The value of the quotient is [tex]\frac{45\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})} = 45(\cos(\frac{\pi}{6}) + i\sin(\frac{\pi}{6}))[/tex]
How to determine the quotient?The expression is given as:
[tex]\frac{90\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{2\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})}[/tex]
Divide 90 by 2
[tex]\frac{45\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})}[/tex]
As a general rule, we have:
[tex]\frac{\cos(\frac{\pi}{A}) i\sin(\frac{\pi}{A})}{\cos(\frac{\pi}{B}) i\sin(\frac{\pi}{B})} = \cos(\frac{\pi}{2B/A}) + i\sin(\frac{\pi}{2B/A})[/tex]
The above means that:
A = 4 and B = 12
So, we have:
2B/A = 2 * 12/4
Evaluate
2B/A = 6
So, the equation becomes
[tex]\frac{\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})} = \cos(\frac{\pi}{6}) + i\sin(\frac{\pi}{6})[/tex]
Substitute [tex]\frac{\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})} = \cos(\frac{\pi}{6}) + i\sin(\frac{\pi}{6})[/tex] in [tex]\frac{45\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})}[/tex]
[tex]\frac{45\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})} = 45(\cos(\frac{\pi}{6}) + i\sin(\frac{\pi}{6}))[/tex]
Hence, the value of the quotient is [tex]\frac{45\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})} = 45(\cos(\frac{\pi}{6}) + i\sin(\frac{\pi}{6}))[/tex]
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Complete question
What is the quotient of [tex]\frac{90\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{2\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})}[/tex]
A glass aquarium with the dimensions shown has a mass of 5 kg when empty what is the mass of the aquarium when it is half full of water I will give you king thing if you answer good
The required mass of aquarium when it is half full of water is 10 kg.
Mass of the aquarium = 5kg
Length = 25 cm, width = 20 cm and height = 10 cm(when half filled)
Volume, is defined as the ratio of the mass of object to its density.
Since, density of the water = 1000 Kg/m³
Now Mass of the water = Volume x density
= 25/100 x 20/100 x 10/100 x 1000
= 0.005 x 1000
= 5 kg
Now, the total mass of the aquarium when half filed by water.
= mass of water + mass of aquarium
= 5 + 5
= 10 kg
Thus, the required mass of aquarium when it is half full of water is 10 kg.
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Anu bought 15 stickers for 225 each and Arjun bought 25 stickers for 215 each. Who paid more? Give a reason for your answer.
Answer: Arjun paid more than Anu of about $2000.
Total cost
unit amount × per unit cost
For Anu total cost:
⇒ 15 × $225
⇒ $3375
For Arjun total cost:
⇒ 25 × $215
⇒ $5375
Anu paid $3375 for each whereas Arjun paid $5375 for each.
Conclusion: Arjun paid more.
URGENT!!! NEED ANSWER SOON!!!!
Pretend that you are the owner of a candy store. You have twenty pounds of cashews, which cost $3.55 a pound, and you have some peanuts, which cost $2.50 a pound. How many pounds of peanuts would you have to mix with the cashews to get a mixture that costs $3.20 per pound?
A. 10 pounds B. 9 pounds C. 7 pounds D. 8 pounds
Answer:
10 pounds
Step-by-step explanation:
So you have some given information:
(Price of cashews per pound) = 3.55
(Amount of cashes) = 20 pounds
(Price of peanuts, per pound) = 2.50
Now what you're looking for is the amount of peanuts you need to get a mixture of 3.20 per pound. So to find the price per pound. You would take the entire price and divide it by the amount of pounds. So generally it can be expressed as: [tex]\text{price per pound} = \frac{\text{price}}{\text{pounds}}[/tex] . In this equation we know we already have 20 pounds of cashews and they cost 3.55 per pound. We also know what the price per pound of the mixture is going to be, it's going to be 3.20. In the equation I'll express the amount of peanuts as "P" So we have the equation:
Plug in known values:
[tex]3.20 = \frac{20(3.55) + P(2.50)}{20+P}[/tex]
Multiply:
[tex]3.20 = \frac{71 + 2.5P}{20+P}[/tex]
Multiply both sides by 20 + P
[tex](20+P)(3.20) = 71+2.5P[/tex]
Distribute the 3.20
[tex]64+3.2P = 71+2.5P[/tex]
Subtract 2.5 from both side and subtract 64 from both sides
[tex]0.7P = 7[/tex]
Divide both sides by 0.7
[tex]P = 10[/tex]
So 10 pounds will be needed
In this activity, you will use multiple representations of relationships to identify key features and solve problems.
Ryan conducted a 6-day study observing the effects of an organic plant food on the growth of his sprouting bean plant. He tracked these two pieces of information:
the amount of plant food remaining in the container after each day’s feeding
the height of the plant over time
Part A
Ryan found that the amount of plant food remaining decreased an equal amount each day, and he used the entire 72 milliliters by the end of his study.
Part B
Ryan also found that he could model the height of his plant with the equation h = 0.5d + 4, where d is the number of days and h is the height in centimeters.
Part C (This is the question that I need help on....PLEASE?)
Explain the similarities and differences between the two relationships in this situation.
The domain will be 0<x<6 and the range will be 0<y<72.
How to illustrate the information?The information given implies that this would be a continuous relationship.
The process of elimination can be used to rule out the sets of numbers that are used in discrete relationships.
X is the amount of days that he was studying the plants.
The inequality is written like this for x: 0<x<6.
For the range, y is the plant food that was used which is 72 milliliters.
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a rectangular tank has Breath ( x + 3 )and length (x + 5) .write an expression for the area and find the area of the triangle if x = 7
Step-by-step explanation:
Length = 5 cm and Breadth = 3 cm
Area of a rectangle = length × breadth
=(5×3) cm
2
=15 cm
2
Hence, Area of rectangle with length 5 cm and breadth 3 cm is 15 cm
evaluate 2/6.341+3/9.222
The evaluation of the given improper fraction is 0.64071.
How do we evaluate fractions?We can evaluate improper fractions by simply determining the L.C.M of the denominators and equating it to the numerators.
Given that:
[tex]=\mathbf{\dfrac{2}{6.341} +\dfrac{3}{9.222} }[/tex]
= The L.C.M for 6.341 and 9.222 is 58.476702.
So, we have:
[tex]\mathbf{= \dfrac{18.444}{58.476702} +\dfrac{19.023}{58.476702} }[/tex]
[tex]\mathbf{= \dfrac{18.444+19.023}{58.476702} } }[/tex]
[tex]\mathbf{= \dfrac{37.467}{58.476702} } }[/tex]
= 0.64071
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Find the volume of a sphere with a diameter of 3 centimeters
Answer: 14.14
Step-by-step explanation:
Volume=(4/3)*π*r³
Given d=3
as we know that d=2r
3/2=r
1.5=r
Volume=(4/3)*π*(1.5)³
Volume =14.14
Each exterior angle of a regular decagon has a measure of (3x + 6)°. What is the value of x?
Ox=8
Ox= 10
Ox=13
Ox=18
find sum of 5, 13, 21, ... 181
Question 10 of 10
Use long division to find the quotient below.
(4x³+ 11x2 +9) + (x+3)
A. 4x²+x+3
OB. 4x²-2x+3
OC. 4x²-x+ 3
OD. 4x²+2x+3
The quotient of the division using the long division rule is 4x^2 - x + 3
Synthetic division of functionsPolynomial functions are functions that has a leading degree of 3 and above. Given the following parameters.
Dividend = 4x³+ 11x2 +9
Divisor = x + 3
Using the synthetic division to determine the quotient
4x^2 - x + 3
x+3 | 4x³+ 11x2 +9
4x³ + 12x²
__________________
-x² + 0x
-x² - 3x
___________________
3x+9
3x+9
___________________
-------
Hence the quotient of the division using the long division rule is 4x^2 - x + 3
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The table shows the educational attainment of the population of Mars, ages 25 and over, expressed in millions. Find the probability that a randomly selected martian, aged 25 and over has completed four years of high school only or is a male. The probability is?
The probability of picking a martian that has completed 4 years of high school or is a male is 72 / 85.
What is the probability?Probability determines the odds that a random event would happen. The odds of the event happening lie between 0 and 1.
The probability = (total number of people who have finished 4 years of high school / total number of martains) + (total number of males / total number of martains)
58 / 170 + 86/170 = 144 / 170 = 72 / 85
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Solve the proportion 2:x x 4:34
[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]
Solve the proportion. [tex]\bf{\dfrac{2}{x}=\dfrac{4}{34}[/tex].
