The quotient for the associated division is -0.5x^(3)-x^(2)+x+1 and the remainder is -9.
What is synthetic division?Synthetic division is a method for dividing polynomials by monomials. It is a simplified form of the long division of polynomials, and is useful when the divisor is a monomial. The method involves arranging the coefficients of the dividend in a row, and then dividing each term by the divisor.
To find P(-2) for P(x)=x^(4)+2x^(3)-2x-7, we simply need to substitute -2 for x and evaluate the expression.
P(-2)=(-2)^(4)+2(-2)^(3)-2(-2)-7
P(-2)=16+2(-8)-2(-2)-7
P(-2)=16-16+4-7
P(-2)=-3
Therefore, the value of P(-2) is -3.
The associated division would be (x^(4)+2x^(3)-2x-7)/(-2), which can be simplified using polynomial long division. The quotient is -0.5x^(3)-x^(2)+x+1 and the remainder is -9.
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Quadrilateral DEFG is a square. What is the value of t?
E
D
t =
3t+46
8t-19
G
F
as the quadrilateral is a square, all the sides will be equal to each other so DE is equal to DG.
3t + 46 = 8t - 19
-5t = -65
5t = 65
so t = 13
Fill in the missing value. Input fractions as( a)/(b). (n^(2))^(2)=n Answer Check
The missing value in this equation is 4, or (4)/(1) in fraction form.
The missing value in this equation is the exponent of n in the final expression. To find this value, we can use the rule of exponents that states that when raising a power to another power, we multiply the exponents. In this case, we have (n^(2))^(2), so we multiply the exponents 2 and 2 to get a final exponent of 4. Therefore, the missing value is 4 and the equation can be written as (n^(2))^(2)=n^(4).
In fraction form, the missing value would be (4)/(1), since any whole number can be written as a fraction with a denominator of 1. So, the equation can also be written as (n^(2))^(2)=n^((4)/(1)).
Overall, the missing value in this equation is 4, or (4)/(1) in fraction form.
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Assume that y = f(x) is a rational function satisfying the following constraints: i. There is a x-intercept at x = 0, and the local approximation here is given by y = ii. There is a vertical asymptote at x = 3, with associated local approximation y 568-332 5(x-3) ili. There is a vertical asymptote at x = -2, with associated local approximation y - 2 5(x+2) iv. There is a horizontal asymptote at y = 2 Sketch and appropriately label the graph of a rational function y = f(x), that displays these four constraints.
The graph of the rational function y = f(x) is represented by the blue line on the graph above. The x-intercept is the point at which the function crosses the x-axis and is labeled (0, 0).
The vertical asymptote at x = 3 is the red line. The local approximation for the vertical asymptote at x = 3 is represented by the black line and is given by y = 568 - 332(x - 3). Similarly, the vertical asymptote at x = -2 is the purple line and the associated local approximation is given by y = -2(x + 2). Finally, the horizontal asymptote at y = 2 is the orange line.
To illustrate the graph, assume the function f(x) is the following: f(x) = (x + 2)(x - 3) / (x + 5). This function is a rational function, as it is the ratio of two polynomials, and it has the given constraints.
To graph the rational function, we begin by finding the x-intercept, which is (0, 0). Then, we look at the vertical asymptote. At x = 3, the local approximation is given by y = 568 - 332(x - 3). We solve the equation y = 568 - 332(x - 3) for x, and get x = 3, thus we mark this point on the graph as the vertical asymptote. We do the same for the vertical asymptote at x = -2 and mark this point on the graph. Finally, we draw the line for the horizontal asymptote at y = 2. This gives us the complete graph of the rational function y = f(x).
In conclusion, the graph of the rational function y = f(x) that displays the four constraints can be sketched and labeled as shown in the figure above.
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Determine if the expression -a^(2)+b^(4)-7a^(3) is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
The expression -a^(2)+b^(4)-7a^(3) is a polynomial.
