1L =1.057 quarts
Answer:
Step-by-step explanation:
To convert the amount of water in gallons to liters, we need to first convert the number of gallons to quarts and then convert the number of quarts to liters.We know that 1 gallon is equal to 4 quarts, so 4.7 gallons is equal to 4.7 gallons * 4 quarts/gallon = 4.7*4=18.8 quarts.We also know that 1 liter is equal to 1.057 quarts, so to convert the number of quarts to liters, we can divide the number of quarts by 1.057 quarts/liter: 18.8 quarts / 1.057 quarts/liter = 18.8/1.057=17.8 liters.Therefore, 4.7 gallons is equal to 17.8 liters.
You are offered a job in sales where you can choose to
either make a salary $500 (constant) every week or
commission of $20 per sale. Write 2 equations that
represent this scenario and solve the system (find two equations)
The linear equation for the first scenario is y = 500 while for the second scenario is y = 20x
The equation of a straight line is given by:
y = mx + b;
where y,x are variables, m is the slope of the line and b is the y intercept.
let x represent the number of sales and y represent the total salary for a weeks.
For scenario 1, there is a constant salary of $500. The linear equation becomes:
y = 500
For scenario 2, there is a commission of $20 per sale. The linear equation becomes:
y = 20x
Travelling at 24 km/h on a snowmobile makes an air temperature of 4°C feel like -6°C because of the wind chill. What is the difference in these temperatures?
The difference in temperature is currently six degrees Celsius. Therefore, the appropriate reaction is six degrees Celsius.
What is the difference in temperatures?When two independent temperature readings are subtracted, or when calculating the amount of temperature rise or fall, the result is a temperature difference, also referred to as a delta temperature (T).
Simply subtract the smaller amount from the larger one to determine the difference in temperature, in this case 19 degrees Celsius from 25 degrees Celsius. We now have a six-degree Celsius temperature difference as a result. Therefore, six degrees Celsius, is the appropriate response.
Due to the varied amounts of radiation the Earth receives from the Sun at various periods of the year, there are variations in climate all over the world. The equator receives more heat from the Sun than the north and south poles, where the angle of the Sun's beams is lower.
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HELP ASAP!
Find the volume of a cone with a radius of 6.5 inches and a height of 12 inches.
A) 670.2 in ³
B) 530.9 in³
C) 414.7 in ³
D) 513.1 in³
At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ship B is sailing north at 21 knots. How fast (in knots) is the distance between the ships changing at 4 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)
At [tex]$5 \mathrm{pm}$[/tex] the distance between the ships is changing at the speed of [tex]$\mathbf{3 0 . 2 1}$[/tex] knots
Firstly we need to an equation to represent both ships and the distance between each. A is moving [tex]$25 \mathrm{knots}$[/tex] west and [tex]$B$[/tex] is moving [tex]$17 \mathrm{knot}$[/tex] north. [tex]$D$[/tex]will be the distance between the two. Drawing it, you'll notice that it creates a right triangle.
So we use the Pythagorean Theorem:
[tex]$$D^{\wedge} 2=A^{\wedge} 2+B^{\wedge} 2$$[/tex]
Differentiate in relation to time:
[tex]$$2 \mathrm{D}(\mathrm{dD} / \mathrm{dt})=2 \mathrm{~A}(\mathrm{dA} / \mathrm{dt})+2 \mathrm{~B}(\mathrm{~dB} / \mathrm{dt})$$[/tex]
Now we must find all of our variables.
[tex]& A=\text { time(speed })+\text { original distance }=5(25)+10=135 \\[/tex]
[tex]& B=5(17)+0=85 \\[/tex]
[tex]& D=V\left(A^{\wedge} 2+B^{\wedge} 2\right)=159.53 \\[/tex]
[tex]& d A / d t=25 \\[/tex]
[tex]& d B / d t=17[/tex]
Plug in all your variables and solve for
[tex]$(\mathrm{dD} / \mathrm{dt})$ :[/tex]
[tex]& 2 \mathrm{D}(\mathrm{dD} / \mathrm{dt})=2 \mathrm{~A}(\mathrm{dA} / \mathrm{dt})+2 \mathrm{~B}(\mathrm{~dB} / \mathrm{dt}) \\[/tex]
[tex]& 2(159.53)(\mathrm{dD} / \mathrm{dt})=2(135)(25)+2(85)(17) \\[/tex]
[tex]& 319.061(\mathrm{dD} / \mathrm{dt})=9640 \\[/tex]
[tex]& \mathrm{dD} / \mathrm{dt}=9640 / 319.061 \\[/tex]
[tex]& \mathrm{dD} / \mathrm{dt}=30.21 \text { knots }\end{aligned}[/tex]
At [tex]$5 \mathrm{pm}$[/tex] the distance between the ships is changing at the speed of [tex]$\mathbf{3 0 . 2 1}$[/tex] knots
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(g) (4 5)(2 -1)
(h) (2 6)(-3 -4)
(i) (1 2)(4 6 5 7)
(j) (0 5)(3 6 4 1)
I don’t know how to do it, please teach me !!!
As described in z-distribution the answers are given below:
a) The 95% confidence interval estimate for the population mean spending by a customer on visiting salon per month is given as follows: (747, 853).
b) The sampling error at 95% confidence level is of: $35.78.
What is a z-distribution ?
The normal distribution with a mean of 0 and a standard deviation of 1 is referred to as the standard normal distribution (also known as the Z distribution) (the green curves in the plots to the right). It is frequently referred to as the bell curve since the probability density graph resembles a bell.
solution:
The bounds of the confidence interval are given as follows:
In which:
is the sample mean.
z is the critical value.
n is the sample size. is the standard deviation for the population.
