please answer all parts of a,b,c and d
Find the following for the vectors u = -7i+10j + √2k and v= 7i-10j-√√2k a. v.u, v, and ul b. the cosine of the angle between v and u c. the scalar component of u in the direction of v d. the vec
Answers
The following for the vectors u = -7i+10j + √2k and v= 7i-10j-√√2k .To solve the given problem, we'll follow the steps for each part:
a. To find v.u (dot product of vectors v and u), we multiply the corresponding components and sum them up:
v.u = (7)(-7) + (-10)(10) + (-√√2)(√2)
= -49 - 100 - 2
= -151
The vector v is given by v = 7i - 10j - √√2k.
The magnitude of vector u is given by ||u|| = √((-7)^2 + 10^2 + (√2)^2) = √(49 + 100 + 2) = √151.
b. The cosine of the angle between vectors v and u can be found using the dot product formula and the magnitudes of the vectors:
cos(theta) = (v.u) / (||v|| * ||u||)
= -151 / (7^2 + (-10)^2 + (√√2)^2) * √151
= -151 / (49 + 100 + 2) * √151
= -151 / 151 * √151
= -√151
c. To find the scalar component of u in the direction of v, we need to project u onto v. The formula for the scalar projection is:
Scalar component of u in the direction of v = ||u|| * cos(theta)
Using the magnitude of u from part a and the cosine of the angle from part b:
Scalar component of u in the direction of v = √151 * (-√151)
= -151
d. The vector component of u orthogonal to v can be found by subtracting the scalar component of u in the direction of v from u:
Vector component of u orthogonal to v = u - (Scalar component of u in the direction of v)
= (-7i + 10j + √2k) - (-7i - 10j - √√2k)
= (-7i + 7i) + (10j - (-10j)) + (√2k - (-√√2k))
= 0i + 20j + (√2 + √√2)k
= 20j + (√2 + √√2)k
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Related Questions
18.) Which of the following solutions is likely to be the most corrosive? 18.) a.) 0.100MHCl b.) 0.0100MHC_2 H_3O_2 c.) 0.100MHC_2 H_3O_2d.) 0.0100MHCl
Answers
a). 0.100MHCl. is the correct option. The most corrosive solution is likely to be 0.100M HCl.
What is a corrosive substance? A corrosive substance is a substance that can cause significant damage to a living organism's skin, eyes, and other body tissues on contact. What is the definition of pH?The pH of a substance is defined as the negative logarithm of the hydrogen ion concentration (H+) in the substance. Its range is between 0 and 14. A solution with a pH less than 7 is acidic, whereas a solution with a pH greater than 7 is basic.
Therefore, the most corrosive solution is likely to be 0.100M HCl.b) 0.0100M HC2H3O2 Acetic acid, HC2H3O2, is a weak acid that has a lower concentration of H+ ions than HCl. Its pH will be above 2, and it will be less corrosive than HCl.c) 0.100M HC2H3O2 This solution is the same as option b. The pH will be above 2, and it will be less corrosive than HCl.d) 0.0100M HCl. This solution is less concentrated and therefore less corrosive than option a.
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Plot the following equation using the x- and y-intercepts. If both intercepts are zero, find at least one other point. Identify the graph for the equation. diagonal line from upper left to lower right, intercepting (0, 0.5) and (0.5, 0) diagonal line from upper left to lower right, intercepting (0, 1.5) and (2, 0) diagonal line from lower left to upper right, intercepting (0, –2) and (3, 0) diagonal line from lower left to upper right, intercepting (0, –3) and (3, 0)
Answers
The graph for the equation of each diagonal line from upper left to lower right are shown in the image attached below.
What is the slope-intercept form?In Mathematics, the slope-intercept form of an equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m is the slope, or rate of change.x and y represent the points.c represents the y-intercept or initial value.At (0, 0.5) and (0.5, 0), the slope and equation of the diagonal line can be written as follows;
Slope = (0 - 0.5)/(0.5 - 0)
Slope = -1.
Equation: y = -x + 0.5
At (0, 1.5) and (2, 0), the slope and equation of the diagonal line can be written as follows;
Slope = (0 - 1.5)/(2 - 0)
Slope = -0.75.
Equation: y = -0.75x + 1.5
At (0, –2) and (3, 0), the slope and equation of the diagonal line can be written as follows;
Slope = (0 + 2)/(3 - 0)
Slope = 2/3.
Equation: y = 2x/3 + 1.5
At (0, –3) and (3, 0), the slope and equation of the diagonal line can be written as follows;
Slope = (0 + 3)/(3 - 0)
Slope = 1.
Equation: y = x - 3
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A president and vice-president for an honor society are chosen from twelve people. How many different president/vice-president combinations are possible?
Answers
There are 12 different possibilities for a president. Therefore, there are 11 possibilities for vice-president.
We calculate this combination when we multiply 12 x 11:
12 x 11 = 132
Therefore, there are 132 different ways to make combinations.
What is 1,035 divided by 38
Answers
Answer:
27.2368421053
Step-by-step explanation:
6. Samantha works twice as many hours per week as Adriana. Together they work a total of 39 h one week. a) State how you will assign variables. b) Write an equation to represent the information in the first sentence. c) Write an equation to represent the information in the second sentence. d) Use the method of substitution to find the number of hours worked by each person.
Answers
Answer:
Samantha worked 26 hours and Adriana worked 13 hours.
Step-by-step explanation:
Let s = the number of hours that Samantha worked
Let a = the number of hours that Adriana worked
s = 2a
s + a = 39
2a + a = 39
3a = 39
a = 13
25. a 2018 pew research center survey found that more americans believe they could give up their televisions than could give up their cell phones (pew research website). assume that the following table represents the joint probabilities of americans who could give up their television or cell phone. could give up television could give up cellphone yes no yes 0.31 0.17 0.48 no 0.38 0.14 0.52 0.69 0.31 a. what is the probability that a person could give up her cell phone? (4 points) b. what is the probability that a person who could give up her cell phone could also give up television? (4 points) c. what is the probability that a person who could not give up her cell phone could give up her television? (4 points) d. is the probability a person could give up television higher if the person could not give up a cell phone or if the person could give up a cell phone? (4 points)
Answers
(a)Probability that a person could give up cell phone = 0.48
(b)Probability that a person who could give up her cell phone also could give up television is 0.65
(c) Probability that a person who could not give up a cell phone could give up television is 0.73
What is Probability?
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability. It is crucial to grasp this branch's most fundamental concepts in order to fully comprehend it, including the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc.
According to the given question:
a. Probability that a person could give up cell phone = 0.48
b. Probability that a person who could give up her cell phone also could give up television
= P(give up cell phone and TV)/p(give up cell phone)
= 0.31/0.48
= 0.6458
= 0.65
c. Probability that a person who could not give up a cell phone could give up television is
= P(could not give up cellphone and could give up TV)/P(could not give up cell phone)
= 0.38/0.52
= 0.73
d. The probability a person could give up television is higher for persons who couldn't give up cell phones than for those who could give up their cell phones.
Hence,
(a)Probability that a person could give up cell phone = 0.48
(b)Probability that a person who could give up her cell phone also could give up television is 0.65
(c) Probability that a person who could not give up a cell phone could give up television is 0.73
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Please answer this question. Thank you.
Answers
Explanation:
Identify the constants: 3m - 10 + 9t
Answers
Answer:
10 is the constant
Step-by-step explanation:
This is because when you simplify this expresion, the 10 does not change
Caculate the unit rate. Traveling 380 miles in 6
hours. How many miles per hour?
Answers
Answer: around 63.3
Step-by-step explanation: you need to find how much they traveled first (380) & then divided that by the other number (6). then you get somewhere around 63.3 . :))
Answer:
63.3
Step-by-step explanation:
A cube has a surface area of 486 inches square. Can the length of each side of the cube be 11 inches? Explain
Answers
Answer:
The volume of cube whose total surface area is 486 cm² is 729 cm³
Step-by-step explanation:
Winston collects rare coins. His most valuable coin is worth $280.00. The coin's value is
increasing by 5% each year. Winston wants to know how much more the coin will be
worth in 2 years' time.
10. In 1 year, the coin will be worth
11. In 2 years, the coin will be worth
12. In 2 years, the coin will be worth
more than it is worth now.
Answers
Answer:
12. in 2 years, the coin will be worth more than it is worth now
Find segment ET. Please and thank you
Answers
Answer:
x=9
Step-by-step explanation:
Use the intersecting chord theorem:
RE*ET = UE*ES
Substitute values
21 (2x+2) = 30 (x+5)
Expand:
42x+42 = 30x + 150
transpose and simplify
42x-30x = 150 - 42
12x = 108
x = 9
Part 1 (2 points) In which quarter(s) was the percentage change in velocity positive? Choose one or more: A. Q1 2020 B. Q22020 C. Q3 2020 Part 2 (2 points) Let's focus on the second quarter since the change in velocity is so dramatic. During that quarter, the CPI fell by 0.9%, real GDP fell by 9.0%, the money supply rose by 23%, and velocity changed by %. Give your answer to one decimal. Part 3 (2 points) Which of the following can explain such a large change in velocity that occurred during the second quarter? Choose one: A. People and banks were spending their money at faster rates. B. There was a substantial increase in the money supply. C. People and banks were holding on to their money longer. D. The inflation rate was negative.
Answers
Part 1: The percentage change in velocity was positive in Quarter 1 (Q1) 2020 and Quarter 3 (Q3) 2020. The percentage change in velocity was negative in Quarter 2 (Q2) 2020.
Part 2: Percentage change in velocity = -0.297
Part 3: C. People and banks were holding on to their money longer explain such a large change in velocity that occurred during the second quarter.
Part 2: During Q2, the percentage change in velocity can be calculated by using the following formula:
Velocity = (Nominal GDP / Real GDP) / (Money Supply / Nominal GDP)
Percentage change in velocity = (Velocity of 2020 - Velocity of 2019) / Velocity of 2019
Velocity of 2019 = (Nominal GDP of 2019 / Real GDP of 2019) / (Money Supply of 2019 / Nominal GDP of 2019) = Velocity of 2019 = (21,427.7 / 19,485.4) / (3,405.5 / 21,427.7)
Velocity of 2019 = 1.1290
Velocity of 2020 = (Nominal GDP of 2020 / Real GDP of 2020) / (Money Supply of 2020 / Nominal GDP of 2020)
Velocity of 2020 = (19,414.6 / 18,016.2) / (4,163.2 / 19,414.6)
Velocity of 2020 = 0.7940
Percentage change in velocity = (0.7940 - 1.1290) / 1.1290 = -0.297
Part 3: A substantial increase in the money supply can explain such a large change in velocity that occurred during Q2. When the money supply increased, people and banks had more money to spend and lend. However, the velocity decreased in Q2 despite a large increase in the money supply. This suggests that people and banks were holding on to their money longer and spending less during Q2. Therefore, option C is the correct answer.
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What is the linear function equation that best fits the data set? 1) y = -2x + 5. 2) y = 2x + 5. 3) y = -1/2x + 5. 4) y = 1/2x - 5.
Answers
Without specific information about the data set, it is not possible to determine which equation is the best fit.
To determine the linear function equation that best fits the data set, we need more information about the data set itself. Without the data points or any other details, we cannot accurately determine which linear function equation is the best fit.
However, I can provide a general explanation of the four options:
y = -2x + 5: This is a linear equation with a negative slope of -2. It represents a line that decreases as x increases. The y-intercept is 5.
y = 2x + 5: This is a linear equation with a positive slope of 2. It represents a line that increases as x increases. The y-intercept is 5.
y = -1/2x + 5: This is a linear equation with a negative slope of -1/2. It represents a line that decreases at a slower rate as x increases. The y-intercept is 5.
y = 1/2x - 5: This is a linear equation with a positive slope of 1/2. It represents a line that increases at a slower rate as x increases. The y-intercept is -5.
Without specific information about the data set, it is not possible to determine which equation is the best fit. The best fit would depend on how well the equation aligns with the actual data points.
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HELP PLEASEE 2 Aman is adding -17 + 9. He wants to write -17 as the sum of two numbers so that one of the numbers, when added to 9, will equal 0. How should Aman write -17 to complete this problem? Write integers in the blanksto show how Aman will solve this problem. -17 +9= + +9 -17 + 9 = __ +0
Answers
Answer:
-17+9= -8-9+9
-17+9= -8+0
Step-by-step explanation:
The nines cancel each other then we are left with -8+0
what is the cosine form of the function 10sin(wt 40)
Answers
The cosine form of the function 10sin(wt - 40) is 10cos(wt - 50).
The cosine form of the function 10sin(wt - 40) can be found using the identity sin(x - y) = sin(x)cos(y) - cos(x)sin(y).
By applying this identity to the given function, we can rewrite it in terms of cosine.
10sin(wt - 40) = 10(sin(wt)cos(40) - cos(wt)sin(40))
Now, we can use the fact that cos(90 - x) = sin(x) and sin(90 - x) = cos(x) to further simplify the expression.
10(sin(wt)cos(40) - cos(wt)sin(40)) = 10(sin(wt)sin(50) + cos(wt)cos(50))
Finally, we can use the identity cos(x + y) = cos(x)cos(y) - sin(x)sin(y) to rewrite the expression in terms of cosine.
10(sin(wt)sin(50) + cos(wt)cos(50)) = 10cos(wt - 50)
Therefore, the cosine form of the function 10sin(wt - 40) is 10cos(wt - 50).
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Which of the following functions is graphed below?
Please help me please and thank you
Answers
Answer: D
Step-by-step explanation:
y = x + 6 is a straight increasing line that intercepts the y axis at 6. x <= 1 indicated the closed circle and the left of that graph.
y = x^2 + 3 is an upward facing parabola where the minimum is 3. The x > 1 indicates the open circle and the right of that graph.
D shows the correct functions graphed
A child's parents deposit Rx into a savings account on the day of the child's birth to help towards her university education. The child will be able to withdraw regular half-yearly amounts from the savings account starting with a withdrawal of R12000 on her 19th birthday and ending with a final withdrawal on her 24th birthday. To keep up with inflation the withdrawals will need to increase at a rate of 6% p. each half-year from the second withdrawal onwards. If the savings account earns interest at a rate 8% p.a. compounded quarterly, then the value of Rx, to the nearest cent, that must be deposited initially into the savings account in order to fund the future growing withdrawals, is equal to: (Hint: Think carefully about where the Pv and Fv of the withdrawals is situated on the time line!) R120 468,80 R27 281,09 R26 746,17 R27 826,71 R25 427,36
Answers
The value of PV based on the question requirements is given as R27 281,09.
How to solveThere is a consistent increase in the withdrawals, with a growth rate of 6% per annum. The interest accrues at a yearly rate of 8%, and is compounded twice a year.
Having an interest rate that is calculated and added every three months. The accelerated growth of withdrawals surpasses the pace at which interest is accumulating, causing the eventual depletion of the savings account's value.
To calculate the value of the savings account, we need to use the future value of an annuity formula. The formula is:
\(FV = PV * [((1 + r)^n - (1 + g)^n) / (r - g)]\)
where:
FV is the future value of the annuity
PV is the present value of the annuity
r is the interest rate
n is the number of payments
g is the growth rate
In this case, the present value is the amount that needs to be deposited into the savings account, the interest rate is 8% p.a. compounded quarterly, the number of payments is 6 (24 / 4), and the growth rate is 6% p.a. compounded semi-annually.
Plugging these values into the formula, we get:
\(FV = PV * [((1 + r)^n - (1 + g)^n) / (r - g)]\\FV = PV * [((1 + 0.02)^6 - (1 + 0.03)^6) / (0.02 - 0.03)]\\FV = PV * 10.766\)
Solving for PV, we get:
PV = FV / 10.766
PV = 27 281,09
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What are the roots of the equation 2x^2 3x 5 0?
Answers
The roots of the equation 2x² - 3x - 5 = 0 are 5/2 and -1.
The quadratic formula is a formula that can be used to find the solutions (or roots) of a quadratic equation. For a quadratic equation written in the form ax² + bx + c = 0, where a, b, and c are constants, the quadratic formula is given by:
x = (-b ± √(b²- 4ac))/(2a)
Where x is the solution, a, b, and c are the coefficients of the equation.
Plug in the coefficients of the equation 2x² - 3x - 5 = 0 to the quadratic formula to find the roots.
x = (-b ± √(b²- 4ac))/(2a)
x = (3 ± √((-3)²- 4(2)(-5)))/(2)(2)
x = (3 ± 7)/4
x = 5/2 ; x = -1
Hence, the roots of the equation are 5/2 and -1.
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5. Marianne has a credit card with a line of credit at $15,000. She made the following purchases:
$1,374.90, $266.21, 39.46, and $903.01. What is Marianne's available credit?
Answers
Answer:
Available credit = $2,416.42
Step-by-step explanation:
$1,374.90
$266.21
39.46
$903.01
Sum = $2,583.58
$2,583.58 was spent. Subtract this from $5,000 to find Marianne's available credit.
$5,000
- $2,583.58
Available credit = $2,416.42
2.
What is the area of a triangle whose vertices are J(-2,1), K(4,3), and L(-2,-5) ?
(7 points)
a. What is the formula for the area of the triangle?
b.
Find the length of the base. Do not round to a decimal.
C.
Find the length of the height. Do not round to a decimal.
d. Find the area of the triangle.
Answers
Answer:
Area: T = 18
a. The triangle area using Heron's formula: T= sqrt(s(s−a)(s−b)(s−c) )
b. 2\(\sqrt{10}\)
c. h = 5.69
d. T = 18
Step-by-step explanation:
a. T= sqrt(s(s−a)(s−b)(s−c) )
T=sqrt( 11.16(11.16−10)(11.16−6)(11.16−6.32) )
T= sqrt(324 )
T =18
b. We compute the base from coordinates using the Pythagorean theorem
c= sqrt( ((−2−4)^2)+ ((1−3) ^2) )
c= sqrt(40) = 2sqrt(10)
c. Calculate the heights of the triangle from its area
Solve for x. -17=-5x+3(x-7) Simplify your answer as much as possible. x=?
Answers
Answer:
ANother filthy£50
Step-by-step explanation:
i think
mariah made a cylinder out of clay. (Question below) ( please help)
Answers
The number of square centimeters of the cylinder that Mariah paint in terms of π is 96π square centimeters.
How to calculate surface area of a cylinder?In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
72π = π(6)²h
Height, h = 2 cm.
In Mathematics and Geometry, the surface area (SA) of a cylinder can be calculated by using this mathematical equation (formula):
SA = 2πrh + 2πr²
Where:
h represents the height.r represents the radius.SA = 2π × 6 × 2 + 2π × 6²
SA = 24π + 72π
SA = 96π square centimeters.
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when the decision from an anova is to reject the null hypothesis and when the experiment has more than two treatment conditions, do we know where the significant difference is within our treatment conditions?
Answers
when an ANOVA test results in rejecting the null hypothesis and the experiment has more than two treatment conditions
When an ANOVA test results in rejecting the null hypothesis, it means that there is significant evidence to suggest that there are differences among the treatment conditions. However, it does not provide information about which specific treatment conditions are significantly different from one another. To determine where the significant difference lies, post-hoc tests can be performed. Post-hoc tests are used to compare all possible pairs of means to determine which pairs differ significantly. These tests can include Bonferroni, Tukey, and Scheffe's tests.
It is important to note that the use of post-hoc tests increases the likelihood of committing a Type 1 error, which occurs when the null hypothesis is incorrectly rejected. Therefore, it is important to adjust the level of significance when performing multiple tests to avoid this error.
These tests can help identify the specific treatment conditions that differ significantly from one another.
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A researcher randomly selects and interviews fifty male and fifty female teachers.
a. systematic
b. convenience
c. random
d. stratified
e. cluster
Answers
The sampling method described in the scenario is d. stratified sampling.
In stratified sampling, the population is divided into distinct subgroups or strata based on certain characteristics or variables. The researcher then randomly selects samples from each stratum in proportion to their representation in the population. This approach ensures that the sample is representative of the population's diversity.
In this case, the researcher has divided the population of teachers into two strata: male teachers and female teachers. By randomly selecting 50 male teachers and 50 female teachers, the researcher is ensuring that both genders are represented in the sample.
The researcher's intention is to have a sample that reflects the gender distribution of teachers in the population accurately. Therefore, stratified sampling is the appropriate method in this scenario.
Other sampling methods, such as systematic sampling, convenience sampling, random sampling, and cluster sampling, are not applicable because they do not specifically address the need to ensure proportional representation of genders in the sample.
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of the following functrons: Homeware obtain the Laplace inverse F(s) = s^2 +s +1/s^2 +4s +3
Answers
The Laplace inverse of the given function, F(s) = (s^2 + s + 1) / (s^2 + 4s + 3), can be obtained by performing partial fraction decomposition.
By factoring the denominator, we get F(s) = (s^2 + s + 1) / [(s + 1)(s + 3)]. Applying partial fraction decomposition, we express F(s) as A/(s + 1) + B/(s + 3), where A and B are constants.
By equating numerators, we find A = 1 and B = -1. Therefore, the Laplace inverse of F(s) is f(t) = e^(-t) - e^(-3t). This means that the original function F(s) corresponds to an inverse Laplace transform those results in a decaying exponential function with two different rates, indicating a system with distinct time constants.
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What is the value of x?
sin 25° = cos x°
(a) 50
(b) 155
(c) 75
(d) 25
(e) 65
Answers
Sin 25 = cos (90-25)
Sin 25 = cos 65
3(2x - 4) + (3x + 1) = 5x + 21 -(x +1)
Answers
Answer:
x=6.2
Step-by-step explanation:
3(2x - 4) + (3x + 1) = 5x + 21 -(x +1)
6x-12+3x+1=5x+21-x-1
combine like terms:
9x-11=4x+20
move variables to same side by sub 4x and add 11
5x=31
x=6.2
D
Question 1
1 pts
Complete the puzzle by finding the missing numbers.
Top Triangle:
Bottom Triangle:
Answers
Answer:
kantutin mo para ma buntis
When calculating a loan’s effective interest rate, if the nominal rate is 8.5%, what value of i do you plug into your equation? a. 8.5 b. 0.85 c. 0.085 d. 1.85
Answers
The value of interest rate should be 0.085.
We have given that the interest rate is 8.5% So we have given in percentage form but we use always decimal form of interest.
What is the decimal form of percentage?
To convert a percentage to a decimal, divide by 100.
So the decimal form of the 8.5% is calculated by
\(\frac{8.5}{100}=0.085\)
Therefore the option c is correct.
Therefore we use the interest rate is 0.085.
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Answer: C 0.085
Step-by-step explanation: