The integral value is approximately 4(π + 1) ≈ 16.5664 when rounded to four decimal places.
To solve the integral ∫(8 + 4cos(x)) dx from π/2 to 0, first, find the antiderivative of the integrand. The antiderivative of 8 is 8x, and the antiderivative of 4cos(x) is 4sin(x). Thus, the antiderivative is 8x + 4sin(x). Now, evaluate the antiderivative at the upper limit (π/2) and lower limit (0), and subtract the results:
(8(π/2) + 4sin(π/2)) - (8(0) + 4sin(0)) = 4π + 4 - 0 = 4(π + 1).
The integral value is approximately 4(π + 1) ≈ 16.5664 when rounded to four decimal places.
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write the equation of a horizontal line that goes through the point (3,7). Explain how you got your answer. I will mark you brainliest!
Answer:
y = 7
Step-by-step explanation:
The equation of a horizontal line is worth memorizing. It is:
y = anumber
(and just in case for future reference the equation of a vertical line is
x= anumber)
Well, you are given one point (3,7).That is in the form (x,y). So x is 3 and y is 7.
y is 7
y = 7
(if it helps...horizontal lines have 0 slope. So m = 0. The equation in point-intercept form is
y = mx + b
y = 0x + b
y = b this is the y= anumber) originally mentioned here)
Part A Without computing, the sum of 2, 3, and -2 is , 1 of 1.. Part B Choose the explanation that supports your answer in Part A. Multiple choice question. cross out A) 2 and -2 are additive inverses and the sum of any number and its additive inverse is zero. The integer 3 is positive, so the sum with be positive. cross out B) There are two positive integers and one negative integer. There are more positive integers than negative integers, so he sum will be positive. cross out C) 2 and 3 multiplied together is 6. Then, 6 and -2 multiplied together is -12. Therefore, the sum of the three integers is negative. cross out D) If there are an odd number of negative integers then the sum is negative. One of the integers is negative, so the sum is negative.
A. Without computing, the sum of 2, 3, and -2 is 3.
B. The explanation that supports the answer in Part A is (A) 2 and -2 are additive inverses and the sum of any number and its additive inverse is zero. The integer 3 is positive, so the sum with be positive.
What is additive inverses?An additive inverse of a number is the value that results in zero when added to the original number. It is the value that we add to a number in order to get zero. If an is the original number, then its additive inverse is minus a, i.e., -a, such that;
a+(-a) = a – a = 0
By changing the sign of a number, we can find its additive inverse. A positive number's additive inverse is negative, while a negative number's additive inverse is positive. Except for the sign, the numerical value will not change. The additive inverse of 8 is -8, for example, while the additive inverse of -6 is 6.
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What does to the power of negative 1 mean?
positive number to the power negative 1 is a number that is always less than 1.
Explanation: a-m = 1/am. when calculate have the result when a positive number is raised to the power of -1, we always get a number that is less than one; for example, 2-1 = 1/2 < 1.
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2 3/4 is between the whole number_____and_____
Answer: 2 and 3
Step-by-step explanation:
How do you solve equations of equality?
Answer:
If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal. When you solve an equation, you find the value of the variable that makes the equation true. In order to solve the equation, you isolate the variable.
Step-by-step explanation:
( x - 8 )( x + 8)
this is Operation Multiplication btw
For the expression (x - 8)(x + 8), using the arithmetic operation the value for x is x = 8.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
The given expression is - (x - 8)(x + 8)
Use the arithmetic operation of multiplication -
(x - 8)(x + 8)
x(x + 8) - 8(x + 8)
x² + 8x - 8x -64
Now, use the arithmetic operation of addition and subtraction -
x² + 8x - 8x -64
x² - 64
Now, collect the like terms on each side -
x² = 64
x = √64
Now, solve the radical form to get the value of x -
x = √64
x = 8
Therefore, the value of x is obtained as x = 8.
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Ella earned $54 last week babysitting. She earns $6 an hour. How many hours did Ella babysit last week?
Answer:
9 hours.
Step-by-step explanation:
Ella earned $54 in total.