A polynomial is a mathematical expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. The given expression satisfies all these conditions, and therefore, it is a polynomial.
The type of the polynomial is determined by the number of terms it has. In this case, the polynomial has 3 terms, so it is a trinomial.The degree of a polynomial is the highest exponent of the variable. In this case, the highest exponent is 4 (in the term b^(4)), so the degree of the polynomial is 4. Therefore, the expression -a^(2)+b^(4)-7a^(3) is a trinomial of degree 4.
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Solve (w-2)^(2)-54=0, where w Simplify your answer as much as If there is more than one solution, If there is no solution, click "No so
The solutions to the equation (w-2)^(2)-54=0 are w = 2, w = 9, and w = -6.
The equation (w-2)2 - 54 = 0 can be solved by factoring.
Let's start by writing the equation as: (w-2)(w-2) - 54 = 0
We can factor out (w-2) to get: (w-2)(w2 - 4w - 54) = 0
Now we can factor the second part of the equation, by splitting the middle term (4w) to get: (w-2)(w-9)(w+6) = 0
Now we have three equations, which we can solve separately:
w - 2 = 0 → w = 2
w - 9 = 0 → w = 9
w + 6 = 0 → w = -6
Therefore, the solutions to the equation (w-2)2 - 54 = 0 are w = 2, w = 9, and w = -6.
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Solve this system of equations using the substitution method.
y = 2x+17
y = 6x - 3
Answer:
this is awnser
Step-by-step explanation:
Answer:
X=5 y=27
Step-by-step explanation:
2x+17=6x-3
Take away 2x both sides
17=4x-3
Add 3 to get x on one side
20=4x
20/4 =5
x=5
Subsitute 5 in, 6 x 5 = 30 30-3=27
25 Points Use Bisection Method to locate the root of f(x) = x/3 + In(x) - 1 on a closed interval [1,2]. Use 17 iterations to extract the root.
The Bisection Method is a numerical method used to find the roots of a function within a given interval. It works by repeatedly dividing the interval in half and checking which half contains the root until the desired level of accuracy is achieved. In this case, we are using 17 iterations to extract the root of the function f(x) = x/3 + In(x) - 1 on the closed interval [1,2].
To locate the root of f(x) = x/3 + In(x) - 1 on a closed interval [1,2] using the Bisection Method with 17 iterations, we will follow the steps below:
1. Define the function f(x) = x/3 + In(x) - 1
2. Set the initial values for the interval: a = 1 and b = 2
3. Start the iteration process by finding the midpoint of the interval: c = (a+b)/2
4. Evaluate the function at the midpoint: f(c) = f((a+b)/2)
5. Determine if the root lies in the left or right half of the interval by checking the sign of f(c)
6. If f(c) is positive, then the root lies in the left half of the interval, so we set b = c and repeat the process from step 3.
7. If f(c) is negative, then the root lies in the right half of the interval, so we set a = c and repeat the process from step 3.
8. Continue the iteration process until we have completed 17 iterations.
After 17 iterations, we will have narrowed down the interval to a very small range and the midpoint of this interval will be an approximation of the root of the function.
The Bisection Method is a numerical method used to find the roots of a function within a given interval. It works by repeatedly dividing the interval in half and checking which half contains the root until the desired level of accuracy is achieved. In this case, we are using 17 iterations to extract the root of the function f(x) = x/3 + In(x) - 1 on the closed interval [1,2].
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A remote controlled car travels 8 feet in 2 seconds Label the other tick marks on the double number line with equivalent rates for the constant speed of the car
The car travels 4 feet in 1 second, 16 feet in 4 seconds, 24 feet in 6 seconds, 32 feet in 8 seconds.
Describe Distance?Distance is a measure of the amount of space between two objects or points. It is the length of the shortest path between the two points, and it is typically measured in units such as meters, kilometers, miles, or feet.