[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]
We multiply 2 by 34, and x by 4 (this is known as cross multiplication)
[tex]\bf{2*34=4*x}[/tex] | simplify
[tex]\bf{68=4x}[/tex] | solve in terms of x
[tex]\bf{17=x}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{17=x}[/tex]
The degree of polynomial, x^4-x^2+2 is
Answer:
4
Step-by-step explanation:
need helpppppppppppppppppppp
Answer:
Its the last option If you ask me.
Step-by-step explanation:
If the price goes up $1.25 every square yard, then I think its the last one.
A suspension bridge with weight uniformly distributed along its length has twin towers that extend 70 meters above the road surface and are 1200 meters apart. The cables are parabolic in shape and are suspended from the tops of the towers. The cables touch the road surface at the center of the bridge. Find the height of the cables at a point 300 meters from the center. (Assume that the road is level.)
Answer:
17.5 m
Step-by-step explanation:
The height of a parabola above its vertex is proportional to the square of the distance from the vertex.
Cable heightThe towers are 1200 m apart, so each is 600 m from center. The location of interest is 300 m from center, so 1/2 the distance to a tower. Since the height is proportional to the square of the distance, the height half-way to the tower will be (1/2)² = 1/4 the height of the tower.
(1/2)²×(70 m) = 17.5 m
The height of the cable 300 m from center will be 17.5 meters.
When 5times a number is increased by 10, the answer is the same as when 100 is decreased by the number. What is the number?
Answer:
x = 15
Step-by-step explanation:
[tex]5x + 10 = 100 - x[/tex]
[tex]6x = 90[/tex]
[tex]x = 15[/tex]
Then what is the value of x?
Answer:
d.) x = -40
Step-by-step explanation:
[tex]\sf Given \ equation: \ log_{5} (-3x+5) = 3[/tex]
Solving steps:
[tex]\rightarrow \sf log_{5} (-3x+5) = 3[/tex]
If logₐ(b) = c then b = aᶜ
[tex]\rightarrow \sf -3x+5 = 5^3[/tex]
[tex]\rightarrow \sf -3x+5 = 125[/tex]
[tex]\rightarrow \sf -3x = 125-5[/tex]
[tex]\rightarrow \sf -3x = 120[/tex]
[tex]\rightarrow \sf x = 120/-3[/tex]
[tex]\rightarrow \sf x = -40[/tex]
Answer:
x= -40
Hope this helps!!
Select three ratios that are equivalent to 11:111:111, colon, 1.
Choose 3 answers:
The three ratios that are equivalent to the given ratio are options B, C and E.
How to determine the equivalent ratios?In order to determine the ratios that are equivalent to the given ratio, we would evaluate by dividing each of them by their respective denominator value:
(11:111:111)/1 = 11:111:111.
For choice A, we have:
1:111:111/11 = 1/11:111:111 (not equivalent).
For choice B, we have:
22:222:222/2 = 11:111:111. (equivalent).
For choice C, we have:
55:555:555/5 = 11:111:111. (equivalent).
For choice D, we have:
9:999:999/99 = 1/11:111:111 (not equivalent).
For choice E, we have:
110:1110:1110/10 = 11:111:111. (equivalent).
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Complete Question:
Select three ratios that are equivalent to 11:111:111, colon, 1. Choose 3 answers: Choose 3 answers: (Choice A) A 1:111:111, colon, 11 (Choice B) B 22:222:222, colon, 2 (Choice C) C 55:555:555, colon, 5 (Choice D) D 9:999:999, colon, 99 (Choice E) E 110:1110:1110, colon, 10.
Solve for x in the following equation:
42x-5=23x+7
O x=-17
O x=-12
O x = 12
Ox=17
Answer:
x = 17
Step-by-step explanation:
1) Make the bases the same then rewrite.
4 = 2²
2^2(2x - 5) = 2^3x + 7
2) Since the bases are the same, set the exponents equal to each other.
2(2x -5) = 3x + 7
4x - 10 = 3x + 7
4x - 3x = 7 + 10
x = 17
You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production of Les Misérables this year, and they need your help planning it.
All the roles have now been cast, and the lead actors playing the following parts are gathered around a large circular table for their first read: Jean Valjean, Inspector Javert, Thénardier, Enjolras, Marius, Fantine, adult Cosette, adult Éponine, and Madame Thénardier. It is your job to seat these 9 actors, the 3 producers, and the director around the table.
