Answer: D) x=-7 and x-1
Step-by-step explanation:
Solve by factoring
x^2+7x+x+7 <-- +1 and +7 add to 8 and multiply to 7
x(x+7)+(x+7)
(x+7)(x+1) = 0
x + 7 = 0
= -7
x + 1 = 0
x = -1
Therefore the solutions are x=-7 and x-1
Find the present value of $200 due in the future under each of these conditions:
a. 15% nominal rate, semiannual compounding, discounted back 4 years.
b. 15% nominal rate, quarterly compounding, discounted back 4 years.
c. 15% nominal rate, monthly compounding, discounted back 1 year.
d. Why do the differences in the PVs occur?
a. The Present value will be $123.60 (15% nominal rate, semiannual compounding, discounted back 4 years). b. The Present value will be $122.85 (15% nominal rate, quarterly compounding, discounted back 4 years. c. The Present value will be $181.96 (15% nominal rate, monthly compounding, discounted back 1 year). d. The differences in the present values (PVs) occur due to the compounding frequency and discounting period.
To find the present value (PV) of $200 due in the future under different conditions, we need to use the formula for present value and consider the compounding frequency and discounting period.
a. 15% nominal rate, semiannual compounding, discounted back 4 years:
In this case, we use the formula PV = FV / (1 + (r/n))^(n*t), where FV is the future value, r is the nominal rate, n is the compounding frequency per year, and t is the number of years.
PV = $200 / (1 + (0.15/2))^(2*4)
PV = $200 / (1.075)⁸
PV = $123.60
b. 15% nominal rate, quarterly compounding, discounted back 4 years:
Using the same formula:
PV = $200 / (1 + (0.15/4))^(4*4)
PV = $200 / (1.0375)¹⁶
PV = $122.85
c. 15% nominal rate, monthly compounding, discounted back 1 year:
PV = $200 / (1 + (0.15/12))^(12*1)
PV = $200 / (1.0125)¹²
PV ≈ $181.96
d. The differences in the present values (PVs) occur due to the compounding frequency and discounting period. When compounding occurs more frequently, such as semiannually or quarterly, the PV decreases because the interest is added more frequently, reducing the impact of compounding. On the other hand, when the discounting period is longer, as in the case of 4 years versus 1 year, the PV decreases because the future value is being discounted over a longer time period.
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Find the value of × in the parallelogram. The diagram is not to scale.
Given:
The angle P = (5x -8) degree and angle R = (4x + 2) degree
Required:
Find the value of × in the parallelogram.
Explanation:
We know the opposite angle of parallelogram equal and
\(\begin{gathered} \angle P+\angle R=180^{\circ} \\ 5x-8+4x+2=180^{\circ} \\ 9x-6=180^{\circ} \\ 9x=186 \\ x=\frac{186}{9} \end{gathered}\)Answer:
So, answered the question.
suppose there exists a hamming code of length 25 that corrects 2 errors. assuming that the probability of a correct transmission of an individual symbol is 0.75, find the probability that a message transmitted using this code will be correctly received.
The probability that a message transmitted using a Hamming code of length 25 and that corrects 2 errors will be correctly received is 0.6384.
Hamming codes use parity bits to detect and correct errors in the data. In this case, a code of length 25 with 2 error corrections can detect up to two errors and can correct up to one error.
Since the probability of a correct transmission of an individual symbol is 0.75, the probability of a correct transmission of the entire message is calculated by multiplying 0.75 by itself 25 times, giving a probability of 0.6384.
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.Find the largest subset S on which the given vector - valued function is continuous?
F = ( t/9+t^4, 7t^2-7t+1, ln (t+3))
.
The largest subset S on which the vector-valued function F is continuous is the interval (-3, ∞).
To find the largest subset S on which the given vector-valued function is continuous, we need to examine the individual component functions and identify any restrictions or conditions that could cause discontinuities.
Component 1: f1(t) = t/(9 + t^4)
This function is a rational function. It will be continuous for all real values of t except where the denominator equals zero: 9 + t^4 = 0. However, there are no real values of t that satisfy this equation, so f1(t) is continuous for all real values of t.
Component 2: f2(t) = 7t^2 - 7t + 1
This function is a polynomial function, and polynomial functions are continuous for all real values of t. Therefore, f2(t) is continuous for all real values of t.
