Find the tangential and normal components of the acceleration vector.
Answers
The tangential component of the acceleration vector represents the change in speed or direction along the path. The normal component of the acceleration vector represents the change in direction perpendicular to the path.
To find the tangential and normal components of the acceleration vector, we need the velocity vector and the curvature of the path. The tangential component of acceleration (at) represents the change in speed or direction along the path. It is given by the derivative of the velocity vector with respect to time. The normal component of acceleration (an) represents the change in direction perpendicular to the path. It is given by the curvature of the path multiplied by the square of the speed.
In mathematical terms:
at = dV/dt
an = (V^2) / R
where:
V is the velocity vector
t is time
R is the radius of curvature of the path.
The tangential component of the acceleration vector represents the change in speed or direction along the path. The normal component of the acceleration vector represents the change in direction perpendicular to the path.
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Related Questions
need help with algebra
Answers
Answer:
a): surjective (only)
b): injective (only)
c): bijective (both injective and surjective)
Step-by-step explanation:
Given the functions F(x)=x(x-4)⁴, G(x)=1/x, and H(x)=x³, you want to know whether each is injective, surjective, and/or bijective.
Injective
A function is injective if its graph passes the horizontal line test. Each unique output must correspond to exactly one unique input.
Surjective
In order to determine whether a function is surjective, you must first define its "codomain," the set of all possible output values of interest. If there is an input function value corresponding to every value in the codomain, the function is surjective.
For example, the floor function produces only integer output values. It is surjective when the codomain is defined as Integers (ℤ), but not when the codomain is defined as Real numbers (ℝ).
Bijective
A function is bijective if it is both injective and surjective.
a): F(x) = x(x -4)⁴The graph in the second attachment show this polynomial function does not pass the horizontal line test: a horizontal line may intersect the graph in more than one place. It is an odd-degree polynomial function, so can produce every possible value in ℝ, the set of real numbers. We can say ...
F(x) is not injective, is surjective on ℝ.
b): G(x) = 1/xThe function passes the horizontal line test, but cannot produce the output value 0. We can say ...
G(x) is injective, not surjective on ℝ.
c): H(x) = x³The function is a non-decreasing odd-degree polynomial function, so it passes the horizontal line test and can produce every possible value in ℝ.
H(x) is injective, surjective, and bijective.
__
Additional comment
We are familiar with the terms "domain" and "range" to describe the sets of input and output values for which a function is defined.
The "codomain" generally includes the range, along with any other output values that we may consider as possible outputs (or that we don't specifically exclude). When we say the range of G(x) is "ℝ except y=0", that function will be surjective on a codomain of {ℝ except 0}, but not on a codomain of ℝ.
Often, the only reason the codomain is different from the range is that we're lazy in describing the codomain. For example, it is easier to say "ℝ" than to say "ℝ except 0". It is easier to say "Natural numbers" than to say "even Natural numbers."
Mr. Green washed 3 8 of his laundry. His son washed 1 3 of it. Who washed most of the laundry? How much of the laundry still needs to be washed?
Answers
Answer:
Mr.Green washed the most laundry with .375 of it done
what remains is .291
Step-by-step explanation:
3/8 or 3 divided by 8 is .375
1/3= .3333 repeating or rounded to .334
.375+.334= .709
1.000 - .709= .291
hopes this helps
Answer:
1. Mr. Green washed more laundry 2. 7/24 of the laundry still needs to be washed
Step-by-step explanation:
If you find a common denominator you can compare them. I used the common denomiator of 24. Next, you need to change both fractions so that they have the same denominator. To do that we have to multiply both the numerator and denominator of 3/8 by 3. When you do that, you end up with 9/24. Then you have to do the same for 1/3 but this time multiplying the numerator and the denominator by 8. That will leave us with 9/24 and 8/24 which proves that Mr. Green did more laundry.
For the second question, we will need to add the two amounts of laundry already washed and then find out how much remains from there. We can use the fractions that already have a common denominator from the explanation above. Now we have to add 9/24 and 8/24 together. Once we add them together, we will get 17/24 which is how much laundry is already done. Now, we need to take the remaining amount from 17/24 which is 7/24, and that represents how much laundry sitll needs to be washed.
(sorry if this is confusing but I hope it helped!)
