The customer will to pay $2,970 in 12 days.
What does 3/10 mean?
3/10 is cash discount term which means that a discount of 3% would be given to the customer if payment for the goods purchased is made within 10 days of purchase.
In this case, 3% is not applicable since the payment was made after 12 days.
What does 1/20 mean?
1/20 is cash discount term which means that a discount of 1% would be given to the customer if payment for the goods purchased is made within 20 days of purchase, the payment is within this range, hence, a 1% discount would be applied to invoice price so as to determine the cash payable
cash payable=$3,000*(1-1%)
cash payable=$3,000*0.99
cash payable=$2,970
What does n/30 mean?
It means a payment is expected latest after 30 days which does not entitle the customer no discount.
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Which list below shows the fractions in order from greatest to least?
A. 3/6, 4/9, 3/7, 3/10
B. 3/10, 3/7, 4/9, 3/6
C. 3/10, 4/9, 3/7, 3/6
D. 3/6, 4/7, 4/9, 3/10
Answer:
Step-by-step explanation:
The following data show the scores of some students in a competition:
13 points
24 points
31 points
24 points
27 points
23 points
11 points
Which box plot represents the data?
A box plot titled "Scores of Participants" and labeled "Score" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 23 to 27 on the number line. A line in the box is at 24. The whiskers end at 11 and 31.
A box plot titled "Scores of Participants" and labeled "Score" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 13 to 27 on the number line. A line in the box is at 24. The whiskers end at 11 and 31.
A box plot titled "Scores of Participants" and labeled "Score" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 13 to 27 on the number line. A line in the box is at 23. The whiskers end at 11 and 31.
A box plot titled "Scores of Participants" and labeled "Score" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 13 to 27 on the number line. A line in the box is at 24. The whiskers end at 10 and 35.
The box plot that represents the data is a box plot titled "Scores of Participants" and labeled "Score" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 13 to 27 on the number line. A line in the box is at 24. The whiskers end at 11 and 31.(second option)
Which box plot represents the data?A box plot is used to study the distribution and level of a set of scores. The whiskers represent the minimum and maximum values.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile. 75% of the scores represents the upper quartile.
The data arranged in ascending order : 11, 13, 23, 24, 24, 27, 31
Median = 24
First quartile = 1/4 x (7 + 1) = 2nd term =13
Third quartile = 3/4 x (7 + 1) = 6th term = 27
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Divide the polynomials.
Answer:
x^4-3x+2
Step-by-step explanation:
There are several different ways to divide algebraic expressions. Here the most simple way to do it (and good idea to try first) is to FACTOR and CANCEL.
see image.
Factor an x from the top. Cancel that x with the bottom x. See image.
(***Also, note: never "cancel" anything connected by a + or a - )
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\frac{x^{5}+(3\times x^{2}) +(2\times x) }{x}} \end{gathered}$}[/tex]
Takes into account expressions that have not yet been taken into account.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\frac{\red{\not{x}}(x-1)(x^{3}+x^{2} +x-2) }{\red{\not{x}} } } \end{gathered}$}[/tex]
Cancel x in both the numerator and the denominator.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{(x-1)(x^{3}+x^{2} +x-2) } \end{gathered}$}[/tex]
The expression expands
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{x^{4}-3x+2 } \end{gathered}$} }[/tex]
The x-intercept of a line is 2 and the y-intercept is 4. Explain how to use this information to write the equation of the line.
Answer:
y = -2x + 4
Step-by-step explanation:
The x-intercept would be the point (2,0) and the y intercept would have the point (0,4). Once we know two points we can write the equation in the line intercept for of y = mx + b.
We need to find the slope and the y intercept. The slope is the steepness of the line and it is the change in y over the change in x.
The ordered pairs are written in the form of (x, y). From our two points, we will subtract the y's to find the top number of our fraction.
0 - 4 = -4 that is the numerator (top number) of our slope. We do the same with the two x numbers that we have been given.
