A particle moves in the xy-plane with position given by (x(t), y(t)) = (5 − 2t, t2 − 3) at time t. In which direction is the particle moving as it passes through the point (3, −2)? Describe the direction in terms of up/down and left/right.
Answers
The velocity vector (-2, -2) points in the direction of the line joining the point (7, -4) to the point (5, -3).
How to determine the direction in which the particle is moving as it passes through the point (3, -2)?To determine the direction in which the particle is moving as it passes through the point (3, -2), we need to find the velocity vector of the particle at that point.
The velocity vector is given by the derivative of the position vector with respect to time:
v(t) = (x'(t), y'(t))
where x'(t) and y'(t) are the derivatives of x(t) and y(t) with respect to t, respectively.
Taking the derivatives of x(t) and y(t), we get:
x'(t) = -2
y'(t) = 2t
So the velocity vector at time t is:
v(t) = (-2, 2t)
To find the velocity vector at the point (3, -2), we substitute t = -1 into the expressions for x(t) and y(t), since the particle passes through the point (3, -2) at time t = -1:
x(-1) = 5 - 2(-1) = 7
y(-1) = (-1)2 - 3 = -4
So the particle is at position (7, -4) when it passes through the point (3, -2).
Substituting t = -1 into the expressions for x'(t) and y'(t), we get:
x'(-1) = -2
y'(-1) = 2(-1) = -2
So the velocity vector at the point (7, -4) is:
v(-1) = (-2, -2)
The velocity vector (-2, -2) points in the direction of the line joining the point (7, -4) to the point (5, -3), which is to the left and slightly down from the point (7, -4). Therefore, the particle is moving in a direction that is slightly to the left and slightly down as it passes through the point (3, -2).
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Related Questions
Evaluate C(9, 3). a)504 b)84 c)60480 d)5040
Answers
Answer:
b
Step-by-step explanation:
Evaluate using the definition
n\(C_{r}\) = \(\frac{n!}{r!(n-r)!}\)
where n ! = n(n - 1)(n - 2)(n - 3)..... × 3 × 2 × 1
Given
9\(C_{3}\)
= \(\frac{9!}{3!(9-3)!}\)
= \(\frac{9.8.7.6.5.4.3.2.2.1}{3!.6!}\)
= \(\frac{9.8.7.6.5.4.3.2.1}{3.2.1(6.5.4.3.2.1)}\)
Cancel 6.5.4.3.2.1 on numerator and denominator, leaving
= \(\frac{9.8.7}{3.2.1}\)
= \(\frac{504}{6}\)
= 84 → b
Here are a few pairs of positive numbers whose sum is 50.
a. Find the product of each pair of numbers.
b. Find a pair of numbers that have a sum of 50
and will produce the largest possible product.
First
Number
1
2
10
Second
Number
49
48
40
c. Explain how you determined which pair of numbers have the largest
product.
tor ic
Product
Answers
Answer:
a. The product of each pair of numbers is:
1 x 49 = 49
2 x 48 = 96
10 x 40 = 400
b. The pair of numbers that will produce the largest possible product is when the two numbers are equal to half of the sum, which is 25. So the pair of numbers is 25 and 25, and the product is 25 x 25 = 625.
c. We can determine the pair of numbers that have the largest product by using the following reasoning: For any two numbers whose sum is fixed, their product is maximized when the two numbers are as close together as possible. This is because the product of two numbers that are far apart is always smaller than the product of two numbers that are closer together and have the same sum. In this case, the sum is 50, so the two numbers that are closest together and add up to 50 are 25 and 25, which give the largest possible product.
help plsssss i dont understand
Answers
Answer:
f(x)= 3x+2
Step-by-step explanation:
math
:)
Kevin is 333 years older than Daniel. Two years ago, Kevin was 444 times as old as Daniel.
Let k be Kevin's age and let d be Daniel's age.
Which system of equations represents this situation?
Answers
Answer:
k = d + 3
k - 2 = 4( d - 2 )
Step-by-step explanation:
Let k be Kevin's age and Let d be Daniel's age.
Given : Kevin is 3 years older than Daniel.
i.e. Age of Kelvin = Age of Daniel+ 3
i.e. In terms of variables , k= d+3 (1)
Two years ago,
Age of Kelvin = k-2
Age of Daniel = d-2
Since Two years ago ,Kevin was 4 times as old as Daniel.
i.e. In terms of variables : k -2 = 4 x (d-2)
k-2=4(d-2) (2)
From (1) and (2) the system of equations represents this situation are
k = d + 3
k - 2 = 4 ( d - 2)
j(x) = 3 - x;j (x) = -5
Answers
Answer:
x = 8, j = -0.625
Step-by-step explanation:
To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.
j(x) = 3 - x; j (x) = -5
j(8) = 3 - 8; j (x) = -5
To find the missing factor, divide the product by the given factor
(-5)/8 = -0.625
-0.625(8) = -5
Therefore, the answer is x = 8 and j = -0.625.
The function g(t) = -16t2 + vt + h represents the height of an object, g, in feet above the ground in relation to the time, t, in seconds, since the object was thrown into the air with an initial velocity of v feet per second at an initial velocity of v feet per second at an initial height of h feet.
A model rocket is launched off the ground at an initial velocity of 80 feet per second.
Part A: Write a function that can be used to describe the flight of the model rocket.
A. g(t) = -16t^2 + 80t + 80
B. g(t) = -16t^2 + 80
C. g(t) = -16t^2 + t + 80
D. g(t) = -16t^2 + 80t
Answers
Select the correct answer.
After four years of college, Erica has to start paying off all her student loans. Her first payment is due at the end of this month. Her bank told her
that she has 10 years to pay off all of her loans, and that starting this month the loans will be compounded monthly at a fixed annual rate of
9.4%.
Erica currently has a total of $29.158.00 in student loans. Using the formula, what is Erica's approximate monthly payment?
Fpli)
P =
1- (1 + i)-
ОА
OB
Erica's approximate monthly payment will be $370.39.
Erica's approximate monthly payment will be $254.94.
Erica's approximate monthly payment will be $375.70.
Erica's approximate monthly payment will be $2.740.10.
Oc.
D.
Answers
Answer:
its $375.70
Step-by-step explanation:
i guessed and got it right. good luck guys. love u. remeber to eat n drink water and try to spend some time outside if you can! i know its hard rn but we can do it! im proud of u all
The value of Erica's approximate monthly payment is $375.70. The correct option is C .
What is the meaning of Rate of Interest ?Rate of Interest is the rate at which a loan is borrowed or the rate at which an investment gives return .
It is given that
Student Loan Total = $29,158
Rate of Interest = 9.4 %
Time Period = 10 years
The monthly payment is given by
\(\rm \dfrac{F p(i) }{ ( 1 - ( 1 + i )^{-n})}\)
Substituting the values in the equation
\(\rm = \dfrac{29158* (0.094/12) }{ ( 1 - ( 1 + (0.094/12) )^{-12*10})}\)
= $ 375.70
Therefore,The value of Erica's approximate monthly payment is $375.70. The correct option is C.
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Identify the domain of the function shown in the graph.
A. -5<x<5
B. 0<x<5
C. x is all real numbers.
D. x > 0
Answers
Answer:
The answer is A choice.
Explanation:
By looking at the graph, we notice that at the left side, the domain/x-value stops at -5 and 5.
Thus, the domain is at the left end side to the right end side.
The domain stops at -5 on the left side and 5 on the right side. Thus the answer is
-5 < x < 5.
The A choice.
Understanding
The domain of a function is basically all the values where x is defined, and by defined, it means it has a y value corresponding to it. In this graph, x is defined from -5 to 5. If you look outside this range of numbers (from -5 to 5 on the x-axis) you will not find any y values for them. We can easily say the solution is A.
Solution:
[A] \(-5<x<5\)
Note: From what I see from the picture -5 and 5 are included in the domain, either the question is incorrectly written, or the picture isn't clear enough. If so, the answer should be \(-5\leq x\leq 5\).
x^2-8x=-15 solve by completing the square
Answers
Answer:
Step-by-step explanation:
I don’t get this problem at all-
Answers
Answer:
2nd option
Step-by-step explanation:
If AB is a tangent to the circle then ∠ B is right angle
Using the converse of Pythagoras' identity.
If the square of the longest side is equal to the sum of the squares on the other 2 sides, then the triangle is right
longest side = 52 and 52² = 2704
48² + (10 + 10)² = 48² + 20² = 2304 + 400 = 2704
Then AB is a tangent to the circle since ∠ B is a right angle
Evaluate $4a$ when $a=7$
Answers
Answer: 4*7=28
Step-by-step explanation: a is 7
At what x-value are the equations equal?
Answers
Answer:
x=2 is the answer to your question
Please I beg you helpppp
Answers
What is the definition of the sine ratio in a right triangle?.
Answers
The trigonometric ratio sine compares the lengths of the right triangle's two sides. Sin, though commonly abbreviated to sin, is actually pronounced sine.
If you know at least one side of the triangle and one of the acute angles, you can use this function to calculate the length of the side.The trigonometric ratio sine compares the lengths of the right triangle's two sides. Sin, though commonly abbreviated to sin, is actually pronounced sine. If you know at least one side of the triangle and one of the acute angles, you can use this function to calculate the length of the side. In a nutshell, the sine, cosine, and tangent ratios are the three basic trig ratios.To learn more about the sine triangle here
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Marilyn wants to use a non-price competitive marketing strategy to gain more customers. Which of the following might she use?
Answers
As Marilyn wants to use a non-price competitive marketing strategy to gain more customers, the strategy that she might use is offering a promotion.
What is a Non-price competition in marketing?In marketing, the non-price competition refers to a marketing strategy in which a firm tries to distinguish its product or service from competing products on the basis of attributes like design and workmanship.
This competition most often occurs in an imperfectly competitive markets because it exists between producers that sell goods and services at same prices but competes to increase their respective market shares through different non-price measures such as marketing schemes and greater quality.
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Prove that he number of spanning trees of a connected graph is the product of the number of spanning trees of each of its blocks.
Answers
The number of spanning trees of a connected graph can be proven to be the product of the number of spanning trees of each of its blocks.
Here are the steps-
1. Consider a connected graph G with blocks B1, B2, ..., Bk. Each block is a maximal connected subgraph with no cut-vertex.
2. The number of spanning trees of G can be denoted as T(G), and the number of spanning trees of each block Bi can be denoted as T(Bi).
3. To prove the given statement, we need to show that\(T(G) = T(B1) * T(B2) * ... * T(Bk).\)
4. We can start by considering a single block B1. Since B1 is a maximal connected subgraph with no cut-vertex, it is a connected graph on its own.
5. The number of spanning trees of B1, T(B1), can be calculated using any method such as Kirchhoff's theorem or counting the number of spanning trees directly.
6. Now, consider the original graph G. We can remove block B1 from G, which leaves us with a graph G' that consists of the remaining blocks B2, B3, ..., Bk.
7. G' is still a connected graph, but it may have cut-vertices. However, the removal of B1 does not affect the connectivity between the other blocks, as each block is a maximal connected subgraph.
8. The number of spanning trees of G', denoted as T(G'), can be calculated using the same method as step 5.
9. Since G' is the remaining part of G after removing B1, the number of spanning trees of G can be expressed as T(G) = T(B1) * T(G').
10. We can repeat this process for the remaining blocks B2, B3, ..., Bk. For each block Bi, we remove it from G and calculate the number of spanning trees of the remaining graph.
11. By repeating steps 6-10 for all blocks, we can express the number of spanning trees of G as-
\(T(G) = T(B1) * T(G')\)
\(= T(B1) * T(B2) * T(G'')\)
= ...
\(= T(B1) * T(B2) * ... * T(Bk).\)
12. Therefore, we have proved that the number of spanning trees of a connected graph G is the product of the number of spanning trees of each of its blocks.
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1. through (0,-1) slope= -1
2. through (-5,4) slope= -2
I don't know how to solve them I need help ASAP!
Answers
Answer:
Step-by-step explanation:
I will give you equations in slope intercept form
1.
y=-x-1
2.
y= -2x - 6
The coefficient of determination, r 2
, indicates A) how closely the data fits a defined curve. B) the sum of the residuals from each data point. C) the linear relationship between two variables. D) the slope of the line of best fit
Answers
The coefficient of determination, r², indicates the linear relationship between two variables.
The coefficient of determination, denoted as r², is a statistical measure that represents the proportion of the variance in the dependent variable (output) that can be explained by the independent variable (input) in a linear regression model. It is a value between 0 and 1.
R^2 is used to assess the goodness of fit of a regression model. It provides a measure of how well the data points fit the regression line. Specifically, r² indicates the proportion of the total variation in the dependent variable that can be accounted for by the variation in the independent variable(s).
Option C is the correct answer because r² is a measure of the linear relationship between two variables. A higher r² value indicates a stronger linear relationship, meaning that the independent variable(s) can better explain the variability in the dependent variable.
Options A, B, and D are not accurate descriptions of the coefficient of determination. While r² does indicate how well the data fits a defined curve (option A), it is specifically related to the linear fit. It is not related to the sum of residuals (option B) or the slope of the line of best fit (option D).
In summary, the coefficient of determination, r², is a valuable measure in regression analysis that quantifies the proportion of the dependent variable's variability explained by the independent variable(s), indicating the strength of the linear relationship between the variables.
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A random variable x is uniformly distributed over the interval [4, 8]. Find the mean, variance, and standard deviation of x. (Note: Remember that standard deviation is the square root of variance
Answers
The mean is 6
The variance is 4/3
The standard deviation is approximately 1.15.
How we Calculate the mean?
The mean (μ) of a uniformly distributed random variable is the average of the endpoints of the interval. So, in this case:
μ = (4 + 8) / 2 = 12 / 2 = 6
How we Calculate the variance?
The variance (σ²) of a uniformly distributed random variable is given by the formula:
σ² = (b - a)² / 12
where a and b are the endpoints of the interval. In this case:
σ² = (8 - 4)² / 12 = 4² / 12 = 16 / 12 = 4 / 3
How we Calculate the standard deviation?
The standard deviation (σ) is the square root of the variance. So, in this case:
σ = √(4 / 3) ≈ 1.15
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Please help me the picture is above, I’ll mark as brainliest.
Answers
if she sells p phones and a accessories = 8p+3.50a
2(3w-6)=5w+8
asap plz
Answers
Answer:
w = 20
Step-by-step explanation:
2 (3w - 6) = 5w + 8
distribute the 2
6w - 12 = 5w + 8
subtract 5w from both sides
w - 12 = 8
add 12 to both sides
w = 20
Answer:
The value of w is 20.
Step-by-step explanation:
Solution :
\({\longmapsto{\tt{2(3w - 6)=5w + 8}}}\)
\({\longmapsto{\tt{(3w \times 2 )- (6 \times 2)=5w + 8}}}\)
\({\longmapsto{\tt{(6w)- (12)=5w + 8}}}\)
\({\longmapsto{\tt{6w - 12=5w + 8}}}\)
\({\longmapsto{\tt{6w - 5w = 8 + 12}}}\)
\({\longmapsto{\tt{w = 20}}}\)
Hence, the value of w is 20.
\(\rule{300}{2.5}\)
Point b is located at (-6,-6). on a coordinate grid. point b is translated 5 units up and 12 units to the right to create b prime.. what is the distance between point b and point b prime. in units?
Answers
The distance between point B and point B prime is 13 units.
Distance Formula: Let (x₁, y₁) and (x₂, y₂) be two points in the coordinate plane.
Then the distance between these points is given by the formula:
d = √[(x₂ − x₁)² + (y₂ − y₁)²]
So, let's begin by finding the coordinates of point B prime.
Since point B is translated 5 units up and 12 units to the right to create B prime, the coordinates of B prime are:
(x,y)(x,y)=(−6+12,−6+5)=(6,-1)
Using the distance formula to find the distance between the points, we have:
d = √[(x₂ − x₁)² + (y₂ − y₁)²]d
= √[(6 − (-6))² + ((-1) − (-6))²]d
= √[(6 + 6)² + (5)²]d
= √[12² + 5²]d
= √(144 + 25)d
= √169d
= 13
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please help______________
Answers
Answer:
49 cm squared. Find the area of all then add.
Which of the following is not included in the cost of merchandise inventory? O Purchase discounts. O Purchase returns and allowances. O Purchase price of the inventory. O Freight costs paid by the seller. O Freight costs paid by the buyer. 4 pts 0 Question 2 Sunshine Cleaning purchased $3,500 worth of merchandise. The seller offered a 2% cash discount. Transportation costs for the buyer were an additional $310. The company returned $240 worth of merchandise and then paid the invoice within the discount period. The total cost of this merchandise is: O $3.570.00. O $3,500.00 O $3,332.00 O $3,430.00. $3,504.80 Question 5 A company has not sales of $759.300 and cost of goods sold of $548.300. Its not income is $10.280. The company's gross margin and operating expenses, respectively, are: O $211.000 and $230,750 $739.550 and $191,720 O $529,020 and $230.750 O $211.000 and $191,720 $230,750 and $529,020 4 pts D D Question 5 A company has not sales of $750,300 and cost of goods sold of $548,300. Its not income is $10.280 The company's groas margin and operating expenses, respectively, arm O $211,000 and $230,750 O $739,550 and $191,720 $529,020 and $230,750 O $211.000 and $191,720 O $230.750 and $529,020 Question 6 Sales less sales discounts, less sales returns and allowances equals: Cost of Goods Sold Net Income O Net Sales O Gross Profit 4 pts 4 pts Goods in transit are included in a purchaser's inventory: O At any time during transit. O After the half-way point between the buyer and seller, When the supplier is responsible for freight charges. When the goods are shipped FOB shipping point. OIf the goods are shipped FOB destination. Question 11 The inventory costing method that smooths out erratic changes in costs is: O LCM. O FIFO. OLIFO. O Specific Identification. O Weighted average. 4 t ne 0 Question 12 Krusty Krab has the following products in its ending inventory Compute lower of cost or market for inventory. applied separately to each product Inventory by Product Product Quantity Cost per Unit 500 $ 500 $ 30 600 Scuba Masks Scuba Sults O $265,000 O $290,000. O $250,000 $268,000 O $275,000. Question 13 Market per Unit $ 550 $ 25 If equity is $368,000 and liabilities are $186,000, then assets equal: O $554,000. $922,000. $368,000. $186,000. O $182,000. 2 pts
Answers
Question 1: The item not included in the cost of merchandise inventory is "Purchase discounts."
2: The total cost of the merchandise is $3,332.00.
5: The company's gross margin and operating expenses, are $211,000 and $191,720.
What is the cost of merchandise inventory?Merchandise inventory expenses normally consist of the price paid for the inventory, deductions from the purchase price resulting from purchase returns and allowances, and freight expenses paid by the purchaser.
Although purchase discounts reduce the cost of merchandise inventory, they are not considered part of it. Instead, they are treated as a distinct discount in the accounting records.
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2 second power 2 * 9 / 3
Answers
Answer:
12
Step-by-step explanation:
2²
=
2+2
=
4
4×9
=
36
36÷3
=
12
The triangle on the right is scaled copy of the triangle on the left identified the scale factor
Answers
Answer:
is there supposed to be a picture with it? i can't solve it without more information. sorry
The measures of three angles of a triangle are 3x, x + 30, and x + 40. Find the measure of all three angles.
Answers
Answer: 66 degrees for 1st angle
52 degrees for 2nd angle
62 degrees for 3rd angle
Step-by-step explanation:
3x+(x + 30)+(x + 40)=180
3x+x+30+x+40=180
3x+x+x+30+40=180
5x+70=180
5x=110
x=22
3x=
3(22)=66 degrees for 1st angle
x+30=
22+30=52 degrees for 2nd angle
x+40=
22+40=62 degrees for 3rd angle
Answer:
3x=66
x+30=52
x+40=62
66,42,62
Step-by-step explanation:
(3x)+(x+30)+(x+40)=180
5x+70=180
5x=110
x=22
3x=66
x+30=52
x+40=62
Assessing the regression model on data other than the sample data that was used to generate the model is known as _____. Group of answer choices approximation cross-validation graphical validation postulation
Answers
Assessing the regression model on data other than the sample data that was used to generate the model is known as cross-validation
How to complete the blank?From the question, we have the following highlights:
Sample data, not usedThe model is a regression modelWhen the sample data is not used in a regression model, then the term is known as cross-validation.
Hence, the term that completes blank is cross-validation
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Rashid solves the following system of equations using the elimination method.
6x−5y=−31
5x+3y=10
What value does he correctly determine for x?
Enter you answer in the box. x =
Answers
Answer:
X = -1 & and for some additional information Y = -5
Step-by-step explanation:
6 x (-1) = (-6)
5 x (-5) = (-25)
(-6) - (-25) = (-31)
_____________
5 x (-1) = (-5)
3 x (-5) = (-15)
(-5) + (-15) = 10
Answer:
x = -1
Step-by-step explanation:
Rashid may have used elimination to solve the problem, but we can use any method we like to find the correct value of x. One method we like is graphing. The attached graph shows the solution is (x, y) = (-1, 5), so we know Rashid found ...
x = -1
__
If we go down Rashid's path, we multiply the first equation by 3 and add that to the second equation multiplied by 5. (This choice of multipliers results in a positive coefficient for x.)
3(6x -5y) +5(5x +3y) = 3(-31) +5(10)
18x -15y +25x +15y = -93 +50 . . . . . . eliminate parentheses
43x = -43 . . . . . . . . . . . . . . . . . simplify
x = -1 . . . . . . . . . . . . . . . . . divide by 43
Four minus n
(choose )
3n + 7
4-n
3n - 7
n-4
Answers
Answer:
the answer is b 4-n. Hope this helps
Answer:
the second one (4-n).
Step-by-step explanation:
lol