Solve for x. -- 2x + 6 = 30 - 6x -6 6 -8 8
Answers
Answer:
6
Step-by-step explanation:
\(-2x+6=30-6x\\\\4x+6=30\\\\4x=24\\\\x=6\)
1. add 6x to both sides
2. subtract 6 from both sides
3. divide both sides by 4
\(\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}\)
-2x+6=30-6x-2x+6x=30-6(-2+6)x=244x=24\(\sf{x=\dfrac{24}{4} }\) x=6Whats the width of a rectangle if the perimeter is 130 ft and the length is 45 but there's no area
Answers
Answer:
Step-by-step explanation:
I hope this helps
Suppose the runtime efficiency of an algorithm is presented by the function f(n)=10n+10 2
. Which of the following statements are true? Indicate every statement that is true. A. The algorithm is O(nlogn) B. The algorithm is O(n) and O(logn). C. The algorithm is O(logn) and θ(n). D. The algorithm is Ω(n) and Ω(logn). E. All the options above are false.
Answers
The given function, \(f(n) = 10n + 10^2\), represents the runtime efficiency of an algorithm. To determine the algorithm's time complexity, we need to consider the dominant term or the highest order term in the function.
In this case, the dominant term is 10n, which represents a linear growth rate. As n increases, the runtime of the algorithm grows linearly. Therefore, the correct statement would be that the algorithm is O(n), indicating that its runtime is bounded by a linear function.
The other options mentioned in the statements are incorrect. The function \(f(n) = 10n + 10^2\) does not have a logarithmic term (logn) or a growth rate that matches any of the mentioned complexities (O(nlogn), O(logn), θ(n), Ω(n), Ω(logn)).
Hence, the correct answer is that all the options above are false. The algorithm's time complexity can be described as O(n) based on the given function.
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guys i really need helpppp plssss
Answers
2x = 18
————
2
leaving you with x=9.
im not sure, i hope that helps, it’s hard to show and explain through this.
Explanation: Divide each term in 2x = 18 by 2. Then cancel the common factor of 2. Then you divide 18 by 2. Finally you have your answer.
by observing a set of data values, thomas used a calculator for the weight (in pounds) and predicted the number of calories burned per minute to get an equation for the least-squares line: ŷ
Answers
A person weighing 173 pounds can burn 10.7 calories per minute.
The given equation is ŷ=2.2+0.05x.
To solve this question, we can use the equation given, ŷ=2.2+0.05x. We can insert the known weight value, 173 pounds, to calculate the anticipated calories burned per minute.
y = 2.2 + 0.05x
y = 2.2 + 0.05 × 173
y = 10.7
Therefore, a person weighing 173 pounds can burn 10.7 calories per minute.
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"Your question is incomplete, probably the complete question/missing part is:"
By observing a set of data values, Thomas used a calculator for the weight (in pounds) and predicted the number of calories burned per minute to get an equation for the least-squares line: ŷ=2.2+0.05x
Based on the information gathered by Thomas, select the statement that is true.
a) A person weighing 149 pounds can burn 9.8 calories per minute.
b) A person weighing 134 pounds can burn 8.9 calories per minute.
c) A person weighing 125 pounds can burn 8.3 calories per minute.
d) A person weighing 173 pounds can burn 10.7 calories per minute.
Answer:
A person weighing 134 pounds can burn 8.9 calories a minute.
Step-by-step explanation:
derive the validity of universal modus tollens from the validity of universal instantiation and modus tollens.
Answers
The validity of Universal Modus Tollens relies on the validity of Universal Instantiation and Modus Tollens, which are well-established logical rules.
The validity of the Universal Modus Tollens can be derived from the validity of Universal Instantiation and Modus Tollens. Let's examine the logic behind each of these rules and how they lead to the validity of Universal Modus Tollens.
Universal Instantiation (UI): This rule allows us to infer a specific instance of a universally quantified statement. For example, if we have the universal statement "For all x, if P(x) then Q(x)," we can instantiate it to a particular instance by replacing the variable x with a specific element, resulting in "If P(a) then Q(a)." This rule is valid and widely accepted in formal logic.
Modus Tollens (MT): Modus Tollens is a deductive rule of inference used to infer the negation of the consequent of a conditional statement. It states that if we have a conditional statement "If P, then Q," and we know the negation of Q (¬Q), we can conclude the negation of P (¬P). This rule is also valid and widely accepted.
