From the given data provided, the probability that number of adults selected in process are 3, less than 5, between 5 and 9, more than 5 but less than 10, 6 or more is 0.096, 0.41, 0.336, 0.232, 0.168 and mean of number of people tested for HIV is 3.6.
(a) The probability that an adult has not been tested for HIV is 1-0.20=0.80. Therefore, the probability that the first adult selected has not been tested for HIV is 0.80. The probability that the first and second adults selected have not been tested for HIV is 0.80 x 0.80=0.64. Continuing in this way, we see that the probability that X adults must be selected until one who has been tested for HIV is found is given by:
P(X≤x) = 1 - 0.80ˣ
(b) Using the formula from (a), we can find the probabilities as follows:
(i) P(X=3) = P(X≤3) - P(X≤2) = (1-0.80³) - (1-0.80²) = 0.096
(ii) P(X<5) = P(X≤4) = 1-0.80⁴ = 0.41
(iii) P(5≤X≤9) = P(X≤9) - P(X≤4) = (1-0.80⁹) - (1-0.80⁴) = 0.336
(iv) P(6≤X<10) = P(X≤9) - P(X≤5) = (1-0.80⁹) - (1-0.80⁵) = 0.232
(v) P(X≥6) = 1 - P(X≤5) = 1 - (1-0.80⁵) = 0.168
(c) To find the mean and variance of X, we first note that X follows a geometric distribution with parameter p=0.20. Therefore, the mean and variance of X are:
Mean of X = E(X) = 1/p = 1/0.20 = 5
Variance of X = Var(X) = (1-p)/p² = 0.8/0.04 = 20
(d) To find the probabilities for a random sample of 18 adults, we use the binomial distribution with parameters n=18 and p=0.20. The probabilities are:
(i) P(X=3) = (18 choose 3) x 0.20³ x 0.80¹⁵ = 0.236
(ii) P(X<5) = P(X≤4) = Σ(18 choose x) x 0.20ˣ x 0.80⁽¹⁸⁻ˣ⁾ for x=0 to 4 = 0.678
(iii) P(5≤X≤9) = Σ(18 choose x) x 0.20ˣ x 0.80⁽¹⁸⁻ˣ⁾ for x=5 to 9 = 0.286
(iv) P(6≤X<10) = Σ(18 choose x) x 0.20ˣ x 0.80⁽¹⁸⁻ˣ⁾ for x=6 to 9 = 0.207
(v) P(X≥6) = 1 - P(X≤5) = 1 - Σ(18 choose x) x 0.20ˣ x 0.80⁽¹⁸⁻ˣ⁾ for x=0 to 5 = 0.322
(e) The mean and variance of X for a sample of 18 adults are:
Mean of X = E(X) = n x p = 18 x 0.20 = 3.6
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Find the value of Sin -¹ (tan 3.14/4)
a. 0
b. 3.14
c. 2
d. 3.14/2
Please select the best answer from the choices provided
Answer:
D.) 3.14/2
Step-by-step explanation:
T = √(2023 2023) (2023 +2023) + (2023 x 2023) + (2023 - 2023).
To simplify the given expression, we can first evaluate each term inside the square root, and then add them up. Using basic algebraic operations, we get:
T = √(2023^2)(4046) + (2023^2) + 0
T = √(2023^2)(4046 + 1)
T = √(2023^2)(4047)
T = 2023√4047
Therefore, the simplified expression for T is 2023√4047.
Determine the power consumed by the resistor
The power consumed by resistor R3 is 0.79 watts.
What is power?The rate at which energy is transferred or converted is known as Power. It is a measure of how much work can be done in a given amount of time. Power is typically measured in watts and is a key factor in determining the efficiency of machines and systems.
To determine the power consumed by resistor R3, we need to first find the current flowing through it.
E₁ = I(R₁ + R₂ + R3 + R4)
I = E₁ / (R₁ + R₂ + R3 + R4)
= 30 / (152 + 202 + 252 + 102)
= 0.056 A
Now that we know the current flowing through R3, we can use Ohm's Law again to find the power consumed by it:
P = I²R3
= (0.056)² x 252
= 0.79 W
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I am an integer in quadrant to my exponent is less than -1 my y-coordinate is more than two my x-coordinate is greater than -3 the sum of the absolute values of my coordinates is five who am I
The integer that satisfies all of these conditions is -4.
Exponentiating -4 gives 16, which is less than -1.
