The ice cream costs $3 for a small serving and $4 for a large serving.
How to determine the ice cream costs for a small serving and a large serving?A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation
Since 3 small servings of ice cream and 1 large serving of ice cream for $13, and 2 small servings of ice cream and 1 large serving of ice cream for $10. We can set up two equations to represent the situation:
Let S and L represent the cost of small servings and large servings respectively
3S + L = 13 --- (1)
2S + L = 10 --- (2)
From (1):
L = 13 - 3S --- (3)
Put (3) in (2):
2S + L = 10
2S + 13-3S = 10
-S + 13 = 10
S = 13-10
S = $3
Put S = 3 into (3):
L = 13 - 3S
L = 13 - 3(3)
L = 13 - 9
L = $4
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can someone help me with this please
2.3 + r = 7.9
r = ?
Answer:
r = 5.6
Step-by-step explanation:
To solve this problem, we need to isolate r on one side of the equation. To do this, we need to subtract 2.3 from both sides, giving us:
2.3 + r = 7.9
r = 5.6
So, r = 5.6
Hope this helped!
Answer:
5.6
Step-by-step explanation:
2.3+r=7.9
r=7.9-2.3
r=5.6
Mario and Carlos, two brothers, play for the same basketball team. Here are the points they scored in 10 games:
The highest point scored is by Carlos with 19 points. Mario's highest was 15. so, Carlos scored 4 points more than Mario.
In the 7th game, Carlos scored 19 points which is the highest point of his game. In the 1st game, Mario scored 15 points which was the highest point he scored. Therefore, Carlos had the highest scoring game between the two of them. Carlos scored 4 points more than Mario did in his highest-scoring game. You can also construct a box plot for this question which will help you visualise this better. The box plot can be made by drawing a number line and marking the following points: minimum, first quartile, median, third quartile and maximum.
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The full question is:
Mario and Carlos, two brothers, play for the same basketball team. Here are the
points they scored in 10 games:
Game 1 2 3 4 5 6 7 8 9 10
Mario 15 X X 12 7 11 12 11 10 11
Carlos 10 X 9 12 15 X 19 11 12 12
(Xs mark games each one missed.) Which brother had the
highest-scoring game? How many more points did he score in
that game than the other brother did in his highest-scoring game?
(7,349) (2,114) slope
Answer:
Slope = 47
Step-by-step explanation:
Slope:Substitute the x and y coordinates in the formula and find the slope.
(7 , 349 ) ; x₁ = 7 ; y₁ = 349
(2 , 114) ; x₂ = 2 ; y₂ = 114
[tex]\sf \boxed{Slope=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf = \dfrac{114-349}{2-7}\\\\=\dfrac{-235}{-5}\\\\=47[/tex]
Answer: m=47
Step-by-step explanation:
[tex]\displaystyle\\The \ slope\ m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Given: (7,349) (2,114) Find: m
x₁=7 x₂=2 y₁=349 y₂=114
[tex]\displaystyle\\m=\frac{114-349}{2-7} \\\\\\m=\frac{-235}{-5} \\\\\\m=47[/tex]
In triangle efg angle e = 5x+6 angle f = 4x-6 and angle g = 5x-2 find angle g
Answer: In any triangle, the sum of the three angles is always 180 degrees. This is known as the triangle angle sum theorem.
So in triangle efg, we can use this theorem to find angle g in terms of x:
angle e + angle f + angle g = 180
5x+6 + 4x-6 + 5x-2 = 180
14x = 180 + 8
14x = 188
angle g = 5x-2 = 5(188/14) - 2 = 5(13.4285714) - 2 = 67.1428571 degrees
So angle g = 67.1428571 degrees
It's important to note that the values of x are the unknowns.
Step-by-step explanation:
what is 6^-2 in a fraction form
Answer:
[tex]\frac{1}{36}[/tex]
Step-by-step explanation:
For negative exponents, you get the original number and make it into its reciprocal, and then whatever power it is to, is the power the bottom number is to, so you get:
[tex]6^{-2} = \frac{1}{6^{2} }[/tex]
Which simplifies to:
[tex]\frac{1}{36}[/tex]
So, [tex]6^{-2}[/tex] in fraction form, is [tex]\frac{1}{36}[/tex].
Hope this helped!
Please give me brainliest if possible!
Determine whether each of the following sentences is a proposition. If the sentence is a proposition, then write its negation (a) Have a nice day. (b) The soup is cold (c) The patient has diabetes.(d) The light is on (e) It's raining today (f) Do you like my new shoes? (g) The sky is purple (h) 2 + 3 = 6 0 Every prime number is even.(i) There is a number that is larger than 17
The sentence which is Proposition is b,c,d,e,g,h, i. We will find its Negation below.
What is Proposition?
An assertion that can be either true or untrue is referred to as a proposition (but not both). For instance, the statements "Paris is in France" (true), "London is in Denmark" (false), "2 equals 4" (true), and "4 Equals 7 (false)" are examples of propositions. The questions "what is your name?" and "complete your homework" are not propositions, nor are the statements "this sentence is wrong" "x is an even number" or "Socrates" (which is not even a phrase). A proposition's truth value refers to whether it is true or false.
What is Negation of Proposition?
The words " ¬" or " ~" are used to denote a statement's denial. For instance, "Arjun's dog has a black tail" is the given sentence. The statement "Arjun's dog does not have a black tail" is the negation of the one that has been said. As a result, the negation of the provided statement is false if the given statement is true.
Our first sentence is “Have a nice day”.
The phrase "Have a nice day" cannot be true or wrong, hence it cannot be a proposition. Additionally, a proposition is a declarative sentence, whereas this sentence is imperative.
The second sentence is "The soup is cold". Its Negation will be "The soup is not cold".
The third sentence is "The patient has diabetes". Its Negation will be "The patient does not have diabetes".
Fourth is "The light is on". Its Negation will be "The light is not on".
Fifth is "It’s raining today". Negation will be "It’s not raining today".
The Sixth is "you like my new shoes". This Sentence is not a proposition.
Seventh is "The sky is purple". Its Negation will be "The sky is not Purple".
Eight is "Every prime number is even". Its Negation will be "It’s not true that every prime number is even".
The ninth sentence is “There is a number that is larger than 17”. Its Negation will be "There is not a number that is larger than 17".
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help with this question pls
Step-by-step explanation:
(a)
the line for time = 0 minutes starts at y (pounds of candy) = 40 pounds
(b)
as the line goes up, when the time goes up, it is clear that the function result (the amount of candy in the container) increases, as the time increases.
so, the second answer option is correct.
to find the rate of pound of candy per minute, we need to find the slope.
one unit on the coordinate grid in the time (x) direction is 1 minute.
one unit in the pounds of candy (y) direction is 40 pounds (0, 40, 80, 120, ...).
when we look at what corners of the coordinate grid units the line goes through (to find integer numbers of the function), we see that the line goes through e.g.
(0, 40)
(1, 160)
(2, 280)
...
we see that x anyways changes by +1, and y anyways charges by +120.
the slope is therefore +120/+1 = 120.
the increase rate of the amount of candy in the container is 120 pounds per minute
PLS HELP I WILL MARK IT BRAINLIEST
Consider the line -7x - 5y = -1
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answer:
I find it best to view these equation in the slope-intercept form.
-7x - 5y = -1
Let's rearrange the terms to isolate the y and put the equation in the y=mx+b form
5y = -1 + 7x
y = -1/5 + (7/1)x
or y = +(7/1) x + -1/5
Here m, the slope, = 7/1
A line parallel to this line will have the same slope or 7/1
A line perpendicular to this line will have a slope that is the negative inverse of this slope, in other words -1/7
Hope this helps - Please mark as Brainliest
Use the distributive property to remove the parentheses.
3y5(5-6y4)
Simplify your answer as much as possible.
Answer:
75y - 360y²
Step-by-step explanation:
ANSWER
3y × 5 (5-6y x 4)
Multiply the monomials
15y (5-24y)
Apply the Distributive Property
15y × 5-15y × 24y
Multiply the monomials
75y - 360y²
I hope it is useful to you.
Does this set of ordered pairs represent a function? why or why not?
(-2,2), (-1, 2), (3, -1), (3, 1), (4, 11))
oa. yes, because there are two xvalues that are the same.
o b. yes, because every xvalue corresponds to exactly one y-value.
o c. no, because two of the y-values are the same.
od. no, because one xvalue corresponds to two different y-values
The ordered set pairs (-2, 2), (-1, 2), (3, -1), (3, 1), (4, 11),
is not a function. Because one x value corresponds to two different y values.
Determine whether or not the function of the set of ordered pairsGiven a set of ordered pairs (-2, 2), (-1, 2), (3, -1), (3, 1), (4, 11),
Function is special relations that pair each member of set A (domain) with exactly one member of set B (codomain).
Discuss the options provided.
a. yes, because there are two x values that are the same that is 3. Then the statement is false, the value of x cannot be the same.
b yes, because every x value corresponds to exactly one y-value. Then the statement is false.
c. no, because two of the y-values are the same. Then the statement is false.
d. no, because one xvalue corresponds to two different y-values. Then the statement is true.
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what percentage of fruits and vegetables is water? 8 to 10 percent 20 to 25 percent ~50 percent 80 to 95 percent\
Answer:
About 50 percent
Step-by-step explanation:
How many answers are there in an absolute value?
Answer: Just 1
Step-by-step explanation:
The absolute value is always positive, so there is just 1.
A boat rental company has two kinds of boats, rowboats and motorboats. The expressions below represent the cost, in dollars, for renting each kind of boat for x number of hours. Cost of a rowboat rental: 8 . 50 x 3 Cost of a motorboat rental: 17 . 50 x 25 Which expression shows how many more dollars it costs to rent a motorboat than a rowboat for x hours
The expression which is correct representing the cost to rent a motorboat than a rowboat for x hours is 9x + 22.
Equation:
An equation is a mathematical formula that contains two algebraic expressions on either side of an equal sign (=). It shows the equivalence relation between the formula written on the left and the formula written on the right. In any formula, L.H.S = R.H.S (left side = right side). You can solve equations to find the values of unknown variables that represent unknown quantities. If a statement doesn't have an equals sign, it means it's not an equation.
According to the question:
The equation of Rowboat rental is Given as:
8.50x + 3
and, the equation of motorboat rental is given as:
17.50x + 25
Now,
the difference between the equation (1) from equation(1):
17.50x + 25 - (8.50x + 3)
⇒ 17.50x - 8.50x + 25 - 3
⇒ 9x + 22
Complete Question:
A boat rental company has two kinds of boats, rowboats and motorboats. The expressions below represent the cost,
in dollars, for renting each kind of boat for x number of hours.
Cost of a rowboat rental: 8.50x +3
Cost of a motorboat rental: 17.50x +25
Which expression shows how many more dollars it costs to rent a motorboat than a rowboat for x hours?
*8x +22
*9x + 22
*9x + 28
*26x + 28
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Is zero positive proof?
No, The number zero is neither positive nor negative.
Aryabhata, who is known as a great astronomer of the classic age of India was the one who invented the digit “0” for which he became immortal but later on is given to Brahmagupta.
The numbers to the right of zero on the number line are positive and those on the left side are negative.
Positive numbers are greater than 0 and located to the right of 0 on a number line. Negative numbers are less than 0 and are located to the left of 0 on a number line.
Positive and negative numbers are sometimes called signed numbers.
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quadrilateral abcd , was dilated to produce the image, quadrilateral A′B′C′D′ . The length of the side between vertices A and B is 5 inches. What is the length of the side between the vertices A′ and B′? Enter your answer as a fraction in simplest form by filling in the boxes. k12
Answer:Dilation is the increase or decrease in the size of a figure by a factor k. If a figure is dilated to produce an image, they are similar, hence the ratio of the corresponding sides are proportional. The length of the side between the vertices A′ and B′ is 16/7 units. Find out more on transformation at: brainly.com/question/1548871 Advertisement
Step-by-step explanation:
during the school year, the 10 members of the chess club play a total of 900 games of chess during their practice matches. each member plays against every other member $n$ times. what is the value of $n$?
On solving the provided question, we can say that by permutation 900 games were actually played; N = 900/45 = 20
what is permutation?The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order.
The number of matches would be if each player faced each other once.
[tex]^{10}C_2[/tex] = 10! / 2! 8!
= 10 X 9 / 2 = 90/2
= 45
Given that 900 games were actually played,
N = 900/45 = 20
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(w2x−3)÷10⋅z when w=−6, x = 1.2, and z=−67
Pls help me my fellow friends, i will answer your question if you want!
Answer:
116.58
Step-by-step explanation:
([tex]\frac{w2x - 3}{10}[/tex]) z Substitute in what you know
[tex](\frac{(-6)(2)(1.2) - 3}{10})[/tex] (-67)
[tex](\frac{-14.4-3}{10})[/tex](-67)
[tex](\frac{-17.4}{10})[/tex](-67)
-1.74(-67)
116.58
Answer:
116,58
Step-by-step explanation:
((-6)·2·1,2-3)÷10·(-67)
(-14,4-3)÷10·(-67)
-17,4÷10·(-67)
-1,74·(-67)
116,58
Does a two-digit number exist such that the digits sum to 9 and when the digits are reversed the resulting number is 9 greater than the original number? identify the system of equations that models the given scenario.
The two digit number is 54 and the system of equations that models the given scenario is x + y = 9 and x - y = -1, where x and y are the digits of the two-digit number.
Let the two-digit number has digit x in tens place value and y in ones place value, then the two digit number is
10x + y
As the sum of the digits is 9
x + y = 9
When the two-digit number is reversed, the resulting two-digit number would be
10y + x
As it is given that this resulting number is 9 greater than original number
10y + x = (10x + y) + 9
Subtracting x and y on both sides
10y + x - y - x = 10x + y + 9 - y - x
9y = 9x + 9
Dividing by 9
y = x + 1
Rearranging
x - y = -1
So the system of equation representing this scenario is
x + y = 9
x - y = -1
To solve for x
Add the equations
(x + y) + (x - y) = 9 + (-1)
2x = 8
Dividing by 2
x = 4
To solve for y, substitute x in first equation
4 + y = 9
Therefore y = 5
Thus the original number is
10x + y = 10×4 + 5
= 45
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The table shows the inputs and corresponding outputs for the function f(x) = (1/8)(2)^x
Answer:
yes
Step-by-step explanation:
Is the absolute value always less than or equal to zero?
No, the absolute value of a number is always non-negative, meaning it is greater than or equal to zero, but it is not always equal to zero.
The absolute value of a number represents the distance of that number from 0 on the number line and a number can be positive or negative.
For example, the absolute value of 5 is 5, which is greater than zero. The absolute value of -5 is also 5, which is also greater than zero. The only time the absolute value of a number is equal to zero is when the number is zero, |0| = 0.
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[tex]\frac{tan(\frac{-2π}{3}} {sin\frac{7π}{4}} -sec (-π)\\[/tex]What is the exact value of the trigonometric expression? State your answer in simplified radical form
The exact value of the trigonometric expression [tex]\frac{tan-(2\pi/3) }{sin(7\pi /4)} - sec(-\pi )[/tex] in the simplified radical form is √6 + 1.
[tex]\frac{tan-(2\pi/3) }{sin(7\pi /4)} - sec(-\pi )[/tex]
We have the angle,
-2π/3 = -120° = (360 - 120)° = 240° = 60°
Put the value of -2π/3 in tan -2π/3, we get
tan -2π/3 = tan (60) = √3
7π/4 × 180/π = 7 × (180/4) = 7 × 45 = 315° = 45°
Put the value of 7π/4 in sin 7π/4, and we get
sin 7π/4 = sin (45°) = √2/2
sec (-π) = sec (π) = -1
Now, substitute all the values in the given equation,
= {√3/(√2/2)} - (-1)
= (2√3/√2) + 1
= (2√3 × √2/√2 × √2) +1
= (2√6/2) + 1
= √6 + 1
--The given question is incorrect, the correct question is
''What is the exact value of the trigonometric expression? [tex]\frac{tan-(2\pi/3) }{sin(7\pi /4)} - sec(-\pi )[/tex] State your answer in simplified radical form."--
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12. One number is one-third another. The lesser number is x. Write an expression that represents the greater number
Answer: The greater number is 3x
Step-by-step explanation:
As the problem states that one number is one third of another number, hence we can set up a proportion
x / (greater number) = 1/3
we can then cross multiply to find out the greater number.
x * 3 = greater number
so the greater number is 3x
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The Expression for greater number is x/3.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the lesser number be x.
So, the one number is x.
Now, the another number is one third of one number.
So, the another number is 1/3 (x)= x/3
Hence, the expression is x/3.
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Multiply 3x (2x - 1) by following these steps: Factor 1 ED +X Product Step 1: Drag tiles to the section labeled Factor 1 to represent the factor 3x.
Answer:
product would be 6x^2-3x
Step-by-step explanation:
don't know the rest
Mary and Ryan each have some sweets.
The ratio of the number of sweets Mary has to the number Ryan has is 3:2
If Mary gave 5 sweets to Ryan they would have the same number of sweets.
Work out how many sweets Mary and Ryan have altogether.
Answer:
Let x be the number of sweets that Ryan has.
Since the ratio of the number of sweets Mary has to the number Ryan has is 3:2, we can say that Mary has 3/2*x sweets.
We know that if Mary gave 5 sweets to Ryan they would have the same number of sweets, so we can write the following equation:
3/2*x -5 = x
By solving this equation, we can find that x = 10. So, Ryan has 10 sweets
Therefore, Mary has 3/2*10 = 15 sweets.
Altogether, Mary and Ryan have 15+10 = 25 sweets.
Answer: 25
Step-by-step explanation:
3x - 5 = 2x, so
x = 5.
And 5x = 5*5 = 25
1.4 unit conversion. (a) convert a mass of 2.2 kg into ounces and lbm. (b) convert 12 lbf /in2 into kpa and mmhg. (c) convert 160 hp into cal/s and btu/s. (d) convert 82 gallons into quarts and ml. (e) convert 34 in into m and cm.
Converted (a) 2.2 kg = 77.6 oz, 4.83 lbm. (b) 12 lbf/in2 = 82.7 kPa, 620.6 mmHg. (c) 160 hp = 119,360 cal/s, 88,000 Btu/s. (d) 82 gallons = 328 quarts, 313,981.8 mL. (e) 34 in = 0.8636 m, 86.36 cm.
What is conversion factor ?
A conversion factor is a ratio of two equivalent measurements used to convert a quantity from one unit to another.
(a) To convert 2.2 kg to ounces, we can use the conversion factor 1 kg = 35.274 oz. So, 2.2 kg = 2.2 * 35.274 oz = 77.6 oz. To convert 2.2 kg to lbm, we can use the conversion factor 1 kg = 2.205 lbm. So, 2.2 kg = 2.2 * 2.205 lbm = 4.83 lbm.
(b) To convert 12 lbf/in2 to kPa, we can use the conversion factor 1 lbf/in2 = 6.894 kPa. So, 12 lbf/in2 = 12 * 6.894 kPa = 82.7 kPa. To convert 12 lbf/in2 to mmHg, we can use the conversion factor 1 lbf/in2 = 51.715 mmHg. So, 12 lbf/in2 = 12 * 51.715 mmHg = 620.6 mmHg.
(c) To convert 160 hp to cal/s, we can use the conversion factor 1 hp = 746 cal/s. So, 160 hp = 160 * 746 cal/s = 119,360 cal/s. To convert 160 hp to Btu/s, we can use the conversion factor 1 hp = 550 Btu/s. So, 160 hp = 160 * 550 Btu/s = 88,000 Btu/s.
(d) To convert 82 gallons to quarts, we can use the conversion factor 1 gallon = 4 quarts. So, 82 gallons = 82 * 4 quarts = 328 quarts. To convert 82 gallons to mL, we can use the conversion factor 1 gallon = 3785.4 mL. So, 82 gallons = 82 * 3785.4 mL = 313,981.8 mL
(e) To convert 34 in to m, we can use the conversion factor 1 in = 0.0254 m. So, 34 in = 34 * 0.0254 m = 0.8636 m. To convert 34 in to cm, we can use the conversion factor 1 in = 2.54 cm. So, 34 in = 34 * 2.54 cm = 86.36 cm.
Converted (a) 2.2 kg = 77.6 oz, 4.83 lbm. (b) 12 lbf/in2 = 82.7 kPa, 620.6 mmHg. (c) 160 hp = 119,360 cal/s, 88,000 Btu/s. (d) 82 gallons = 328 quarts, 313,981.8 mL. (e) 34 in = 0.8636 m, 86.36 cm.
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Renee knows that there is 700 calories in 12 oz of chocolate. She wants to calculate how many calories would be in 30 oz of Chocolate. Below is her work. Did she calculate correctly? If not explain and correct her mistake.
Answer: 1750 calories
Step-by-step explanation:
[tex]\frac{700calories}{12oz} * 30 oz = 1750 calories[/tex]
Mr. brown's statistics class consists of 21 seniors. the class took two quizzes in one week, and 12 of the students in the class passed both quizzes. what is the probability that the same students who passed the first quiz also passed the second quiz given that 19 students passed the first quiz? a. b. c. d.
Given that 19 students completed the first quiz, the probability that the same children who finished the first exam also passed the second quiz is P(S/F) = 0.63.
How is probability determined?How possible something is to happen is determined by its probability. By dividing the whole significance level by the total number of ways an event could occur, one can calculate the likelihood.
In this situation, conditional probability is used. P represents the conditional probability like an occurrence, A, given that B has occurred (AIB). We would estimate the likelihood as
P(AIB) is defined as (Probability of A and B)/Probability of B.
Probability of S and F in the iven question is 12/21. (12 of the students in the class passed both quizzes)
Probability of S = 19/21
Therefore,
P(SIF) = (12/21) / (19/21)
(PSIF) = 12/21 * 21/19
(PSIF) = 12/19 = 0.63
The correct option is A
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The complete question is-
Mr. Brown's statistics class consists of 21 seniors. The class took two quizzes in one week, and 12 of the students in the class passed both quizzes. What is the probability that the same students who passed the first quiz also passed the second quiz given that 19 students passed the first quiz?
A. P(S/F) = 0.63
B. P(S/F) = 0.2
C. P(S/F) = 0.8
D. P(S/F) = 1.31
A particle is located at vector r = (0.54,)i + (-36m)j +(p.85m)k constant force of magnitude 2.6 N acts on the particle. Find the components of the torque about the origin when the force acts in (a) the positive x direction and (b) the negative z direction.
The components of the torque about the origin when the force acts in
(a) the positive x direction is 1.4N.
(b) the negative z direction is 2.21N.
What is constant force of magnitude?
The motion of a particle occurs on a plane and is influenced by a force of constant magnitude that is always perpendicular to the particle's velocity.
Given:
A particle is located at vector r = (0.54m)i + (-36m)j +(.85m)k constant force of magnitude 2.6 N acts on the particle.
We have to find the torque about positive x direction and negative z direction.
At the positive x direction the torque is (T)
= the x component of position vector . F
= 0.54 x 2.6
= 1.4 N
At negative z direction Torque = - (z component of position vector).F
= .85 x 2.6
= 2.21 N
Hence,
The components of the torque about the origin when the force acts in
(a) the positive x direction is 1.4N.
(b) the negative z direction is 2.21N.
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Can someone please help me with this math problem, ASAP? I've been trying to figure it out, but still couldn't get the right answer for it, Thanks!
The linear function with a slope of -1/4 and intercept of -5 is given as follows:
f(x) = -0.25x - 5.
How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change of the output variable y relative to the input variable x.The intercept b represents the value assumed by y when x = 0.The parameters for this problem are given as follows:
Slope of -1/4 -> m = -1/4 = -0.25.f(0) = -5 -> b = -5.Comparing to the standard definition, the linear function is defined as follows:
f(x) = -0.25x - 5.
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sam wishes to cross a circular lake with diameter 1 km. he can row across the water at a rate of 4 km/hour, or he can walk along the shore (carrying the rowboat) at a rate of 6 km/hour. what is the minimum amount of time necessary to cross the lake?
25 minutes. The time it would take to row across the lake is 15 minutes (1 km/4 km/hour = 0.25 hour), and the time it would take to walk around the lake is 10 minutes (1 km/6 km/hour = 0.1666 hour). Thus, the minimum amount of time necessary to cross the lake is 25 minutes (15 + 10).
1 km/4 km/hour = 0.25 hour (time to row across the lake)
1 km/6 km/hour = 0.1666 hour (time to walk around the lake)
Minimum amount of time necessary to cross the lake = 0.25 + 0.1666 = 0.4166 hour
0.4166 hour x 60 minutes/hour = 25 minutes
Sam can row across the lake in 15 minutes (1 km/4 km/hour = 0.25 hour) or walk around it in 10 minutes (1 km/6 km/hour = 0.1666 hour). The minimum amount of time necessary to cross the lake is 25 minutes (15 + 10), as this is the lowest total time to get from one side to the other.
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