In circle S with m/RST = 126 and RS = 3 units, find the length
of arc RT. Round to the nearest hundredth.
Answers
RT arc length 3.31 units (rounded to two decimal places).
What is a circle and what is its formula?A circle is indeed a closed arc that extends outward from a set point known as the center, with each point on the curve being equally spaced from the center. [tex](x-h)2 + (y-k)2 = r2[/tex] is the equation for a circle having a (h, k) center and a r radius.
We may employ the following equation to determine that length of a circle's arc:
length of arc =[tex](central angle / 360 degrees) x 2πr[/tex]
Where the circle's radius, r, is.
According to the information provided in this problem, m/RST = 126, the arc RT's center angle is 126 degrees. We are also told that RS = 3 units, which indicates that the circle's radius is 3 units (since all radii of a circle have the same length).
Applying the formula with these values, we obtain:
length of arc [tex]RT = (126 / 360) x 2π(3) ≈ 3.31 units[/tex]
We obtain the final response by rounding to the closest hundredth:
RT arc length 3.31 units (rounded to two decimal places).
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Related Questions
Who ever helps me, Get 100 points
Answers
Step-by-step explanation:
a) Area=144m²
side²= 144
side=12m
b) perimeter=32m
4×side=32
side=32/4
side=8m
Please help me with this question.
Answers
Substitute known values into formula:
448π = πr^2 x 7
Divide by 7 then by π to find the radius squared:
64 = r^2
Find r with square root of 64:
r = 8ft
Check:
π x 8^2 x 7 = 448π
Hope this makes sense and helps you out :)
A battery is charged. The percentage of the battery’s capacity that is charged as a function of time (in minutes) is graphed.
Answers
Answer:
what
Step-by-step explanation:
what
3) Jiya walks 6 km due east and then 8 km due north. How far is she from her
starting place?
6 km
8 km
Answers
Answer:
10km
Step-by-step explanation:
Pythagoras
Formula=[tex]a^2+b^2=c^2[/tex]
[tex]6^{2} +8^{2} =c^2\\c^2=100\\c=\sqrt{100} \\c=10km[/tex]
X^2=8^2+6^2
The 1948 and 2018 temperatures at 197 random locations across the globe were compared and the mean difference for the number of days above 90 degrees was found to be 2.9 days with a standard deviation of 17.2 days. The difference in days at each location was found by subtracting 1948 days above 90 degrees from 2018 days above 90 degrees.
What is the lower limit of a 90% confidence interval for the average difference in number of days the temperature was above 90 degrees between 1948 and 2018?
What is the upper limit of a 90% confidence interval for the average difference in number of days the temperature was above 90 degrees between 1948 and 2018?
What is the margin of error for the 90% confidence interval?
Does the 90% confidence interval provide evidence that number of 90 degree days increased globally comparing 1948 to 2018?
Does the 99% confidence interval provide evidence that number of 90 degree days increased globally comparing 1948 to 2018?
If the mean difference and standard deviation stays relatively constant would decreasing the degrees of freedom make it easier or harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.
If the mean difference and standard deviation stays relatively constant does lowering the confidence level make it easier or harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.
Answers
The lower limit of a 90% confidence interval for the average difference in the number of days the temperature was above 90 degrees between 1948 and 2018 is -22.8 days and the upper limit is 28.6 days.
The margin of error for the 90% confidence interval is 25.4 days.
The 90% confidence interval does provide evidence that the number of 90-degree days increased globally comparing 1948 to 2018.
The 99% confidence interval also provides evidence that the number of 90-degree days increased globally comparing 1948 to 2018.
If the mean difference and standard deviation stay relatively constant, decreasing the degrees of freedom would make it harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.
Lowering the confidence level would also make it harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.
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i need help with this
Answers
Answer:
1) [tex]y\leq 2x-3[/tex]
2)See below photo, or graph it yourself using [tex]y < 2 - \frac{1}{2} x[/tex]. This would look like the line for that equation, but dotted and shaded in below.
3) I disagree with Oscar. Because the equation for the second line is less than, not less than OR equal to, and that point falls right on the line for [tex]y < 2 - \frac{1}{2} x[/tex], it is not a valid solution.
Step-by-step explanation:
1) First, I found the slope. It's rising 2 over 1, so the slope is 2/1 or 2. Then, the y-intercept, which is -3. From there I created the equation.
2) I had to put this into slope-intercept form by subtracting x from both sides to get [tex]2y < 4-x[/tex]. Then I divided both sides by two to get [tex]y < 2 - \frac{1}{2} x[/tex]. Then I put it into an online graphing program (I used desmos's).
3) Explains itself!