Now, let's demonstrate how the validity of Universal Instantiation and Modus Tollens leads to the validity of Universal Modus Tollens:
Universal Modus Tollens (UMT): If we have the universally quantified statement "For all x, if P(x) then Q(x)," and we know the negation of Q for a specific instance, ¬Q(a), then we can conclude the negation of P for that same instance, ¬P(a).
To derive UMT, we can apply the following steps:
Apply Universal Instantiation (UI) to the universally quantified statement, replacing x with a specific element, let's say a. This gives us "If P(a) then Q(a)."
Assume the negation of Q for that specific instance, ¬Q(a).
Apply Modus Tollens (MT) to the conditional statement "If P(a) then Q(a)" and the negation of Q, which allows us to conclude the negation of P, ¬P(a).
Thus, by using Universal Instantiation to instantiate a universally quantified statement, and then applying Modus Tollens to the instantiated conditional statement and the negation of the consequent, we can derive Universal Modus Tollens.
It's important to note that the validity of Universal Modus Tollens relies on the validity of Universal Instantiation and Modus Tollens, which are well-established logical rules.
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Solve the Inequality
9w-4w+6≥1+5w
Answers
Answer: All real numbers :)
Choose the graph of the following function:
f(x) = sin(1/2= x)
Answers
The graph of the function f(x) = sin(1/2x) is attached accordingly. It is to be noted that it is erroneous to include an equal sign within the parenthesis, that is sin(1/2= x). Hence the correct function is f(x) = sin(1/2x).
What is a graphed function?A graphed function simply means drawing a graph that is representative of a mathematical function.
What is the interpretation of the graphed function?The task of the mathematician here is to first redefine the formula such that one can identify the:
AmplitudePeriodPhase shift; andVertical shift.The form to be used is:
a sin(bx - c) + d where
a = 1
b= 1/2
c =0
d =0.
What is the Amplitude?The absolute value of the amplitude |a| is given as
Amplitude = 1
Using 2π/ |b|
Lets substitute b with 1/2
thus we have
2π/ |1/2|
= 4π
How to solve for the Phase shift?With the aid of the formula, c/b
Given that c = 0
Hence, c/b which is 0/1/2
Phase shift = 0
How to solve for vertical shift?The vertical shift is simply given as zero (0)
Thus all the properties of the trigonometric function are:
Amplitude = 1
Period = 4π
Phase Shift = 0
Vertical Shift = 0
See the attached graph.
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I need help again This does not make sense-
Answers
Answer:
Step-by-step explanation:
Two corresponding angles when the lines are parallel, are situated in the same relative position. That really is a mouthful. Look at angle 7. It is on the lower left of the intersection where 4 angles meet. The 4 angles are 5,6,7,8.
Now move up to the meeting place of the 4 other angles (1,2,3,4). Which one is on the lower left? Isn't it angle 3. If you agree, then the answer is <3
Which problem could be solved with the expression 3 x (5 - 2) - 1?
Choose 1 answer:
Stephanie had 3 apples. She then found 5 more but immediately ate 2 of them. Several
minutes later, she ate 1 more. How many apples does she still have?
Orlando had 5 action figures but decided to give 2 of them to his younger brother. His parents
were so impressed with his kindness that they tripled the action figures he had left. Since he
got so many new action figures, he then gave 1 more to his brother. How many action figures
does he now have?
Of Ralph's 5 toy cars, he gave 2 to his sister. After that, he found 1 more toy car. Then, he
decided to go to the store and triple his number of cars. How many toy cars does Ralph have
now?
Answers
Lauren has a choice of two health care plans. Option A charges $500 for the year and $65 each time she visits the doctor. Option B charges only $300 for the year but $95 for each doctor's visit. How many visits will she have to make in a year for Option A to be the better deal?
part A Define your variable
part B Write an inequality to represent the situation.
part C Solve the inequality, showing all work in the box below. Write your answer in a complete sentence.
Answers
Answer:
I don't know how to answer all the different parts but Lauren would have to have 6 doctor visits to make Option A the better deal.
Step-by-step explanation:
The table of values represents a quadratic function f(x).
x f(x)
−8 7
−7 2
−6 −1
−5 −2
−4 −1
−3 2
−2 7
−1 14
0 23
What is the equation of f(x)?
Answers
The equation of f(x) is f(x) = -6x^2 - 3x + 23.To find the equation of the quadratic function f(x) using the given table of values, we need to determine the coefficients of the quadratic equation in the form of f(x) = ax^2 + bx + c.
We can start by analyzing the pattern of the y-values (f(x)) corresponding to the x-values. Looking at the table, we notice that the y-values increase and then decrease, indicating that the quadratic function has a concave-down shape.
Next, we observe that when x = 0, f(x) = 23. This gives us the value of c, which is the constant term in the quadratic equation. Therefore, c = 23.To find the other coefficients, we can choose any two points from the table and substitute them into the general quadratic equation. Let's choose (-3, 2) and (1, 14).Substituting (-3, 2):
2 = a(-3)^2 + b(-3) + 23
9a - 3b + 23 = 2Substituting (1, 14):
14 = a(1)^2 + b(1) + 23
a + b + 23 = 14Simplifying both equations, we have:
9a - 3b = -21 ---(1)
a + b = -9 ---(2)
Solving equations (1) and (2), we find a = -6 and b = -3.
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5(x+1)-x=3(x-1)+7no solution one solution and what does x= or all real numbers are solutions
Answers
The equation 5(x + 1) - x = 3(x - 1) + 7 has one solution which is x = -1.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
The given equation is,
5(x + 1) - x = 3(x - 1) + 7
Using the distributive property,
5(x + 1) = 5x + 5 and 3(x - 1) = 3x - 3
Substituting,
5x + 5 - x = 3x - 3 + 7
(5x - x) + 5 = 3x + (-3 + 7)
4x + 5 = 3x + 4
4x - 3x = 4 - 5
x = -1
Hence the solution of the given equation is -1.
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In △ABD, altitude AC¯¯¯¯¯ intersects the right angle of triangle ABD at vertex A. BC=4.2 in. and CD=9.6 in..
What is the length of AC¯¯¯¯¯?
Answers
Answer:
AC = 6.35 in.
Step-by-step explanation:
BC times CD
4.2(9.6) = 40.32
The square root of 40.32 = 6.3498031465550174172038778087342
Round your answer to the nearest hundredth
AC = 6.35 in.
John recorded the number of cars passing a traffic signal at intervals of 2 minutes. He plotted
Cars
y 45
40
35
8
30
25
20
15
10
5
24
6 8 10 12 14 16 18 20
Time (minutes)
The slope of the line is
and the y-intercept is
Answers
The slope of the line and the y-intercept are slope = 20/7 and y-intercept = 0
How to calculate the slope of the line and the y-interceptFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have
(0, 0) and (14, 40)
The slope is calculated as
slope = change in y/change in x
So, we have
slope = 40/14
Evaluate
slope = 20/7
For the y-intercept, we have
y-intercept = 0
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Please help with this SAT question. A solution gets Brainliest!
Answers
Answer:
i think Chope its help
C is my answer
ASAP!!!
Determine the perimeter of the right triangle shown. Round your final answer to the nearest whole number, if necessary.
5 units
12 units
16 units
25 units
Answers
The perimeter of the triangle ABC is 12 units. Hence, option (B) is correct.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
In the given right angle triangle,
The vertices are A(-3, 2), B(-3, -1) and C(1, -1)
The distance between AB = 3,
And the distance between BC = 4
To find the distance of AC, use Pythagoreans theorem,
AC² = AB² + BC²
= 3² + 4²
= 9 + 16
AC² = 25
AC = 5
The perimeter of triangle ABC = AB + BC + AC
= 3 + 4 + 5
= 12
The perimeter of the triangle ABC is 12 unit.
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Marco's class is painting a mural on the side of their school. The mural covers a 3 m high,
rectangular wall. It has an area of 28 m².
What is the length of the mural?
Answers
Answer:
28/3 = 9 1/3 ≈ 9.33 meters
Step-by-step explanation:
You want the length of a 28 square meter mural that is a rectangle 3 meters high.
AreaThe area of a rectangle is given by ...
A = LW
Solving for L, we have ...
L = A/W = (28 m²)/(3 m) = 28/3 m
The length of the mural is 28/3 meters, or 9 1/3 meters, about 9.33 meters.