In mathematics, distance is often calculated using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The car travels 4 feet in 1 second, which is equivalent to a rate of 4 feet per second.
The car also travels 16 feet in 4 seconds, which is also equivalent to a rate of 4 feet per second.
Similarly, the car travels 24 feet in 6 seconds, 32 feet in 8 seconds, and so on, all at a constant rate of 4 feet per second.
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cups pineapple juice 24 cups orange juice 46 cups seltzer 72 How many servings can be made from 108 cups of punch?
Answer:
First, find the total number of cups of liquid in the punch:
24 cups pineapple juice + 46 cups orange juice + 72 cups seltzer = 142 cups
Then, divide the total cups of liquid by the amount of liquid in each serving:
108 cups / 142 cups per serving = 0.76 servings
Therefore, approximately 0.76 servings can be made from 108 cups of punch.
2x3+3x2-12x+5 criterio de la primera derivada
Answer:
To apply the first derivative test to the function f(x) = 2x^3 + 3x^2 - 12x + 5, we need to find its derivative:
f'(x) = 6x^2 + 6x - 12
Then, we need to find the critical points by solving for f'(x) = 0:
6x^2 + 6x - 12 = 0
Dividing both sides by 6, we get:
x^2 + x - 2 = 0
Factoring the left side, we get:
(x + 2)(x - 1) = 0
So the critical points are x = -2 and x = 1.
To determine the intervals where f(x) is increasing and decreasing, we need to evaluate f'(x) on each side of the critical points. We can use a sign chart to do this:
x | -2 | 1 |
------|-----|----|
f'(x) | -12 | 0 |
Since f'(x) is negative to the left of x = -2 and positive to the right of x = -2, the function is decreasing to the left of x = -2 and increasing to the right of x = -2. Since f'(x) changes sign at x = 1, there is a local minimum at x = 1.
Therefore, using the first derivative test, we can conclude that the function has a local minimum at x = 1.
Step-by-step explanation:
A watch was bought for 2,700 including 8% VAT. Find its price before the VAT was added.
Answer:
Let's assume that the price before adding the VAT is x.
We know that the VAT rate is 8%, which means that the VAT amount is 8% of x, or 0.08x.
The total price including VAT is the sum of the price before VAT and the VAT amount, so we can write:
Total price = price before VAT + VAT amount
or
2,700 = x + 0.08x
Simplifying this equation, we can combine like terms on the right-hand side to get:
2,700 = 1.08x
To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 1.08:
x = 2,700 / 1.08
x = 2,500
Therefore, the price before VAT was added is 2,500.
Use the image to determine the direction and angle of rotation.
90° clockwise rotation
270° clockwise rotation
90° counterclockwise rotation
180° counterclockwise rotation
After comparing the image and the figure, we found that the direction and angle of rotation are 180° counterclockwise rotation.
What is meant by the rotation of figures?A transformation known as a rotation involves turning the figure either clockwise or counterclockwise. The centre of rotation is the fixed location where the rotation occurs. The term "angle of rotation" refers to the amount of rotation. A figure can be rotated 90 degrees, or a quarter turn, in either a clockwise or counterclockwise direction. You have rotated the figure 180 degrees when you have spun it exactly halfway. The figurine may be rotated 360° by turning it all the way around. A counterclockwise turn has a positive magnitude because a clockwise rotation indicates a negative magnitude. Rotational symmetry exists in every regular polygon. When an object is rotated around its centre, it retains its original appearance. The object is then referred regarded as having rotational symmetry.
Let's write the coordinates of the original figure,
A = (1, -5)
B = (6, -2)
C = (6, -5)
D = (1, -8)
Now, if we rotate it 90 degrees counterclockwise, the coordinates are:
A' = ( 5, 1)
B' = (2, 6)
C' = (5, 6)
D' = (8, 1)
Now if we rotate it again 90 degrees counterclockwise, the coordinates are:
A'' = ( -1, 5)
B'' = (-6, 2)
C'' = (-6, 5)
D'' = (-1, 8)
Now from the figure, let's write the coordinates.