The y-coordinate of -4 on the coordinate plane is above 2.
The x-coordinate of -4 on the coordinate plane is greater than -3.
And, the sum of the absolute values of the coordinates of -4 is 7, which is equal to five.
5^x+1+5^x-1 simply using the law of exponents
Answer:
5^x+x
Step-by-step explanation:
5^x+1+5^x-1
First of all 1- 1 = 0
so we are here with 5^x +5^x
What is the result when the number 94 is decreased by 50%?
Step-by-step explanation:
94 - 50% * 94 =
94 - .50 * 94 =
94 - 47 = 47
Answer:
47
Step-by-step explanation:
50 × 94 ÷ 100 =
47,00 ÷ 100=
47
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
The answer you're looking for is x = 6, and the missing angle is 30º
Step-by-step explanation:
In order to find the answer we need to find out what the angle amount actually is. We can use the equation 180º = 110+ 40 + (8x-18).
Now there are two ways to solve this equation you could solve it by starting with the equation actually is or you can find out the missing angle using another equation.
First Method:
Using 180º = 110+ 40 + (8x-18), you first need to do is to combine like terms such as combining 110, 40, and -18, giving you 132.
Now you have 180 = 132 + 8x.
Then you will have to make sure that 8x is left by itself so do the opposite operation and to keep the equation balanced you do it on both sides giving you 48 = 8x. The only step left to do is to do the opposite operation on both sides which is dividing by 8, giving you 6 = x
Now with that, you replace x, with 6, and go from there.
(8x-18) = (8×6-18) = (48 - 18) = 30.
With that, we are finished with the equation.
However, the other method you could use, which is easier in my opinion, can be found below.
Second Method:
The first thing we do is find out immediately what the missing angle (m) is using the equation 180 = 110 + 40 + m.
You combine like terms 110 and 40, giving 150 and then get,
180 = 150 + m.
You then do the inverse of operations, which is subtracting 150 from both sides and you get 30 = m.
Now that we complete that we start with our other equation which is:
30 = 8x-18. You then do inverse of -18, which adds 18 to both sides giving: 48 = 8x.
Finally doing the inverse operation of multiplying is dividing 8 by both sides giving 6 = x as the correct answer.
I will give Brainliest! =D
Determine the rest of the side lengths, and describe your strategies!
Considering the figure, the missing lengths are
the topmost is 15the other length is 4What is similar triangles?In geometry, the phrase "similar triangles" refers to triangles whose respective sides are proportionate and whose corresponding angles are congruent.
Hence, if the triangle's corresponding angles are congruent, the side should be in proportion.
The proportions are as follows
say the side on top of 10 (in horizontal line) is y
y / (10 + 15 + 12.5) = 10 / (10 + 15)
y / 37.5 = 10 / 25
cross multiplying
25y = 37.5 * 10
25y = 375
y = 15
say the side below side 10 (in horizontal line) is x
x / 10 = 10 / (10 + 15)
x / 10 = 10 / 25
cross multiplying
25x = 100
x = 4
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NEED HELP ASAP (100 points)
Answer:
Ill help you figure out how to graph.
Step-by-step explanation:
The value in front of x (like 2x or 7x) is the slope (rise over run) rise is how much the line goes up, and run is how much it goes to the side. the second number (in the bottom left graph, it is -5) is the y intercept. it is where the line crosses the y axis. (in this case on -5) Here is an example. (of the problem y=x-5)
A bottle filling machine fills 25 bottles per minute. A second machine fills 15 bottles per minute. The second machine starts filling bottles 20 minutes after the first machine starts. Both machines stop filling bottles after 300 minutes after the first machine started. Which equation represents the situation of how many bottles will be filled?
A) 300(25)+290(15)
B) 300(25)+280(25)
C) 300(25)+300(25)
D) 300(25)+280(15)
25 bottles every minute are filled using a filling and capping machine in [tex]11700[/tex]
What use does a machine serve?Even though both pressures and movements are involved in a machine's functioning, one of its principal functions can either be force amplification or motion modification. A lever essentially adds force, but a gearbox often acts as a speed reducer.
What in mathematics is a machine diagram?A machine diagram represents a function operation on a variable x to create a variable output y diagrammatically. If x falls inside the scope of the f(x, the machine will accept x as an input and output y in accordance with the function's rules.
