Answer:For the first 40 hours, Mr. Smith earned:
$23.20/hour × 40 hours = $928.00
For the additional 11.5 hours, he earned:
$23.20/hour × 1.5 = $34.80/hour
So, for these hours, he earned:
$34.80/hour × 11.5 hours = $400.20
Adding these amounts together, we get:
$928.00 + $400.20 = $1,328.20
Therefore, Mr. Smith earned $1,328.20 last week.
Step-by-step explanation:
The store sells a television for $1000. customers can choose to receive 10% discount and pay it off at a simple interest rate of 4% or they can choose to pay the full price and pay it off in 3 years with no interest. which option is better
Option 1 with the discount and 4% simple interest has a total cost of $972, while Option 2 with no discount and no interest has a total cost of $1000. Option 1 is the better choice as it has a lower total cost.
What is simple interest?Simple interest is a type of interest that is calculated on the original principal amount of a loan or investment. It is a fixed percentage of the principal amount that is paid by the borrower or earned by the lender over a specific period of time.
According to question:To compare the two options, we need to calculate the total cost of each option and compare them.
Option 1: 10% discount and pay off with 4% simple interest
The discount reduces the price of the television to $1000 x 0.9 = $900. If the customer chooses to pay it off at 4% simple interest, the total cost would be:
Total cost = $900 + ($900 x 0.04 x 3) = $972
Option 2: Full price and pay off in 3 years with no interest
The total cost of this option would be simply the full price of $1000 paid over 3 years, so:
Total cost = $1000 / 3 = $333.33 per year x 3 years = $1000
Comparing the two options, we see that Option 1 with the discount and 4% simple interest has a total cost of $972, while Option 2 with no discount and no interest has a total cost of $1000. Therefore, Option 1 is the better choice as it has a lower total cost.
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The complete question is: The store sells a television for $1000. customers can choose to receive 10% discount and pay it off at a simple interest rate of 4% or they can choose to pay the full price and pay it off in 3 years with no interest. which option is better?
Option 1 with the discount and 4% simple interest.
Option 2 with no discount and no interest.
Of first-time college students who matriculate to a certain university, the odds in favor of having graduated in the top 25 percent of their high school class are 2.06 to 1. Of transfer students who matriculate to the same university, 0.666666666666667 proportion graduated in the top 25 percent of their high school class.
(a) For first-time college students, what is the proportion who graduated in the top 25 percent of their high school class (rounded to three decimal places)?
(b) For transfer students, what is the ratio in favor of having graduated in the top 25 percent of their high school class?
Odds and Probability:
Odds in favor of an event is expressed as a ratio:
O
(
f
)
=
favorable cases
:
unfavourable cases
Similarly odds against are expressed as:
O
(
a
)
=
unfavorable cases
:
favourable cases
.
Odds and probability are closely related, as the probability in favor of an even is computed as:
P
=
favorable cases
favorable cases+unfavorable cases
The answers to the questions (a) the proportion who graduated in the top 25 percent of their high school class will be 0.672 and (b) the ratio in favor of having graduated in the top 25 percent of their high school class is 2:3.
(a) For first-time college students, the proportion who graduated in the top 25 percent of their high school class (rounded to three decimal places) is 0.672.
(b) For transfer students, the ratio in favor of having graduated in the top 25 percent of their high school class is 0.67:1. It is said that 0.666666666666667 proportion graduated in the top 25 percent of their high school class. This can be simplified as follows:0.666666666666667=20/30=10/15=2/3. Therefore, the ratio in favor of having graduated in the top 25 percent of their high school class is 2:3.
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Marty graphs the hyperbola (y+2)236−(x+5)264=1 . How does he proceed? Drag a value, phrase, equation, or coordinates in the boxes to correctly complete the statements. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
To construct the graph of the hyperbola, the procedure is as follows:
Marty first identifies the center of the hyperbola as (-5,2), and that the hyperbola opens up and down. Since a = 6, the coordinates of the vertices are (-5, -4) and (-5, 8).The slopes of the asymptotes of this parabola are a = ± 3/4, and the asymptotes pass through the center of the hyperbola. The equations of the asymptotes are y - 2 = ± 3/4(x + 5).Equation of an hyperbolaThe equation of a vertical hyperbola with center (x*, y*) is given according to the following equation:
(y - y*)²/a² - (x - x*)²/b² = 1.
A vertical hyperbola opens up and down.
In this problem, the equation is:
(y + 2)²/36 - (x + 5)²/64 = 1.
Hence the center is:
(-5, 2).
The value of coefficient a is:
a² = 36 -> a = 6.
Then the vertices of the hyperbola are:
(-5, 2 - 6) = (-5,-4).(-5, 2 + 6) = (-5,8).The slopes of the asymptotes of the parabola are given as follows:
±a/b.
Hence:
a/b = 6/8 = 3/4.-a/b = -6/8 = -3/4.Since the asymptotes pass through the center, the equation is:
y - 2 = ± 3/4(x + 5).
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On a cold winter day, Joel and Duncan brought a container of hot chocolate with them to go sledding. There were 15 ounces of hot chocolate, and they split it evenly. How much hot chocolate did each boy get?
If Joel and Duncan split the 15 ounces of hot chocolate evenly, then they each got half of the container.
To find out how much hot chocolate each boy got, we need to divide the total amount of hot chocolate by the number of people sharing it. Since there are two boys, we can divide 15 by 2 to get the amount of hot chocolate each boy received: 15 ÷ 2 = 7.5
Therefore, each boy got 7.5 ounces of hot chocolate to drink while they went sledding.It's important to note that when dividing something equally between two people, we divide by two since there are two individuals.
In this case, each boy received half of the container, or half of the total amount of hot chocolate. This type of division is known as "fair" or "equal" sharing, as both parties receive an equal portion.
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a different pattern is made using 20 straight lines and 14 arcs
The total cost of metal in the pattern would be £24.6.
What is the total cost of the pattern?
Let's assume that the cost of one arc is 3x, then the cost of one straight line would be 2x.
The total number of lines and arcs is given as 20 + 14 = 34.
Since 20 straight lines cost £12, the cost of one straight line is £12/20 = £0.6.
Therefore, the cost of one arc is (3/2) * £0.6 = £0.9.
The total cost of the 20 straight lines would be 20 x £0.6 = £12.
The total cost of the 14 arcs would be 14 x £0.9 = £12.6.
So, the total cost of metal in the pattern would be £12 + £12.6 = £24.6.
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The complete question is below:
A different pattern is made using 20 straight lines
and 14 arcs.
The straight lines and arcs are made from metal.
20 straight lines cost £12
cost of one straight line : cost of one arc = 2 : 3
Work out the total cost of metal in the pattern.
A simplified carbon cycle with aerobic and anaerobic processes is depicted here. Although much of the emphasis on global climate change has been on increasing carbon dioxide levels, methane is also a greenhouse gas whose levels are increasing due to human and other activity. Which of these actions would increase methane levels in the atmosphere and potentially affect global climate change? Select ALL that apply.
--------------------------------------------------------------------------------------------------------------------------------
A Agricultural practices in rice cultivation releases methane.Agricultural practices in rice cultivation releases methane.
B Anaerobic digestion of cellulose by cows produces methane.Anaerobic digestion of cellulose by cows produces methane.
C Photosynthesis by phytoplankton converts carbon dioxide into the atmosphere.Photosynthesis by phytoplankton converts carbon dioxide into the atmosphere.
D Industrial combustion of fossil fuels releases methane into the atmosphere.Industrial combustion of fossil fuels releases methane into the atmosphere.
E Anaerobic decomposition of landfill material releases methane into the atmosphere.