The parameters for this problem are given as follows:
Hence the lower bound of the interval is of:
800 - 200 x 1.96/square root of 55 = 747.
The upper bound of the interval is of:
800 + 200 x 1.96/square root of 55 = 853.
The sampling error for a sample size of 120 is calculated as follows:
200 x 1.96/square root of 120 = $35.78.
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A rectangular piece of metal is 5 in longer than it is wide. Squares with sides 1 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 456 in³, what were the original dimensions of the piece of metal?
The width of the piece of metal will be 21 inches while the length will be 26 inches.
What is a rectangle?
A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Main body:
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
Let's say the width of metal w then the length will be w + 5
Now if we cut 1 inch square from the corner of the metal and then fold then the resultant cuboid will have;
Length = w+5 - 2 -= w + 3
Width = w - 2
Height = 1
So,
Volume = (w+3)(w-2)1
456 = w² - 2w + 3w - 6
w² + w - 462 = 0
By solving this
w = 21 so width will be 21 and length will be 21 + 5 = 26.
Hence "The width of the piece of metal will be 21 inches while the length will be 26 inches".
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Kyle buys last years best selling hardcover for $19.50 . This is with a 25% discount from the original price. What was the original price of the novel ,
Use variable x to set up an equation to solve the given problem. DONT TAKE STEPS TO SOLVE
Answer:
original price is 26 dollars
Step-by-step explanation:
19.50/0.75=26
1. Calculate the expected value of the number of cups of coffee Alex drinks each day. 00.200 cups 00.163 cups 00.976 cups 01.881 cups
The expected value of the number of cups of coffee Alex drinks each day is 00.805 cups.
the mean/ average is gotten by dividing the sum of the values in the set by their number.
The concept of mean/average is used in this ques to calculate the expected value of the number of cups of coffee Alex drinks each day.
Mean/ Average= sum of values
number of values
Substituting the values into the equation we have:Mean/ Average= 00.200 cups +00.163 cups+ 00.976 cups+ 01.881 cups
4
Mean/ Average= 00.805 cups
Hence, The expected value of the number of cups of coffee Alex drinks each day is 00.805 cups.
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what is the area of the convince store
Answer:
please add screenshots of the question and/or illustrations
Need help please:
show that the two quadrilaterals are congruent
The two quadrilaterals JKLQ and LMNP are congruent.
What is congruent quadrilaterals?
You will always have two opposite pairs of parallel sides if the two pairs of opposite sides in a quadrilateral are congruent. They must measure similarly to be considered congruent. Consider this: two congruent sides must always maintain the same separation between the opposing lines to maintain the other pair of opposite sides.
To prove that all corresponding pairs of sides and angles are congruent, you must put the interior angles and sides of one quadrilateral in correspondence with those of another.
For the given quadrilaterals JKLQ and LMNP it is given that,
JK ≅ MN, JQ ≅ NP, QL ≅ PL and KL ≅ ML
Also,
∠J ≅ ∠N, ∠Q ≅ ∠P, ∠K ≅ ∠M, and ∠L is the common for both quadrilaterals.
Here the corresponding sides and angles of the quadrilaterals are congruent.
Hence, the two quadrilaterals JKLQ and LMNP are congruent.
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A variable needs to be eliminated to solve the system of equations below. Choose the correct first step
X-7y=-45
-x+8y=51
Step-by-step explanation:
x - 7y = -45
-x +8y = 51
the X's cancel out
-7y + 8y = -45 + 51
y = 6
A high - powered model rocket is traveling at 150 mph What is the rockets speed in feet per second ?
Speed of rocket travelling at 150 m/h into feet per second is 0.1367 feet per second
How to covert meter to feet ?3.28084 feet is about equal to one meter. Multiply 3.28084 feet to the given meter value to convert
According to the given information
Speed of rocket in meter per hour is 150 m/h
To know the speed of rocket in feet per second
1 meter = 3.280 feet
15o meter = 150 × 3.280
= 492 feet
1 hour = 60 × 60
= 3600 second
So,
speed of rocket in feet per second = [tex]\frac{492}{3600}[/tex]
= 0.1367 feet per second
Speed of rocket travelling at 150 m/h into feet per second is 0.1367 feet per second
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Find f(-2) for f(x) = 2 • 3^x
Function f(x) is 2/9.
Which is a function example?F(x) = sin x, F(x) = x2 + 3, F(x) = 1/x, F(x) = 2x + 3, etc. are a few further instances of functions. Mathematical functions come in many different varieties. Among the crucial kinds are: injection technique or One-to-one relationship: when there is a mapping between two sets for a range for each domain.If a function depends on another variable, you write it as f(x), g(x), or even h(t), depending on the dependant variable. You read f(x) and h(t) as "f of x" and "h of t," respectively. Not all functions must be linear. The nonlinear function g(x) = -x2 -3x + 5 is defined as follows.f(-2) for f(x) = 2 • 3^x is 2/9.
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A time series-based forecast is a form of ____ or, assuming that patterns observed in historical data will prevail in the future.
Time series forecasts are developed based on time series analysis, which comprises methods for analyzing time series data to extract meaningful statistics and other characteristics of the data.
One of the most often used data science techniques in business, finance, supply chain management, production, and inventory planning is time series forecasting.
A time component is often present in prediction difficulties, necessitating the extrapolation of time series data or time series forecasting. Another crucial field of machine learning (ML) is time series forecasting, which may be viewed as a supervised learning issue.
It can be subjected to ML techniques including regression, neural networks, support vector machines, random forests, and XGBoost. Using models created from historical data to anticipate future observations is known as forecasting.
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