Vectors and Complex numbers Part AYou drive 30 miles due east in a half hour. Then, you turn left and drive 30 miles north in 1 hour. What are your average speed andvelocity, and what are the rectangular and polar coordinates of your position?Part BYou have already travelled 30 miles east and then 30 miles north. To get back to the start, you travel 30 miles west in 1 hour and then 30 minutes south in a half hour. What are your average speed and average velocity for the whole rally?
Answers
Part A.
30 miles east in half hour next
turn left and drive 30 miles north in 1 hour
The average speed is given by
the total distance divided by the total amount of time.
In this case,
[tex]\begin{gathered} \text{average velocity=}\frac{30+30}{1.5+1} \\ \text{average velocity=}\frac{60}{2.5} \\ \text{average velocity=}24\text{ }\frac{miles}{hour} \end{gathered}[/tex]Now, the position in rectangular coordinates is (30,30)
In polar coordinates, we must find the angle theta and the lenght r.
This can be given as
[tex]\begin{gathered} r=\sqrt[]{x^2+y^2} \\ \end{gathered}[/tex]In our case x=30 and y=30, hence
[tex]\begin{gathered} r=\sqrt[]{30^2+30^2} \\ r=\sqrt[]{2\cdot30^2} \\ r=30\sqrt[]{2} \end{gathered}[/tex]On the other hand, angle theta is given by,
[tex]\theta=tan^{-1}\frac{y}{x}[/tex]hence,
[tex]\begin{gathered} \theta=tan^{-1}\frac{30}{30} \\ \theta=tan^{-1}1 \\ hence, \\ \theta=45\text{ degr}ees \end{gathered}[/tex]Therefore, in polar coordinates, point (30,30) is given by
[tex](r,\theta)=(30\sqrt[]{2},45)[/tex]Part B
Until now, we drove 30 miles east, next 30 miles north. Now, we must drive 30 miles west and 30 miles south.
Hence, we will drive 30+30+30+30=4*30=120 miles. Therefore, the average velocity is
[tex]\begin{gathered} \text{average velocity=}\frac{120}{1.5+1+1.5+1.5} \\ \text{average velocity=}\frac{120}{5.5} \\ \text{average velocity=}21.81\text{ }\frac{miles}{hour} \end{gathered}[/tex]Part A. Velocity.
Velocity is a vector. In this case, we must add to vectors:
vector V1 is given by
[tex]\begin{gathered} v_1=(\frac{30}{1.5},0) \\ \text{which is equal to } \\ v_1=(20,0) \end{gathered}[/tex]Vector V2 is given by
[tex]\begin{gathered} v_2=(0,\frac{30}{1}) \\ v_2=(0,30) \end{gathered}[/tex]then, resultant vector velocity is
[tex]\begin{gathered} v=v_1+v_2 \\ v=(20,0)+(0,30) \\ v=(20,30) \end{gathered}[/tex]
Related Questions
Write an equation in slope-intercept form for the line with y-intercept 3 and slope 2.
Answers
Answer:
y=2x+3
Step-by-step explanation:
Slope intercept form: y=mx+b
mx(slope)=2
(b)y-intercept=3
y=2x+3
Hope this helps :)
The farm raises its own produce and meat. Will has a cow that produces milk. She gives 2.3 gallons of milk aday. How many gallons does she give in a month that has 30 days?
Answers
Cow produces:
2.3 gallons of milk per day
To obtain the number of gallons that she will give in a month of 30 days, simply multiply the amount she gives per day (2.3) by the numbe rof days (30):
2.3 g/day x 30 day
An individual's income varies with age. The table
shows the median income I of individuals of
different age groups within the United States for
a certain year. For each age group, let the class
midpoint represent the independent variable x.
For the class "65 years and older," assume that
the class midpoint is 69.5.
Complete parts (a) through (e).
Answers
Considering the relation between the two variables in the table, it is found that:
A quadratic relation with a < 0 exists between the two data-sets.The quadratic relation is given by: y = -46.359 x^2 +4385.3 x -57255.975.How to find the type of relation of the variables?We have to look at the behavior of the relation over the entire domain as follows:
If it only increases, or only decreases, it is a linear relation.If it increases and then decreases, or vice-versa, then it is a quadratic relation.In the context of this problem, the median income increases until a age group of 45-54 years, then it decreases. Since it increases then it decreases, the relation is concave down quadratic, that is, quadratic with a < 0.