2 - 0 = 2 This is our numerator (or bottom number of our slope)
Our slope is -4 /2 to simplify, we divide the top and bottom number by 2 to get -2 / or just -2
Now that we have the slope we need to find the y-intercept. We can use either of our original two points and our slope to determine the y-intercept. It does not matter if you use the point (2,0) or (0,4). I will use (2,0) and the slope of -2
y = mx + b
0 = -2(2) + b
0 = -4 + b add 4 to both sides of the equation
4 = b
Now that we have the slope and the y-intercept, we can write the equation
y = mx + b
y = -2x + 4
Alec starts up a monthly subscription potato box. It costs 18.20 dollars per month,
and comes with 16 potatoes in each box. Each subscriber may order any amount of
”luxury potatoes”, that are separate from the 16 that normally come in the box, for
an additional 5 dollars each.
(a) Write a formula for the monthly revenue, R in dollars, earned by Alec as a function
of s, the number of monthly subscribers, and n, the total number of luxury potatoes that his clients order. R(s, n) =
(b) Using your formula from above, find R(10, 3)
A. The formula (mathematical function) for the monthly revenue, R, earned by Alec, R(s, n) = $18.20s + $5n.
B. Using the formula above, the value of R(10, 3) is $197.
What is a function?A function is an expression, rule, or law defining the relationship between an independent variable and a dependent variable.
Functions are used to define physical relationships between variables.
Data and Calculations:Cost monthly subscription = $28.20 per box
Number of normal potatoes in each box = 16
Cost of additional luxury potatoes = $5 per potato
If the monthly revenue function, R, is given as R(s, n) where:
s = number of monthly subscribers
n = total number of luxury potatoes ordered
The monthly revenue, R, earned by Alec, R(s, n) = $18.20s + $5n.
The value of R(10, 3) is $197 ($18.20 x 10 + $5 x 3)
Thus, using the formula above, the value of R(10, 3) is $197.
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The measure of the second angle of a triangle is three times the measure of the first. The measure of the third angle in the triangle is 12 degrees less than twice the measure of the first angle. Find the measures of each angle in the triangle.
Answer:
First angle:
x =32
Second angle:
3x
3(32) = 96
Third angle:
2x - 12
2(32) -12 =52
Step-by-step explanation:
x + 3x + 2x - 12 = 180 The sum of the interior angles of a triangle is 180
6x -12 = 180 Combine the x terms
6x = 192 add 12 to both sides
x = 32
Check: 52 + 96 + 32 = 180
1. Based on the circular
angle below. What is the
best measurement
the angle?
for
a. less than 90°
b. more than 90°
C. more than 180°
d. less than 60°
Answer:
B. More than 90
Step-by-step explanation:
Hope this helps!
3.5.3 Test (CST): Functions
Does this graph show a function? Explain how you know.
-5
5-
OA. No; there are y-values that have more than one x-value.
B. No; the graph fails the vertical line test.
OC. Yes; there are no y-values that have more than one x-value.
D. Yes; the graph passes the vertical line test.
Jhy
Answer:
D
Step-by-step explanation:
It pass the vertical line test.
Hope this helps <3
As per the given graph, the graph fails the vertical line test. The correct option is B.
What is graph?A graph is a visual representation of data that uses lines, bars, or other symbols to show how different values are related to each other.
Graphs are often used to display information in a way that is easy to understand and interpret.
The vertical line test is a way to determine whether a given graph represents a function.
According to this test, if any vertical line intersects the graph at more than one point, then the graph does not represent a function.
In the given graph, we can see that there are some vertical lines that intersect the graph at more than one point, such as the vertical line passing through x = 2.
Therefore, the graph does not pass the vertical line test and does not represent a function.
Thus, the correct answer is B.
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I need help ASAP please
Answer:
8.1
Step-by-step explanation:
[tex]\sqrt{(-1-0)^2 + (5-(-3))^2}=\sqrt{65} \approx 8.1[/tex]
Which graph is the result of reflecting f(x) = (8)* across the y-axis and then across the x-axis? O 8- 6- 8 7
I assume you meant [tex]f(x)=8^x[/tex].
Reflecting across the x-axis would give [tex]y=-8^x[/tex].
Reflecting across the y-axis would give [tex]y=8^{-x}[/tex].
Simplify the following
Answer is 6
Firstly changing mixed fraction.
[tex] \frac{3}{2} - \frac{5}{4} + \frac{23}{4} [/tex]
By taking the LCM
[tex] \frac{6 - 5 + 23}{4} [/tex]
-5 + 23 (-) (+) = (-)
[tex] \frac{6 + 18}{4} [/tex]
[tex] \frac{24}{4} [/tex]
[tex]6[/tex]
Hope it helps you, any confusions you may ask!
Answer:
6 (work below)
Step-by-step explanation:
1 1/2 = 3/2
1 1/4 = 5/4
5 3/4 = 23/4
The least common multiple of the denominators is 4, so 3/2 will become 6/4.
6/4 - 5/4 = 1/4 + 23/4 = 24/4 = 6
Brainliest, please :)
18. Which TWO linear inequalities are shown in the
graph below?
y
A.
B.
C.
D.
E.
F.
G.
H.
y> -2
y < -2
x<-2
X > -2
x+y<1
x-y<-1
x+y>1
x-y> -1
Answer: A and H
Step-by-step explanation:
y=x+1 is shaded below and dotted, so [tex]y < x+1 \implies x-y > -1[/tex].
Also, y=-2 is dotted and shaded above, so it represents [tex]y > -2[/tex]
A family has two cars. The first car has a fuel efficiency of miles 15 per gallon of gas and the second has a fuel efficiency of 20 miles per gallon of gas. During one particular week, the two cars went a combined total of 975 miles, for a total gas consumption of 55 gallons. How many gallons were consumed by each of the two cars that week?
The first car consumed 25 gallons of fuel while the second car consumed 30 gallons of fuel.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the first car consumption and y represent the second car consumption, hence:
x + y = 55 (1)
Also:
15x + 20y = 975 (2)
From both equations:
x = 25, y = 30
The first car consumed 25 gallons of fuel while the second car consumed 30 gallons of fuel.
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Express the following
The sum of the exponential expression is e^8x + e^2x
Simplifying exponential functionExponential functions are inverse of logarithmic function
Given the exponential function below;
(e^4x)² + e^2x
Expand
e^8x + e^2x
Hence the sum of the exponential expression is e^8x + e^2x
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The graph of the function f(x) = (x - 3)(x + 1) is shown.
Ty
-10-8-6
10
8
6
-6
8
-10-
6
10
X
Which describes all of the values for which the graph is
positive and decreasing?
O all real values of x where x < -1
O all real values of x where x < 1
O all real values of x where 1
O all real values of x where x > 3
Answer:
all real values of x where x < -1
The correct statement is all real values of x where x < -1.
Option A is the correct answer.
We have,
To determine the values for which the graph of the function
f(x) = (x - 3)(x + 1) is positive and decreasing, we need to analyze the behavior of the function.
Let's consider the factors individually:
(x - 3): This factor is positive for x > 3 and negative for x < 3.
(x + 1): This factor is positive for x > -1 and negative for x < -1.
To determine the overall sign of the function, we need to consider the signs of both factors together.
When both factors are positive or both factors are negative, the function is positive.
When the factors have opposite signs, the function is negative.
From the above analysis, we can conclude the following:
When x > 3, both factors are positive, so the function is positive.
When -1 < x < 3, the factor (x - 3) is negative, while the factor (x + 1) is positive. Therefore, the function is negative.
When x < -1, both factors are negative, so the function is positive again.
Since we are looking for values where the function is positive and decreasing, we can eliminate the options that include positive and increasing regions (such as x > 3).
Thus,
The correct statement is all real values of x where x < -1.
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Calculate the geometric center of the graph the function
The geometric center of the graph under the function is 5/3
How to determine the geometric center of the graph under the function?The equation of the function is given as:
f(x) = 3 - |x - 2|
The interval is given as:
x ∈ [0, 3]
The geometric center (gc) of the graph under the function is calculated using
gc = ∫x f(x) dx/∫f(x) dx
Substitute the known values in the above equation
gc = ∫x * (3 - |x - 2|) dx/∫3 - |x - 2| dx
Integrate the numerator and the denominator of the above equation
gc = [-1/6(x - 2)((2|x -2| - 9)x + 2|x - 2| - 18)]/[3x - 1/2[|x - 2|(x - 2)]]
Recall that the interval is given as x ∈ [0, 3]
Substitute the interval values in the above equation.