We know she makes $6 an hour, so we just divide 54/6 to find the amount of hours she babysat last week.
54/6 = 9 hours
Side note: You are obviously competent enough to make this question, so I am sure you can do the basic math too.
Answer: 9 hours.
Step-by-step explanation:
Divide 54 by 6. 54/6 = 9.
the admision to a local fair is $10 each for adult and $6 for each child. Each ride costs $1.50 for an adult and $1 for a child.
An adult and child will each go on 7 ride. How much more did the adult spend?
Answer:
7.5
Step-by-step explanation:
10 + ( 7 × 1.5) = 20.5
6 + ( 7 × 13 ) = 13
20.5 - 13 = 7.5
Answer!! What is Simplified?
On solving the provided question, we can say that Volume of cuboid = 2x(3x+4)(3x-4)
Volume = [tex]18x^3 + 48x^2 + 32x[/tex]
what is cuboid?A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.
here,
we have a cuboid
Volume of cuboid = 2x(3x+4)(3x-4)
Volume = [tex]18x^3 + 48x^2 + 32x[/tex]
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The scatter plot shows a hiker's elevation above sea level during a hike from the base to the
top of a mountain. The equation of a trend line for the hiker's elevation is y=9.16x +659, where x
represents the number of minutes and y represents the hiker's elevation in feet. Use the equation of
the trend line to estimate the hiker's elevation after 150 minutes.
The trend line equation to estimate the hiker's elevation after 150 minutes is 2033 feet.
What is the hiker's elevation?Given that,
A trend line's equation for the hiker's elevation is y = 9.16x + 659.
We must determine,
The trend line equation is used to calculate the hiker's elevation after 150 minutes.
In response to the question,
A trend line's equation for the hiker's elevation is y = 9.16x + 659.
Where x is the number of minutes and y is the elevation of the hiker in feet.
Substitute the value of x = 150minute in the given equation to find the trend line to estimate the hiker's elevation after 150minutes.
Therefore,
y = 9.16x + 659
x = 150
y = 9.16(150) + 659
y = 1374 + 659
y = 2033
As a result, the trend line equation for estimating the hiker's elevation after 150 minutes is 2033 feet.
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Help Answer this math question
Answer:
c.
Step-by-step explanation:
Bo i buying a board game that uually cot BBB dollar. The game i on ale, and the price ha been reduced by 18\%18%18, percent
The expressions that could represent the amount Bo would pay for the game: 0.82B and B - 0.18B
The correct options are: option (a) and option (e)
Given that the board game costs B dollars.
And the price is reduced by 18%.
So, the discount percentage is 18%
i.e., the price is reduced by 0.18
To find out discount amount on the board game, we multiply cost of the board game by discount percentage.
So, we get an expression for the discount amount = 0.18B
Now we calculate total price of the board game.
Subtract the discount amount from original price B
So, we get an expression for the total price of the board game.
B - 0.18B
As the discount percentage is 18%, then the original percentage of pay is about 100 - 18 = 82%
i.e., total price of the board game would be 0.82B
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The complete question is:
Bo is buying a board game that usually costs BBB dollars. The game is on sale, and the price has been reduced by 18\%18%18, percent.Which of the following expressions could represent how much Bo pays for the game?
a) 0.82B
b) 1.18 B
c) B - 0.18
d) B - 18
e) B - 0.18B
Jenna has 34 pennies. Mandy has 48 pennies. Mandy says that 72 pennies in all. what should Mandy do to fix her mistake
Re-write the quadratic function below in Standard Form y= -3(x+2)(x-3)
Answer:
-3x^2 +3x +18
Step-by-step explanation:
Y= -3(x+2)(x-3)
= - 3 (x^2 - x - 16)
= - 3x^2 - 3(-x) - 3(-6)
= - 3x^2 +3x +18
Solve for y
6x+8y=10
identify the slope and y-intercept
Therefore , the solution to the given problem of slope intercept comes out to be y = 3/4x + 2 * 1/5.
