Find the component form of u + v given the lengths of u and v and the angles that u and v make with the positive x-axis. ||u|| = 5, 0u = 9
||v|| = 1, 0v = 5
u + v = ...
Answers
The component form of u + v is simply the component form of v, which is (1, 0).
Howto determined the component form of the vector?Given the lengths of vectors u and v, we have:
||u|| = 5 and ||v|| = 1
We are also given the angles that u and v make with the positive x-axis.
Let the angle that vector u makes with the positive x-axis be θu and the angle that vector v makes with the positive x-axis be θv. Then we have:
cos(θu) = 0 and sin(θu) = 1 (since u makes a 90-degree angle with the positive x-axis)
cos(θv) = 1 and sin(θv) = 0 (since v makes a 0-degree angle with the positive x-axis)
Now we can find the component form of vectors u and v as follows:
u = (||u||cos(θu), ||u||sin(θu)) = (5cos(0), 5sin(0)) = (5, 0)
v = (||v||cos(θv), ||v||sin(θv)) = (1cos(0), 1sin(0)) = (1, 0)
so we can use that information to find the component form of u + v as follows:
5u + v = u + v
4u = 0
u = 0
Substituting this value of u into the equation 5u + v = u + v, we get:
v = v
Therefore, the component form of u + v is simply the component form of v, which is (1, 0).
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Related Questions
Which statement best explains the relationship between numbers divisible by 5
and 10?
Some of the numbers that are divisible by 10 are also divisible by 5.
1) Numbers that are divisible by 10 are never divisible by 5.
A number that is divisible by 10 is also divisible by 5 because all factors of 10 are also
factors of 5
A number that is divisible by 10 is also divisible by 5 because 5 is a factor of 10.
Done
Answers
Answer:
a number that is divisible by 10 is also divisible by 5 since all factor of 10 are also factor of 5
Find the unknown number in the proportion 1/9 = x/109
Answers
Answer:
I think it's 12.11
Step-by-step explanation:
1/9=x/109
1×109=9×x
109/9=12.11 so it should be this answer
Sweatshirts at the school store cost $30. They currently sell about 4 shirts per month. They have decided to decrease the price of the shirts. They found the for each each $1.50 decrease, they will sell 2 more shirts per month. How many decreases in prices will give the max value?
A. 30
B. 9
C. 363
D. 16.50
Answers
for every $2 increase in price, there will be a drop of 60 sales a year.
What price they should charge for each shirt to maximize the revenue?
:
Let x = no. of $2 increases
also
Let x = no. 60 shirt sales reductions
:
Price = (20 + 2x)
No. of shirts = (1200 - 60x)
:
Revenue = price * no. of shirts sold, therefore:
R = (20 + 2x)*(1200 - 60x)
FOIL
R = 24000 - 1200x + 2400x - 120x^2
Arranges as a quadratic equation
R = -120x^2 + 1200x + 24000
Find the axis of symmetry to find the price for max revenue: x = -b/(2a)
In this equation; a=-120; b=1200
x = %28-1200%29%2F%282%2A-120%29
x = %28-1200%29%2F%28-240%29
x = +5 ea $2 increases
and
5*60 = 300 reduction in shirt sales:
:
Price for max sales; 20 +2(5) = $30, will sell 1200 - 300 = 900 shirts
:
Max revenue: 30 * 900 = $27,000
a spring has a natural length of 18 inches and a force of 20 lbs is required to stretch and hold the spring to a length of 24 inches. what is the work required to stretch the spring from a length of 21 inches to a length of 26 inches?
Answers
The work required to stretch the spring is 91.6 Ibs-inch
What is work?
Work is defined as force applied across a distance. Work examples include pushing an object against gravity, driving a car up a hill, and lowering a captive helium balloon. Work is the mechanical expression of energy.