To find the equation that models the relation, we insert the data-points given as follows into the calculator:
(19.5, 10963), (29.5, 32131), (39.5, 41636), (49.5, 46693), (59.5, 41477), (69.5, 22500).
Using the calculator with these points, the quadratic equation of best-fit is given as follows:
y = -46.359 x^2 +4385.3 x -57255.975
More can be learned about quadratic functions at https://brainly.com/question/24737967
#SPJ1
Answer:
-46.537x^2 + 4409.695x - 57770.475
Step-by-step explanation:
1) Convert the improper fraction to a mixed number. 17 3 II ») 3 3 5 3 6 6.
Answers
write an equation parallel to y=3x+6 that passes through the point (4,7).
Answers
The equation of a line in the slope intercept form is expressed as
y = mx + c
Where
m represents slope
c represents y intercept
The given equation is
y = 3x + 6
If we compare the given equation with the slope intercept equation, we can see that slope = 3
If two lines are parallel, it means that they ahve the same slope. Thus, the slope of the line
that passes through the point (4,7) is 3
We would find it's y intercept, c by substituting m = 3, x = 4 and y = 7 into the slope intercept equation. It becomes
7 = 3 * 4 + c
7 = 12 + c
c = 7 - 12
c = - 5
Thus, we would substitute m = 3 and c = - 5 into the slope intercept equation to get the equation of the line. Thus, we have
y = 3x - 5
Keaton needs to fill juice cups for her little sister's birthday party. There are 22 juice cups and each juice cup holds 12 fluid ounces. The juice comes in 1-gallon bottles. How many 1-gallon bottles of juice will Debbie need to purchase?
(1 quart = 32 fluid ounces, 1 gallon = 4 quarts)
Answers
Answer: 3 Gallons
Step-by-step explanation:
To find the total number of ounces she needs of juice we need to multiply the 22 cups by 12 ounces.
22 x 12 = 264
Now to find the number of quarts we need to convert the ounces into quarts by dividing by 32.
264 / 32 = 8.25
To find the number of gallons we need you have to convert it into gallons by dividing by 4.
8.25 / 4 = 2.0625
Because you cannot purchase .0625 of a gallon, we need to round up and purcahse 3.
if d=3, does d+d+d =3d?
Answers
Yes, d + d + d = 3d
Explanations:d + d + d can also be written as:
1d + 1d + 1d
which equals to 3d
Therefore, no matter what the value of d is,
d + d + d = 3d
The scatter plot shows the relationship between the number of chapters and the total number of page’s for several books
Answers
we have
x ----> number of chapters
y ---> number of pages
In this problem
we have a proportional relationship between the variables x and y (because the line passes through the origin)
so
The linear equation is of the form
y=Kx
where k is the constant of proportionality
K=y/x
looking at the graph
we take the point (4,40)
so
k=40/4=10
the equation is
y=10x
For y=180
substitute
180=10x
solve for x
x=180/10
x=18
the answer is 18 chaptersSolve the systems of equations. List variables a, b, and c.
a-2b+c=8
2a+b-c=0
3a-6b+ 3c = 24
Answers
a = 2b-c+8
b = (-a-c+8)/ 2
c = -a+2b+8
variable a ,b & c for 2a+b-c=0
a = (-b+c) / 2
b=-2a+c
c = 2a+b
variable a ,b & c for 3a-6b+ 3c = 24
a=2b-c+8
b = - (-a-c+8)/ 2
C = -a+2b+8
How to find variables a,b,c ?