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Simplify the following: 2y + 9 + 8y + 7
Answers
Answer:
10y + 16
Step-by-step explanation:
Given
2y + 9 + 8y + 7 ← collect like terms
= (2y + 8y) + (9 + 7)
= 10y + 16
write the slope-intercept equation for a line that goes through the point (0,4) and is parallel to the line whose equation is y = 3x + 2 ?
Answers
Answer:
its y = 3x + 4
Step-by-step explanation:
it is because the y intercept is 4 and the slope is 3/1
Answer this - wrong answers will be reported/deleted
Answers
Answer:
58.03 ft
Step-by-step explanation:
To solve for the total circumference of circle F, we can create a ratio of section angle measure to circumference. We know that these two attributes of a circle have a linear relationship because the formula for arc length (\(S = 2\pi r \cdot \frac{\theta}{360\°}\)) relies proportionately on the radius and angle measure of the section.
angle measure : circumference
290° : 46.75 ft
We can multiply this ratio by \(\frac{360}{290}\) to get the corresponding circumference for a 360° section (which is the entire circle).
\(\frac{360}{290}(290\° : 46.75 \text{ ft})\)
\(= 360\° : \boxed{58.03 \text{ ft}}\)
Therefore, the circumference of circle F is approximately 58.03 ft.
A square has a perimeter of 32ft. What is the length of each side?
Answers
Answer: 2.378.
Step-by-step explanation:
perimeter of square= 4×side
32= 4×side
32/4= side
8= side
hope it helps you friend!!
Eight pairs of data yield r = 0.708 and the regression equation = 55.8 2.79x. also, = 71.125. what is the best predicted value of y for x = 9.9?
Answers
The best predicted value of y for x = 9.9 is y = 83.42.
What is linear equation if two variables?Linear equations with two variables are equations with one, zero, or infinitely numerous solutions where every of a two variables has the highest exponential order of 1.
Some key features regarding linear equation if two variables are-
The two-variable linear equation has the conventional form ax + by + c = 0, where x and y are the variables. These solutions might also be expressed in pairs, such as (x, y). A graphical representation of a linear equation system in two variables involves two straight lines that can be intersecting, parallel, or coincident.Now, according to the question;
The given equation is;
y = 55.8 + 2.79x
Calculate the value of y by substituting the value of x = 9.9.
y = 55.8 + 2.79×9.9
y = 83.42
Therefore, the best predicted value of y for x = 9.9 is 83.42.
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The correct question is-
Eight pairs of data yield r = 0.708 and the regression equation y = 55.8 + 2.79x. Also, the mean y-value is 71.125. What is the best predicted value of y for x = 9.9?
Deeni bought 1000 units of stock at a price of RM 2.50 per unit. he sold all the shares at a price of rm 3.10 per unit. calculate the profit obtained
Answers
Answer:
RM 600
Step-by-step explanation:
1 unit -> bought for RM 2.50
sold for RM 3.10
Selling price is higher than buying price, hence a profit is made.
Profit (for 1 unit) = Selling price - Buying Price
= RM 3.10 - RM 2.50
= RM 0.60
Since Deeni bought 1000 units of stock,
Profit Obtained = 1000 x RM 0.60
= RM 600
can yall help me with this one WILL GIVE BRAINLIEST
Answers
Answer:
c=12
Step-by-step explanation:
Peace's average mark on her 5 maths tests was 88. If her lowest score was dropped, her new average would be 90. What is her lowest mark?
Answers
Her average score on the four remaining tests is indeed 90, which confirms that her lowest score was 80.
Let's assume Peace's lowest score on the five math tests is x.
According to the problem statement, her average mark on all five tests is 88. This means that the sum of her scores on all five tests is:
5 * 88 = 440
If her lowest score was dropped, then the sum of her scores on the remaining four tests would be:
4 * 90 = 360
We know that the sum of her scores on all five tests is 440, so we can write an equation:
440 - x = 360
Solving for x, we get:
x = 80
Therefore, her lowest mark was 80. We can check this by finding her average score after dropping her lowest score:
(88 + 88 + 88 + 88 + 90) / 5 = 90
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Once again i need help its worth 90 points so id say its worth it
Answers
Answer:
EXPLANATION BELOW
Step-by-step explanation:
7 | 0, 4, 8
8 | 0, 8, 9
9 | 5
10 | 1, 9
11 | 6, 7
hope this helps!! you basically just divide the number into two-
what is 5 divided by 3/4 in simplest form