Δx : displacement from equilibrium position
f = k Δ x (force due to spring = -kΔx)
where, k is the spring constant
Given,
f = 20ibs
Δx = 24 -18 Inches = 6 inches
∴ k = 20/6 ibs/inch
Now, PE stored in spring = 1/2 k (Δx)²
Δx : displacement from equilibrium position
Work done = change in PE
= 1/2K (Δx₂)² -1/2k (Δx₁)²
given,
Δx₁ = 21-18 inches = 3 inches
Δx₂ = 26-18 inches = 8 inches
∴work done = 1/2 * 20/6 (8² - 3²)Ibs-inches
=10/6 *5*11
work done = 91.6 ibs-inch
The spring must be stretched with 91.6 Ibs-inch of force.
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A random sample of 64 sat scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240. the 95onfidence interval for the population mean sat score is: ________
a. 1.96. b. 1.998.
c. 1.645. d. 1.28.
Answers
The 95% confidence interval for the population mean SAT score is given as follows:
(1340, 1460).
How to calculate the confidence interval?The confidence interval is calculated using the t-distribution, as the standard deviation for the population is not known, only for the sample.
The bounds are obtained according to the equation defined as follows:
\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)
In which the variables of the equation are presented as follows:
\(\overline{x}\) is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.In the context of this problem, the values of these parameters are given as follows:
\(\overline{x} = 1400, n = 64, s = 240\)
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 64 - 1 = 63 df, is t = 1.998.
Then the lower bound of the interval is of:
1400 - 1.998 x 240/sqrt(64) = 1340.
The upper bound of the interval is of:
1400 + 1.998 x 240/sqrt(64) = 1460.
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what is the quotient of 6 1/4 ÷ (-5/8)
Answers
Answer: -10
Step-by-step explanation:
1. Convert 6 1/4 to an improper fraction
25/4
2. Find the quotient using the keep, change, flip method
- Keep the first fraction (25/4)
- Change the division sign to a multiplication sign
- Flip the second fraction (i.e. find the reciprocal)
-5/8 -> -8/5
3. Multiply and solve by multiplying the numerators and denominators together respectively
25/4 * -8/5
25*-8 = -200
4*5 = 20
-200/20 = -10
Answer:
\(-\frac{12}{5}\)
Step-by-step explanation:
Using the 100/50/20 Rule for daily fluid requirements (DFR). Calculate the following questions, do not round the patient's weight but round all final answers to a whole number. 1-10 kg = 100ml/kg/day 11-20 kg = 50ml/kg/day (+ 1000 mL/day for 1* 10kg) Over 20kg = 20mL/kg/day (1500 mL/day for 1s 20kg) 18. An infant weighs 11 pounds. What is the required amount of fluid per day in ml? I 19. A child weighs 31 lbs and 8 ozs. What is the required amount of fluid per day in ml? If no oral fluids are consumed, what is the hourly IV flow rate to maintain proper hydration?
Answers
18. An infant weighs 11 pounds which is equivalent to 4.98 kg. Using the 100/50/20 Rule, the required amount of fluid per day for an infant between 11-20 kg is 50 ml/kg/day. So, the required amount of fluid per day in ml is 4.98 kg x 50 ml/kg/day = 249 ml/day.
19. A child weighs 31lbs and 8 ozs which is equivalent to 14.21 kg. Using the 100/50/24 Rule, the required amount of fluid per day for a child over 20 kg is 20 ml/kg/day. So, the required amount of fluid per day in ml is 14.21 kg x 20 ml/kg/day = 284.2 ml/day.
If no oral fluids are consumed, the hourly IV flow rate to maintain proper hydration would be: 284.2 ml/day / 24 hours/day = 11.8 ml/hour.
Daily Fluid Requirements (DFR)The question is about fluid requirements for infants and children, and it is using the 100/50/20 Rule for Daily Fluid Requirements (DFR) to calculate the required amount of fluid per day for different weight ranges. The 100/50/20 Rule is a guideline used to determine the appropriate amount of fluid that infants and children should receive on a daily basis based on their weight. The rule states that for infants and children up to 10 kg, the recommended fluid intake is 100 ml/kg/day, for those between 11-20 kg it is 50 ml/kg/day, and for those over 20 kg it is 20 ml/kg/day.
The question also asking about the hourly IV flow rate to maintain proper hydration if no oral fluids are consumed.