1) Finding variable a ,b & c for a-2b+c=8
Finding a=(a-2b+c) + (2b-c)=8+ (2b-c)
a -2b+c+2b-c=8+2b-c
a-2b+2b+c-c=2b-c+8
a = 2b-c+8
Finding b =a-2b+c=8
(a-2b+c) + (−a − c) = 8+ (-a-c)
a-2b+c-a-c=8-a-c
b = (-a-c+8)/ 2
Finding c =a-2b+c8
(a-2b+c)+(-a+2b)=8+(-a+2b)
c = -a+2b+8
2) Finding variable a ,b & c for 2a+b-c=0
Finding a=2a+b-c=0
(2a+b-c)+(-b+c) = -b+c
2a+b-c-b+c = -b+c
a = (-b+c) / 2
Finding b =2a+b-c=0
(2a + b-c) + (-2a + c) = -2a + c
b=-2a+c
Finding c =2a+b-c=0
(2a+b-c) + (-2a - b) = -2a-b
c = 2a+b
3) Finding variable a ,b & c for 3a-6b+ 3c = 24
Finding a=3a-6b+3c = 24
(3a-6b+3c) + (6b-3c) = 24 + (6b- 3c)
3a-6b+3c+6b-3c = 24 + 6b-3c
a=2b-c+8
Finding b =3a-6b+3c=24
(3a-6b+3c) + (−3a - 3c) = 24 + (-3a - 3c)
3a-6b+3c-3a-3c-24-3a-3c
3a-6b+3c=24
(3a-6b+3c) + (−3a - 3c) = 24 + (-3a - 3c)
b = - (-a-c+8)/ 2
Finding c =3a-6b+3c=24
(3a-6b+3c) + (-3a+6b)=24+ (-3a+6b)
3a-6b+3c-3a+6b-24-3a+6b
C = -a+2b+8
System of equations :In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.A system of equations is a set of one or more equations involving a number of variables.The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect. A system of equations can be classified in a similar manner as single equations.The following set of equations is an example of system of equations,2x - y = 12
x - 2y = 48
Solving a system of equations means finding the values of the variables used in the set of equations.We compute the values of the unknown variables still balancing the equations on both sides.The main reason behind solving an equation system is to find the value of the variable that satisfies the condition of all the given equations true.To learn more about System of equations refer :
https://brainly.com/question/13729904
#SPJ13
In the middle school math class of 30 students, 24 got a grade over 90 points on a unit test. What decimal and the percent of the students got a grade above 90 points?
Answers
The percentage of students who got above 90 point is 80%
the decimal student got grade above the 90 points is 0.8
What is Decimal?
The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the name for the method of representing numbers in the decimal system.
Given,
Total no. of students = 30
No. of students who score above 90 points = 24
We have to find the percentage of the students who got above 90 points
So, to calculate,
24 / 30 x 100 = 80%
Now, we have to convert percent into decimal
so, we have,
80 / 100 = 0.8
Hence, 80% percent student got grade above 90 points
And 0.8 of the student got grade above the 90 points
To learn more about Decimal click on the link
https://brainly.com/question/703656
#SPJ9
Use the binomial theorem to expand the binomial.(x – 3)^5
Answers
The binomial theorem tells us how to expand an expression of the form (a + b)^2 like this:
[tex](a+b)^n=nC_0a^nb^0+nC_1a^{n-1}b^1+\cdots nC_na^0b^n[/tex]And nCr is given by the following formula:
[tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]Then, for this polynomial, we can apply the binomial theorem with a = x, b = -3 and n = 5 to get:
[tex](x-3)^5=5C_0x^5(-3)^0+5C_1x^4(-3)^1+5C_2x^3(-3)^2+5C_3x^2(-3)^3+5C_4x^1(-3)^4+5C_5x^0(-3)^5[/tex][tex]\begin{gathered} 5C_0=1 \\ 5C_1=5 \\ 5C_2=10 \\ 5C_3=10 \\ 5C_4=5 \\ 5C_5=1 \end{gathered}[/tex]Simplifying, we get:
[tex]\begin{gathered} (x-3)^5=(1)x^5(-3)^0+(5)_{}x^4(-3)^1+(10)_{}x^3(-3)^2+(10)x^2(-3)^3+(5)x^1(-3)^4+(1)x^0(-3)^5 \\ (x-3)^5=x^5+(5)_{}x^4(-3)^{}+(10)_{}x^3(9)+(10)x^2(-27)+(5)x^1(81)^{}-243 \\ (x-3)^5=x^5-15_{}x^4^{}+90_{}x^3-270x^2+405x^{}^{}-243 \end{gathered}[/tex]Then, the expanded polynomial is:
x⁵ - 15x⁴ + 90x³ - 270x² + 405x - 243
6r = 726r − 6 = 72 − 6r = 66Is Brooke’s solution correct? If the solution is incorrect, explain why it is incorrect and show the correct steps to solve the equation.