The equation is then simplified using a graphing calculator.
So, we have
gc = (65/6)/(13/2)
Express the quotient expression as a product
gc = (65/6) * (2/13)
Divide 65 by 13
gc = 5/6 * 2
Divide 2 by 6
gc = 5/3
Hence, the geometric center of the graph under the function is 5/3
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What is the value of x
83
58
50
70.5
Answer:
58
Step-by-step explanation:
[tex]x = \frac{141 - 25}{2} = 58[/tex]
When Billy's asked how old he is, he replies, "In two years I will be twice as old as I was five years ago." How old is he?
brainliest to whoever answers
Answer:
12 years old
Step-by-step explanation:
Set up the following equation:
x + 2 = 2(x - 5) (distribute the 2)
x + 2 = 2x - 10 (subtract 2 from both sides)
x = 2x - 12 (subtract 2x from both sides)
-x = -12 (multiply both sides by negative 1)
x = 12
Brainliest, please :)
Answer: 12
Step-by-step explanation:
Let's algebraically represent this situation. Say his current age is x. We can rephrase the sentence to say that in two years, his age is the same as twice his age 5 years ago.
The phrase "in two years" means when his age is 2 more than his current age, or x + 2.
The phrase "same as" represents equality. The expressions on both sides have the same value.
The phrase "twice his age 5 years ago" is his age minus 5, multiplied by 2. We can write this as 2*(x-5).
Now that we have "translated" the equation from words to numbers, let's put it all in one equation and solve:
[tex]x+2=2(x-5)[/tex]
[tex]x+2=2x-10[/tex] [Distributive Property]
[tex]x+2-2x-2=2x-10-2x-2[/tex] [Adding -2x-2 to both sides]
[tex]-x=-12[/tex] [Combining like terms and simplifying]
[tex]x=12[/tex] [Multiplying both sides by -1 to remove the negative]
Hence, Billy's age is 12.
Suppose that 37% of college students own cats. If you were to ask random college students if they own a cat what would the probability that:
a) a single student doesn’t own a cat?
b) 3 students own cats?
c) 2 students own cats while 2 students don't own cats?
Using the binomial distribution, the probabilities are given as follows:
a) 0.37 = 37%.
b) 0.5065 = 50.65%.
c) 0.3260 = 32.60%.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the fixed parameter is:
p = 0.37.
Item a:
The probability is P(X = 1) when n = 1, hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{1,1}.(0.37)^{1}.(0.63)^{0} = 0.37[/tex]
Item b:
The probability is P(X = 3) when n = 3, hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.37)^{3}.(0.63)^{0} = 0.5065[/tex]
Item c:
The probability is P(X = 2) when n = 4, hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{4,2}.(0.37)^{2}.(0.63)^{2} = 0.3260[/tex]
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will give brainliest
The equation of a hyperbola is [tex]x^{2}[/tex]/9 - [tex]y^{2}[/tex]/4 = 1
What are the steps to Hyperbola equation ?
To find the equation of hyperbola, the following steps must be taken. You need to identify;
The coordinate of the centerThe coordinate of the verticesThe coordinate of the fociThe general equation of a hyperbola can be expressed as
[tex]x^{2}[/tex]/[tex]a^{2}[/tex] - [tex]y^{2}[/tex]/[tex]b^{2}[/tex] = 1
From the graph, we have the following parameters
a = 3
[tex]a^{2}[/tex] = [tex]3^{2}[/tex] = 9
b = 2
[tex]b^{2}[/tex] = [tex]2^{2}[/tex] = 4
The equation of a hyperbola can be expressed as
[tex]x^{2}[/tex]/9 - [tex]y^{2}[/tex]/4 = 1
The vertices = V(+/-a,0) = (+/-3,0)
The center = C(0,0)
The focus = F(+/-C, 0)
Where [tex]C^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex]
C = [tex]\sqrt{9 + 4}[/tex]
C = [tex]\sqrt{13}[/tex]
Focus = F(+/- [tex]\sqrt{13}[/tex], 0)
The general equation for asymptote = +/- b/a X
= +/-2/3X
Therefore, the equation of a hyperbola can be expressed as
[tex]x^{2}[/tex]/9 - [tex]y^{2}[/tex]/4 = 1
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Complete the frequency table:
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 18 165
Age 15 and above 65 195
Column totals 152 110 98 360
What percentage of students age 15 and above travel to school by bus? Round to the nearest whole percent.
The percentage of students age 15 and above travel to school by bus is 47%
How to complete the table?The table of values is given as:
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 18 165
Age 15 and above 65 195
Column totals 152 110 98 360
Using the column total of column 1, we have:
Under age 15 + 65 = 152
This gives
Under age 15 = 87
Using the column total of column 2, we have:
Age 15 and above + 18 = 110
This gives
Age 15 and above = 92
Using the row total of row 1, we have:
Car + 87 + 18 = 165
This gives
Car = 60
Using the row total of row 2, we have:
Car + 65 + 92 = 195
This gives
Car = 38
So, the complete frequency table is
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 87 18 60 165
Age 15 and above 65 92 38 195
Column totals 152 110 98 360
The percentage of students age 15 and above travel to school by bus is:
Percentage = 92/195 * 100%
This gives
Percentage = 47%
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anybody answer me please with step by step explanation need complete detailed answer
Answer:
A = 55
Step-by-step explanation:
take the two identical triangles and join them so that you get a rectangle wih sides 5 and 11. now multiply them togeter to get the are of the polynom
The area of triangle is 55 square centimeters.
What is area?Area is the amount of space occupied by a two-dimensional figure.
What is the formula for the area of triangle?The formula for the area of triangle is
[tex]Area = \frac{1}{2} \times base\times height[/tex]
According to the given question.
We have a figure of a quadrilateral which is made up of four right angled tringles.
Now,
The area of a triangle with base 5cm and height 7 cm
= [tex]\frac{1}{2} \times 5\times 7[/tex]
[tex]=\frac{35}{2}[/tex]
[tex]= 17.5[/tex] square centimeters
And, the area of triangle with base 4cm and height 5cm
= [tex]\frac{1}{2} \times 4\times 5[/tex]
[tex]= 10[/tex] square centimeters
Since, the quadrilateral is made up of 2 right angled triangle with base 5cm and height 7cm and 2 right angled triangle with base 4cm and height 5cm.
Therefore, the area of quadrilateral or the given fiure
= 2( area of triangle with height 7cm and base 5cm + area of triangle with base 4cm and height 5cm )
= 2(17.5 + 10) square centimeter
= 2 × 27.5
= 55 square centimeters
Hence, the area of triangle is 55 square centimeters.
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Janet Lopez is establishing an investment portfolio that will include stock and bond funds. She has $720,000 to invest, and she does not want the portfolio to include more than 65% stocks. The average annual return for the stock fund she plans to invest in is 18%, whereas the average annual return for the bond fund is 6%. She further estimates that the most she could lose in the next year in the stock fund is 22%, whereas the most she could lose in the bond fund is 5%. To reduce her risk, she wants to limit her potential maximum losses to $100,000.
a. Formulate a linear programming model for this problem.
Based on the amounts that Janet Lopez has to invest in stocks and bonds, the linear programming model would be:
0.18x + 0.06y = maximized returns 0.22x + 0.05y ≤ 100,000x + y ≤ 720,000x/ y + y ≤0.65What is the linear programming model?The return on stocks (x) is 18% and the return on bonds (y) is 6%, The objective function:
= 0.18x + 0.06y
There are constraints to watch out for:
Maximum to lose on stocks is 22% and on bonds is 5% but these are to be less than the total amount of $100,000.
0.22x + 0.05y ≤ 100,000
The total amount to invest is $72,000 which means that both bonds and stocks need to be less than this amount:
x + y ≤ 720,000
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Please help ASAP! Clear explanations are greatly appreciated!
Using a system of equations, it is found that her normal week is of €285.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: Her normal hours.Variable y: Her time and a half hours.The first equation, considering the first sentence, is given by:
x + 8y = 375.
