The temperature in Buenos Aires can be modeled using the equation T(t) = 5 sin(2π(t - 182.5)/365) + 27, where t is the number of days since January 1.
How to model temperature in Buenos Aires?To model the temperature in Buenos Aires using a trigonometric function, we can use the sine function.
First, we need to find the amplitude, period, phase shift, and vertical shift.
Amplitude: The difference between the maximum and minimum temperatures is (37 - 17) / 2 = 10 degrees, so the amplitude is 10/2 = 5 degrees.Period: The period of the function is 365 days, which is the length of a year.Phase shift: January 7 is in the summer, so we want to shift the function to the right by half a year (182.5 days).Vertical shift: The average temperature over the year is (37 + 17) / 2 = 27 degrees, so the vertical shift is 27 degrees.Putting it all together, the equation for the temperature in Buenos Aires as a function of time is:
T(t) = 5 sin(2π(t - 182.5)/365) + 27
Where t is the number of days since January 1 and T(t) is the temperature in degrees Celsius.
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What is the graph of g?
Answer:
Vertical Compression by factor of 1/4
Step-by-step explanation:
Two methods:
Method 1. Transformations
Method 2. Algebraic input-output tables
Method 1. Transformations
The Main concept of this question is about Transformations of functions -- specifically, multiplying on the outside by a positive number less than 1.
The transformation that occurs when multiplying a function by a positive number on the outside of the function is a vertical stretch or compression.
Positive numbers larger than 1 will stretch it vertically, whereas positive numbers smaller than 1 will compress it vertically.
Therefore, multiplying by 1/4 on the outside, a positive number less than 1, will vertically compress the function down to one-fourth the size.
This means that for g(x), all points on the original function f will have their heights reduced to 1/4 their original height (or depth) -- making all points on g(x) 1/4 their previous distance from the x-axis on the "f" function.
Method 2. Algebraic input-output tables
Observe on the graph three points on the function f:
(0,0), (1,4) and (3,0) --- points on the function "f"In function notation, this means [tex]f(0)=0[/tex], [tex]f(1)=4[/tex], and [tex]f(3)=0[/tex]Using the equation relating f and g, [tex]g(x)=\frac{1}{4}f(x)[/tex], we can find how those points would look like on the new function g(x).
For [tex]f(0)=0[/tex]
[tex]g(0)=\frac{1}{4}[f(0)]\\g(0)=\frac{1}{4}[0]\\g(0)=0[/tex]
For [tex]f(1)=4[/tex]
[tex]g(1)=\frac{1}{4}[f(1)]\\g(1)=\frac{1}{4}[4]\\g(1)=1[/tex]
For [tex]f(3)=0[/tex]
[tex]g(3)=\frac{1}{4}[f(3)]\\g(3)=\frac{1}{4}[0]\\g(3)=0[/tex]
These known points should correctly identify the graph from the possible choices.
Solve the write an equation of the line that passes through a pair of points a. y=x+3 b. y=x-3 c. y=-x+2 d. y=-x-2
The equation of the line passing through the points (0,-2) and (2,0) is y = x - 2.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division, and can be represented using symbols and/or words. Equations are used to solve problems in mathematics, science, engineering, and other fields.
In the given question,
We can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
First, we need to find the slope of the line passing through the points (0,-2) and (2,0):
slope = (change in y)/(change in x)
slope = (0 - (-2))/(2 - 0)
slope = 2/2
slope = 1
Now that we have the slope, we can use one of the given equations and substitute the coordinates of one of the points to find the y-intercept:
y = mx + b
-2 = 1(0) + b
b = -2
So the equation of the line passing through the points (0,-2) and (2,0) is y = x - 2.
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What value of x is in the solution set of the inequality 8x – 6 > 12 + 2x?
a. –1
b.0
c. 3
d. 5
Answer:
D.5
Step-by-step explanation:
8x – 6 > 12 + 2x
= 8x−2x>12+6= 6x>18
= x>38x−2x>12+6
= 6x>18
= x>3
From the given options the only value which is greater than 3 is Option (D) 5
48 X 25 = 24 x is what
Answer:
x=50
Step-by-step explanation:
1. multiply the numbers
48x25=24x
1200=24x
2. Divide both sides by the same factor
1200/24 = 24/24x
simplify the expression
x=50
Use the rules to find derivatives of the following functions at the specified values. a. f(x) = 2x³ at x = 2 f' (2)= g(z) =13x ½ at x = 3 g' (3)= h(z)= hx at x = 4 j(z) 130x¯¹ at x = 5 j' (5)=
The power rule for derivatives is -26/5.