Answers
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the given solution
[tex]\begin{gathered} 6r=72 \\ 6r-6=72-6 \\ r=66 \end{gathered}[/tex]STEP 2: Determine whether Brooke's solution is correct
Brooke's solution is incorrect because Brooke subtracted the co-efficient of r which is 6 from both sides. Brooke can not use this method since 6 is multiplied to the unknown value which ir and not added to both sides.
The correct step will be to divide both sides by the coefficient of r as seen below:
[tex]\begin{gathered} 6r=72 \\ Coefficeint\text{ of r is 6} \\ Divide\text{ both sides by 6} \\ \frac{6r}{6}=\frac{72}{6} \\ r=12 \end{gathered}[/tex]A line passes through (-1, 7) and (1, 3).
Which answer is the equation of the line?
Answers
Answer:
hgg
Step-by-step explanation:
Solve for z. 5z - 7 = 2z + 2
Answers
Solution
[tex]5z_-7=2z+2[/tex]Collect the like terms
[tex]\begin{gathered} 5z-2z=2+7 \\ 3z=9 \end{gathered}[/tex]Divide both sides by 3
[tex]\begin{gathered} \frac{3z}{3}=\frac{9}{3} \\ \\ z=3 \end{gathered}[/tex]The final answer
[tex]z=3[/tex]If answer is decimal should be rounded to hundredths place
Answers
A rectangular prism has a volume that can be obtained using the formula
[tex]V=A\text{ x h}[/tex]where
[tex]\begin{gathered} A=\text{base area of the prism} \\ h=\text{height of the prism} \end{gathered}[/tex]Substituting the given values of
[tex]\begin{gathered} V=150 \\ A=10 \\ \end{gathered}[/tex]Into the equation, we will obtain
[tex]150=10\times h[/tex]If we make h the subject of the formula
[tex]h=\frac{150}{10}[/tex][tex]h=15\text{ units}[/tex]Sal has invested in two different stocks over the past few years. He has 22 shares of Company A's stock, which is currently selling at $45 per share. He also has 130 shares of Company B's stock, which is currently selling at $75 per share. What is the total value of Sal's stock holdings?
Answers
Total value of Sal's stock holdings is $10740
What is stock holding?The quantity of stocks, or shares, that a person or organization owns in a corporation is referred to as their stock holdings. Along with futures, bonds, mutual funds, and other assets, these make up an element of an investment portfolio. Each of these is an investment that has the potential to appreciate in value, bringing its owner a profit.
Stock holdings can comprise securities such as stocks, bonds, futures, mutual funds, ETFs, and other types of assets.
Preferred stock and ordinary stock are the two main categories of stock holdings.
Money earned on selling stocks of company A
= 22×45
= $990
Money earned on selling stocks of company B
= 130×75
= $9750
Total money earned on selling stocks of company A and B
= 990 + 9750
= $10740
To know more about stock holding please visit:
https://brainly.com/question/13397492
#SPJ13
Final and of the non side round your answer to the nearest 10th 18 and 4
Answers
In the right triangle, there is a relation between its sides
(hypotenuse)^2 = (leg1)^2 + (leg2)^2
The hypotenuse is the side opposite to the right angle
leg1 and leg 2 are the sides of the right angle
In the given figure
The hypotenuse = 18
leg1 = 4
(18)^2 = (4)^2 + (leg2)^2
324 = 16 + (leg2)^2
Subtract 16 from both sides
324 - 16 = 16 - 16 + (leg2)^2
308 = (leg2)^2
Take square root for both sides
17.54992877 = leg2
Round it to the nearest tenth
leg2 = 17.5
In what form is water returned to earths surface?
A. Vapor
B. Precipitation
C. Wind
Answer asap for brainlist please nobody will help me
Answers
Answer:
B. Precipitation
Step-by-step explanation:
Precipitation is atmospheric water vapor that condenses to a liquid and then falls back to earth due to gravity.
Based on the diagram below, find the following lengths:BX208E1A7 XDС44AB =AEED =FC =AC =DC =
Answers
Answer:
AB = 14
ED = 10
AC = 16
AE = 7
FC = 10
DC = 8
Explanation:
In a medial triangle, larger triangle is similar to the smaller triangle; therefore, the ratio of the side lengths is the same:
15) Cost of a computer game: $4.99
Markup: 40%
Discount: 55%%
Tax: 1%
Answers
Answer:
$3.18
Step-by-step explanation:
(4.99×0.4)+4.99=6.986
6.986-(6.986×0.55)=3.1437
(3.147×0.01)+3.147=3.175137
4. Which equation does NOT have like terms to collect?
3y - 2(y-1) + y = −42
-8(b-3) = -56 - 6
15t+19r = 2
8.5d +7.5 10d +3
Answers
Answer:
15t + 19r = 2
Step-by-step explanation:
None of the unknowns are common
Hi I need help rewriting this equation so there is no fractions in it
Answers
We will rewrite the equation as follows:
[tex]8+\frac{2}{3}x=\frac{5}{6}\Rightarrow6(8+\frac{2}{3}x)=6(\frac{5}{6})[/tex][tex]=48+4x=5[/tex]So, the equation without fractions is:
[tex]48+4x=5[/tex]Consider a collection of envelopes consisting of 2 red envelopes, 2 blue envelopes, 2 green envelopes, and 3 yellow envelopes. If three envelopes are selected at random, without replacement, determine the probability that they are all yellow envelopes.
Answers
The probability that all three randomly selected envelopes are yellow without replacement is 1/84.
What is a combination?It is an arrangement of a set of numbers from a total set where the order of the set is not relevant.
We have,
2 red envelopes
2 blue envelopes
2 green envelopes
3 yellow envelopes.
Total number of envelopes = 9
The probability that all three randomly selected envelopes are yellow without replacement.
= [tex]\frac{^3C_1}{^9C_1} \frac{^2C_1}{^8C_1} \frac{^1C_1}{^7C_1}[/tex]
= (3/9) x (2/8) x (1/7)
= (3x2x1)/(9x8x7)
= 1/84
Thus,
The probability that all three randomly selected envelopes are yellow without replacement is 1/84.
Learn more about combination here:
https://brainly.com/question/14355408
#SPJ1
are the events mutually exclusive?event A: rational numbersevent B: irrational numbers
Answers
Given:
There are given that the statement to find them mutually exclusive.
Explanation:
According to the concept of mutually exclusive:
Tw events A and B of any sample space are mutually exclusive if the occurrence of any one of them excludes the occurrence of the other event.
Then, twp events A and B cannot occur simultaneously.
Now,
From the given question:
Event A and events B, which means, rational numbers and irrational numbers are mutually exclusive because they have no numbers in common.
So, they span the entire set of real numbers which means both are real numbers.
Final answer:
Hence, the correct option is Yes-Mutually exclusive.
I might not respond for a little while, please don’t end the session! Need help on #3 and 4
Answers
We have a right triangle with a 15m hypotenuse and a 8m leg. If we use x for the missing leg then the Pythagorean Theorem states that:
[tex]15^2=8^2+x^2[/tex]Then we have to solve that equation for x:
[tex]\begin{gathered} x^2=15^2-8^2=225-64 \\ x^2=161 \\ x=\sqrt[]{161} \end{gathered}[/tex]So the answer is the square root of 161.
Use the order of operations to evaluate the expression.7 + { 6 + (3 x 2 )} x 5A. 67B. 95C. 97D. 125
Answers
ANSWER
67 (Option A)
EXPLANATION
Given:
[tex]7+\lbrace6+(3\times2)\rbrace\times5[/tex]Desired Outcome:
Evaluate the expression
Using the order of operations
Note: Follow the following ORDER to evaluate the expression
1. The parenthesis are completed first.
2. The exponents come next.
3. Multiplication and division are done from left to right when they are encountered.
4. Addition and subtraction are done from left to right when they are met.
1. Complete parenthesis first
[tex]\begin{gathered} 7+\lbrace6+6\rbrace\times5 \\ 7+\lbrace12\rbrace\times5 \end{gathered}[/tex]2. Multiplication and division are done from left to right when they are encountered.