The meaning of slope interceptThe place where the the line slope intersects the y-axis is known as the intersection point. where, on a line or a curve, the una crosses that location. This is demonstrated by using y = changes in different as the formula for the single direction, where m denotes the slope while c denotes the y-intercept. In the intercepting form of the equation, the line's slope (m) the y-intercept (b) are indicated. Slope and y-intercept are, respectively, m and b for equations with the intercept form (y=mx+b). Additionally, certain equations might be modified to look like slope intercepts. When y=x is written as y=1x+0, for example, the slope and una become 1 and 0, respectively.
Here,
In this case, you must first set up your equation in the "Slope intercept" form.
6x=8y+10
Because your y should be alone, add 8y to each of your sides.
8y + 6x = 10
Since subtraction is the exact reverse of addition, multiply 6 times on both sides.
8y = 6x + 10
You will now divide both sides by 8. You will be alone yourself while completing this.
y= 6/8x + 10/8
Though you might leave it as is, you should probably simplify.
either y = 3/4x + 2 1/5 or y = 3/4x + 5/2
Therefore , the solution to the given problem of slope comes out to be
y = 3/4x + 2 * 1/5.
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The perimeter (y) of a given shape is a function of its longest side (x). The equation for this function is y = 2.5x + 14. What does a solution of (15 feet, 51.5 feet) represent in the context of the problem?
The solution of (15 feet, 51.5 feet) represents the perimeter of a shape with a longest side of 15 feet.
What is Equation?Equation is a mathematical statement that express the equality of two expression use in equal sign.
The equation for this perimeter can be written as y = 2.5x + 14, where y is the perimeter of the shape and x is the longest side of the shape.
Thus, when x is 15 feet, the perimeter of the shape is 51.5 feet, as represented by the solution (15 feet, 51.5 feet).
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Ade and Ola share a sum of 4000.00 in the ratio of 3:5 find the amount Ade received solutions
The number of shares that Ade and Ola possess will be 1500 and 2500, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Ade and Ola share a sum of 4000.00 in a ratio of 3:5.
Let 'x' and 'y' be the number of shares that Ade and Ola have, respectively. Then the equations are given as,
x / y = 3 / 5 ...1
x + y = 4000 ...2
From equations 1 and 2, then we have
(3/5)y + y = 4000
(8/5) y = 4000
y = 2500
Then the value of the variable 'x' is calculated as,
x + 2500 = 4000
x = 1500
The number of shares that Ade and Ola possess will be 1500 and 2500, respectively.
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Is there a triangle whose sides have lengths 10.2 5.8 cm and 4.5 cm?
It is possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm because the sum of two sides are smaller than third sides.
In the given question, we have to check that it is possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm.
The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.
To check this we firstly add the 10.2 and 5.8
10.2 + 5.8 > 4.5
16 > 4.5
Now we add 10.2 and 4.5
10.2 + 4.5 > 5.8
14.7 > 5.8
Now we add 5.8 and 4.5
5.8 + 4.5 > 10.2
10.3 > 10.2
It is possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm because the sum of two sides are smaller than third sides.
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A survey asks 50 people if they prefer to stream movies or rent dvds. The result of the survey indicate that 25 people prefer to stream, 20 people prefer to rent dvds and 5 people had no preference what is the ratio of people who prefer streaming to the people surveyed
The ratio of people who prefer streaming to the people surveyed is 25:50, or 1:2.
What is ratio?Ratio is a comparison of two or more numbers or quantities that indicates the relative size of the quantities. Ratios are expressed in the form of a fraction or decimal, and they are used in mathematics, statistics, and other sciences. Ratios can be used to compare the sizes of different objects or values, or to compare the relationships between different numbers. Ratios are often used to measure the efficiency of a process or the relationship between different variables.
This ratio indicates that half of the people surveyed prefer to stream movies, while the other half prefer to rent DVDs.
Of the 50 people surveyed, 5 had no preference, meaning that 45 out of the 50 people had a preference for either streaming or renting DVDs.
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Use the Triangle Sum Theorem to find the measure of each angle. Drag and drop the angle measures into the correct boxes to show the measure of each angle.