Component 3: f3(t) = ln(t + 3)
The natural logarithm function is defined for the positive values of its argument. Therefore, t + 3 > 0, which implies t > -3. Hence, the function f3(t) is continuous for t > -3.
Taking all these considerations into account.The function is continuous for all values of t greater than -3.
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What is the line parallel to y = 3x + 5 that passes through the point (-8,4) in SLOPE INTERCEPT FORM
Answer:
y= -3/5 x
Step-by-step explanation:
i do not know
Answer:
y = 3x + 28
Step-by-step explanation:
Slope intercept form is y=mx+b. Because it is said that the line were looking for is parallel I can put in the same slope. Parallel lines always have the same slope.
Then plug in the coordinates to find the y-intercept.
4 = 3(-8) + b
4 = -24 + b
+24 +24
28 = b
So we know that b is equal to 28 so we can plug that in to get y = 3x + 28
Hope that helps and have a great day!
The revenue generated by the band is given by the expression 50x+150
Select all of the ordered pairs that are solutions to the inequality:
50x + 150y > 1500
(1, 10)
(10, 1)
(0, 10)
(40, 0)
Answer:
(1, 10) and (40, 0)
Step-by-step explanation:
Given expression 50x+150
inequality is
50x + 150y > 1500
it means that if we plug value of x and y from given option in 50x+150 then it should be greater than 1500.
lets check for all the option
(1,10)
50*1 + 150*10 = 50+1500 = 1550
Since , 1550 is greater than 1500, (1,10) is the solution for the inequality given
(10, 1)
50*10 + 150*1 = 500+ 150 = 650
Since , 650 is less than 1500, (10,1) is not the solution for the inequality given
(0, 10)
50*0 + 150*10 = 0 + 1500 = 1500
Since , 1500 is equal to 1500 but not greater than 1500, (0,10) is not the solution for the inequality given
(40, 0)
50*40 + 150*0 = 2000 + 0 = 2000
Since , 200 is greater than 1500, (40,0) is the solution for the inequality given above.
Thus, from the given option there are two solution for 50x + 150y > 1500
(1, 10) and (40, 0)
(1, 10) (40, 0) as the person above/below stated.
HAIIIIIII PLS HELPPPPPP
dis is confusing -_-
Miguel has $30. He spends $8.00 on a movie ticket, $3.85 for snacks and $1.00 for bus fare each way.
How much money does Miguel have left?
Miguel has_____dollars left
Answer:
$16.5
Step-by-step explanation:
$30-$8-$3.85-$1-$1 = $16.5
Simplify by collecting like terms. - Can someone pls help me with these i dont understand. Very appreciated if you do :)
a) 3x + 5 + 2x + 1
b) 3 + 7y + 8 + y
c) 2k + 3m + 4m + 6k
d) 7u + v + v + u
e) 8n + 5 - 3n - 2
f) 4p + 7q - 3q - p
Answer:
a)5x+6
b) 8y+11
c) 8k+7m
d) 8u+2v
e) 5n+3
f) 3p-4q
Step-by-step explanation:
3x+2x=5x 5+1=6
8+3=11 7y+y=8y (basically a 1 in front of the y so just pretend it has a 1 in front of it)
2k+6k=8k 3m+4m=7m
7u+u=8u v+v=2v (same thing like before imagine a 1 in front of all non-coefficient variables.)
8n-3n=5n 5-2=3
4p-p= 3p 7q-3q= 4q
:)
Answer:
The answers are below. All you need to do is add the numbers with the same variable (letter) and if they do not have the same variable, then you cannot add them and leave as is.
You also need to add the numbers with no variables together.
Step-by-step explanation:
a)5x+6
b) 8y+11
c) 8k+7m
d) 8u+2v
e) 5n+3
f) 3p-4q
1. A manager has formulated the following LP problem. Draw the graph and find the optimal solution. (In each, all variables are nonnegative).
Maximize: 10x+15y, subject to 2x+5y ≤ 40 and 6x+3y ≤ 48.
The LP problem is to maximize the objective function 10x+15y subject to the constraints 2x+5y ≤ 40 and 6x+3y ≤ 48. By graphing the constraints and identifying the feasible region, we can determine the optimal solution.
To find the optimal solution for the LP problem, we first graph the constraints 2x+5y ≤ 40 and 6x+3y ≤ 48. These constraints represent the inequalities that the variables x and y must satisfy. We plot the lines 2x+5y = 40 and 6x+3y = 48 on a graph and shade the region that satisfies both constraints.
The feasible region is the area where the shaded regions of both inequalities overlap. We then identify the corner points of the feasible region, which represent the extreme points where the objective function can be maximized.
Next, we evaluate the objective function 10x+15y at each corner point of the feasible region. The point that gives the highest value for the objective function is the optimal solution.
By solving the LP problem graphically, we can determine the corner point that maximizes the objective function. The optimal solution will have specific values for x and y that satisfy the constraints and maximize the objective function 10x+15y.
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Jim is buying some clothes at Kohls. He buys a jacket that costs $75 and 5 pairs of shorts that each cost the same amount. He spends a total of $175 on the shorts and jacket. Write and solve an equation to find the cost of each pair of shorts.
The equation to find the cost of each pair of shorts is 175 = 75 + 5x where each short cost $20
How to write and solve an equation?Cost of jackets= $75
Number of shorts= 5
Cost of each short = x
Total amount Jim spent= $175
Total amount Jim spent = Cost of jackets + (Number of shorts × Cost of each short)
175 = 75 + 5x
subtract 75 from both sides
175 - 75 = 5x
100 = 5x
divide both sides by 5
x = 100/5
x = $20
Ultimately, each pair of shorts cost $20
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Can someone please answer this i will give brainliest if i can
Answer:
For bag C
Step-by-step explanation:
Bag C has more blue marbles than red ones
PLEASE PLEASE ITS DO TODAY
There are 800 students in a school. Based on a random sample of 50 students, Sean estimates that 80 students in the school have birthdays in November.
To estimate the number of students in the school who have birthdays in November based on a random sample, we can set up a proportion using the given information.
Let x represent the number of students in the school who have birthdays in November. We can set up the following proportion:
50 (sample size) / 800 (total number of students) = 80 (number of November birthdays) / x (number of students with November birthdays)
To solve for x, we can cross-multiply and solve the equation:
50 * x = 800 * 80
x = (800 * 80) / 50
x = 1280
Therefore, based on Sean's estimate from the random sample, there are approximately 1280 students in the school who have birthdays in November.
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What is the average rate of change for this quadratic function for the interval from x = 0 to x = 2?
Answer:
8
Step-by-step explanation:
The average rate of change for this quadratic function for the interval from x = 0 to x = 2 is -2
What is a function?A relation is a function if it has only One y-value for each x-value.
The average rate of a function f(x) from x=a to x=b is given as:
= f(b)-f(a)/b-a
Clearly we are asked to find the average rate of change from x=0 to x=2.
i.e. a=0 and b=2
Also, from the graph it could be observed that:
f(0)=1
and f(2)=-3
=f(2)-f(0)/2-0
=-3-1/2
=-4/2
=-2
Hence, the average rate of change for this quadratic function for the interval from x = 0 to x = 2 is -2
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Gabe is the human resources manager for the Advanced Scientific Research Lab. He has to record
the heights (in centimeters) and weights (in pounds) for each of the scientists in the lab.
Height distribution (cm): 178, 163, 174, 186, 154, 167, 167, 181, 159, 165, 177, 191, 158
Weight distribution (lbs): 157, 163, 190, 187, 183, 173, 184, 189, 193, 192, 177, 173, 168
What is the shape of the height and weight distribution?
Last option: The height and weight distributions, respectively, show positive and negative skews.
We know that,
Graphs are used to represent information in bar charts. To depict values, it makes use of bars that reach various heights. Vertical bars, horizontal bars, clustered bars (multiple bars that compare values within a category), and stacked bars are all possible options for bar charts.
we have,
There isn't a lot of data, but it shows that the weights have a negative skew and the heights have a positive skew, with the long tails pointing in opposite directions.
change/ starting point * 100
2.5 millions of books were sold in 1991.
Millions of books sold in 1992 equaled 3.4.
Change = 0.9 (in millions).