[tex]\begin{gathered} 7+\lbrace12\rbrace\times5 \\ 7+60 \end{gathered}[/tex]3. Addition and subtraction are done from left to right when they are met.
[tex]\begin{gathered} 7+60 \\ =67 \end{gathered}[/tex]Hence, the answer is 67 (Option A)
Reese is selling lemonade at the parade. He gets to keep 10% of the money he collects. A large lemonadeis $4.00 and a small lemonade is $3.00.The expression represents 10% of the money he collects.0.10(4/ +35)Use the Distributive Property to expand the expression.The simplified expression is
Answers
ANSWER
[tex]0.40l+0.30s[/tex]EXPLANATION
We want to use the distributive property to expand the expression:
[tex]0.10(4l+3s)[/tex]To do this, use the term outside the bracket to multiply each of the terms in the bracket:
[tex]\begin{gathered} (0.10\cdot4l)+(0.10\cdot3s) \\ 0.40l+0.30s \end{gathered}[/tex]That is the simplified expression.
The diagonal of a square measures 12 inches. What is the length of the sides
Answers
It is given that the diagonal of a square is 12 inches.
The square is given by the diagram shown below:
In the triangle ABC by pythagorean theorem it follows:
[tex]\begin{gathered} AB^2+BC^2=AC^2 \\ 2AB^2=12^2 \\ AB^2=\frac{144}{2} \\ AB^2=72 \\ AB=\sqrt[]{72}=6\sqrt[]{2} \end{gathered}[/tex]Hence the side is given by:
[tex]s=6\sqrt[]{2}\text{ inches}[/tex]Find the value of the test statistic z.The claim is that the proportion of peas with yellow pods is equal to 0.25 (or 25%). The sample statistics from one experiment include 430 peas with 126 of them having yellow pods.
Answers
You have to calculate the z-value or value of the test statistic z, for the proportion of yellow pods. The form of the z-statistic used to study the population proportion is:
[tex]Z=\frac{\hat{p}-p}{\sqrt[]{\frac{p(1-p)}{n}}}\approx N(0,1)[/tex]The population proportion of the yellow pods is p=0.25.
From a sample of 430 peas, 126 of them had yellow pods, using this information you have to calculate the sample proportion p-hat (^p)
The sample proportion is equal to the quotient between the number of successful outcomes "x" (number of yellow pods) and the total number of outcomes "n" (number of peas sampled)
[tex]\begin{gathered} \hat{p}=\frac{x}{n} \\ \hat{p}=\frac{126}{430} \\ \hat{p}=0.29 \end{gathered}[/tex]Once determined the sample proportion, you can calculate the z-value as follows:
[tex]\begin{gathered} Z=\frac{0.29-0.25}{\sqrt[]{\frac{0.25(1-0.25)}{430}}} \\ Z=\frac{0.04}{\sqrt[]{\frac{0.25\cdot0.75}{430}}} \\ Z=\frac{0.04}{\sqrt[]{\frac{0.1875}{430}}} \\ Z=1.915\approx1.92 \end{gathered}[/tex]The value of the test statistic is 1.92.
*-*-*-*-*
The standard deviation of the distribution of the sample proportion:
To simplify the calculations you can calculate the standard deviation separately, the formula for this measure is the denominator of the formula of the Z-statistic:
[tex]\sigma=\sqrt[]{\frac{p(1-p)}{n}}[/tex]Using p=0.25
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{0.25(1-0.27)}{430}} \\ \sigma=\sqrt[]{\frac{0.25\cdot0.75}{430}} \\ \sigma=\sqrt[]{\frac{0.1875}{430}} \\ \sigma=\sqrt[]{\frac{3}{6880}} \\ \sigma=0.0208 \end{gathered}[/tex]Then you can replace the result in the denominator of the formula to determine the Z-value:
[tex]\begin{gathered} Z=\frac{\hat{p}-p}{\sqrt[]{\frac{p(1-p)}{n}}} \\ Z=\frac{0.29-0.25}{0.0208} \\ Z=\frac{0.04}{0.0208}\approx1.92 \end{gathered}[/tex]795,860,913,789 in word form