A' = ( -1, 5)
B' = (-6, 2)
C' = (-6, 5)
D' = (-1, 8)
This is the same as the coordinates of the second 90 degrees counterclockwise rotation.
Since we did two 90 degrees rotations, we can say we did a total of 180° counterclockwise rotation.
Therefore after comparing the image and the figure, we found that the direction and angle of rotation are 180° counterclockwise rotation.
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Answer: 180 degrees counterclockwise rotation.
you buy an nft hoping it will increase in value at a compounded rate of 8% each year. if you pay $500 for the nft now. how much do you expect it to be worth in 20 years?
Using cοmpοund interest , the tοtal wοrth after 20 years is $2,330.48.
What is cοmpοund interest?The interest that is calculated using bοth the principal and the interest that has accrued during the previοus periοd is called cοmpοund interest. It differs frοm simple interest in that the principal is nοt taken intο accοunt when determining the interest fοr the subsequent periοd with simple interest.
Here the principal P= $500
Rate οf interest r = 8%
Number οf years = 20 years,
Nοw using cοmpοund interest fοrmula then,
=> Total amount = [tex]P(1+\frac{r}{100})^t[/tex]
=> A = [tex]500(1+\frac{8}{100})^{20}[/tex]
=> A = [tex]500(1+0.08)^{20}[/tex]
=> A = [tex]500(1.08)^{20}[/tex]
=>A = $2,330.48
Hence after 20 years , nft's total worth is $2,330.48.
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A probability of 4/5 indicates an event is likely to happen.
Yes, a probability of 4/5 indicates that an event is likely to happen.
What is Probability?Probability refers to the measure of the likelihood of an event occurring, typically expressed as a number between 0 and 1. It is used to quantify uncertainty and is widely used in various fields such as mathematics, statistics, economics, science, and engineering.
Yes, a probability of 4/5 indicates that an event is likely to happen. It means that out of 5 possible outcomes, 4 outcomes are favorable to the event. In other words, there is an 80% chance that the event will occur.
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Alex has kept within his budget during this 4-week period! He also earned an extra $12 one week for cleaning his neighbor’s garage. If Alex wants to save the $10 he has left over every 4-week period, how much less time will it take for him to earn enough money for the shoes? Remember, the shoes cost $45.99 plus tax.
The time it will take for Alex to earn enough money to purchase his shoes is given as follows:
13.6 weeks.
How to obtain the time needed to earn the money?The time needed to obtain enough money to purchase the shoes is obtained applying the proportions in the context of the problem.
Alex saves $10 every 4 weeks. He earned an extra $12 for cleaning his neighbor’s garage, hence the amount he must save is of:
45.99 - 12 = $33.99.
Considering that he saves $10 each week, and he must save $33.99 to purchase the shoes, the number of periods of four weeks that he needs is of:
33.99/10 = 3.399 periods of four weeks.
As each period is composed by four weeks, the number of weeks that he needs to save enough money is obtained as follows:
4 x 3.399 = 13.6 weeks.
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Mr. K math class is one 1 over four hours long after working problems on the board for 55 minutes 11/12 hours he gave the students the rest of the class. To work on homework how long did students have to work on homework right your answer in simplest form
We can conclude that the students did not have any time left to work on homework.
The duration of Mr. K's math class is 1 and 1/4 hours, or 5/4 hours.
We need to determine how much time is left for the kids to do their assignment after working on problems on the board for 55 minutes and 11/12 hours. To achieve this, we must take the time spent solving issues out of the overall class time:
Total class time = 5/4 hours
Time spent on working problems = 55 minutes + 11/12 hours
= (55/60) hours + (11/12) hours
= (11/12 + 55/60) hours
= (11/12 + 11/12) hours
= (22/12) hours
= (11/6) hours
Overall class time minus the amount of time spent solving problems equals the amount of time remaining for homework.