[tex]25 bottles/minute * 20 minutes = 500 bottles.[/tex]
During the remaining [tex]280[/tex] minutes, both machines are running and together they fill
[tex]25 bottles/minute + 15 bottles/minute = 40 bottles/minute[/tex]
So, the total number of bottles filled during this period is
[tex]40 bottles/minute * 280 minutes = 11,200 bottles.[/tex]
[tex]500+ 11,200= 11,700[/tex]
None of the given options represents this equation.
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Consider 3 individuals in a small town: Alice, Bianca, and Claire. There is an NGO who can provide an art museum for their town with the help of local contributions. The higher the contributions, the larger the art collection of the museum. Their respective direct marginal benefits from N works of art are: MBA=7-N, MBB=7-½N, MBC=23-½N2, and their respective marginal costs are: MCA=2, MCB=3, MBC=5.
a. Find each person’s optimal number of art works.
b. Who will contribute and how many works of art will be provided?
Altruism: now consider the case where each individual cares about the benefit from the museum to the other two. For example any additional utility to Alice or Bianca is also a utility gain for Claire.
c. Find each person’s optimal number of art works.
d. Who will contribute and how many works of art will be provided?
Now consider the case where each individual cares only about their direct marginal benefit from the public good plus an additional warm-glow marginal benefit from giving as follows: WMBA=6-NA, WMBB=6-NB, and WMBC=24-NC, where NA, NB, and NC respectively represent Alice, Bianca, and Claire’s individual contributions. For example, Alice’s total marginal benefit is TMBA=MBA+WMBA=7-N+6-NA.
e. Who will contribute and how many works of art will be provided?
The Bianca will contribute 14.6 works of art, and Claire will contribute 8.7 works of art.
a. In order to find each person's optimal number of art works, one must solve for the point at which the marginal benefit and the marginal cost intersect. For Alice, that point is when N = 7 and MBA = MCA, resulting in an optimal number of works of art of 7. For Bianca, the intersection point is when N = 14 and MBB = MCB, resulting in an optimal number of works of art of 14. For Claire, the intersection point is when N = 8.3 and MBC = MCC, resulting in an optimal number of works of art of 8.3.
b. Without considering altruism, Alice will contribute 7 works of art, Bianca will contribute 14 works of art, and Claire will contribute 8.3 works of art.
c. With altruism, the optimal number of art works for each individual can be calculated in the same way as without altruism, but with the warm-glow benefit added to their respective total marginal benefits. For Alice, that point is when N = 7.3 and TMBA = MCA, resulting in an optimal number of works of art of 7.3. For Bianca, the intersection point is when N = 14.6 and TMBB = MCB, resulting in an optimal number of works of art of 14.6. For Claire, the intersection point is when N = 8.7 and TMBC = MCC, resulting in an optimal number of works of art of 8.7.
d. With altruism, Alice will contribute 7.3 works of art, Bianca will contribute 14.6 works of art, and Claire will contribute 8.7 works of art.
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Two 10 by 10 grids are shown. The first grid has 4 columns and 6 squares shaded green. On the same grid, 6 squares and 4 columns are shaded red. On the same grid, 8 squares are shaded blue. On the second 10 by 10 grid, 3 columns and 8 squares are shaded blue. Part A Write the multiplication expression shown by the model. Do not solve the problem. Part B Explain the expression written in Part A. Include the final product and how it is shown with the model. 1000
a) Tοtal squares shaded is 4*10+(1*6) + 4*10+(1*6) + (1*8) + 3*10+(1*8)
b) The expressiοn gives the tοtal number οf squares.
Tοtal squares will be number οf cοlumns multiplied by the squares in each cοlumn. dοing same fοr all cοlοrs and adding them, we will get the Tοtal squares shaded
c) On simplifying the expressiοn, we get 138 squares
What is an expressiοn?Mathematical expressiοns cοnsist οf at least twο numbers οr variables, at least οne arithmetic οperatiοn, and a cοmplete sentence. Any οne οf the fοllοwing mathematical οperatiοns can be used. A sentence has the fοllοwing structure: Number/variable, Math Operatοr, Number/Variable is an expressiοn.
In each cοlumn, there are 10 squares
The first grid has 4 cοlumns and 6 squares shaded green
=> 4*10+(1*6) = 46 green squares
On the same grid, 6 squares and 4 cοlumns are shaded red.
=> 4*10+(1*6) = 46 red squares
On the same grid, 8 squares are shaded blue. => (1*8) blue squares
On the secοnd 10 by 10 grid, 3 cοlumns and 8 squares are shaded blue.