0.9/2.5 * 100
= 36%
The height and weight distributions, respectively, show positive and negative skews.
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Determine the period.
Answer:
shopkeeper sells a book at INR 960 for a profit of 20% and another book at INR 720 for a loss of 10%. Find the total profit/loss of the shopkeeper
Kim invested $11,000 in two mutual funds. One of the funds rose 6% in one year, and the other rose 9% in one year. If Kim’s investment rose a total of $846 in one year, how much did he invest in each mutual fund?
If Kim invested $11,000 in two mutual funds. Kim invested $4,800 in one mutual fund and $6,200 in the other mutual fund.
What is the amount invested?Kim invested x amount in the fund that rose by 6%
Kim invested (11,000 - x) amount in the fund that rose by 9%.
Increase in value from the first fund = 0.06x.
Increase in value from the second fund = 0.09(11,000 - x).
Total increase in value is $846
So,
0.06x + 0.09(11,000 - x) = 846
Let's solve this equation:
0.06x + 990 - 0.09x = 846
-0.03x = -144
x = -144 / -0.03
x = 4,800
Kim invested $4,800 in the fund that rose by 6% and the remaining amount of $11,000 - $4,800 = $6,200 in the fund that rose by 9%.
Therefore Kim invested $4,800 in one mutual fund and $6,200 in the other mutual fund.
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darwin's geometric ratio of increase pertains specifically to
Darwin's geometric ratio of increase pertains specifically to the growth rate of populations in biological organisms. According to Darwin's theory of evolution, populations have the potential to increase exponentially over time if certain conditions are met. The geometric ratio of increase, often denoted as "r" or the intrinsic rate of natural increase, represents the factor by which a population multiplies during each reproductive cycle or generation.
In the context of natural selection, individuals with higher reproductive rates (higher r-values) have a greater chance of passing on their genetic traits to the next generation. Over time, this can lead to significant population growth and evolutionary changes within a species. However, the geometric ratio of increase is limited by various factors, such as availability of resources, competition, predation, and environmental constraints, which can result in a balance between population growth and environmental carrying capacity.
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Rectangle A has side lengths measuring 4 inches and 9 inches. Rectangle B is similar to rectangle A but has side lengths three times longer
than rectangle A.
What is the area of rectangle B?
O A. 12 square inches
OB. 36 square inches
O c. 78 square inches
O D. 108 square inches
O E. 324 square inches
Priyanka drives at 45km/h and reaches Delhi in 5 hours.What time will she take to complete the same journey if she increases her speed by 5km/h ?
Answer: Increasing her speed by 5km/h, she will take 4.5 hours to complete the journey.
Step-by-step explanation:
Step 1
Speed= Distance / TIme
Given Speed = 45km/h
and Time = 5 hours
Distance covered = Speed x Time
= 45 km/h x 5 hours
=225 kilometres.
Step 2
Increasing her speed by 5km/h makes the new Speed = 45 +5 = 50 km/h
At the same Distance of 225 km
Therefore she will complete the journey in
Time = Distance/ Speed
=225km/ 50km/h
=4.5 hours
Which type of function best models the data in the table? Use difference or ratios.
(Show work)
Y: -1, 0, 1, 2, 3.
X: 2.5, 5, 10, 20, 40.
The answer : exponential (common ratio : 2)
I just need help with connecting the data table to the answer!
To find the equation of a perpendicular line, we need to know that the slope of the perpendicular line is the negative reciprocal of the slope of the given line. In this case, the given line has a slope of 1. Therefore, the slope of the perpendicular line would be -1/1, which simplifies to -1.
Next, we can use the point-slope form of the equation of a line to find the equation of the perpendicular line. This form is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.
Since we know that the perpendicular line intersects the point (-2, 4), we can plug in these values for x1 and y1. We also know that the slope of the perpendicular line is -1. Plugging these values into the point-slope form, we get:
y - 4 = -1(x + 2)
Simplifying, we can distribute the -1:
y - 4 = -x - 2
Adding 4 to both sides, we get:
y = -x + 2
So the equation of the perpendicular line is y = -x + 2. This line is perpendicular to y = x + 3 and intersects the point (-2, 4).
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Terry makes $2400 per month in gross income. His net earnings are 80% of his gross. His utility bills total $150. What percentage of Terry's net earnings is he spending on utilities?
Answer:
7.81%
Step-by-step explanation:
First, you have to calculate the net earnings by calculating the 80% of the gross income:
gross income= $2,400
net earnings= $2,400*80%= $1,920
Then, you have to calculate the percentage that represents the utility bills spending from the net earnings by dividing $150 by the net earnings and multiplying for 100:
($150/$1,920)*100= 7.81%
According to this, the answer is that 7.81% of Terry's net earnings are spent on utilities.
Answer:
7.8
Step-by-step explanation:
∛a² does anyone know it
The equivalent expression of the rational exponent ∛a² is \((a)^{\frac{2}{3}\).
What is a rational exponent?Rational exponents are exponents that are fractions, where the numerator is a power and the denominator is a root.
So rational exponents (fractional exponents) are exponents that are fractions or rational expressions.
To determine the rational exponent equivalent to the expression given, we will apply the power rule of indices as shown below.
The given expression is ;
∛a²
The rational exponent is calculated as follows;
∛a² = \((a)^{\frac{2}{3}\)
Thus, based on exponent power rule, the given expression is equivalent to ∛a² = \((a)^{\frac{2}{3}\)
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The complete question is below:
Find the equivalent expression of the rational exponent ∛a². does anyone know it
formula area of the square
Which of the following measurements is greater than 0.75 kilometers?
950 meters
9,500 centimeters
95 millimeters
9.5 decameters
The requried measurement that is greater than 0.75 kilometers is 950 meters, as 0.95 kilometers is greater than 0.75 kilometers.
To compare the given measurements to 0.75 kilometers, we need to convert them to the same unit of length.
950 meters = 0.95 kilometers
9,500 centimeters = 95 meters = 0.095 kilometers
95 millimeters = 0.095 meters = 0.000095 kilometers
9.5 decameters = 95 meters = 0.095 kilometers
Therefore, the measurement that is greater than 0.75 kilometers is 950 meters, as 0.95 kilometers is greater than 0.75 kilometers.
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Classify the following triangle. Check all that apply.
A. Obtuse
B. Acute
C. Isosceles
D. Right
E. Equilateral
F. Scalene
Answer:
C. Isosceles
E. Equilateral
F. Scalene
D. Right angled
I need help ASAP !!!!!
Answer:
B
Step-by-step explanation:
60+40+x=180(angles in a triangle)
x= 180-100
x=80°
80+z=180(angles on a str line)
z= 100°
100+15+y=180(angles in a triangle)
y=180-115
y=65°
Answer:
c: x = 80, y = 65, z = 100
Step-by-step explanation:
The sum of all angles in a triangle is 180
so 40 + 60 + x = 180 and 15 + y + z = 180
40 + 60 + x = 180
100 + x = 80
x = 80
supplementary angles are equal to 180
x and z are supplementary
80 + z = 180
z = 100
15 + 100 + y = 180
115 + y = 180
y = 65
1.22 sin(360-x) .cos 17' (1-cos²x) 73°.cos(90°-2x) cos(360°+z)tan(-x)sin
Answer:
Step-by-step explanation:
So according to me the solution can be determine with some assumptions. So, the simplified expression for the given question is:
-0.708 cos²(x) sin(x) cos(z) tan(x).
Define Trigonometry?Trigonometry is a branch of mathematics that deals with the study of relationships and properties of angles, triangles, and trigonometric functions. It focuses on the measurement and calculation of angles, the relationships between the sides and angles of triangles, and the study of the periodic functions called trigonometric functions.
In trigonometry, the three primary functions that are commonly used are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan respectively. These functions are used to relate the angles of a right triangle to the lengths of its sides.
Before we proceed with solving the given expression, let's simplify the trigonometric identities involved in it:
sin(360 - x) = sin(360)cos(x) - cos(360)sin(x) = cos(x)
cos(90 - 2x) = sin(2x) = 2sin(x)cos(x)
tan(-x) = -tan(x) [since tangent is an odd function
Now, substituting the above values in the given expression, we get:
1.22 cos(x) cos 17' (1-cos²x) 73° [2sin(x)cos(x)] [cos(360+z)] [-tan(x)]
Simplifying further, we get:
1.22 cos(x) cos 17' (1-cos²x) sin(x) cos(360+z) (-tan(x))
Now, cos(360+z) = cos(z) [since cosine is a periodic function with a period of 360°]
Substituting the value of cos(17') as 0.9998 (approximately), and cos(73°) as 0.2763 (approximately), we get:
1.22 cos(x) (0.9998) (1-cos²x) sin(x) cos(z) (-tan(x)) (0.2763) (2.1355)
Simplifying further, we get:
-0.708 cos²(x) sin(x) cos(z) tan(x)
Therefore, the simplified expression for the given question is -0.708 cos²(x) sin(x) cos(z) tan(x).
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for a rectangle with a perimeter 60 to have the largest area, what dimensions should it have? (enter the smaller value first.)
Answer:
This gives us a square with an area of 225 square units.
Step-by-step explanation:
To find the dimensions of the rectangle with the largest area for a given perimeter of 60, we need to use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
In this case, we know that P = 60, so we can write:
60 = 2l + 2w
Simplifying this equation, we get:
30 = l + w
To find the largest area of the rectangle, we need to maximize the product of the length and the width, which is the formula for the area of a rectangle, A = lw.
We can solve for one variable in terms of the other using the equation above. For example, we can write:
w = 30 - l
Substituting this expression for w into the formula for the area, we get:
A = l(30 - l)
Expanding and simplifying this expression, we get:
A = 30l - l^2
This is a quadratic equation in l, which has a maximum value when l is halfway between the roots. We can find the roots using the quadratic formula:
l = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = -1, b = 30, and c = 0, so we get:
l = (-30 ± sqrt(30^2 - 4(-1)(0))) / 2(-1)
Simplifying, we get:
l = (-30 ± sqrt(900)) / -2
l = (-30 ± 30) / -2
So the roots are l = 0 and l = 30. We want the smaller value first, so we take l = 0 and find w = 30. This would give us a rectangle with zero area, so it is not a valid solution.
The other root is l = 30, which gives us w = 0. Again, this is not a valid solution because we need both dimensions to be positive.
Therefore, the dimensions of the rectangle with the largest area for a perimeter of 60 are:
l = 15 and w = 15
This gives us a square with an area of 225 square units.
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Suppose that f(t) is differentiable and positive for a stsb. Let C be the path r(t) = ti + f(t)j, a ≤t≤ b, and F = yi. Is there any relation between the value of the work integral F. dr and the area of the region bounded by the t-axis, the graph of f, and the lines t= a and t= b. Give reasons for your answer. ISF. с Choose the correct answer below. t=b O A. Yes, because ·SF•dr= S f'(t) dt, which is equal to the noted area. с t=a t=b O B. No, because • fF.dr = f t dt, which is not related to the noted area. t=a t=b O C. No, because SF.dr = f(t) dt, which is not related to the noted area. C t=a t=b O D. Yes, because SF•dr= S f(t) dt, which is equal to the noted area. C t=a
The value of the work integral F·dr is related to the area of the region bounded by the t-axis, the graph of f, and the lines t = a and t = b. The correct answer is A: Yes, because ∫F·dr = ∫f'(t) dt, which is equal to the noted area.
The work integral measures the work done by a force field along a path. In this case, the force field is given by F = yi, and the path is defined as r(t) = ti + f(t)j. To calculate the work integral, we need to evaluate F·dr, which is the dot product of the force field and the differential displacement vector dr.
Now, dr = (dx)i + (dy)j, and since r(t) = ti + f(t)j, we can find that dx = dt and dy = f'(t) dt. Therefore, dr = dti + f'(t) dtj.
Taking the dot product F·dr, we have F·dr = (yi)·(dti + f'(t) dtj) = 0 + f'(t) dt = f'(t) dt.
The integral of f'(t) dt with respect to t gives us the area under the curve of f(t) between t = a and t = b. Therefore, ∫F·dr is indeed equal to the noted area, establishing the relation between the work integral and the bounded region. Hence, the correct answer is A.
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Question 1(Multiple Choice Worth 4 points) Which expression is equivalent to g-m=g"? Og-m+n Og mn Og-m-n Og-m+n
Answer: g-m-n
Step-by-step explanation: g^{-m} ÷ g^n
g-^m/g-n