= 5/4 hours - 11/6 hours
= (15/12) hours - (22/12) hours
= (-7/12) hours
We can infer that the kids ran out of time to finish their homework because the response is illogical because we cannot have negative time.
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The diameter of the human hair is 9x10 to the -5th power. The diameter of a spider silk is 3x10 to the -6th power. Answers in scientific notation
Darrell measured a city and made a scale drawing. The scale of the drawing was 1 inch : 4 yards. The actual width of a neighborhood park is 60 yards. How wide is the park in the drawing?
This question does not require a diagram to be drawn, so based on the scale factor or ratio of 1 inch : 4 yards and since the actual width of the neighborhood park is 60 yards, the width of the drawing is 15 inches.
What is the scale factor?The scale factor is the ratio of a scale drawing or model to the actual dimension of the object.
The scale factor is also measured as the dimension of the new shape ÷ dimension of the original shape.
The Ratio of the scale drawing = 1 inch : 4 yards
The actual width of the park = 60 yards
The scaled-down width of the drawing = 15 inches (60/4).
Thus, we can conclude that the scale drawing's width that Darrell made was 15 inches.
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On an analog clock, the hour hand rotates 30 degrees as the second hand rotates 21,600 degrees. Which equation correctly relates the variables defined below?
h: angular motion of the hour hand, in degrees
s: angular motion of the second hand, in degrees
Step-by-step explanation:
the ratio is 30/21600 = 3/2160 = 1/720
that means for every degree the hour hand moves, the second hand does 2 full rotations (2×360°).
h = s×30/21600 = s/720
FYI :
as there are 12 hours on a clock, every hour means 360/12 = 30° rotation for the hour hand.
so, for each hour the second hand moves 21600°.
that means 21600/360 = 60 full rotations.
that means one rotation of the second hand is 1 minute.
so, the second hand is truly a second hand (counting the seconds).
60 seconds in a minute (a full rotation by the second hand), that means each second corresponds to 360/60 = 6° rotation of the second hand.
Multiple choice. Choose the letter of the correct answer and write it on the blank provided
before the number.
___1. The Addition Property of Equality, If a=b, then a+c=b+c depicts which notion?
a. If equals are subtracted from equals, then the remainders are equal.
b. Things which coincide with one another equal one another.
c. The whole is greater than the part.
d. Things which are equal to the same thing are also equal to one another.
e. If equals are added to equals, then the wholes are equal.
The Addition Property of Equality, If a=b, then a+c=b+c depicts the notion that "If equals are added to equals, then the wholes are equal". The correct answer is option e.
Addition Property of Equality is a law that describes the possibility of adding the same quantity on both sides of an equation to maintain equality. If a=b, then a+c=b+c represents the Addition Property of Equality. It denotes that if you add the same quantity on both sides of an equation, the result will remain equal.
The Addition Property of Equality also mentions that if two numbers are equal to each other, then adding the same number to both of them will also result in two equal numbers. This means that if a=b, then a+c=b+c. Therefore, the correct answer is option "e.
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20% of $509 and how to work it out
Answer:
101.80
Step-by-step explanation:
Well this is fairly simple, if you can use a calculator. There not much to it so first you convert 20% to a decimal which is 0.2 or 0.20 either works. Then you multiply 0.2 by 509 to get 101.80. I used a calculator to multiply those two but Im not sure how else to do it without a calculator. Hope this helps.
What is the area of the following composite figure? Round to the nearest whole. I NEED THE ANSWER ASAP.
Answer:
141 inch^2
Step-by-step explanation:
13×7= 91 for the rectangle
13-5=8
diameter of circle=8
radius=4
area if circle=4^2 times π
=16×π
=16π
16π+91=141.2654....
to the nearest whole= 141 inch^2 I think
The relative frequency of a 6 on a biased dice is 0.25. The dice land on 6 150 times. How many times was the dice thrown?