=> 3*10+(1*8) blue squares
a)Tοtal squares shaded
= shades οn first grid + shades οn secοnd grid
= ( green squares + red squares + blue squares ) + ( blue squares )
= 4*10+(1*6) + 4*10+(1*6) + (1*8) + 3*10+(1*8)
b) The expressiοn gives the tοtal number οf squares.
Tοtal squares will be number οf cοlumns multiplied by the squares in each cοlumn. dοing same fοr all cοlοrs and adding them, we will get the Tοtal squares shaded
c) On simplifying the expressiοn, we get
= 46+46+8+38
= 138 squares
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Lucia fue a comprar el regalo de cumpleaños de la abuela. Le compró un vestido que tiene un precio de $750 pesos, pero la tienda cuenta con el 20% de descuento en todas las prendas. ¿Qué cantidad terminó pagando Lucia por el vestido?
Answer:
[tex]\boxed{ \$600}[/tex]
Step-by-[tex]\boxed{/$600}[/tex]step explanation:
El enunciado nos dice que toda la tienda cuenta con 20% de descuento, así que por cada artículo paga el 80% de su valor (100%-20%).
Una forma rápida de resolver el ejercicio es con regla de 3.
[tex]\$750 \Rightarrow 100 \% \newline x \Rightarrow 80\%[/tex]
para encontrar [tex]x[/tex]:
[tex]x=\frac{80*750}{100} \\x=\$600[/tex]
Por lo que la cantidad que termina pagando por el vestido es de $600.00
[tex]\text{-B$\mathfrak{randon}$VN}[/tex]
The height of a student is measured as 1.6m to the nearest tenth of a meter. Find to one significant figure, the greatest possible percentage error
Answer: 7.4
Step-by-step explanation:
What is this written as an algebraic expression? the sum of number and 9.
Answer:
The sum of a number and 9 can be written as:
x + 9
where "x" represents the number being referred to.
Alternatively, if we want to use a different variable, we can write it as:
n + 9
where "n" represents the number being referred to.
Hope this helped, if not I'm sorry! If you need more help, feel free to ask! :]
A school sports team contains 68 students. 33 do field events, 40 do track events, 23 do swimming, 14 do both field and track events. If 15 students do field events only and 10 do both swimming and track events, how many students do a) swimming knly b)track events only c) all three events?
Answer:
9, 20 and 4
Step-by-step explanation:
Swimming only 9
Track only 20
All 3 events
14 did track and field
10 did track and swimming
Those who sis all 14- 10 = 4
The answers are the students do a) swimming only = 9, b)track events only = 20 and c) all three events = 4
What is a Venn diagram?A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things.
Given that, a school sports team contains 68 students. 33 do field events, 40 do track events, 23 go swimming, 14 do both field and track events. If 15 students do field events only and 10 do both swimming and track events,
Please refer to picture attached
Therefore,
15+a+c+d = 33.......1
b+c+d+e = 40.........2
a+b+d+f = 23..........3
c+d = 14...............4
a+d = 8.............5
b+d = 10.............6
Now, solving for variables,
From 1 and 4,
a = 4
Therefore, from 5,
d = 4
From 6,
b = 6
Put these in eq 3,
f = 9
c = 10
e = 20
Therefore,
Swimming only = 9
Track events = 20
All three = 4
Hence, the answers are the students do a) swimming only = 9, b)track events only = 20 and c) all three events = 4
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Please refer to the photo
Which expression is equivalent to….
What is the length of DE? and What is the length of AD? and What is the length of EC?
Answer:
DE's length is 1/2 of BC's length, due to it being a mid segment (13)((You can tell it is a mid segment due to the congruency lines)). AD's length is 12, due to there being a midpoint. EC's length is 10, also due to the congruency lines.
Aisha wants to work out 764+3+2
show two ways she can do this
Answer:
769
764 + 3 + 2 = 769
1. She can do 764 + 3 = 767 767 + 2 = 769
2. OR She can do 2 + 3 = 5 5 + 764 = 769
Elizabeth is mountain climbing with Frank and has just climbed a 16-meter vertical rock face. Frank is standing 30 meters away from the bottom of the cliff, looking up at Elizabeth. How far away are Elizabeth and Frank?
Pythagorean theorem: word problems ⬆️
Please respond.
Answer:
34m
Step-by-step explanation:
To find:-
Distance between Frank and Elizabeth.Answer:-
We are here given that Elizabeth climbed up the mountain vertically 30m , and the distance between frank and the bottom of the mountain is 30m .
We are interested in finding out the distance between frank and Elizabeth. For that we will have to use Pythagoras theorem , in which;
[tex]\rm\implies a^2+b^2 = h^2 \\[/tex]
Where h is the longest side of the triangle and a and b are two other sides. here we need to find out the longest side ( see attachment) .
So on substituting the respective values, we have;
[tex]\rm\implies h^2 = (16m)^2+(30m)^2 \\[/tex]
[tex]\rm\implies h^2 = 256m^2 + 900m^2 \\[/tex]
[tex]\rm\implies h^2 = 1156m^2\\[/tex]
[tex]\rm\implies h =\sqrt{1156 \ m^2} \\[/tex]
[tex]\rm\implies \red{h = 34 m} \\[/tex]
Hence the distance between Elizabeth and Frank is 34m .
factorise fully
[tex]x {}^{2} + x[/tex]
[tex]15a {}^{2} + 19a - 8[/tex]
[tex]8x {}^{2} - 6xy - 9y {}^{2} [/tex]
[tex]a {}^{2} - ab - a + b[/tex]
Answer:
1 . x(x+1)
2.(3a-1)(5a+8)
3.(4x + 3y) ( 3x - 3y)
4.(a+b)
Which is the better buy? 3-pound bag of rice for $2.25 9-pound bag of rice for $6.66
Answer:
Step-by-step explanation:
To see which bag is the better buy, calculate how much each pound of rice would cost.
To do that divide the price by the amount of costs for each then compare those numbers
$2.25/3 = $0.75 per pound
$6.66/9 = $0.74 per pound
So the 9 pound bag of rice would cost 1 cent less per pound making it the better buy.
Maria is a baker. Her cost to make a cake is $4.00. She sells her cakes to local grocery stores at a price which includes a 20% markup for profit. The grocery stores then sell the cakes at a price which includes an additional 25% for their profit. What is the price of one of Maria's cakes at a grocery store?
Answer : 6 Dollars
Explanation : 4.00 × 20/100 = 0.8 + 4 = 4.8 * 25/100 = 6
Answer : 6 doolarz ThanK me
What is equivalent to the answer in
8(2y+1/4)?
FYI the “1/4” is not divided it’s a fraction
Answer:
[tex]\boxed{\textsf{16y + 2 is Equivalent to 8 (2y + 1/4).}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to find an \underline{equivalent expression}.}[/tex]
[tex]\textsf{This expression is set up to allow us to use the \underline{Distributive Property}.}[/tex]
[tex]\Large\textsf{What is the Distributive Property?}[/tex]
[tex]\textsf{The \underline{Distributive Property} is a property that allows us to distribute.}[/tex]
[tex]\large\underline{\textsf{For this problem;}}[/tex]
[tex]\textsf{We can use the Distributive Property to distribute the 8 into values in the Parentheses.}[/tex]
[tex]\large\underline{\textsf{Distribute:}}[/tex]
[tex]\mathtt{8(2y+\frac{1}{4} )}[/tex]
[tex]\mathtt{(8 \times 2y) + (8 \times \frac{1}{4}) .}[/tex]
[tex]\boxed{\textsf{16y + 2 is Equivalent to 8 (2y + 1/4).}}[/tex]
Answer:
16y + 2
Step-by-step explanation:
Now we have to,
→ Find the equivalent expression.
The expression is,
→ 8(2y + (1/4))
Let's simplify the expression,
→ 8(2y + (1/4))
→ 8(2y) + 8(1/4)
→ 16y + (8/4)
→ 16y + 2
Hence, the answer is 16y + 2.
HELP SOMEONE PLEASE I'LL GIVE BRAINLIEST AND 5 STARS IF CORRECT
The Uniform Federal Accessibility Standards specify that a wheelchair ramp may not have an incline greater than 4.76°
. You want to build a ramp with a vertical rise of 8 inches. You want to minimize the horizontal distance taken up by the ramp. Label the diagram (in inches) to show the approximate dimensions of your ramp. Round decimal answers to the nearest tenth.