Answer:
Step-by-step explanation:
so basically Use the Triangle Sum Theorem to find the measure of each angle. Drag and drop the angle measures into the correct boxes to show the measure of each angle.
your welcome lol. -_-
(16-8x-7x^2+2x^3)/(x-4)
The division of 16 - 8x - 7x² + 2x³ by x - 4 will have a quotient of 2x² + x - 4 and a remainder of 0 using synthetic division.
Dividing with synthetic divisionThe procedure for synthetic division involves the following steps:
Divide.
Multiply.
Subtract.
Bring down the next term, and
Repeat the process to get zero or arrive at a remainder.
We shall rearrange 16 - 8x - 7x² + 2x³ to become 2x³ - 7x² - 8x + 16 and then divide by x - 4 as follows;
2x³ divided by x equals 2x²
x - 4 multiplied by 2x² equals 2x³ - 8x²
subtract 2x³ - 8x² from 2x³ - 7x² - 8x + 16 will give x² - 8x
x² divided by x equals x
x - 4 multiplied by x equals x² - 4x
subtract x² - 4x from x² - 8x will give us -4x + 16
-4x divided by x equals -4
x - 4 multiplied by -4 equals -4x + 16
subtract -4x + 16 from -4x + 16 will result to a remainder of 0
Therefore by synthetic division, 16 - 8x - 7x² + 2x³ divided by x - 4 is equal to the quotient of 2x² + x - 4 with a remainder of 0.
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What is the formula of triangle and square?
The formula for a triangle is the area of a triangle = ½ × base × height. The formula for a square is the area of a square = side2.
This formula is used to calculate the area of any triangle when the base and height are known. For example, if the base of a triangle is 10 cm and the height is 5 cm, the area of the triangle is 25 cm2.
The formula for a square is the area of a square = side2. This formula is used to calculate the area of any square when the side length is known. For example, if the side of a square is 10 cm, the area of the square is 100 cm2. To calculate this, we can use the formula by squaring 10 (102 = 100).
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What is n to the power of 6?
n to the power of 6, also written as n⁶, is a mathematical operation that raises the number n to the sixth power. This means that n is multiplied by itself six times.
For example, if n = 2, then n⁶ = 2 × 2 × 2 × 2 × 2 × 2 = 64.
Exponentiation is a mathematical operation that is used to represent repeated multiplication. The number that is being multiplied is called the base, and the number that represents how many times the base is being multiplied is called the exponent. In the case of n⁶, the base is n and the exponent is 6.
In general, when raising a number to a power, the result is the product of that number multiplied by itself the number of times represented by the exponent. For example, n³ = n × n × n and n⁴ = n × n × n × n.
In addition to being a mathematical operation, exponentiation also has practical applications in fields such as computer science, engineering, and physics.
For example, in computer science, exponentiation is used to perform fast computations, such as in the process of encryption and decryption. In engineering and physics, exponentiation is used to calculate rates of growth, such as in the case of compound interest and radioactive decay.
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Use the diagram to determine which triangle similarity theorem is the most appropriate to justify the similarity relationship.
ABC DEF by ___________ Similarity.
Both triangles ABC and DEF are similar to each other based on angle angle similarity
What are similar triangles?Two triangles are said to be similar if the ratio of the corresponding sides of both triangles are proportional to each other. Also, all the three angles of one triangle are equal to that of the other triangle.
The angle angle (AA) similarity theorem states that two triangles are similar if two angles of one triangle is equal to that of the other triangle.
Both triangles ABC and DEF are similar to each other
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In a lab experiment, a population of 50 bacteria is able to quadruple every hour. Which equation matches the number of bacteria in the population after 3 hours?
The exponential equation that matches the number of bacteria after 3 hours is given as follows:
y = 50(4)^3.
What is an exponential function?An exponential function is used to model this situation as the output is multiplied for each unit of the input.
The general format of an exponential function is given as follows:
y = a(b)^x.
In which:
a represents the initial value.b represents the rate of change.In a lab experiment, a population of 50 bacteria is able to quadruple every hour, hence the parameters a and b are given as follows:
a = 50, b = 4.
Thus the exponential function that gives the population after x hours is of:
y = 50(4)^x.
After three hours, we have that x = 3, hence the population is given as follows:
y = 50(4)^3.
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What is midpoint formula Class 11?
The midpoint formula is a mathematical formula used to find the midpoint of a line segment, given the coordinates of the two endpoints of the segment. In class 11, it is defined as:
Midpoint = ( (x1 + x2)/2 , (y1 + y2)/2 )
Where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment, and (x, y) are the coordinates of the midpoint of the segment.
For example, if the two endpoints of a line segment are (5,6) and (9,11)
Midpoint = ( (5 + 9)/2 , (6 + 11)/2 )
Midpoint = (7,8.5)
The midpoint of the line segment with endpoints (5,6) and (9,11) is (7,8.5)
It's worth noting that this formula can be adapted for three-dimensional points, where the midpoint formula would be
((x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2)
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consider the differential equation dy /dx = 2x-y
100 points + Brainliest Let C represents the cost in dollars and R represents the revenue in dollars. What is the break-even point? Use a table to help if necessary.
C=36x+200
R=76x
Break-even point: ([],[])
Answer:
The break even point is 380.
Step-by-step explanation:
36x + 200 = 76x
200 = 76x - 36x
200 = 40x
200/40 = x
5 = x
C = 36(5) + 200 R = 76(5)
C = 180 + 200 R = 380
C = 380
Answer:
The breakeven point is 5 units
Step-by-step explanation:
C is the cost ($) and R is the revenue ($).
We are told that :
R=76x
C=36x+200
Profit would be the Revenue minus the Cost:
Profit = R - C
The "breakeven point" is the situation in which there is neither a profit nor a loss. That means that the total profit equals the total cost for x units. We want to find the value of x that would result in no profit or loss: Profit = 0.
0 = R-C
====
Profit = 76x - (36x+200)
Profit = 40x - 200
0 = 40x - 200 [The Breakeven Point]
-40x = -200
x = 5 units
5 units results in 76*5 or $380 in revenue.
5 units results in a cost of 36*(5)+200 or $380 in costs.
The result is breakeven (Profit = $390 - $380) of $0.00
Gustave imagen es Space And Time And The for him steps Make Up one mile one day gusta e walked 6300 steps which one was 3 miles
Based on the information, it can be inferred that Gustave gives 2,100 steps for every mile he walks.
How to calculate the number of steps Gustave takes in a mile?To calculate the number of steps Gustave takes in a mile, we must take into account the information available about the ratio of steps to the distance he covers. In this case, we know that for every 3 miles, Gustave takes 6,300 steps.
To find how many steps he takes in a mile we must divide the number of steps into the number of miles he walked as shown below:
6,300 / 3 = 2,100According to the above, Gustave takes 2,100 steps for every mile he walks.
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A spinner with 4 equal sections is spun 20 times. The frequency of spinning each color is recorded in the table below.
Outcome Frequency
Pink 6
White 3
Blue 7
Orange 4
What statement best compares the theoretical and experimental probability of landing on blue?
The theoretical probability of landing on blue is one fourth, and the experimental probability is 35%.
The theoretical probability of landing on blue is one fourth, and the experimental probability is 50%.
The theoretical probability of landing on blue is one fifth, and the experimental probability is 35%.
The theoretical probability of landing on blue is one fifth, and the experimental probability is 50%.
The statement that best compares the theoretical and experimental probability for a spin to land on blue is A. The theoretical probability of landing on blue is one fourth, and the experimental probability is 35%.
How does theoretical probability compare to experimental probability ?Theoretical probability is calculated by analyzing the total number of possible outcomes of an event and the number of favorable outcomes. Experimental probability, on the other hand, is calculated by conducting an experiment and observing the results.
This means that the theoretical probability of landing on blue is:
= Number of sections of blue / Number of total sections
= 1 / 4
The experimental probability of landing of blue is :
= Number of times blue is spun / Number of spins
= 7 / 20
= 35 %
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Answer: A 35%
Step-by-step explanation: