The issue with the claim that a heat engine takes in 21 kJ of heat, discharges 16 kJ of heat to the environment, and performs 3 kJ of work is that the work performed does not equal the difference between the heat input and the heat output. Therefore, the correct option is A.
1. According to the first law of thermodynamics, the work performed by a heat engine is equal to the difference between the heat input (Qin) and the heat output (Qout).
2. In this case, Qin is 21 kJ and Qout is 16 kJ.
3. The difference between the heat input and heat output is 21 kJ - 16 kJ = 5 kJ.
4. However, the claim states that the work performed is 3 kJ, which is not equal to the difference between the heat input and the heat output (5 kJ).
Hence, the claim is incorrect because the work performed does not equal the difference between the heat input and the heat output. The correct answer is option A.
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Find the length of the segment indicated.
Answer:
11.281
Step-by-step explanation:
For this question, since we see a right angle triangle, we know that we can use Pythagoras' Theorem to solve for this question.
By Pythagoras' Theorem,
[tex] {c}^{2} = {a}^{2} + {b}^{2} \\ {x}^{2} = {4.6}^{2} + {10.3}^{2} \\ \\ {x}^{2} = 127.25 \\ x = \sqrt{127.25} \\ = 11.281 \: or \: \frac{ \sqrt{509} }{2} [/tex]
Which of these is a zero of the polynomials p(y) = 3y^3 - 16 y - 8? * - 8 0 2 - 2
The zero of polynomials is -2. The polynomials is p(y) = [tex]3y^{3} - 16 y - 8[/tex].
According to the question,
The polynomials is p(y) = [tex]3y^{3} - 16 y - 8[/tex]. In order to find the zero of polynomials only if we substitute the value and polynomials become zero.
p(-2) = [tex]3(-2)^{3} - 16 (-2) - 8[/tex]
= 3(8) + 32 -8
= 0
Hence, the zero of polynomials is -2. The polynomials is p(y) = [tex]3y^{3} - 16 y - 8[/tex].
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3x-2y=10 find the y intercept and the x intercept
Answer:
(0, -5) (10/3, 0)
Step-by-step explanation:
First, convert the given equation into the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
3x - 2y = 10
2y = 3x - 10
y = 3/2x - 5
The y-intercept is -5.
Next, to find the x-intercept, let y = 0 and solve for x. X-intercept is the point where the graph intersects the x-axis, so the y-coordinate of x-intercepts are always 0.
3x - 2*0 = 10
3x - 0 = 10
3x = 10
x = 10/3
X-INTERCEPT
Plug y=0 into the equation and solve the resulting equation 3x=10 for x.
The x-intercept:
[tex]\left(\frac{10}{3},0\right)\approx \left(3.33333333333333,0\right)[/tex]
Y-INTERCEPT
Plug x=0 into the equation and solve the resulting equation −2y=10 for y.
The y-intercept:
[tex]\left(0, -5\right)[/tex]
please help with this
Answer:
a) x = 1, x = -7
b) (-3, -48)
c) x = -3
d) upwards
Step-by-step explanation:
Given quadratic equation:
[tex]y=3(x-1)(x+7)[/tex]
Part (a)Intercept form of a quadratic equation:
[tex]y=a(x-p)(x-q)[/tex]
where:
p and q are the x-interceptsa is some constantComparing the formula with the given equation:
⇒ p = 1
⇒ q = -7
Therefore, the x-intercepts of the given equation are x = 1 and x = -7.
Part (b)The midpoint between the two x-intercepts is the x-coordinate of the vertex.
[tex]\implies \textsf{Midpoint}=\dfrac{x_2+x_1}{2}=\dfrac{1+(-7)}{2}=-3[/tex]
Therefore, the x coordinate of the vertex is -3.
To find the y-coordinate of the vertex, substitute this into the given equation:
[tex]\implies y=3(-3-1)(-3+7)=-48[/tex]
Therefore, the coordinates of the vertex are (-3, -48).
Part (c)The x-coordinate of the vertex is the axis of symmetry.
Therefore, the axis of symmetry is x = -3.
Part (d)If the leading coefficient of a quadratic equation is positive, the parabola opens upwards.
If the leading coefficient of a quadratic equation is negative, the parabola opens downwards.
From inspection of the given equation, the leading coefficient is 3.
Therefore, the parabola opens upwards.
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A dindercal container close at boat and have a radius 7cm and hight 6cm find total surface area of the container what is the volume of this container
A) The total surface area of the given cylindrical container is 571.76 cm² and B) The volume of the given cylindrical container is 923.62 cm³.
What are the formulae for the total surface and volume of the cylinder?Consider a cylinder with height 'h', and radius 'r'.
The total surface area of the cylinder(TSA) = 2πr (r + h) square units
and
The volume of the cylinder V = πr²h cubic units.
Calculation:It is given that,
A cylindrical container closed on both ends has a radius r = 7 cm and a height h = 6 cm.
So,
TSA = 2πr (r + h)
= 2× π × 7 × (7 + 6)
= 14 × π × 13
= 571.76 cm²
and
Volume = πr²h
= π × 7² × 6
= π × 49 × 6
= 923.62 cm³
Therefore, the total surface area and volume of the cylindrical container are 571.76 cm² and 923.62 cm³ respectively.
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Graph the image of this triangle after a dilation with a scale factor of 2 centered at the origin. Use the polygon tool to graph the triangle.
The triangle is illustrated below.
How to explain the triangle?The first thing you should find are the new vertices:
(x, y) ---> (2x, 2y) ---> (x', y')
(0, 0) ---> (2 (0), 2 (0)) ---> (0, 0)
(-4, 4) ---> (2 (-4), 2 (4)) ---> (-8, 8)
(-4, -2) ---> (2 (-4), 2 (-2)) ---> (-8, -4)
Then, you must join the ordered pairs and graph the new triangle.
See the attached graph.
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Problem: A piece of farmland is a watering plot of land in a circular pattern. A sewer line needs to be installed from a new housing project to a processing plant The city does not want the sewer line to cross the farm land. Can a direct line be installed?
● Let 1 unit = 100 feet.
● The entry to the sewer plant is at (2,3)
● The sewage exit from the housing project is at (12,6)
● The sprinkler system extends 200 ft and the center of the land is at (8,3)
Questions: (1) Will the sewer line cross the farmland? If so then at what points?
(2) If the farmer wants to maximize the farming area and does not want to cross the sewer line, what is the longest sprinkler system that could be installed?
The entry and exit points of (2, 3), and (12, 6), and 200 ft. extension of the sprinkler system gives;
(1) The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)
(2) The longest installable sprinkler system is approximately 172.4 feet
How can the points where the line crosses the farmland be found?1. The slope of the sewer line is found as follows;
m = (6 - 3)/(12 - 2) = 3/10 = 0.3The equation of the sewer line can be expressed in point and slope form as follows;
(y - 3) = 0.3×(x - 2)y = 0.3•x - 0.6 + 3
y = 0.3•x + 2.4
The equation of the circumference of the sprinkler can be expressed as follows;
(x - 8)² + (y - 3)² = 2²Therefore;
(x - 8)² + (0.3•x + 2.4 - 3)² = 2²
Solving gives;
x= 6.53, or x = 8.48
y = 0.3×6.53 + 2.4 = 4.36
y = 0.3×8.48 + 2.4 = 4.9
Therefore;
The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)2. When the farmland does not cross the sewer line, we have;
sewer line is tangent to circumference of farmland
Slope of radial line from center of the land is therefore;
m1 = -1/0.3
Equation of the radial line to the point the sewer line is tangent to the circumference is therefore;
y - 3 = (-1/0.3)×(x - 8)
Which gives;
y = (-1/0.3)×(x - 8) + 3
The x-coordinate is therefore;
0.3•x + 2.4 = (-1/0.3)×(x - 8) + 3
x ≈ 7.5y = 0.3 × 7.5 + 2.4 ≈ 4.65The longest sprinkler system is therefore;
d = √((7.5 - 8)² + (4.65 - 3)²) ≈ 1.724
Which gives;
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The sum of a positive number and 56 times its reciprocal is equal to its cube. What is the number?
Answer:
2×sqrt(2) = 2.828427125...
Step-by-step explanation:
x = "a positive number"
x + 56/x = x³
x² + 56 = x⁴
x⁴ - x² - 56 = 0
(x² + 7)(x² - 8) = 0
this is true only for
x² = -7
or
x² = 8
x² = -7 would mean that x is an imaginary number. so, that is not a valid solution here.
x² = 8 means
x = sqrt(8) = sqrt(4×2) = 2×sqrt(2) = 2.828427125...
You select one red marble from the full bag in exercise 20. what is the probability that the next marble you select will be green without replacement of the first marble?
P(blue) = 1/3
Step-by-step explanation:
Probability for any event A is given by
p(A) = no of times of happening of event A/ total no of occurrence of all the events given under the situation.
A bag contains 5 blue marbles, 6 red marbles, and 4 green marbles
So, total no of occurrences of all the events given under the situation
one can either pick blue, red, or 4 green marbles
Total no. of occurrence of all the event = 5 + 6 + 4 = 15
Now, no occurrence of selecting blue.
since there are 5 blue marbles, there is a chance of selecting blue as 5.
no occurrence of selecting blue = 5
Therefore,
P(blue) = no of occurrence of selecting blue /total no of occurrence of picking any color ball
P(blue) = 5/15 = 1/3.
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Kim's softball team was playing in the championship game. When there were 444 innings left, the team was losing by a score of 171717 to 666 runs. In the last 444 innings, her team scored the same number of runs per inning, and the other team did not score any more runs. Kim's team won with the most runs.
Write an inequality to determine the number of runs per inning, ppp, Kim's team could have scored.
Find the minimum whole number of runs per inning Kim's team could have scored.
The inequality to determine the number of runs per inning, p Kim's team could have scored is; 4r + 6 > 17
How to write an Inequality?
Let r represent the number of runs per inning. Thus for 4 innings, we have 4r.
The team already has 6 runs. Now add the additional runs to this to get;
4r + 6
The team wants to score more than the other team, this means they need more than 17 and so the inequality required is;
4r + 6 > 17
Subtract 6 from each side to get;
4r + 6 - 6 > 17 - 6
4r > 11
Divide both sides by 4 to get:
r > 2.75
Approximating to a whole number gives;
r > 3
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Answer:
6+4p> 17
3
Step-by-step explanation:
A math club is researching a golf tournament fund-raiser. it will cost $1,000 to host the tournament. if it rains, the club will lose the investment. if it is sunny, it is expected that the club will collect $4,500 from the participants. if the chance of rain is 20%, what is the expected value for the tournament?
The expected value of tournament is $2600.
According to the statement
we have given that the tournament will cost $1000 and if it is sunny, it is expected that the club will collect $4,500 from the participants. And we have to find the expected value of a tournament.
So, we know that the
Cost of hosting the tournament : $1,000
If it rains, the club will lose the investment: $ -1,000
If it is sunny, the club will collect $4,500 ;
From all this the profit they will get
profit: 4,500 - 1000 = 3,500
And
There is a chance of 20% then
The club will loss the investment is
-1000*20 = -200
And
Effect on their profit if there is a rain then
3500*80 = 2800
then
The expected value of tournament is 2800-200=2600.
So,The expected value of tournament is $2600.
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Answer:
C
Step-by-step explanation:
on edge
PLEASE HELP! Solve each of the following by using the general quadratic formula.
Using the quadratic formula, the solutions are:
a) [tex]x = \frac{3 \pm \sqrt{41}}{4}[/tex]
b) [tex]x = 1 \pm 2i[/tex]
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]
In which:
[tex]\Delta = b^2 - 4ac[/tex]
Item a:
The coefficients are a = 2, b = -3, c = -4, hence:
[tex]\Delta = (-3)^2 - 4(2)(-4) = 41[/tex][tex]x_1 = \frac{3 + \sqrt{41}}{4}[/tex][tex]x_2 = \frac{3 - \sqrt{41}}{4}[/tex]Item b:
The coefficients are a = 1, b = 2, c = 2, hence:
[tex]\Delta = (2)^2 - 4(1)(2) = -4[/tex][tex]x_1 = \frac{2 + \sqrt{-4}}{2} = 1 + 2i[/tex][tex]x_2 = \frac{2 - \sqrt{-4}}{2} = 1 - 2i[/tex]More can be learned about quadratic equations at https://brainly.com/question/24737967
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When multiplying or dividing measured quantities, what determines the number of significant figures in the result?.
The quantity with the fewest number of significant figures.
The least number of significant figures is used to calculate the product's or quotient's number of significant figures when multiplying or dividing measurable numbers. While 5.25 has three major figures, 3.5 only has two.What is significant figures?
Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit. Calculate the number of significant figures for an assortment of numbers.When multiplying two measured values the number of significant figures should be equal to the?
For multiplication or division, the rule is to count the number of significant figures in each number being multiplied or divided and then limit the significant figures in the answer to the lowest count. An example is as follows: The final answer, limited to four significant figures, is 4,094.Learn more about significant figures
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Evaluate each expression for the given values of the variables: 4|a|+8-a, if a =-2
The value of expression is 18.
modulus of functionA modulus function is a function that determines a number or variable's absolute value. A function with absolute values is another name for it. This function's result is always positive. let's suppose if you want to find modulus of -2 then you will get 2 as the answer.
now according to question
4|a|+8-a at a=-2
here a is negative that means modulus will give us positive value.
put a =-2 in the expression and get the answer. modulus of -2 will give us +2
so
=4(2)+8-(-2)
=8+8-(-2)
=8+8+2
=18
hence the answer is 18.
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Find the indicated term of the geometric sequence.
5th term of 1,
1 /4,1/16,…
Answer:
[tex]\frac{1}{256}[/tex]
Step-by-step explanation:
So generally a geometric sequence can be defined as: [tex]a_n=a_1(r)^{n-1}[/tex] which is the explicit form. The r, is what each previous term is being multiplied by to get the next value which is evident in the recursive form: [tex]a_n = r(a_{n-1})\\[/tex]. Knowing this we can take two values which are "next" to each other to find what r is. In this case I'll just is 1 and 1/4, given these two values we know that: [tex]\frac{1}{4} = 1 * r[/tex], 1*r is just r... so what each term is being multiplied by is 1/4. So let's plug the values into the explicit formula: [tex]a_n=(\frac{1}{4})^{n-1}[/tex] (I didn't put an a_1 value in front, since it's just 1... so it's a bit redundant). Anyways using this formula we simply plug in 5 as n into the equation to find the 5th term: [tex]a_5 = (\frac{1}{4})^{5-1} = (\frac{1}{4})^4 = \frac{1^4}{4^4} = \frac{1}{256}[/tex]
Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
The equations which are true for the values of x given are; x²-4 =0 and 4x²= 16.
Which equations are true for the values of x?The values of x given according to the task content are; x = –2 and x = 2.
By considering equation; x²-4 =0
x² = 4
x = ±2
Also, by considering 4x²= 16;
x² = 16/4 = 4
x = ±4.
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Hat is the area of the shaded face of the cylinder is 22m give your answer to the nearest whole number and give the correct units
The area of the shaded face of the cylinder is 1,520 mm².
How to find the area of the shaded area?We can see that the shaded area of the cylinder is circular in shape.
This means that we can find the area of the shaded area by finding the area of the circle.
The radius of the circle is given as 22 mm.
The formula for finding the area of a circle is given as:
Area = πr²
= 3.14 × 22 × 22
= 1,519.76
≈ 1520 mm²
Therefore, we have found the area of the shaded face of the cylinder to be 1,520 mm².
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Disclaimer: The question was incomplete, the complete question is attached below.
Can someone help with this problem please.
A sheet of paper, 12 inches by 18 inches, is folded so that 2 opposite corners touch, as shown in the figures below. What is the area, in square inches, of the shaded triangle formed as the result of the overlap. (Please look at the picture!)
The area of the shaded triangle formed as the result of the overlap is = 62.35 inches ²
Calculation of the equilateral triangleAfter folding the rectangle with length of 12 inches and width of 18 inches, an equilateral triangle was formed.
An equilateral triangle is a type of triangle where by all the three sides are equal.
To determine the value of one of the sides, CB or CD is used because the folding didn't affect these sides.
Using the formula for the area of an equilateral triangle,
A = √¾ a²
a= 12 inches
A = √¾ ×12²
A = 62.35 inches ²
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Answer:
Its 78!!!!
Solution:
1/2(12 * 18 - 5 * 12) = 78
9x/4y=1 and y= 18, what is the value of x
Answer:
x = 8
Step-by-step explanation:
[tex]\frac{9x}{4y}=1[/tex]
[tex]\frac{9x}{4*18} =1[/tex]
9x = 72
x = 8
Are the triangles similar? If so, state the similarity and the postulate or theorem that justifies your answer.
Answer: The triangles are not similar.
Step-by-step explanation:
Two figures are similar simply if they have the same shape, but not necessarily the same size. In a more mathematical sense, similar figures have the same angle measures and proportionate side lengths.
For reference, side lengths are proportionate when the ratios between corresponding/matching sides are the same.
Since we do not have any angles, we will try using the SSS Similarity Theorem, which states that if all three sides of both triangles are in proportion, then the triangles are similar. We will first list all the side lengths and match corresponding ones.
[tex]\triangle ABC \rightarrow 18,20,32\\ \triangle UVT \rightarrow 14,15,24[/tex]
Since we matched corresponding sides, we can now check whether they have the same ratio).
[tex]\frac{18}{14}=\frac{20}{15}=\frac{32}{24}[/tex]
[tex]\frac{9}{7}=\frac{4}{3}=\frac{4}{3}[/tex]
Not all of the side lengths have the same ratio, so these triangles aren't similar. you must multiply 14 by 9/7 to get to 18, but you need to multiply the other two sides by 4/3 to get to their
-6-5
(-5-4)
(-2,2)
2-
4
--2-1₁
4-
2
4 9
(0, -3)
X
What is the equation of the line that is parallel to the
given line and passes through the point (-2, 2)?
Oy=x+4
Oy = x + ¹/2
Oy = -5x + 4
Oy=-5x + ¹2
The equation of the line that is parallel to the given line and passes through the point (-2,2) is:
[tex]y = \frac{x}{5} + \frac{12}{5}[/tex]
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.When two lines are parallel, they have the same slope. In this problem, the given line passes through (-5,-4) and (0,-3), hence the slope is:
m = (-3 - (-4))/(0 - (-5)) = 1/5.
Hence the equation is:
[tex]y = \frac{x}{5} + b[/tex]
When x = -2, y = 2, then:
[tex]y = \frac{x}{5} + b[/tex]
[tex]2 = \frac{-2}{5} + b[/tex]
[tex]b = \frac{12}{5}[/tex]
Hence:
[tex]y = \frac{x}{5} + \frac{12}{5}[/tex]
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Please help with this
Answer: Circle lines
Step-by-step explanation:
Hopefully the attached image helps, it is a diagram of all the labeled lines on a circle excluding the radius (BG or GE)
Jamie and owen joined a monthly walking challenge at their youth center. jamie has already walked 120 minutes and plans to walk 20 minutes per day. owen plans to walk 30 minutes per day. let x represent the number of days and y represent the total number of minutes walked during the challenge. which system of equations can be used to find the number of days it will take for owen and jamie to have walked the same number of minutes? a system of equations. y equals 20 x plus 120. y equals 30 x. a system of equations. y equals 20 x. y equals 30 x plus 120. a system of equations. y equals 120 x plus 20. y equals 30 x. a system of equations. y equals 120 x. y equals 30 x plus 20.
Answer:
The system of equation y=120+20x and y=30x
Step-by-step explanation:
Let the number of days be x and y be the total number minutes
Jamie has walked 120 mins. She will walk at a rate of 20 mins per day.
y=120+20x
Owen walks 30 mins a day. So
y = 30x
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Causes of variation that can be identified and eliminated are called what?
The causes of variation that can be identified and eliminated are called; Assignable Causes.
What are the causes of Variation?There are two primary causes of variation in the quality of a product or process. These two primary causes are called;
Common causes.Assignable causes.Now, Common causes of variation are defined as random causes that we cannot identify. However, Assignable causes of variation are those that can be identified and eliminated.
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David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour, but realizes that he will be 1 hour late if he continues at this speed. He increases his speed by 15 miles per hour for the rest of the way to the airport and arrives 30 minutes early. How many miles is the airport from his home
The distance between David's home and the airport is 210 miles.
Distance traveled after 1 hour
let the distance traveled after first 1 hour = y
distance/speed = time
after 1 hour his speed = (35 + 15) = 50 mph
total time after 1 hour and 30 mins = 1.5 hr
y/50 + 1.5 = y/35
multiply through by350
7y + 525 = 10y
3y = 525
y = 525/3
y = 175 miles
In the first 1 hour, at 35 mph, distance covered = 35 miles
Distance from his home to airport = 175 miles + 35 miles = 210 miles
Thus, the distance between David's home and the airport is 210 miles.
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What criteria might CBR researchers use to select and specify which units will be sampled as well as the sampling frame and methods to be used
The criteria which CBR researchers might use to select and specify which units will be sampled as well as the sampling frame and methods to be used is the population.
What is Population?This is defined as the total number of organisms found in a particular place at any given point in time and varies based on the number of variables present. In some cases, head counts are done to ascertain the exact value of individuals present.
The probability sampling method is ideal for a large population and involves random selection of the organisms so as to find out the statistical features of the group being used such as the range, mean etc. This tool is very important in the area of giving estimates for ascertain type of activity or job.
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Given the following results from a spinner game after spinning 20 times.
What is the experimental probability of landing on red?
The experimental probability of landing on red is 7/20 or 0.35 or 35%
How to determine the experimental probability of landing on red?The complete question is added as an attachment
From the question, we have the following outcomes:
Red = 7
Green = 5
Blue = 5
Yellow = 3
The total number of spins is
Total = Red + Green + Blue + Yellow
This gives
Total = 7 + 5 + 5 + 3
Evaluate the sum
Total = 20
The experimental probability of landing on red is the calculated as:
P(Red) = Red/Total
Substitute the known values in the above equation
P(Red) = 7/20
Evaluate
P(Red) = 0.35
Express as percentage
P(Red) = 35%
Hence, the experimental probability of landing on red is 7/20 or 0.35 or 35%
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What is the explicit formula for this sequence?
-9,-3,3,9,15
Answer: A
Step-by-step explanation:
Normally in choice questions, I would choose to substitute the values into the formulas but I think it is better if I explain to you.
In a sequence, if the numbers increase by d each time and the first number in the sequence is [tex]a_{1}[/tex], then the explicit formula is [tex]a_{1}[/tex] + (n - 1)d when n is the order of the number in the sequence, like n = 1 for the first number, n = 2 for the second number and so on. Using this, we get that the answer to this problem is [tex]a_{n}[/tex] = -9 + (n - 1)6 so the answer is A
Vector u has initial points at (21,12) and it’s terminal point at (19,-8). Vector v has a direction opposite that of u. Who’s magnitude is five times the magnitude of v. Which is the correct form of vector v expressed as a linear combination of the unit vectors i and j?
The correct form of vector v expressed as a linear combination of the unit vectors i and j is [tex]\vec v = 10\,\hat{i} + 100\,\hat{j}[/tex].
What is the value of a vector with respect to another vector?
First, we need to determine the value of the vector u by subtracting two vectors whose initial points are at the origin:
[tex]\vec u = (19\,\hat{i} - 8\,\hat{j}) - (21\,\hat{i} + 12\,\hat{j})[/tex]
[tex]\vec u = - 2\,\hat{i} - 20\,\hat{j}[/tex] (1)
According to the statement, vector v is antiparallel to vector u and its magnitude is five times as the magnitude of vector v, which means that (1) must be multiplied by two scalars:
[tex]\vec v = - 1 \,\cdot \, 5\cdot \vec u[/tex] (2)
Please notice that antiparallelism is represented by the scalar - 1, whereas the dilation is represented by the scalar 5.
[tex]\vec v = 10\,\hat{i} + 100\,\hat{j}[/tex]
The correct form of vector v expressed as a linear combination of the unit vectors i and j is [tex]\vec v = 10\,\hat{i} + 100\,\hat{j}[/tex].
Remark
The statement presents typing mistakes, correct form is shown below:
Vector u has initial points at (21, 12) and its terminal point at (19, - 8). Vector v has a direction opposite that of u, whose magnitud is five times the magnitud of v. Which is the correct form of vector v expressed as a linear combination of the unit vectors i and j?
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In the diagram below, ABC ~ DEC. What is the value of x?
A. 2
B. 3.5
C. 2.5
D. 3
Answer:
x = 3
Step-by-step explanation:
Please refer to the attached photo. (Apologies for the terrible drawing.)
Since we know triangles ABC and DEC are similar, we can use the ratio method to find x.
[tex] \frac{ec}{bc} = \frac{ed}{ba} \\ \frac{25}{5} = \frac{18 - x}{x} \\ \frac{18 - x}{x} = 5 \\ 18 - x = 5x \\ 18 = 5x + x \\ 6x = 18 \\ x = \frac{18}{6} \\ = 3[/tex]