I need help with this practice problem solving The subject, I believe, is complex numbers and vectors
Answers
Given:
Given that
[tex]r=\frac{5}{3\sin\theta-\cos\theta}[/tex]Required: Convert to rectangular form.
Explanation:
The given equation in polar can be written as
[tex]\begin{gathered} r(3\sin\theta-\cos\theta)=5 \\ 3r\sin\theta-r\cos\theta=5 \end{gathered}[/tex]Substitute
[tex]x=r\cos\theta,y=r\sin\theta[/tex]Then the equation becomes 3y - x = 5.
Solve for y.
[tex]\begin{gathered} 3y=x+5 \\ y=\frac{1}{3}x+\frac{5}{3} \end{gathered}[/tex]Final Answer:
[tex]y=\frac{1}{3}x+\frac{5}{3}[/tex]Related Questions
The area of the base of a prism is 96 square centimeters and the height is 9 centimeters. Find the volume of the prism.288 cm3864 cm3932 cm37776 cm3
Answers
Given:
Area of base of the prism, B = 96 square centimeters
Height of prism, H = 9 centimeters
Let's find the volume of the prism.
To find the volume of the prism, apply the formula below:
[tex]V=B\ast H[/tex]Where:
V is the volume in cubic units
B is the area of the base = 96 square centimeters
H is the height = 9 centimeters
Hence, we have:
[tex]\begin{gathered} V=96\ast9 \\ \\ V=864\operatorname{cm}^3 \end{gathered}[/tex]Therefore, the volume of the prism is 864 cubic centimeters
ANSWER:
[tex]864\operatorname{cm}^3[/tex]A corporation reported profits of approximately 3,500 million with approximately 67000 million in revenues. Compare the profit to revenue by writing a fraction in lowest terms
Answers
The profit for te corporation is 235,00 million.
The revenue for the corporation is 6700e million.
ExplanationTo determine th fractio in lowest terms for thr e profit and revenue is
[tex]\begin{gathered} \frac{3500}{67000}=\frac{35}{670} \\ \frac{35}{670}=\frac{7}{134} \end{gathered}[/tex]AnswerHencenthe answer s [tex]\frac{7}{134}[/tex]E is located at ( − 6 , − 3 ) (−6,−3) on the coordinate plane. Point E E is reflected over the x x-axis to create point E ′ E ′ . What ordered pair describes the location of E ′ ? E ′ ?
Answers
Answer:
(-1,-6) --> (1,-6) --> (1,6)
(1,6) is E''
Find the perimeter of the figure given to the right. Use the approximation 3.14
Answers
To answer this question we will use the following diagram as a reference:
Notice that the perimeter of the given figure is the sum of 2 times the perimeter of the semicircles and 48m, the perimeter of each semicircle is:
[tex]\begin{gathered} P_S=\pi\times radius=6\pi m \\ \approx18.84m. \end{gathered}[/tex]Therefore the perimeter of the given figure is:
[tex]P=2*18.84m+48m=85.68m.[/tex]Answer: 85.68m.
Alejo had 115.25 in his bank account. He made three equivalent
transactions. His new balance is $-77.73. How much was each transaction?
Answers
Answer:
So,
let the amount of each transaction be x.
3x= 115.25+77.73
x= 192.98÷
x= 64.327
each transaction was of 64.327
Step-by-step explanation:
since the amount left is -77.73 then three equal transaction will also include 115.25+77.73= 1 92.98
192.98 was the total amount used
write a paragraph reflecting on the different methods (graphing technology, tables of values, and successive approximation) of solving f(x) =g(x). state which of the three methods you prefer, and explain why.
Answers
The three methods that are generally used to solve f(x) =g(x) are Graphing technology, Tables of values, and Successive approximation.
Determine the exact value of x by replacing the values of x with f(x) and g(x).
The hit-and-trial technique is used in f(x) = g(x) to compute the exact value of x by selecting an interval and then substituting the value of x in that interval.
This is a bit longer and takes more time.
Graph Technique: Create a graph that contains both f(x) and g(x). The values of x given by these two functions are the same. Some features are difficult to plot, but once plotting is done, the right solution is obtained. The graphics technique is prioritised in determining f(x) = g(x) and x.