Consider the following linear programming problem:Maximize 6x+5y (OBJ)Subject tox+y≤6 (1)2x+y≤8 (2)y≤5 (3)
The maximum value of the objective function is 33, which occurs at the corner point (3, 3)
According to the question we have to maximize 6x+5y (OBJ)Subject tox+y≤6 (1)2x+y≤8 (2)y≤5 (3).Linear programming is a mathematical method that aims to maximize or minimize an objective function subject to a set of linear constraints. In this problem, we are asked to maximize the objective function 6x + 5y subject to the constraints given by the inequalities 1, 2, and 3.
The inequalities 1, 2, and 3 define a feasible region in the xy-plane, which is a region that satisfies all the constraints. The feasible region can be found by graphing the three inequalities and shading in the region that satisfies all of them.
In this case, the feasible region is a triangle with vertices (0, 0), (3, 3), and (4, 1), as shown below:
The objective function 6x + 5y is evaluated at each corner point as follows:
At (0, 0), 6(0) + 5(0) = 0, At (3, 3), 6(3) + 5(3) = 33, At (4, 1), 6(4) + 5(1) = 29. Thus, the optimal solution is x = 3 and y = 3, and the maximum value of the objective function is 33.
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List 3 sides to a right triangle. explain how you can use three pythagorean theorem to know that your three sides will create a right triangle.
The 3 sides to a right triangle are:
Leg 1 (a)Leg 2 (b)Hypotenuse (c)State the pythagorean theorem?The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides (called the legs) is equal to the square of the length of the longest side (called the hypotenuse).
So, if we have three sides of a triangle and we want to know if it forms a right triangle, we can use the Pythagorean Theorem in the following three ways:
Check if a² + b² = c², where a and b are the lengths of the two legs and c is the length of the hypotenuse. If this equation is true, then the triangle is a right triangle.
Check if b² + c² = a², where b and c are the lengths of the two legs and a is the length of the hypotenuse. If this equation is true, then the triangle is a right triangle.
Check if a² + c² = b², where a and c are the lengths of the two legs and b is the length of the hypotenuse. If this equation is true, then the triangle is a right triangle.
If none of these equations are true, then the triangle is not a right triangle.
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Evaluate 1/3 · 5/6
GIVING 20 POINTS
If sec(x) = -root2 and pi/2
Answer: x = π - π/4 = 3π/4
Step-by-step explanation:
If sec(x) = -√2 and x is in the second quadrant (between π/2 and π), we can use the identity:
sec^2(x) - 1 = tan^2(x)
to find the value of tan(x):
sec^2(x) - 1 = tan^2(x)
(-√2)^2 - 1 = tan^2(x)
2 - 1 = tan^2(x)
1 = tan^2(x)
Taking the square root of both sides, we get:
tan(x) = ±1
Since x is in the second quadrant, the angle that satisfies tan(x) = 1 is π/4. Therefore, we have:
x = π - π/4 = 3π/4
Note that the angle that satisfies tan(x) = -1 is in the fourth quadrant, so it is not relevant to this problem.
xplain how you would calculate the area of a cross section of the dam without using calculus. use your explanation to calculate the area of the cross section. is the area you found exact? why or why not?
Cross-sectional area of the dam can be calculated without using calculus as explained below:
Step 1: Draw the cross-section of the dam on a graph paper and divide it into simple shapes like triangles, rectangles, and circles.
Step 2: Calculate the area of each shape separately using the appropriate formulae. For example, the area of a rectangle is length times width, area of a triangle is 1/2 times base times height and the area of a circle is pi times radius squared.
Step 3: Add the areas of all the shapes to find the total cross-sectional area of the dam. This gives an approximate value of the area since the actual shape of the cross-section is not perfectly regular.If we take a concrete example of a dam with a cross-section of a trapezoid,
we can calculate the cross-sectional area using the above steps:
Step 1: Draw the cross-section of the dam on a graph paper as shown below. The cross-section of the dam can be divided into a rectangle and a triangle.
Step 2: Calculate the area of the rectangle and the triangle separately using the formulae for the area of the rectangle and the triangle respectively.Area of the rectangle = base times height = 10 m times[tex]4 m = 40 m²[/tex]Area of the triangle = 1/2 times base times height = 6 m times 4 m = 12 m²
Step 3: Add the areas of the rectangle and the triangle to get the total cross-sectional area of the dam.Area of the cross-section = area of rectangle + area of triangle= [tex]40 m² + 12 m²= 52 m²[/tex]The area found using the above method is not exact since it is an approximation of the actual area of the cross-section of the dam. It can be more accurate by dividing the cross-section into smaller and simpler shapes and calculating their areas individually.
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