The second equation, considering the second sentence, is given by:
x + 4y = 330.
Then the system is:
x + 8y = 375.x + 4y = 330.Multiplying the second equation by -2, the system is:
x + 8y = 375.-2x - 8y = -660.Adding the equations, we have that her normal week is given by:
x = 660 - 375 = €285.
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Can anyone help me find all the calculations to these cups?
The volume of the glasses is as follows;
glass 1 = 170 cm³glass 2 = 141 cm³glass 3 = 60 cm³How to find volume ?The volume of cylinder glass 1 = πr²h
The volume of cylinder glass 1 = 3.14 × 3² × 6
The volume of cylinder glass 1 = 3.14 × 9 × 6
The volume of cylinder glass 1 = 169.56 cm³ = 170 cm³
The volume of the glass 2 = 2 / 3 π r³ + πr²h
The volume of the glass 2 = 2 / 3 × 3.14 × 3³ + 3.14 × 3² × 3
The volume of the glass 2 = 56.52 + 84.78
The volume of the glass 2 = 141.3 cm³ = 141 cm³
The volume of conical glass 3 = 1 / 3 πr²h
The volume of conical glass 3 = 1 / 3 × 3.14 × 3² × (√7² - 3² = √40)
The volume of conical glass 3 = 9.42 × √40
The volume of conical glass 3 = 59.5773111176
The volume of conical glass 3 = 60 cm³
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5.5(x+6 1/2)-(x+9 1/3) - (19-x)
The simplest form of the expression given in the task content is; 5.5x +7.42.
What is the simplest form of the expression?The expression given in the task content is;
5.5(x+6 1/2)-(x+9 1/3) - (19-x)
Hence, the expression can be written in its simplest form as follows;
5.5x + 35.75 -x -9.33 -19 +x
= 5.5x +7.42.
Remarks: The complete task requires that the expression be written in its simplest form.
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I need help with my work
The area of the interior above the polar axis is -0.858 square units
The area bounded by a polar curveThe area bounded by a polar curve between θ = θ₁ and θ = θ₂ is given by
[tex]A = \int\limits^{\theta_{2} }_{\theta_{1} } {\frac{1}{2}r^{2} } \, d\theta[/tex]
Now, since we have the curve r = 1 - sinθ and we want to find the area of the interior above the polar axis, we integrate from θ = 0 to θ = π, since this is the region above the polar axis.
So, [tex]A = \int\limits^{\theta_{2} }_{\theta_{1} } {\frac{1}{2}r^{2} } \, d\theta\\= \int\limits^{\pi}_{0} {\frac{1}{2}(1 - sin\theta)^{2} } \, d\theta\\= \int\limits^{\pi}_{0} {\frac{1}{2}[1 - 2sin\theta + (sin\theta)^{2}] } \, d\theta\\= \int\limits^{\pi}_{0} {\frac{1}{2}\, d\theta - \int\limits^{\pi}_{0} 2sin\theta \, d\theta+ \int\limits^{\pi}_{0} (sin\theta)^{2} } \, d\theta\\[/tex]
[tex]A = \int\limits^{\pi}_{0} {\frac{1}{2}\, d\theta - 2\int\limits^{\pi}_{0} sin\theta \, d\theta+ \int\limits^{\pi}_{0} \frac{(1 - cos2\theta)}{2} } \, d\theta\\= \int\limits^{\pi}_{0} {\frac{1}{2}\, d\theta - 2\int\limits^{\pi}_{0} sin\theta \, d\theta+ \int\limits^{\pi}_{0} \frac{1}{2} } \, d\theta -\int\limits^{\pi}_{0} \frac{cos2\theta}{2} } \, d\theta\\[/tex]
[tex]A = \int\limits^{\pi}_{0} \, d\theta - 2\int\limits^{\pi}_{0} sin\theta \, d\theta -\int\limits^{\pi}_{0} \frac{cos2\theta}{2} } \, d\theta\\= [\theta]_{0}^{\pi} - 2[-cos\theta]^{\pi} _{0} - [\frac{sin2\theta}{4}]_{0}^{\pi} \\= [\theta]_{0}^{\pi} + 2[cos\theta]^{\pi} _{0} - [\frac{sin2\theta}{4}]_{0}^{\pi}\\= [\pi - 0] + 2[cos\pi - cos0] - \frac{ [sin2\pi - sin0]}{4}\\= \pi + 2[-1 - 1] - \frac{ [0 - 0]}{4}\\= \pi + 2[-2] - \frac{ [0]}{4}\\= \pi - 4 - 0\\= \pi - 4\\= 3.142 - 4\\= -0.858[/tex]
So, the area of the interior above the polar axis is -0.858 square units
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Lamonte has 50 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 288 square meters. List each set of possible dimensions (length and width) of the field.