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A box contains 13 large marbles and 20 small marbles. Each marble is either green or white. 5 of the large marbles are green, and 13 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is small or green? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answers
Answer:
The probability of selecting a small or white marble is 10/13
Step-by-step explanation:
The total number of marbles is 15 + 11 = 26 marbles
The probability that we want to calculate is if the marble selected is small or white.
So we need to find the number of small marbles as well as the number of white marbles
We can construct a table to see the distribution of the marbles. Please check the attachment for this.
From the table , we can see that there are 11 small marbles and a total of 9 white marbles
The probability of selecting a white marble is;
number of white marbles/total number of marbles = 9/26
The probability of selecting a small marble will be ;
number of small marbles/total number of marbles = 11/26
In probability, whenever we have or, we tend to add
So therefore, the probability of selecting a white or small marble = Probability of selecting a white marble + Probability of selecting a small marble
Mathematically, that would be 9/26 + 11/26 = 20/26
So the probability is 10/13
influence of education on south african economy
Answers
Children's academic success, literacy, numeracy, and scientific knowledge are all directly impacted by their schooling. A child's education in school helps them learn all the fundamentals that will benefit them in the future.
Explain about influence of education on south African economy?The study confirmed that reducing the proportion of people with lower levels of education, as in primary school or no education at all, has a positive effect on economic growth. In that regard, South Africa has done a good job of lowering the proportion of people with Grade 7 education or less to under 20%.Families with educated members have a better probability of improving their living situations than families without educated members. The working class, their families, and their communities are all assured of financial stability when a stable income is supplied to them.Children in South Africa struggle to enter the workforce without even a basic education, making it impossible for them to escape poverty. Education fosters the development of critical abilities like effective communication and social skills in addition to teaching fundamental skills like reading and writing.To learn more about education on south African refer to:
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Complete sheet given
Answers
Answer:
20 hyenas
Step-by-step explanation:
locate number of lions 28 on the horizontal axis , then go up vertically to meet the line, then cross horizontally to meet the vertical axis at 20
that is 20 hyenas are contained
Select the correct answer.
What is the simplest form of this expression?
x-3/x-1 + 6/x-3
A. x²+12x+15 / (x-1)(x-3)
B. x²+3 / (x-1)(x-3)
C. x+3 / (x-1)(x-3)
D. x²-6x+3 / (x-1)(x-3)
Answers
x² + 3 / (x-1)(x-3) is simplest form of the given expression
What will the expression be?Given: x-3/x-1 + 6/x-3
First, find the LCM of x-1 and x-3. The LCM is c
(x-3)(x-3) + 6(x-1) / (x-1)(x-3)
Remove the bracket of the numerator
x² - 6x + 9 + 6x - 6 / (x-1)(x-3)
Add and subtract like terms
x² + 3 / (x-1)(x-3)
Therefore, the expression has the simplest form of x² + 3 / (x-1)(x-3). This shows the concept of expression.
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A road crew must repave a road that is 3/4 miles long. They can repave 1/48 miles each hour. How long will it take the crew to repave the road?Write your answer in simplest form.
Answers
Let's use a rule of three to solve this:
This way,
[tex]x=\frac{\frac{3}{4}}{\frac{1}{48}}\rightarrow x=36[/tex]The crew will take 36 hours to repave the road
24 Finding Cylinder Dimensions < Next > 14.2: What's the Dimension? Volume formula for cylinder V=12h The volume of this cylinder with radius 5 units is 50T cubic units. Volume=undefined i cubic unit What does the height of this cylinder have to be? Explain how you know. radius=1.5 unit height:4 unit Submit and Explain height slid radius slid Igal DIN-
Answers
Explanation:
The volume formula is:
[tex]V=\pi r^2h[/tex]We know that the radius is r = 5 and the volume is V = 50pi. We have to replace these values into the formula above and solve for h:
[tex]\begin{gathered} 50\pi=\pi5^2h \\ 50\pi=25\pi h \\ h=\frac{50\pi}{25\pi}=\frac{50}{25}=2 \end{gathered}[/tex]Answer:
h = 2
A rectangle has a length that is 7 less than 4 times the width. The perimeter is 100 in. Find the length and the width.
Answers
Answer:
136 m
Step-by-step explanation:
Let w = the width of the rectangular field.
Let l = the length of the rectangular field.
The formula for the perimeter P of the rectangular field is:
P = 2w + 2l
Since the length l is 7 m less than 4 times the width w, then we can write the following equation that relates l and w:
l = 4w - 7 m
Since l = 4w - 7 and it's given that perimeter P = 136 m, then we can substitute this information into the perimeter formula as follows:
P = 2w + 2l
136 m = 2w + 2(4w - 7 m)
136 m = 2w + 2(4w) - 2(7 m)
136 m = 2w + 8w - 14 m
136 m + 14m = 10w - 14 m + 14 m
150 m = 10w + 0
10w = 150 m
(10w)/10 = 150 m/10
(10/10)w = 150 m/10
(1)w = 15 m
w = 15 m
Therefore, l = 4w - 7 m
l = 4(15 m) - 7 m
l = 60 m - 7m
l = 53 m
CHECK:
P = 2w + 2l
136 m = 2(15 m) + 2(53 m)
136 m = 30 m + 106 m
136 m = 136 m
jeanscah estimates that 475 songs will fit on her iphone.the actual amount of the songs that fit Is 380.find the percent error.
Answers
Data:
Estimate: E= 475 songs
Actual amount: A=380
To find the percent of error you use the next formula:
[tex]\text{error}=\frac{\mleft|E-A\mright|}{A}\cdot100[/tex][tex]\begin{gathered} \text{error}=\frac{\mleft|475-380\mright|}{380}\cdot100 \\ \text{error}=\frac{\mleft|95\mright|}{380}\cdot100 \\ \text{error}=0.25\cdot100 \\ \text{error}=25 \end{gathered}[/tex]Then, the percent error is 25%What is y=-2/9x+3 written in standard form using integers?A. 2/9x+y=3 B. y + 2/9x – 3 = 0 C. 2x + 9y = 3D. 2x + 9y = 27
Answers
Given:
[tex]y=-\frac{2}{9}x+3[/tex]The equation above is written in slope intercept form:
y = mx + b
To rewrite in standard form, use the standard form of linear equations below:
Ax + By = C
Thus, we have:
[tex]y=-\frac{2}{9}x+3[/tex]Multiply through by 9 to eliminate the fraction:
[tex]\begin{gathered} 9y=(-\frac{2}{9}x\ast9)+(3\ast9) \\ \\ 9y=-2x+27 \end{gathered}[/tex]Add 2x to both sides:
[tex]\begin{gathered} 2x\text{ + 9y = -2x + 2x + 27} \\ \\ 2x\text{ + 9y = 27} \end{gathered}[/tex]Therefore, the equation in standard form is:
2x + 9y = 27
ANSWER:
D. 2x + 9y = 27
1 cm plus what equals 100cm
Answers
Answer:99cm.l
Step-by-step explanation:100-1
100-1=99
So then the answer is 99, because 99+1 is also equal to 100.
And if you subtract 1 from 100, you get 99.
Answer: 99cm
Step-by-step explanation:
1cm + x = 100cm
100cm - 1cm = x
Which means,
99cm is the correct answer.
Mia makes a cold drink she calls iced punch. She uses vanilla ice-cream, grape juice and
ginger ale in the ratio 1:4:5. Mia has plenty of vanilla ice-cream, but only 2250ml of grape
juice and 2750ml of ginger ale. She makes as much iced punch as she can with these
ingredients. How much of each ingredient does she use?
Answers
Now she has 2250ml juice and 2750ml ale
Given that juice and ale are needed in the ratio 4 to 5
So here we find according to the bigger value.
5x=2750 => x= 550ml
=> 4x= 2200ml
So she uses 550ml ice cream , 2200ml juice and 2750ml ale
Please help on how I would start these
Answers
Answer:
a) -15 (b)25/2 (c)-31.2 (d)15
Step-by-step explanation:
(a)f(-24)=5/6×24+15
-15
(b)f(9)=5/6×9+15
25/2
(c)f(x)=5/6x+15
5/6x+15=-11
5x+90=-66
5x=-66-90
5x=-156
5x/5=-156/5
x=-31.2
(d)f(0)=5/6×0+15
0+15
15
Open Ended Question is an incorrect hypothesis valuable? Why or why not?