This subject is part of pediatrics, more specifically in the field of fluid and electrolyte balance and management.
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The federal unemployment tax act (futa) is a payroll tax paid by employers on employee wages. The tax is 6. 0% on the first $7,000 an employee earns each year. If walmart has 1. 5 million employees in the u. S. , about how much does it pay in futa taxes annually?.
Answers
The amount of tax that Walmart pay annually in FUTA is $630 million .
In the question ,
it is given that ,
the amount that an employee earns in 1 year(E) = $7000
the tax rate (r) = 6%
number of employees in Walmart = 1.5 million = 1.5 × 10⁶
So , the amount of tax paid by Walmart in Federal Unemployment Tax Act(FUTA) can be calculated using the formula
Amount = r × n × E
Substituting the values of r , n , E in the amount formula ,
we get ,
Amount = 0.06 × 1.5 × 10⁶ × 7000
= 630,000,000
= 630 million .
Therefore , The amount of tax that Walmart pay annually in FUTA is $630 million .
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what is the the difference between a repeating decimal and a nonstop decimal on the rational numbers chart
Answers
Repeating decimals are those numbers that, following the decimal point, continue to repeat the same value. The term "non-repeating rational numbers" refers to decimal numbers that do not repeat their value after the decimal point.
Repeating decimals are those numbers that, following the decimal point, continue to repeat the same value. Recurring numbers is another name for these figures. The term "non-repeating rational numbers" refers to decimal numbers that do not repeat their value after the decimal point.
A repeating decimal can be a rational number, and any integer is a rational number since it can be expressed as a fraction by simply assigning it a denominator of 1. Then, by multiplying and dividing the decimal according to its place values, we can also state that a terminating decimal can be expressed as a fraction.
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What is the answer please hurry I need helpp
Answers
The given function is f(x) = 15(1.02)^x, where x is the number of years from the date at which money is initially deposited.
This means that $15 were initially deposited into the account, and the amount grows at an annual rate of 2% (which is represented by 1.02 being raised to the power of x).
Therefore, the correct answer is: $15 were initially deposited into the account, which grows at an annual rate of 2%.
Hope I helped you...
A. $15 dollars were initially deposited into the account, which grows at a annual rate of 2%
UNDERSTAND why:
this shows the initial amount then the rate of growth while the X in this equation is the eXponential
Formalize the following in terms of atomic propositions r, b, and w, first making clear how they correspond to the
English text. (a) Berries are ripe along the path, but rabbits have not been seen in the area.
(b) Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.
(c) If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.
(d) It is not safe to walk along the path, but rabbits have not been seen in the area and the berries along the path are ripe.
e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to
pave been seen in the area.
Walking is not safe on the path whenever rabbits have been seen in the area and berries are ripe along the path.
Answers
Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path. This is formalized by using the →(if-then) and ∧(logical and) operators.
Given information and corresponding atomic propositions:
We need to formalize the given statements in terms of atomic propositions r, b, and w, which are defined as follows:
r: Rabbits have been seen in the area.
b: Berries are ripe along the path.
w: Walking on the path is safe.
Now, let us formalize each of the given statements in terms of these atomic propositions:
a) Berries are ripe along the path, but rabbits have not been seen in the area.
b: Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.
c: If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.
d: It is not safe to walk along the path, but rabbits have not been seen in the area, and the berries along the path are ripe.
e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.
Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path.
The formalizations in terms of atomic propositions are:
a) b ∧ ¬r.b) ¬r ∧ w ∧
b.c) (b → w) ∧ (¬r → w).
d) ¬w ∧ ¬r ∧
b.e) (¬r ∧ ¬b) → w.b ∧
Berries are ripe along the path, but rabbits have not been seen in the area.
This is formalized by using the ∧(logical and) operator.
(¬r ∧ ¬b) → w: It means For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.
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HURRY THIS IS DUE IN A COUPLE OF MINUTES!!!!
Answers
Answer: The model is 16.67 ft tall 16 feet, 8 inches
Step-by-step explanation: Divide the real height by the scale.