The dimensions of the length and width are 25 meters and 12. 5 meters respectively.
How to determine the valuesArea of a rectangle
area of rectangle = l × w
where
l = length
w = width
Note that,
Perimeter = 2w+ l
50 = 2w + l
l = 50 - 2w
Hence,
area = w(50 - 2w)
288 = 50w - 2w²
-2w² + 50w - 288 = 0
-w² + 25w - 144 = 0
The dimension w can be found as follows;
w = - b / 2a
where
a = -1
b = 25
w = - 25 / 2 × -1
w = 12.5 meters
Then, we have that
l = 50 - 2w
Substitute the value of w
l = 50 - 2(12.5)
l = 50 - 25
I = 25 meters
Thus, the dimensions of the length and width are 25 meters and 12. 5 meters respectively.
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PLEASE HELP PLEASE I DONT KNOW THIS QUESTION AND IVE BEEN STUCK ON THIS FOR A DAY
Answer:
A = -5
B = 1
Step-by-step explanation:
Hello!
You simply plug in the given x-value into the equation to find the missing y-value.
Solve for APlug in -1 for x into y = 2x - 3.
y = 2x - 3y = 2(-1) - 3y = -2 - 3y = -5Solve for BPlug in 2 for x into y = 2x - 3.
y = 2x - 3y = 2(2) - 3y = 4 - 3y = 1100 POINTS
Find the volume of the composite solid.
A ) 1099.01 m^3
B) 104.67 m^3
C) 889.67 m^3
D) 785 m^3
Volume of a cylinder: PI x radius^2 x height
= 3.14 x 5^2 x 10 = 785 m^3
Volume of a cone: pi x radius^2 x height/3
= 3.14 x 5^2 x 4/3 = 104.67 m^3
Total volume = 785 + 104.67 = 889.67 M63
Answer: C. 889.67 M^3
Answer:
[tex]\textsf{C)}\quad \sf 889.67\: m^3[/tex]
Step-by-step explanation:
The given composite solid is made up of a cylinder and a cone.
To find the volume of the composite solid, find the volume of the cylinder and the volume of the cone, then add them together.
Volume of a cylinder:
[tex]\sf V=\pi r^2 h[/tex]
(where r is the radius and h is the height)
Given:
r = 5 mh = 10 mSubstitute the given values into the formula and solve for V:
[tex]\begin{aligned}\implies \sf Volume\:of\:the\:cylinder & = \sf \pi (5)^2(10)\\ & = \sf 250 \pi \:\:m^3 \end{aligned}[/tex]
Volume of a cone:
[tex]\sf V=\dfrac{1}{3} \pi r^2 h[/tex]
(where r is the radius and h is the height)
Given:
r = 5 mh = 4 mSubstitute the given values into the formula and solve for V:
[tex]\begin{aligned}\implies \sf Volume\:of\:the\:cone & = \sf \dfrac{1}{3} \pi (5)^2(4)\\ & = \sf \dfrac{100}{3}\pi \:\:m^3 \end{aligned}[/tex]
Therefore, the volume of the composite solid is:
[tex]\begin{aligned}\implies \sf Volume\:of\:composite\:solid & = \sf Cylinder\:volume+Cone\:volume\\ & = \sf 250\pi + \dfrac{100}{3}\pi \\ & = \sf \dfrac{850}{3} \pi \\ & = \sf \dfrac{850}{3} \times 3.14 \\ & = \sf 889.67\:m^3\:(2\:d.p.)\end{aligned}[/tex]