Answers
A hypothesis can be seen as an assumption about something, If the hypothesis is wrong, you have information about that something, and you can be sure that the behavior you assumed is never going to happen. In conclusion, you also learn from the mistakes made
Federal standards require that the angle ramp for the wheel chair to be less than 5 degrees, if the length of the ramp is 20 feet and vertical rise is 15 inches, does it meet federal standards?
Answers
ANSWER:
The ramp does meet federal standards
STEP-BY-STEP EXPLANATION:
The first thing we must do is sketch the situation of the statement in order to better understand it.
Now, we need to convert feet to inches, so they are the same units. We know that 1 foot is equal to 12 inches, so:
1 ft = 12 in
20 ft = 20 ft *12 in/ft = 240 in
Now, we calculate the angle of the ramp by means of the trigonometric sine function that relates the side opposite the angle to the hypotenuse.
Therefore:
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \text{ opposite = 15} \\ \text{ hypotenuse = 240} \\ \text{ Replacing} \\ \sin \theta=\frac{15}{240} \\ \theta=\arcsin \mleft(\frac{15}{240}\mright) \\ \theta=3.58\text{\degree} \end{gathered}[/tex]The value of the angle is 3.58°, which is less than 5°, which means that it meets federal standards.
The value of y varies directly with x. When y = 21, x = 3. What is the value of y when x is 14
Answers
Answer:
43
Step-by-step explanation:
The value of y varies directly with x. When y = 21, x = 3. What is the value of y when x is 14.
when y = 21 and x = 3 the ratio of y to x is 21 to 3 or (reduced) 3 y to 1 x
This means y is three times the size of x.
When x = 14 then y = 14 × 3 = 42
Estimate the average rate of change from x = 4 to x = 7.
Answers
The average rate of change of the function from x = 4 to x = 7 is: -1/3.
How to Estimate the Average Rate of Change of a Function?The formula used to estimate the average rate of change of a function is given as:
f(b) - f(a) / b - a.
Given the function as shown in the diagram below, we are required to find the average rate of change of the function within the interval, x = 4 to x = 7, therefore:
a = 4
b = 7
f(a) = f(4) = 4
f(b) = f(7) = 3
To find the average rate of change of the given function for the interval of x = 4 to 7, substitute the above stated values into the formula for the average rate of change, f(b) - f(a) / b - a:
Average rate of change = 3 - 4 / 7 - 4
Average rate of change = -1/3
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the first step in determining the solution to the system of equations, y=-x² - 4x-3 and y= 2x + 5, algebraically isthe two equations equal as -x² - 4x - 3= 2x + 5. What is the next step?et y = 0 in y=-x2 - 4x-3.actor each side of the equation.se substitution to create a one-variable equation.ombine like terms onto one side of the equation.
Answers
Given -
Equations:
y = -x² - 4x -3 and y = 2x + 5
To Find -
Next step =?
Step-by-Step Explanation -
We know first step:
-x² - 4x - 3= 2x + 5
-x² - 4x - 3 - 2x - 5 = 0
-x² - 6x - 8 = 0
-(x² + 6x + 8) = 0
x² + 6x + 8 = 0
x² + 2x + 4x + 8 = 0
x(x+2) +4(x +2) = 0
(x+4)(x+2) = 0
So,
x = -4 or x = -2
So,
The next step is to combine like terms onto one side of the equation.
Final Answer -
Option (d)
Combine like terms onto one side of the equation
12. The length of time that a particular type of blue cheese will keep in
refrigerator can be modelled by the exponential function
H(T) = 130 (12
T
43.3
where H(T) represents the number of hours after the cheese is p
the refrigerator and T represents the temperature of the refrigerator in
degrees Celsius.
is set at a
Answers
The refrigerator is to be set at 5 degrees celsius for the cheese to keep for 5 days.