Answer: 600
Step-by-step explanation:150=.25*X Divide both sides by .25 to get rid of it on the right and move it to the left so now 150/.25=X 600=X
Find the area of each shaded region.
The area of the shaded region which is a triangle will be 32 square inches.
What is the area?Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.
From the graph, the height of the triangle is given as,
2h = L
2h = 16 inches
h = 8 inches
And the base of the triangle is half of the base of the rectangle. Then we have
b = L / 2
b = 16 / 2
b = 8 inches
Then the area of the shaded region is given as,
A = 1/2 x 8 x 8
A = 32 square inches
The area of the shaded region which is a triangle will be 32 square inches.
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At a carnival game, it cost Taylor $6 to toss 63 rings. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
Graph is the collection of all points whose coordinates satisfy a given relation (such as a function).
What is coordinates?Coordinates of a point in a 2D plane, also known as cartesian coordinates, are two numbers or sometimes a combination of a letter and a number that tell us the exact location of a specific point on a grid. Here, the grid is known as a coordinate plane.
Let tosses be x and and dollars be y
Then we have, (x, y) as (63, 6)
So if in 6 dollars you get 63 tosses then 1 dollar you get = 63/6 = 10.5 tosses.
Then in 2 dollars we have = 10.5 × 2 = 21 tosses
As 21 tosses = 2 dollars
Then 42 tosses = 2 × 2 = 4 dollars
Thus, we have the table:
[tex]\boxed{\begin{array}{cc}\underline{\text{Tosses}}&\underline{\text{dollars}}&\\ \boxed{10.5}&2&\\42&\boxed4&\\63&6&\end{array}}[/tex]
To graph the given points, just correspond x as tosses and y as dollars.
Graph given in attachment
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What is the solution of the inequality: b+1>-8
Answer: The answer would be b<-9 for the nonsimplified version though.
Step-by-step explanation:
b+1>-8
first, -1 from each side.
then you will have -9>b
But you are going to divide by a negative number, so you are going to flip the inequality.
( b>-9 )
I remember learning this is like 7th grade haha. Let me know if you have any questions
Please help!! I'll give 20 points!
[tex]\stackrel{a}{-117}+\stackrel{b}{44}i \\\\[-0.35em] ~\dotfill\\\\ \theta =\tan^{-1}\left( \cfrac{44}{-117} \right)\implies \theta \approx 339.39^o~\hfill r=\sqrt{(-117)^2 + 44^2}\implies r=125 \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\sqrt[n]{z}=\sqrt[n]{r}\left[ \cos\left( \cfrac{\theta+2\pi k}{n} \right) +i\sin\left( \cfrac{\theta+2\pi k}{n} \right)\right]\quad \begin{array}{llll} k\ roots\\ 0,1,2,3,... \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \boxed{k=0}\hspace{3em} \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 339.39^o + 360^o( 0 )}{3} \right) +i \sin\left( \cfrac{ 339.39^o + 360^o( 0 )}{3} \right)\right] \\\\\\ \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 339.39^o }{3} \right) +i \sin\left( \cfrac{ 339.39^o }{3} \right)\right][/tex]
[tex]5[ \cos(113.13^o) +i \sin(113.13^o)]\approx \boxed{-1.96~~ + ~~4.60i} \\\\[-0.35em] ~\dotfill\\\\ \boxed{k=1}\hspace{3em} \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 339.39^o + 360^o( 1 )}{3} \right) +i \sin\left( \cfrac{ 339.39^o + 360^o( 1 )}{3} \right)\right] \\\\\\ \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 699.39^o }{3} \right) +i \sin\left( \cfrac{ 699.39^o }{3} \right)\right] \\\\\\ 5[\cos(233.13^o)+i\sin(233.13^o)]\approx \boxed{-3.00~~ - ~~4.00i} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\boxed{k=2}\hspace{3em} \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 339.39^o + 360^o( 2 )}{3} \right) +i \sin\left( \cfrac{ 339.39^o + 360^o( 2 )}{3} \right)\right] \\\\\\ \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 1059.39^o }{3} \right) +i \sin\left( \cfrac{ 1059.39^o }{3} \right)\right] \\\\\\ 5[\cos(353.13^o)+i\sin(353.13^o)]\approx \boxed{4.96~~ - ~~0.60i}[/tex]
Cube roots of complex number - 117 + 14i are,
- 1.96 + 4.60i
- 3.00 - 4.00i
4.96 - 0.60i
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
Complex number is,
⇒ - 117 + 14i
Let a = - 117
b = 44
Then, tan ⁻¹ (44/117) = 339.39°
⇒ θ = 339.39°
And, r = √117² + 44² = 125
Hence, We have;
[tex]\sqrt[n]{z} = \sqrt[n]{r} [cos (x + 2\pi k/n) + i sin (x + 2\pi k/n)][/tex]
Where, k = 0,1,2, 3, ..