In attempts to reduce greenhouse gas emissions and the effects of climate change, these sources must be taken into account.
what is equation ?A mathematical equation is a claim that two expressions are equal, typically represented with an equal sign (=) between them. The terms "left hand side" (LHS) and "right hand side" (RHS) of the equation, respectively, refer to the expressions on either side of the equal sign. Equations are a common tool for problem solving because they may be used to depict relationships between variables or quantities and to determine the value(s) of the unknown variable(s) that satisfies the equation. For instance, the link between the variables x and the integers 2, 5, and 11 is represented by the equation 2x + 5 = 11. Finding the value of x that makes the left and right sides of the equation equal is necessary to solve this equation.
given
A) Rice farming operations release methane into the atmosphere.
B) Methane is created when cows break down cellulose anaerobically.
E) Methane is released into the atmosphere when landfill material decomposes anaerobically.
Any of the aforementioned behaviours would raise the atmospheric methane concentrations and may have an impact on climate change globally.
Methane is a greenhouse gas that causes the atmosphere of the Earth to warm.
It is produced by both natural and artificial processes. Examples of human activities that contribute to methane emissions into the atmosphere include the production of rice, cattle digestion, and landfill decomposition.
In attempts to reduce greenhouse gas emissions and the effects of climate change, these sources must be taken into account.
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25. Students in a class took an algebra test if 15 students passed the test what percent pass the test
Answer:
15/x * 100 %
Step-by-step explanation:
Since we don't know the total, we have 15/x * 100 % as the percent of how many people passed the test. (x is amount of people, 15 or greater.)
Sunflower canola oil is a cooking oil sold in south african supermarkets a 750ml bottle cost R28 and a 2litre bottle cost R63 evaluate which option will be the most cost effective option
A 2-liter container costs R0.032 per milliliter, which is less than a 750-milliliter bottle, which costs R0.037 per milliliter.
A milliliter is it an ML?a volumetric measurement using the metric system. One litre is equivalent to 1,000 milliliters. Additionally known as cc, mL, and cubic centimetre.
To evaluate which option is the most cost-effective, we need to calculate the cost per milliliter of each bottle of cooking oil.
For the 750ml bottle, the cost per milliliter is:
R28 / 750ml = R0.037 per ml
For the 2-liter bottle, the cost per milliliter is:
R63 / 2000ml = R0.032 per ml
Therefore, the 2-liter bottle is the more cost-effective option, as it has a lower cost per milliliter than the 750ml bottle. The cost per milliliter of the 2-liter bottle is R0.032, which is cheaper than the cost per milliliter of the 750ml bottle, which is R0.037.
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The velocity of an object is
v(t) = 36-t^2, 0≤ t ≤ 6
where v is measured in meters per second and t is the time in seconds. Find the velocity and acceleration of the object when t = 3. What can be said about the speed of the object when the velocity and acceleration have opposite signs?
In calculus, the derivative is a fundamental concept that measures how a function changes with respect to its input variable. It is a mathematical tool used to study the behavior of functions and is used in many areas of mathematics, physics, engineering, and economics.
When t = 3, the velocity of the object is 27 meters per second, and its acceleration is -2 meters per second squared.
When the velocity and acceleration have opposite signs, the speed of the object is decreasing. The acceleration of an object can be calculated using the derivative of the velocity of the object with respect to time.
v(t) = 36 - t², 0 ≤ t ≤ 6
Let us take the derivative of the velocity, v(t), to obtain acceleration, a(t) = v'(t) = -2t.When t = 3, v(3) = 36 - 3² = 27 meters per second.Therefore, when t = 3, the velocity of the object is 27 meters per second. When t = 3, a(3) = -2(3) = -6 meters per second squared. The object's acceleration is -6 meters per second squared.
The speed of the object is decreasing when the velocity and acceleration have opposite signs.
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An Ixl question from sixth grade IXL:FF.15 Rectangles: relationship between perimeter and area
The dimensions of the gray rectangle are approximately 61.9 km by 218.1 km.