Remember that there are 5 lead male roles and 4 lead female roles. If you must seat the male leads together, the female leads together, the 3 producers together, and the director by himself, how many different ways can you seat the 13 people around the circular table?
103,680
479,001,600
6,227,020,800
17,280
Answer:
6227020800
is mi answer
What are the x-intercepts of this function?
g(x) = -0.25x2 − 0.25x + 5
Answer:
(-5,0) and (4,0)
x= -5 and x= 4
Step-by-step explanation:
The length of a rectangle is 8 inches and the width is x inches. What is the perimeter, in inches?
A. 16+ 2x
B. 10+2x
C. 16+ x
D. 10+ x
The mean useful life of xar batteries is 48 months. They have a standard deviation of 5
A circle has a radius of 17cm. Find the radian measure of the central angle θ that intercepts an arc of length 5cm.
Answer:
3.14 PIE
Step-by-step explanation:
Use Pie the method we all learned I think it’s 3.14
For a population with μ = 165 , z-score =2.46, and data value = 206. Find the standard deviation σ . Round your answer to the nearest hundredths place.
Answer:
The standard deviation is 16.67
================
GivenMean μ = 165 , z - score z = 2.46, Data value x = 206.To findThe standard deviation σ.SolutionUse z-score formula to find the missing value:
z = (x - μ )/σ ⇒ σ = (x - μ)/zSubstitute values into equation and find the standard deviation:
σ = (206 - 165)/2.46 = 16.67 (rounded).I need help with number 15 and 16
Answer:
please see explanations
Step-by-step explanation:
For the first question,
Sum of angles in a triangle equal180°3x + 4x + 2x = 180
9x = 180°
Dividing bothsides by 9
9x/9 = 180/9
x = 20
The measure of the interior angles are :
3x = 3(20) = 60
4x = 4( 20) = 80
2x = 2(20) = 40
For the second question,
Let's find x first.
Angles on a straight line equal 180°.x + 92 = 180
x = 180 - 92 = 88°
To find A note that:
Exterior angle equal sum of opposite interior angles.A = 88° + 43°
A = 131°
Adi used algebra tiles to represent the product (negative 2 x minus 1)(2 x minus 1). please help!
The true statement is (b) she did not represent the two original factors correctly on the headers
How to determine the true statement?The product expression is given as:
(-2x - 1)(2x - 1)
Expand the expression
(-x - x - 1)(x + x - 1)
This means that the header of the algebra tiles would be:
-x, -x, 1 and x, x and -1
From the figure, we can see that this is incorrectly represented
Hence, the true statement is (b)
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2. In factored form, a quadratic function can be written as y= (-2- x) (x-8). This parabola goes through the points (-2, 0) and (8, 0). Use your knowiedge of the symmetry of the parabola to find the vertex. Show all work. 4 marks
show the parabola please
The vertex of the given parabola is the point (3, 25).
How to get the vertex of the parabola?
If the parabola has roots x₁ and x₂, then the vertex of the parabola is at:
xₙ = (x₁ + x₂)/2
Here the parabola is:
y = (-2 - x)*(x - 8)
We can rewrite that to:
y = -(x + 2)*(x - 8)
Then the two roots are:
x = -2 and x = 8
Then the vertex is at:
xₙ = (8 - 2)/2 = 6/2 = 3
To get the y-value of the vertex, we evaluate the equation in x = 3:
y = -(3+ 2)*(3 - 8) = -5*(-5) = 25
The vertex is (3, 25).
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Choose the most convenient method to graph the line y=−13x+5
Select the correct answer below:
Recognize the equation as that of a vertical line passing through the x-axis at 5
Recognize the equation as that of a horizontal line passing through the y-axis at 5
Identify the slope and y-intercept and then graph
Find the x- and y-intercepts and then graph
The most convenient method to graph the line y=−13x+5 is C. Identify the slope and y-intercept and then graph.
How to illustrate the information?From the information given, the equation has been given. It's important to identify the slope. This is the gradient of the line.
Also, the y intercept should be identified. Therefore, the most convenient method to graph the line y=−13x+5 is to identify the slope and y-intercept and then graph.
In conclusion, the correct option is C.
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Find the equation of this line.
1
y = [? ]x + [
Simplify your answer and enter as an integer.