Now, At k = 0
[tex]\sqrt[3]{z} = \sqrt[3]{125} [cos (339.39 + 0/3) + i sin (339.39 + 0/n)][/tex]
= - 1.96 + 4.60i
At k = 1;
[tex]\sqrt[3]{z} = \sqrt[3]{125} [cos (339.39 + 360/3) + i sin (339.39 + 360/n)][/tex]
= - 3.00 - 4.00i
At k = 2;
[tex]\sqrt[3]{z} = \sqrt[3]{125} [cos (339.39 + 360*2/3) + i sin (339.39 + 360*2/3)][/tex]
= 4.96 - 0.60i
Thus, All Cube roots of complex number - 117 + 14i are,
- 1.96 + 4.60i
- 3.00 - 4.00i
4.96 - 0.60i
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A photocopier can copy 4 pages every 2 seconds. How long will it take to copy 120 pages draw a digram to solve the problem
Answer: First we have to check the information they are giving in the problem. do we can see that the photocopier can copy 4 pages every 2 seconds.
so with this info we can calculate the ratio, or the number of copies that can be done in one second:
So we made a rule of 3 to solve that
So, if the photocopier can print 2 copys every second, the we can calculate the the time that takes to print 120 pages:
solving this rule of 3:
so is going to take 60 seconds to copy 120 pages.
In a Poisson distribution with µ = 7
a. What is the probability that x = 10?
b. What is the probability that x > 5?
a. The probability that x=10 in a Poisson distribution with µ = 7 is 0.0942.
b. The probability that x > 5 in a Poisson distribution with µ = 7 is 0.4790.
A discontinuous probability distribution is a Poisson distribution. It provides the likelihood that an occurrence will occur a specific number of times (k) over a predetermined period of time or place. The mean number of occurrences, denoted by the letter "lambda," is the only component of the Poisson distribution.
When a discontinuous count variable is the subject of concern, poisson distributions are used. Many financial and economic data are count variables, such as how frequently someone is laid off in a given year, which makes them amenable to study using a Poisson distribution.
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Find the balance of a savings account after 212 years if the simple interest earned each quarter is 0. 35% and the principal is $450
A $450 principal and a simple interest rate of 0.35% each quarter for 212 years would result in a savings account balance of $3768.
Amount and simple interestWe can use the formula for simple interest to solve this problem:
Simple Interest = Principal x Rate x Time
where Rate is the interest rate as a decimal, and Time is the time in years.
The quarterly interest rate is 0.35% / 4 = 0.00875, and the time is 212 years, or 848 quarters.
Plugging in these values, we get:
Simple Interest = $450 x 0.00875 x 848 = $3318
Therefore, the balance of the savings account after 212 years would be:
Balance = Principal + Simple Interest = $450 + $3318 = $3768
Therefore, the balance of the savings account after 212 years with a simple interest rate of 0.35% each quarter and a principal of $450 would be $3768.
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