What is perimeter of a rectangle?The distance around a rectangle's outside edge is known as its perimeter. It is computed by summing the measurements of the rectangle's four sides. The perimeter P of a rectangle with sides of length l and width w is given by:
P = 2l + 2w.
By understanding that a rectangle contains two pairs of equal sides (length and breadth), and that the distance around the rectangle is equal to the total of these four sides, one may deduce this formula.
Let us suppose the dimensions of the gray triangle as x and y.
The perimeter of rectangle is given as:
P = 2(1 + b)
For the blue triangle we have:
P = 2(72 + 68)
For the gray triangle we have;
P = 2(x + y)
Equating the two since they are equal we have:
2(72 + 68) = 2(x + y)
280 = x + y
We also know the area of the gray triangle thus:
xy = 3876
Substituting y = 280 - x into the second equation, we get:
x(280 - x) = 3876
x² - 280x + 3876 = 0
x = (280 ± √(280² - 4(1)(3876))) / 2
x ≈ 62.7 or x ≈ 61.9
We may discard the negative answer since a rectangle's dimensions cannot be negative.
Substituting the value of x we have:
y = 280 - 61.9 = 218.1 km.
Hence, the dimensions of the gray rectangle are approximately 61.9 km by 218.1 km.
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the number of minutes needed to complete a job, m, varies inversely with the number of workers, w. three workers can complete a job in 30 minutes. how many minutes would it take 6 workers to complete the job?
The number of minutes needed to complete a job, m, varies inversely with the number of workers, w.
Three workers can complete a job in 30 minutes.
To find, out how many minutes would it take 6 workers to complete the job.
The formula used for inverse variation is, m1w1 = m2w2
Where, m1 = 30,
w1 = 3,
m2 = ?
and w2 = 6
Substitute the given values in the above formula, 30 × 3 = m2 × 6
Simplify the above expression,90 = 6m2
Divide both sides by 6,90 / 6 = m2m2 = 15
Hence, it will take 15 minutes for 6 workers to complete the job.
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Solve each system of equations algebraically. y=x + 15, y= 2x
The solution to the system of equations is (15, 30).
What is system of equations?A group of two or more equations that must be solved all at once is known as a system of equations. The system's equations each show how two or more variables relate to one another. The variables' values that satisfy every equation in the system can be discovered using algebraic techniques.
Algebraic systems of equations can be solved using a variety of techniques, such as substitution, elimination, and graphing. The substitution approach involves solving one equation for one variable in terms of the other variable, and then substituting the result for that variable's expression into the other equation.
The given system of equations are y=x + 15, y= 2x.
Substitute the value of y from equation 2 in equation 1:
x + 15 = 2x
15 = x
Substitute the value of x to get the value of y:
y = 2x = 2(15) = 30
Hence, the solution to the system of equations is (15, 30).
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What was the total number of hours worked by the 15 employees? Write the expression of total number he total number of hours worked by the 15 employees and solve it.
The expression of total number of hours worked by the 15 employees is 505 .
What is an expression?An expression is a mathematical statement that combines numbers, variables, and/or operators to represent a quantity or relationship. It can be evaluated or simplified, but does not have an equals sign and is not a complete equation.
To find the total number of hours worked by the 15 employees, we need to add up the hours worked by each individual employee.
Let's say that employee 1 worked x1 hours, employee 2 worked x2 hours, and so on, up to employee 15 who worked x15 hours. Then, the total number of hours worked by the 15 employees can be expressed as:
Total number of hours = x1 + x2 + ... + x15
To solve this expression, we need to know the specific number of hours worked by each employee. If we are given this information, we can simply substitute the values into the expression and add them up to find the total number of hours.
we can calculate the total number of hours worked as:
Total number of hours = 40 + 30 + 35 + ... + 20
= 505
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In a recent election 65% of eligible voters actually voted. A simple random sample of 1000 people is taken from the population of eligible voters. Which of the following represents the probability that less than 70% of the people sampled voted?