The derivative is a fundamental concept that measures how much a function changes as its input changes. It is a mathematical tool used to find the instantaneous rate of change of a function at a specific point. The derivative of a function f(x) at a point x=a, denoted by f'(a), is the slope of the tangent line to the graph of f(x) at the point (a, f(a)).
a. f(x) = 2x³
Using the power rule for derivatives, we have:
f'(x) = 6x²
So, f'(2) = 6(2)² = 24.
b. g(x) = 13x^(1/2)
Using the power rule for derivatives, we have:
g'(x) = (1/2) * 13x^(-1/2) = (13/2√x)
So, g'(3) = (13/2√3).
c. h(x) = hx
Using the power rule for derivatives, we have:
h'(x) = h
So, h'(4) = h.
d. j(x) = 130x^(-1)
Using the power rule for derivatives, we have:
j'(x) = -130x^(-2)
So, j'(5) = -130(5)^(-2) = -130/25 = -26/5.
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Max's niece pushed a playground merry-go-round so that it travels 4. 5 feet along the
curve. The radius of the merry-go-round is 5 feet. Find, to the nearest degree, the
central angle.
The central angle is approximately 51.6 degrees.
How to find the Arc length of a central angle?To solve this problem, we can use the formula for arc length of a circle:
arc length = θ × r
where θ is the central angle in radians, and r is the radius of the circle.
We know that the arc length is 4.5 feet and the radius is 5 feet. So we can rearrange the formula to solve for θ:
θ = arc length / r
θ = 4.5 / 5
θ = 0.9 radians
To find the central angle in degrees, we can convert radians to degrees by multiplying by 180/π:
θ = 0.9 × (180/π)
θ ≈ 51.6 degrees
Therefore, the central angle is approximately 51.6 degrees.
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Find the volume of the solid generated when the right triangle below is rotated about
side IK. Round your answer to the nearest tenth if necessary.
The volume of the solid generated when the right triangle below is rotated about side IK is: 37.7 units²
What is the volume of a cone?The three-dimensional figure that is formed by rotating a triangle about it's height is called a Cone.
Where:
The triangle base length will be seen to become the radius of the cone
The triangle height will be seen to become the height of the cone
The formula for the volume of a cone is expressed as:
V = ¹/₃πr²h
Where:
r refers to the radius
h refers to the height
Therefore, we can say that the volume will be expressed as:
V = ¹/₃ * π * 2² * 9
V = 37.7 units²
Thus, that is the volume of the solid generated when the right triangle below is rotated about side IK.
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Solve for x. Assume that lines which appear tangent are tangent.
How do I do number 3?
Answer:
V = 1,728 mi³
SA = 864 mi²
Step-by-step explanation:
We can find the volume of the triangular prism by multiplying the area of one of the triangle faces by the prism's depth.
First, we can solve for the area of one of the triangle sides:
A(triangle) = (1/2) · b · h
A(triangle) = (1/2) · 24 · 18
A(triangle) = 12 · 18
A(triangle) = 216 mi²
Next, we can get the volume of the prism by multiplying the area of the triangle face by the prism's depth.
V = A(triangle) · depth
V = 216 · 8
V = 1,728 mi³
__
We can find the surface area by finding the area of each side, then adding all of those areas together.
We already know that the area of each of the triangle sides is 216 mi².
Now, we can solve for the area of the base.
A(base) = length · width
A(base) = 24 · 8
A(base) = 192 cm²
Then, we can find the area of the top side.
A(top) = length · width
A(top) = 30 · 8
A(top) = 240 mi²
Finally, we can solve for the surface area of the prism by adding the areas of each of its sides.
SA = (2 · A(triangle)) + A(base) + A(top)
SA = 2(216) + 192 + 240
SA = 432 + 192 + 240
SA = 624 + 240
SA = 864 mi²
Simplify (4x − 6) + (5x + 1). Group of answer choices 9x + 5 9x − 5 x − 5 −x − 5
Answer:
Combining like terms,
(4x - 6) + (5x + 1) = 9x - 5
Beckett asked his classmates, "How many days do you floss your teeth
typical week?" The table shows Beckett's data.
Days of Flossing per Week
7
7
7
4
3
1
0
6
6
7
2.
6
5
3
N
4
How many observations did he record?
A. 20
B. 12
O c. 4
O D. 16
Answer: B
Step-by-step explanation: I did the quiz :p
Hope this helps
The correct answer is B. 12. There are 12 numbers in the table, which represents the number of observations Beckett recorded.
The table shows the number of days each of Beckett's classmates floss their teeth in a typical week. The number of observations recorded is simply the number of classmates, or the number of entries in the table. In this case, there are 12 entries, so the answer is 12.
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PLEASE ANYONE 100 POINTS LOL
a ⃗=⟨-9,6⟩ and b ⃗=⟨3,1⟩. What is the component form of the resultant vector 1/3 a ⃗- 2b ⃗ ?
Show all your work.
The resultant component of the vector addition, 1/3a - 2b is (-9, 0).
What is the resultant component of the vectors?The resultant component of the vector is calculated as follows;
a = (-9, 6)
b = (3, 1)
The result of 1/3a = ¹/₃ (-9), ¹/₃(6) = (-3, 2)
The result of 2b = 2(3, 1) = (6, 2)
The result of the vector addition is calculated as follows;
1/3a - 2b
= (-3, 2) - (6, 2)
= (-3 -6, 2 -2)
= (-9, 0)
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Pediatricians prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of a child's weight. how many milliliters of acetaminophen will the doctor prescribe for jocelyn, who weighs 40 pounds?
The doctor would prescribe 8 milliliters of acetaminophen for Jocelyn, who weighs 40 pounds.
According to the given information, pediatricians prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of a child's weight. So, if a child weighs 50 pounds, the doctor would prescribe 10 ml of acetaminophen.
Now, let's apply this formula to Jocelyn's weight. As Jocelyn weighs 40 pounds, we need to calculate how many 25-pound increments her weight contains. To do this, we can divide her weight by 25:
40 pounds ÷ 25 pounds = 1.6 increments
This means that Jocelyn's weight is equivalent to 1.6 times the 25-pound increment used in the prescription. To determine the amount of acetaminophen she needs, we can multiply 5 ml (the prescribed dose for 25 pounds) by 1.6:
5 ml × 1.6 = 8 ml
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How many more cubic inches of popcorn does the jumbo size hold compared to the regular size round to the nearest tenth
Cubic inches of popcorn does the jumbo size hold compared to the regular size round to the nearest tenth
To determine how many more cubic inches of popcorn the jumbo size holds compared to the regular size, you would need to:
1. Find the volume (in cubic inches) of both the jumbo and regular size popcorn containers.
2. Subtract the volume of the regular size container from the volume of the jumbo size container.
Unfortunately, without specific dimensions for the jumbo and regular size popcorn containers, I cannot provide a numerical answer. Please provide the dimensions, and I would be happy to help you with the calculations.
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A point on the rim of a wheel moves with a velocity of 100 feet per second. Find the angular velocity of the point if the diameter of the wheel is 8 feet.
The angular velocity of the point on the rim of the wheel is 25 radians per second.
The linear velocity of a point on a wheel's rim is determined by:
v = rω
v = linear velocity
r = radius of the wheel
ω = angular velocity.
In this case, the diameter of the wheel is 8 feet, so the radius is 4 feet. The linear velocity is given as 100 feet per second, so we have:
100 = 4ω
Solving for ω, we get:
ω = 25 radians per second
Therefore, the angular velocity of the point on the rim of the wheel is 25 radians per second.
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determine the value of the following line segment lengths and angle measures. round
your answers to the nearest tenth of a yard for line segments and the nearest degree for
angles.
ap =
bp =
ac =
bc =
mzcab =
algebranations
mlacb =
algebra
ou
I'm sorry, but I cannot determine the values of the line segment lengths
and angle measures without further information or context about the
geometry problem. Please provide me with more details or the specific
problem in question.
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In 1980, there were 1. 2 million elephants living in Africa. Because the natural grazing lands for the elephant are disappearing due to increased population and cultivation of the land, the number of elephants has decreased by about 6. 8% per year. In 1987, what was the population of elephants? Round up to the nearest elephant
There were approximately 586,800 elephants in Africa, rounded up to the nearest elephant.
In 1980, there were 1.2 million elephants in Africa. With a decrease of 6.8% per year, we need to calculate the population in 1987, which is 7 years later.
To find the population in 1987, we use the formula:
Final population = Initial population * (1 - decrease rate) ^ number of years
Final population = 1,200,000 * (1 - 0.068) ^ 7
Final population ≈ 1,200,000 * 0.489
Final population ≈ 586,800
In 1987, there were approximately 586,800 elephants in Africa, rounded up to the nearest elephant.
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A telephone calling card company allows for $0.25 per minute plus a one-time service charge of $0.75. If the total cost of the card is $5.00, find the number of minutes you can use the card.
Answer:
Answer:17
Explanation: 5-0.75=4.25 4.25÷0.25=17
Hope this helps
The stem-and-leaf plot shows the number of push-ups done by each student in a Physical Education class. What is the mode of the number of push-ups?
The mode of the number of push-ups is 40.
What is the mode of the number of push-ups shown in the stem-and-leaf plot for a Physical Education class?A stem-and-leaf plot is a way of organizing data where the stems (the tens digit) and leaves (the ones digit) are separated. Each row represents a stem and the leaves represent the values that belong to that stem.
Here's the stem-and-leaf plot for the number of push-ups:
3 | 5 6 8
4 | 0 0 1 2 2 3 5 6 8 9
5 | 0 1 3 4 5 5 7 8 9
6 | 0 1 2 2 3 4 5 7 8 9
7 | 0 2 5 8
8 | 1 2 4
9 | 0
To find the mode, we look for the value that appears most frequently. In this case, the number 40 appears three times, which is more than any other value. Therefore, the mode of the number of push-ups is 40.
Note that the stem-and-leaf plot makes it easy to see the distribution of the data. For example, we can see that there are a lot of values between 40 and 49, and relatively few values above 60.
We can also see that there are no values between 90 and 99.
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WILL GIVE BRAINLY AND 100PTS DUE IN A COUPLE HOURS BIG PROBLEM BUT PLS HELP MEAN THE WORLD.
Project Option 1—Individually
Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.
Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.
Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences.
Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology.
Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different.
02.03 Key Features of Linear Functions—Option 1 Rubric
Requirements Possible Points Student Points
Student changes equation to slope-intercept form. Student shows all work and identifies the slope and y-intercept of the equation. 4
Student writes a description, which is clear, precise, and correct, of how to graph the line using the slope-intercept method. 4
Student changes equation to function notation. Student explains clearly what the graph of the equation represents. 4
Student graphs the equation and labels the intercepts correctly. 4
Student writes at least three sentences explaining how the graphs of the two equations are the same and how they are different. 4
Note that where the above function is given, the equation in function notation is f(x) = (-2/3)x + 490. This function represents the profit Sal makes from lunch specials based on the number of sandwich and wrap lunch specials sold. See the graph attached.
What is the explanation for the above response?To change the given equation to slope-intercept form, we need to solve for y.
2x + 3y = 1470
3y = -2x + 1470
y = (-2/3)x + 490
Therefore, the slope of the line is -2/3 and the y-intercept is 490.
To graph this line using the slope-intercept method, we can plot the y-intercept first, which is (0, 490). Then, using the slope of -2/3, we can find another point by moving 2 units to the right and 3 units down from the first point. We can continue this pattern to plot additional points and then draw a straight line through them.
The equation in function notation is f(x) = (-2/3)x + 490. This function represents the profit Sal makes from lunch specials based on the number of sandwich and wrap lunch specials sold.
To graph the function, we can plot the intercepts (0, 490) and (735, 0), where 735 is the x-intercept. Then, using the slope of -2/3, we can find other points and draw a straight line through them.
If Sal's total profit on lunch specials for the next month is $1,593, then the equation would be 2x + 3y = 1593. The graphs of the functions for both months would have the same slope of -2/3, indicating that the profit per lunch special sold remains constant.
However, the y-intercept would be different, indicating a different starting profit for the month. The graphs would have different intercepts and intersect the y-axis at different points, reflecting the difference in starting profits.
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Which pair of adjacent angles is complementary?
A. Pair A
B. Pair B
C. Pair C
D. Pair D
Pair C of adjacent angles is supplementary because both the angles make the sum of 180°.
Adjacent angles are those angles which have a common vertex and supplementary angles are those which on adding make sum of 180°. In the given question, only the adjacent angles of Pair C make the sum of 180°.
Supplementary angles are those that total 180 degrees. Angles 130° and 50°, for example, are supplementary angles since the sum of 130° and 50° equals 180°.
Complementary angles, on the other hand, add up to 90 degrees. When the two additional angles are brought together, they form a straight line and an angle.
It should be emphasized, however, that the two supplementary angles do not have to be adjacent to each other. As a result, any two angles can be supplementary if their sum is equal to 180°.
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Correct question:
Which pair of adjacent angles is complementary?
A. Pair A
B. Pair B
C. Pair C
D. Pair D
Image is attached below.
Which of these words has a vertical line of symmetry? A BOB B HOD с TOT D KID E COOK
Answer:
A BOB, C TOT
Step-by-step explanation:
If we draw a vertical line throgh the word the left side is the mirror image of the right.
Among the 30 largest U. S. Cities, the mean one-way commute time to work is 25. 8 minutes. The longest one-way travel time is in New York City, where the meantime is 39. 7 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 7. 5 minutes.
A. What percent of New York City commutes are for less than 30 minutes?
B. What percent are between 30 and 35 minutes ?
A. Approximately 9.85% of New York City commutes are less than 30 minutes
B. Approximately 16.91% of New York City commutes are between 30 and 35 minutes.
How to find the commute time?A. To find the percent of New York City commutes that are less than 30 minutes, we need to calculate the z-score using the formula:
z = (x - μ) / σ
where x is the value we are interested in (30 minutes), μ is the mean commute time (39.7 minutes), and σ is the standard deviation (7.5 minutes).
z = (30 - 39.7) / 7.5 = -1.29
We can use a standard normal distribution table or calculator to find the area to the left of z = -1.29, which gives us:
P(z < -1.29) = 0.0985
Therefore, approximately 9.85% of New York City commutes are less than 30 minutes.
B. To find the percent of New York City commutes that are between 30 and 35 minutes, we need to calculate the z-scores for both values using the same formula:
z1 = (30 - 39.7) / 7.5 = -1.29
z2 = (35 - 39.7) / 7.5 = -0.62
We can then find the area between these two z-scores using a standard normal distribution table or calculator, which gives us:
P(-1.29 < z < -0.62) = P(z < -0.62) - P(z < -1.29) = 0.2676 - 0.0985 = 0.1691
Therefore, approximately 16.91% of New York City commutes are between 30 and 35 minutes.
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Find f'(-2) for f(x) = ln((x^4 + 5)^2). Answer as an exact fraction or round to at least 2 decimal places.
Using the chain rule, we have: f'(x) = 2ln(x^4 + 5) * 2(x^4 + 5)^1 * 4x^3
f'(x) = 16x^3 * ln(x^4 + 5) * (x^4 + 5)
To find f'(-2), we plug in -2 for x:
f'(-2) = 16(-2)^3 * ln((-2)^4 + 5) * ((-2)^4 + 5)
f'(-2) = -128 * ln(21) * 21
f'(-2) ≈ -599.92 (rounded to 2 decimal places)
Therefore, f'(-2) is approximately -599.92.
To find f'(-2) for the function f(x) = ln((x^4 + 5)^2), we will first find the derivative of the function, and then evaluate it at x = -2.
1. Differentiate the function using the chain rule:
f'(x) = (d/dx) ln((x^4 + 5)^2) = (1/((x^4 + 5)^2)) * (d/dx) ((x^4 + 5)^2)
2. Differentiate the inner function:
(d/dx) ((x^4 + 5)^2) = 2(x^4 + 5) * (d/dx) (x^4 + 5) = 2(x^4 + 5) * (4x^3)
3. Combine the derivatives:
f'(x) = (1/((x^4 + 5)^2)) * (2(x^4 + 5) * (4x^3)) = (8x^3(x^4 + 5))/((x^4 + 5)^2)
4. Evaluate the derivative at x = -2:
f'(-2) = (8(-2)^3((-2)^4 + 5))/((-2)^4 + 5)^2 = (-128(21))/(21^2) = -128/21
So, f'(-2) is -128/21 as an exact fraction.
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which rule explains why these triangles are congruent
Answer:
SSA
Step-by-step explanation:
It would be SSA (Side-Side-Angle). They are congruent where they intersect at B (opposite angles). Since CF is congruent to GH, and CB is congruent to HB, you have an angle and two sides congruent, in the order SSA.
3.
A local town has a population of 3,500 people and has grown by 2.5% each year. Write an exponential function that models the total population p after t years.
The exponential function that models the total population p after t years is p = 3,500 x 1.025^t.
What is the exponential?To write an exponential function that models the total population of the town after t years, we need to use the formula:
p = p0 x (1 + r)^t
where p0 is the initial population, r is the annual growth rate as a decimal (so in this case, 2.5% = 0.025), and t is the number of years.
In this case, we know that the initial population is 3,500, and the annual growth rate is 2.5%, or 0.025. So we can substitute these values into the formula to get:
p = 3,500 x (1 + 0.025)^t
Simplifying this expression gives:
p = 3,500 x 1.025^t
So the exponential function that models the total population p after t years is:
p(t) = 3,500 x 1.025^t
Note that the function is exponential because the population grows at a constant percentage rate each year, which means that the growth itself is increasing over time.
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Find all solutions of the equation algebraically.
|x| = x2 + x − 35
The solutions of the equation algebraically are x = 5 and x = -7
How to determine the valueFrom the information given, we have the quadratic equation;
|x| = x2 + x − 35
The sign , '| |' represents the modulus sign and says that the value must be a positive value.
Then, we have;
x² + x + x - 35
add the like terms
x² + 2x - 35
Find the pair factors of -35 that add up to 2, we have;
x² + 7x - 5x - 35
Group the expression in pairs
(x² + 7x) - (5x - 35)
factorize the expression
x(x + 7) - 5(x + 7)
Then, we have that;
x - 5 = 0
x = 5
x + 7 = 0
x = -7
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If Tara spends $219 a month for her car payment and she makes $3,200 a month, what percent of her monthly income is spent on her car payment? A. 8. 6% B. 680% C. 6. 8% D. . 68%
Answer:
Step-by-step explanation:
To find the percentage of Tara's monthly income spent on her car payment, we need to divide her car payment by her monthly income and then multiply by 100 to get the percentage:
$219 / $3,200 = 0.0684375
0.0684375 * 100 = 6.84375
So, Tara spends approximately 6.8% of her monthly income on her car payment.
The closest answer choice is C. 6.8%.
Answer:
C
Step-by-step explanation:
I got just did it and got it right
Find-F+2G+H-R using the Graphical Tail-to-Tip method.
F = 45.0 N [S 45° W]
G= 25.0 N[35° N of W]
H=70.0 N [E 15° S]
To find -F+2G+H-R using the Graphical Tail-to-Tip method, measure the magnitude and direction of this resultant vector to find the sum F+2G+H-R.
How to solveTo find the vector sum F+2G+H-R using the graphical tail-to-tip method, follow these steps:
Draw vector F: 45.0 N [S 45° W]Draw 2G: Multiply G by 2: 2 x 25.0 N [35° N of W] = 50.0 N [35° N of W]Draw vector H: 70.0 N [E 15° S]Draw vector R: Since we want to find the sum F+2G+H-R, R should be drawn in the opposite direction to balance the equation.Now, place the vectors tail-to-tip in the following order: F, 2G, H, and R (in opposite directions).
The sum of these vectors can be found by connecting the starting point (tail of F) to the endpoint (tip of R in the opposite direction).
Measure the magnitude and direction of this resultant vector to find the sum F+2G+H-R.
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how would you work the image attached out
The ratio of a : b : c : d is 3 : 7 : 2 : 7.
What are the ratios?The ratios are determined as follows from the data given.
The given data is:
7a = 2b
b = (7/2)a.
a and b have no common factors, thus a must be even and b must be odd.
c : d is 2 : 7
For an integer x, c = 2x and d = 7x
a : d is 3 : 1
So for an integer y, a = 3y and d = y
Substituting into 7a = 2b:
7(3y) = 2(7/2)y a
21y = 7y * b
b = 3a
Substituting these expressions for a and b into c : d = 2:7, we get:
2x : 7x = 3 : 1
2x = 3y and 7x = y
y = 14x/3
a : b : c : d = 3y : 7y : 2x : 7x
a : b : c : d = 3(3y) : 3(7y) : 3(2x) : 3(7x)
a : b : c : d = 9y : 21y : 6x : 21x
a : b : c : d = 3 : 7 : 2 : 7
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