Since we are given the relation for the exponential function
H(T) = 130 (1/2) ^(T/43.3), where H(T) is the number of hours
since we are asked for a cheese to keep for 5 days, so
H(T)= 5 * 24 = 120 hours
so the equation we will have
=>120 =130 (1/2) ^(T/43.3)
we multiply both sides by 120
=> 12/13= (1/2) ^(T/43.3)
taking logarithms on both sides, we get
=> ln (12/13) = (T/43.3) ln(1/2)
=>43.3 ln (12/13) = T ln (1/2)
dividing both sides by ln (1/2), we get
=> T = 43.3 ln (12/13) / ln (1/2)
=> T= 5.0016
=> T = 5.0 celsius
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The length of time that a particular type of blue cheese will keep in the refrigerator can be modeled by the exponential function H(T) = 130 (1/2) ^(T/43.3) where H(T) represents the number of hours after the cheese is put in the refrigerator and T represents the temperature of the refrigerator in degrees Celsius. If you want the cheese to keep for 5 days, at what temperature should the refrigerator be set ; round your answer to the nearest tenth of a degree.
HELP PLEASE
Review the objective below, and rate your knowledge of the topic from 0-4, with 0
being the lowest rating and 4 being the highest rating.
"I can factor an expression using the GCF."
0
1
2
3
4
Answers
Answer:
Step-by-step explanation:
Comment
Well my response is, I know how it is done and most of the time I get it right, but mistakes make me give myself about a 3.4.
I hope this answers your question. It will likely be taken down.
7x + 4 + 8x + 6. equals
Answers
Answer: [tex]15x + 10[/tex]
Step-by-step explanation:
[tex]7x + 4 + 8x + 6[/tex]
First you have to combine like terms. You combine like terms by adding them so u would add 7x and 8x and get 15x. Then u would add 4 and 6 and get 10.
[tex]15x + 10[/tex]
15x + 10 would be your final answer in simplest form.
How many liters each of a 20 % acid solution and a 30 % acid solution must be used to produce 90 liters of a 25 % acid solution? (Roundto two decimal places if necessary.)
Answers
Let x = volume of 20% solution=0.2
Let y = volume of 30% solution=0.3
Equation of total volume:
x + y = 90
Equation of amount of acid:
[tex]\begin{gathered} 0.2x+0.3y=0.25(90) \\ 0.2x+0.3y=22.5 \\ Solve\text{ x+y = 90 , for x} \\ x=90-y \end{gathered}[/tex]Substitute into the second equation
[tex]\begin{gathered} 0.2(90-y)+0.3y=22.5 \\ 18-0.2y+0.3y=22.5 \\ 0.1y=22.5-18 \\ 0.1y=4.5 \\ \text{divide both side by 0.1} \\ \frac{0.1y}{0.1}=\frac{4.5}{0.1} \\ y=45 \\ \sin ce\text{ x=90-y} \\ x=90-45 \\ x=45 \end{gathered}[/tex]Therefore 45 liters of 20% solution and 45 liters of 30% solution
Hence the volume of 20% acid = 45 litres
the volume of 30% acid = 45 litres
Solve each triangle. Round answers to the nearest tenth, if necessary.
Answers
Given the triangle DEF.
Angle E = 71.2˚
e = 29.5 cm
f = 30.3 cm
We are to solve for each triangle.
Using laws of sine:
a = b = c
sinA SinB SinC
In this case we will have:
e = f
SinE SinF
29.5 = 30.3
sin 71.2˚ sinF
cross multiply
sinF(29.5) = sin 71.2˚(30.3)
sinF = sin 71.2˚(30.3)
sin 29.5
sinF = 0.9466 * 30.3
0.4924
sinF = 58.2524
Please help solve the problem.
-2/5x+3=2/3x+1/3
Answers
Answer: -6/5=2/9
Step-by-step explanation:
If f(x) = 2x + 1, find f(1).
Answers
Answer: 3
Step-by-step explanation:
if x = 1 then 2(1) +1 is 2+1 which is 3
f(1) means that in the place of x you plug in 1 and simplify.
[tex]f(1) = 2(1) + 1 \\ f(1) = 2 + 1 \\ f(1) = 3[/tex]
ATTACHED IS THE SOLUTION