The probability that less than 70% of the people sampled voted is 0.9992.
Step 1: Calculate the mean of the sample. µ = p = 0.65 (since the percentage of eligible voters who actually voted in the recent election is 65%).
Step 2: Calculate the standard deviation of the sample.σ = sqrt{[p(1 - p)]/n} = sqrt{[(0.65)(0.35)]/1000} = 0.01578
Step 3: Calculate the z-score for the given probability. z = (0.7 - 0.65)/0.01578 = 3.16Step 4: Use the standard normal distribution table to find the area to the left of the z-score (since we want to find the probability that less than 70% of the people sampled voted).P(z < 3.16) ≈ 0.9992Therefore, the probability that less than 70% of the people sampled voted is approximately 0.9992 (or 99.92%).
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A linear function maps input numbers to output numbers.
Complete the input-output table for this function.
Input
1
2
5
10
Output
4
10
28
n
Step-by-step explanation:
after a little bit of thinking and experimenting we find that the function multiplied x by 6 and subtracts 2.
y = 6x - 2
formally, we find this by using the normal linear form
y = ax + b
and we use the given data points to find a and b.
4 = a×1 + b = a + b
10 = a×2 + b = 2a + b
so, by adding a on one side and adding 6 on the other side, we keep the balance.
therefore, a = 6
the first equation gives us then
4 = 6 + b
b = -2
and that's it.
so,
for x = 10 we get as output (y)
6×10 - 2 = 58
for x = n we get as output (y)
6n - 2
Operación de vectores
Answer:
operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.
Answer:
operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.
Step-by-step explanation:
there are 20 rows of seats on a concert hall: 25 seats are in the 1st row, 27 seats on the 2nd row, 29 seats on the 3 rd row, and so on. if the price per ticket is $32, how much will be the total sales for a one-night concert if all seats are taken?
Answer:
Step-by-step explanation:
To solve this problem, we need to find out how many seats there are in total, and then multiply that by the price per ticket.
To find the total number of seats, we need to add up the number of seats in each row. We can use the formula for an arithmetic sequence to do this:
S = n/2 * (a + l)
where S is the sum of the sequence, n is the number of terms, a is the first term, and l is the last term.
In this case, we have:
n = 20 (since there are 20 rows)
a = 25 (since there are 25 seats in the first row)
d = 2 (since the difference between each row is 2 seats, the common difference is 2)
We can use d to find the last term as well:
l = a + (n-1)*d
l = 25 + (20-1)*2
l = 25 + 38
l = 63
Now we can plug these values into the formula:
S = 20/2 * (25 + 63)
S = 10 * 88
S = 880
So there are 880 seats in total.
To find the total sales, we just need to multiply by the price per ticket:
total sales = 880 * $32
total sales = $28,160
Therefore, the total sales for a one-night concert with all seats taken would be $28,160.
The speed s (in miles per hour) of a car can be given by s = √(30fg), where fis the
coefficient of friction and d is the stopping distance (in feet). The table shows the
coefficient of friction for different surfaces. You are driving 35 miles per hour on an
icy road when a deer jumps in front of your car. How far away must you begin to
brake to avoid hitting the deer? Round your answer to the nearest whole integer. NO
UNITS NEEDED
Answer:
Step-by-step explanation:
lknk
pihpin
87647fpom';
oiy69877t7gbkjb
Answer:
s= 6
Step-by-step explanation:
The speed s (in miles per hour) of a car can be given by s = √(30fg), where fis the
coefficient of friction and d is the stopping distance (in feet). The table shows the
coefficient of friction for different surfaces. You are driving 35 miles per hour on an
icy road when a deer jumps in front of your car. How far away must you begin to
brake to avoid hitting the deer? Round your answer to the nearest whole integer. NO
UNITS NEEDED
Denisha has already read 42 pages
novel for her English class. For the rest of
the month, she plans to read 24 pages
every 3 days. What is the constant rate of
change in this situation?