1250÷ 75 = 16.667
This is a quick Short cut for working out the ratio x/1250 : 1/75
suppose the correlation matrix for three variables (v1, v2, and v3) is as seen here. what would be the best conclusion regarding the relationships between the variables?
Answers
the three vectors are linearly dependent and they cant generate a 3 dimensional vector subspace.
Lets take v1 = (1,0,0), v2 = (1,1,0) and v3 = (0,1,0). Neither of the vectors are a multiple of the other, however they dont generate R³ because for example the vector (0,0,1) is not a linear combination of v1, v2 and v3.
Not that, despite not being a multiple of v1 or v3, v2 is a linear combination of v1 and v3, because it is the sum of both of them. Therefore, the three vectors are linearly dependent and they cant generate a 3 dimensional vector subspace.
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use lagrange multipliers to find the maximum and minimum
Answers
an urn contains five balls numbered 1, 2, 2, 6, and 6. how many ways can a person choose two balls at random from the urn?
Answers
There are six possible ways a person can choose two balls at random from an urn containing five balls numbered 1, 2, 2, 6, and 6.
To understand how to calculate the number of combinations, let's break it down into two parts: selecting the first ball, and then selecting the second ball. Since there are five balls in the urn, the first ball can be chosen in five possible ways. Then, when selecting the second ball, the number of possible selections is reduced to four because one ball has already been selected. This can be expressed mathematically as: n(A)=5x4.
To calculate the total number of combinations, we then multiply the two numbers: 5x4=20. This result is then divided by two because the order of selection does not matter. As a result, 20/2=10, which means that there are ten possible combinations when choosing two balls at random from the urn. In conclusion, if an urn contains five balls numbered 1, 2, 2, 6, and 6, there are six possible ways a person can choose two balls at random. This can be expressed mathematically as n(A)=6 or n(A)=5x4/2.
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B) work out (3. 6 * 10 ^ - 5) / (1. 8 * 10 ^ 2) give your answer in standard form.
Answers
The expression (3.6 * 10^-5) / (1.8 * 10^2) can be calculated as = 2 * 10^-7
A canonical, normal, or standard form of a mathematical object is a conventional manner of presenting that item as a mathematical expression in mathematics and computer science. It is frequently the one that gives the simplest representation of an item and allows it to be identified in a unique fashion.
A quantity is said to be stated in standard form if it is written as the product of a power of ten and a number higher than or equal to one but less than ten (or scientific notation).
The expression (3.6 * 10^-5) / (1.8 * 10^2) can be calculated as follows:
=3.6 * 10^-5 / (1.8 * 10^2)
= (3.6 / 1.8) * (10^-5 / 10^2)
= 2 * 10^-7
Therefore, the answer in standard form is 2 * 10^-7.
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Answer plz I will correct answer as brainliest
Answers
y=180-50
=130 degrees (angles in a straight line equal to 180)
z=180-130-30 (angle sum of a triangle equal to 180)
z=20 degrees
a recent study reported that americans spend an average of 300 minutes a day watching tv.. suppose that the distribution of minutes per day watching tv follows a normal distribution with a standard deviation of 26 minutes.
Answers
The average time Americans spend watching TV per day is reported to be approximately 300 minutes, following a normal distribution with a standard deviation of 26 minutes.
To address this question, we can use the provided information to describe the distribution of minutes per day spent watching TV by Americans.
Given that the distribution follows a normal distribution, we can assume that the data is symmetrically distributed around the mean. The mean of the distribution is given as 300 minutes.
The standard deviation, which measures the spread of the data, is stated as 26 minutes. This indicates that most people fall within one standard deviation of the mean.
Using the properties of a normal distribution, we can make various probabilistic statements. For example, approximately 68% of Americans would spend between 274 minutes (mean - 1 standard deviation) and 326 minutes (mean + 1 standard deviation) watching TV per day.
By understanding the characteristics of the normal distribution and the provided parameters (mean and standard deviation), we can analyze and make predictions about the amount of time Americans spend watching TV on a daily basis.
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Which list correctly orders the coefficients of the following terms from least to greatest?
81, – 4z, – 1ly, w
(1 point)
0-1ly, - 4z, w, 8z
Ow, – 4z, 81, - lly
O -1ly, - 41, 8z, u
O w, 87, - fly, – 4z
Answers
Answer:
−11y, −4z, w, 8x
Step-by-step explanation:
Description of Data
The data being used for this lab are based on data collected after the 2009 war ended that was between Israel and the Hamas militias in the Gaza Strip. Responses were obtained from 200 individuals that were exposed to rocket attacks during that period. The variables in the study include:
ID: Used to indicate the ID# of the participant
family income: The household income of the individuals (expressed in thousands)
gender: The gender of the individuals that responded to the survey
family in range: Indicates whether or not the participant’s family decided to stay in the range of the rockets (Not in rocket range vs. In rocket range)
family size: The size of the family (Small, Medium, Large)
anger: Respondents were asked to estimate the level of anger they felt during the war on a sliding scale of 1 to 100
fear: Respondents were asked to estimate the level of fear they felt during the war on a sliding scale of 1 to 100
perceived threat: Respondents reported the level of threat they perceived in the area (Low, High)
A subset of this data is shown in the image below:
Question 1
You decide to run a statistical test to evaluate whether gender predicts the perceived threat someone feels. In this test, gender would be your:
-independent variable
-dependent variable
Answers
gender would be the independent variable in this statistical test.
: In a statistical test, the independent variable is the variable that is manipulated or chosen by the researcher, and it is expected to have an effect on the dependent variable. In this case, the researcher is interested in evaluating whether gender has an effect on the perceived threat someone feels, so gender would be the independent variable. The dependent variable, on the other hand, is the variable that is expected to be affected by the independent variable, which in this case is the perceived threat someone feels.
The answer is that the researcher can use a statistical test, such as a t-test or ANOVA, to compare the perceived threat levels between males and females in the sample. The independent variable (gender) would be used to group the participants into two categories: male and female. The dependent variable (perceived threat) would be the variable that is being measured and compared between these two groups. The statistical test would then determine whether there is a significant difference in the perceived threat levels between males and females.
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When conducting a one sample hypothesis test of means or proportions, I am comparing the mean or proportion of a sample to a benchmark mean or proportion. true or false?
Answers
The statement "When conducting a one sample hypothesis test of means or proportions, I am comparing the mean or proportion of a sample to a benchmark mean or proportion" is true.
When conducting a one sample hypothesis test, the goal is to determine whether the sample mean or proportion is significantly different from a known or hypothesized population mean or proportion. This known or hypothesized value serves as the benchmark for comparison, and the hypothesis test assesses the likelihood of obtaining the observed sample result under the assumption that the benchmark value is true.
The null hypothesis represents the assumption that there is no significant difference between the sample and the benchmark, and the alternative hypothesis represents the possibility that the sample result is statistically different from the benchmark. By comparing the sample to the benchmark, we can determine whether the sample provides evidence to reject or fail to reject the null hypothesis, and ultimately make inferences about the population based on the sample data.
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One of the altitudes of the parallelogram shown is the square root of 22.5. What is the other altitude?
Answers
Answer:
Step-by-step explanation:
12x/3x
12x divided by 3x
Answers
Answer:
= 4
Step-by-step explanation:
12x / 3x
12/3 = 4
x/x = 1
then:
12x / 3x = 4*1 = 4
= 4
We have
=12x/3x
Here 12 is divided by 3 with 4 times
and x cuts x
Hence, answer=4
Please help: describe how the graph of each function compares with the graph of the parent function, y=logb^X
Answers
Answer:
The graph of the function is the graph of the parent function shifted 1 unit to the left and 5 units down.
Explanation:
If we have a function y = f(x + c), the graph of y will be the graph of f(x) shifted c units to the left.
If we have a function y = f(x) - c, the graph of y will be the graph of f(x) shifted c units down.
In this case, the parent function is f(x) = log₆x, then y = log₆(x + 1) - 5, so
y = f(x + 1) - 5
It means that the graph of the function is the graph of the parent function shifted 1 unit to the left and 5 units down.
if you have 3 cups of glue u use 2/3 cup of glue how much slime can u make?
Answers
I did 3/1 times 2/3 which would equal to 2
So in the numerator 3 times 2 equals 6 and in the denominator 1 times 3 equals to 3 which you’ll know have 6/3. so now you divide both of them by three since you can simplify it and it would left as 2.
Therefore you can make 2 slimes.
HELP ASAP.....NO LINKS & NO TROLLING
which statement about of y=5x^2+17x+6 is true
A. the zeros of y=5x^(2)+17x+6 are 3 and( 2)/(5), because y=(x+3)(5x+2)
B. the zeros of y=5x^2+17x+6 are 3 and 2/5, because y=(x-3)(5x-2)
C. the zeros of y=5x^2+17x+6 are -3 and -2/5, because y=(x+3)(5x+2)
D. the zeros of y=5x^2+17x+6 are -3 and -2/5, because y=(x-3)(5x-2)
Answers
Answer:
C
This is the answer
\((x + 3)(5x + 2) \\ x = - 3 \: \: or \: \: x = - \frac{2}{5} \)
When you solve an equation and you end with a TRUE STATEMENT, the solution set will be:
Answers
Answer:
false
Step-by-step explanation:
Answer:
equal
Step-by-step explanation:
3(x+2)=3x+6
3x+6=3x+6
-3x -3x
6=6
john went from weighing 140 pounds to 155 pounds. what is the percent of change and is it an increase or decrease?
Answers
Weight of the John increased by 10.71 percent as he is weighing 140 pounds to 155 pounds.
As given in the question,
Original weight of John is equal to 140 pounds
John's changed weight is equal to 155 pounds
155 is greater than 140 pounds
Increase in John's weight.
Change in weight = Increased weight - actual weight
Percent of change in John's increased weight
= [ | change in weight| / Actual weight ] × 100
= [(155 - 140 ) / 140] × 100
= (15 / 140)× 100
= 10.71%
Therefore, the percent of change in John's weight is increased by 10.71%.
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Two supplementary angles are in the ratio of 5 to 7. Find positive difference of the measure of the two angles. Do the same problem, only do it for complementary angles instead of supplementary angles.
Answers
Answer:
30° is the difference if they are supplement
15° is the difference if they are complementary
Step-by-step explanation:
Let 5x = the measure of the smaller angle
and 7x = the measure of the larger angle
If they are supplementary, then 5x + 7x = 180
12x = 180
x = 15
5x = 5(15) = 75 = the measure of the smaller angle
7x = 7(15) = 105 = the measure of the larger angle
105 - 75 = 30 = difference of the measures
Now, if they are complementary, then 5x + 7x = 90
12x = 90
x = 7.5
5x = 7(7.5) = 37.5 = the measure of the smaller angle
7x = 7(7.5) = 52.5 = the measure of the larger angle
52.5 - 37.5 = 15 = difference of the measures
which of the following equations represent a line that is parallel y=5x-4 ad passes through the point (3,4)
Answers
The equation that represents a line that is parallel to y = 5x - 4 and passes through the point (3, 4) is y = 5x - 11.
How to write the point-slope form equation?We are given that
The slope of given line = 5And passed through point (3, 4)Slope of parallel lines is the same, so slope of the line parallel to the given line will be m = 5
We have the slope and a point, using the point-slope form we can write the equation of the line:
\(\rightarrow\text{y} - 4 =5 \ (\text{x} - 3)\)
\(\rightarrow\text{y} = 5\text{x} - 15 + 4\)
\(\rightarrow\bold{y = 5x - 11}\)
Hence, the equation that represents a line that is parallel to y = 5x - 4 and passes through the point (3, 4) is y = 5x - 11.
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Your question is incomplete. The complete question is-
Which of the following equations represents a line that is parallel to y = 5x - 4 and passes through the point (3, 4)?
A. y = 5x - 7
B. y = 5x + 19
C. y = -1/5x -4
D. y = 5x - 11