A.
page per day
B. 6 pages per day
C. 8 pages per day
D. 24 pages per day
Answer:
B.6 pages per day
Martina made $60 for 5 hours of work. At the same rate, how many hours would she have to work to make $204 ?
Answer:
WELL 17
Step-by-step explanation:
60 DIVED BY 5 IS 12
SO 12 DIVIDED BY 204 IS 17 SOOOOOO 17 IS THE ANS
Find the outer perimeter.
10 ft
8 ft
P = [?] ft
Round to the nearest
hundredth.
The outer perimeter is 76.12 ft according to given question.
what is perimeter?
Perimeter is a term used in geometry to refer to the total distance around the outside of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, in a rectangle, the perimeter is calculated by adding the length of all four sides. In a circle, the perimeter is called the circumference and is calculated as the distance around the edge of the circle.
The perimeter of a semicircle is the sum of the length of its straight edge and half the circumference of the circle.
In this case, the radius of the semicircle is given as 8 units, so the circumference of the corresponding full circle is 2πr = 2π(8) = 16π units.
Half the circumference of the circle is therefore 8π units.
The straight edge of the semicircle is simply the diameter of the circle, which is twice the radius, or 2(8) = 16 units.
So, the perimeter of the semicircle is the sum of the straight edge and half the circumference:
Perimeter = 16 + 8π
Using approximate value for pi (π = 3.14), the perimeter can be expressed as:
Perimeter ≈ 16 + 8(3.14) ≈ 40.12 units.
The perimeter of a rectangle is given by the sum of the lengths of its four sides.
In this case, the length of the rectangle is given as 10 units and its width is given as 8 units.
Therefore, the perimeter of the rectangle is:
Perimeter = 2(Length + Width) = 2(10 + 8) = 2(18) = 36 units.
So, the perimeter of the rectangle with length 10 units and width 8 units is 36 units.
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Math question please help
TU is a perpendicular bisector.
What is perpendicular bisector?
A line that divides a line segment into two equal halves and forms a 90-degree angle at the point of intersection is called a perpendicular bisector.
To put it another way, a perpendicular bisector separates a line segment at its midpoint, creating a 90-degree angle.
A line or line segment that divides a given line segment into two equal portions is known as a perpendicular bisector.
The word "bisect" refers to dividing equally.
The line segment that perpendicular bisectors overlap forms four 90° angles on either side.
A line or line segment is said to be perpendicular when it forms a 90° angle with another line or line segment.
Hence, TU is a perpendicular bisector.
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A cylindrical garbage can has the dimensions shown.
A cylinder has a diameter labeled twelve inches and height labeled fifteen inches.
Question 1
Part A
What is the area of the horizontal cross section of the cylinder? Use 3.14
for π
.
Enter the correct answer in the box.
about
square inches
Question 2
Part B
What is the area of the vertical cross section of the cylinder through the centers of the bases?
Enter the correct answer in the box.
Check the picture below.
so the horizontal cross-section is simply the area of a circle with a radius of 6, and the vertical cross-section is simply a 12x15 rectangle.
[tex]\stackrel{ \textit{\LARGE horizontal cross-section} }{\pi (6)^2\implies 36\pi \implies 36(3.14)\implies \text{\LARGE 113.04}~in^2} \\\\\\ \stackrel{ \textit{\LARGE vertical cross-section} }{(12)(15)\implies \text{\LARGE 180}~in^2}[/tex]
I am too lazy to search it up on brainly tell me what is the answer
Answer:
no lol im too lazy
Step-by-step explanation:
give me brain
Answer:
x = 9/10.
Step-by-step explanation:
0.5(4x + 9) = 3x * 7/3
2x + 9/2 = 3x * 7/3
2x + 9/2 = 7x
5x = 9/2
x = 9/10.
What is the surface area?
5 yd
6 yd
5 yd
5 yd
4 yd
prove that g(x)= 2x^6-x^2+4 is an even function
We can also check this by graphing the function, which would show us the symmetry about the y-axis.
What is function?In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is associated with exactly one output. This means that for every value of the input, there is a unique corresponding value of the output.
by question.
To prove that a function is even, we need to show that it satisfies the property:
g(-x) = g(x) for all x in the domain of g.
So, let's substitute -x for x in g(x) and simplify:
g(-x) = 2[tex](-x)^{6}[/tex] - [tex](-x)^{2}[/tex] + 4
= 2[tex]x^{6}[/tex] -[tex]x^{2}[/tex] + 4
Notice that we obtained the same expression as g(x), which means that g(x) is even. Therefore, we can write:
g(x) = g(-x)
This means that the graph of the function is symmetric with respect to the y-axis, since for any value of x, the value of g(x) is the same as the value of g(-x).
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5. Solve the following problems. Note: In those problems the geometric multiplicity is less than algebraic multiplicity. (a)d/ dx = ( 1 −44 −7) x2−30
Answer:
-130
Step-by-step explanation:
Use Euler’s formula to write in exponential form.
Answer:
(A) 10e^(i7π/4)
Step-by-step explanation:
You want the exponential form of 5√2 -5i√2.
Complex number notationThere are numerous ways a complex number can be written in "polar form".
The usual choices are ...
a +bi . . . . . . . . . . . . . rectangular form
A(cos(θ) +i·sin(θ)) . . . . a sort of hybrid form
A·cis(θ) . . . . . . . . . . an abbreviation of the above
A∠θ . . . . . . . . . . . . polar form
A·e^(iθ) . . . . . . . . . using Euler's formula
ConversionThe conversion from rectangular form to any of the others makes use of trig identities and the Pythagorean theorem.
A = √(a² +b²)
θ = arctan(b/a) . . . . . with attention to quadrant
ApplicationFor the given number, ...
A = √((5√2)² +(-5√2)²) = (5√2)√(1 +1) = 5·2
A = 10
θ = arctan(-5√2/(5√2)) = -1 . . . in the 4th quadrant
θ = 7π/4
Then the desired exponential form of the complex number is ...
10e^(i7π/4)
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Additional comment
Spreadsheets and some calculators have an ATAN2(x, y) function that performs a quadrant-sensitive angle conversion.
If a certain apple tree grew 2 feet and then tripled its height, it would become 4 feet
shorter than the pine tree that grows on the other end of the street. Which
of the formulas below describes the relation between the height of the apple tree a
and the height of the pine tree p?
A) P-4=3a+2
B) P=2(a+3)+4
C) P=3(a+2)-4
D) P=3a+10
Answer:
Step-by-step explanation:
C.) P = 3(a+2)-4
The formula which describes the relation between the height of the apple tree and the height of the pine tree p is P=3(a+2)-4, the correct option is C.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
We are given that;
Growth of apple tree= 2feet
Now,
Let's call the original height of the apple tree "h". According to the problem, if the apple tree grew 2 feet and then tripled its height, it would become 4 feet shorter than the pine tree. So we can write:
3(h+2) - 4 = p
Simplifying, we get:
3h + 2 = p
Now we can see that option (D) P=3a+10 is very similar to our expression, but it has a constant term of 10 instead of 2. This constant term does not match the problem statement, which says that the apple tree would be 4 feet shorter than the pine tree, not taller. Therefore, option (D) is not the correct answer.
Option (A) P-4=3a+2 also does not match the problem statement. If we solve for p, we get:
P = 3a + 6
This means that the apple tree would be 6 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.
Option (B) P=2(a+3)+4 also does not match the problem statement. If we solve for p, we get:
P = 2a + 10
This means that the apple tree would be 10 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.
Option (C) P=3(a+2)-4 matches our expression from earlier. If we solve for p, we get:
P = 3a + 2
Therefore, by equation the answer will be P=3(a+2)-4.
Learn more about linear equations;
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If l is parallel to m find the values of x and y