Let me know if this helped by hitting thanks or brainliest. If not, please comment and I'll get back to you ASAP!
venus is known as the ''cloudy planet'' because it is covered with thick, yelllow clouds. The gravity of venus is 90% of earths gravity. To calculate your weight on venus, multiply your weight by 0.9
Answers
Answer:
Step-by-step explanation:
How does Priestley present the theme of social class in Act 1? 3 paragraphs 80 POINTS!!!
INTRODUCTION: What are Priestley’s overarching ideas about the class system? How are Priestley’s ideas about class seen in Act 1 of the play?
PARAGRAPH 1 -
PARAGRAPH 2-
PARAGRAPH 3-
CONCLUSION: What are Priestley’s overarching ideas about the class system? How are Priestley’s ideas about class seen in Act 1 of the play?
in fig. 8-25, a block slides along a track that descends through distance h.the track is frictionless except for the lower section. there the block slides to a stop in a certain distance d because of friction. (a) if we decrease h,will the block now slide to a stop in a distance that is greater than, less than, or equal to d? (b) if, instead, we increase the mass of the block, will the stopping distance now be greater than, less than, or equal to d?
Answers
a block slides along a track that descends through distance h. The track is frictionless except for the lower section. There the block slides to a stop in a certain distance d because of friction. If we decrease h, will the block now slide to a stop in a distance that is greater than, less than, or equal to d?As per the given information, when a block slides along a track that descends through a distance h, the track is frictionless except for the lower section. There the block slides to a stop in a certain distance d because of friction. Now if we decrease h, then the distance covered by the block before it comes to rest will also decrease. So the block will slide to a stop in a distance that is less than d. Hence the answer is less than d.If we increase the mass of the block, will the stopping distance now be greater than, less than, or equal to d?
As the mass of the block increases, the force of friction acting on the block will also increase. Hence the stopping distance will also increase. So the stopping distance now will be greater than d. Hence the answer is greater than d.In conclusion, the answer to (a) is less than d, and the answer to (b) is greater than d.
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60 identical machines in a factory pack 150 crates of limes per day
between them.
a) Write the ratio of the number of machines to the number of crates
packed per day in the form 1: n.
b) How many crates of limes would 70 of these machines pack per day?
Give any decimals in your answers to 1 d.p.
Answers
a) To write the ratio of the number of machines to the number of crates packed per day in the form 1: n, we need to find the number of crates packed per day per machine. We can do this by dividing the total number of crates packed per day by the number of machines:
Number of crates packed per day per machine = 150 crates/day ÷ 60 machines = 2.5 crates/machine/day
Therefore, the ratio of the number of machines to the number of crates packed per day in the form 1: n is 1:2.5 or 2:5.
b) To find out how many crates of limes 70 of these machines would pack per day, we can use the ratio from part (a) to set up a proportion:
1 machine : 2.5 crates/day = 70 machines : x crates/day
Solving for x, we get:
x = (70 machines × 2.5 crates/day) / 1 machine = 175 crates/day
Therefore, 70 of these machines would pack 175 crates of limes per day.
Step-by-step explanation:
a) The ratio of the number of machines to the number of crates packed per day can be written as:
60 : 150
To simplify this ratio, we can divide both sides by 10:
6 : 15
Finally, we can divide both sides by 3 to get the ratio in the form 1 : n:
1 : 2.5
Therefore, the ratio of the number of machines to the number of crates packed per day is 1 : 2.5.
b) If 60 machines can pack 150 crates per day, then one machine can pack:
150/60 = 2.5 crates per day
So, 70 machines can pack:
70 × 2.5 = 175 crates per day
Therefore, 70 machines can pack 175 crates of limes per day.
A principal gathered data about the distance in miles that his teachers and bus drivers live from the school
Answers
A principal gathered data about the distance in miles that his teachers and bus drivers live from the school. then, the interquartile range of the distances for the bus drivers in 5 miles less than the interquartile range of the distance for the teacher.
Interquartile Range:
In descriptive statistics, the interquartile range (IQR) is a measure of the statistical distribution, the distribution of data. IQR can also be referred to as bad reading, 50% mean, fourth distribution, or H-distribution. It is defined as the difference between the 75th and 25th percentile of the data. To calculate the IQR, the data set is divided into quartiles, or four parts of equal rank by linear interpolation. These quartiles are represented by Q1 (also known as the lower quartile), Q2 (the median) and Q3 (also known as the upper quartile).
The lower quartile is the 25th percentile and the upper quartile is the 75th percentile, so IQR = Q3 − Q1
Basically, the interquartile range represents the width or “spread” of the collection. The interquartile range is determined by the difference between the upper quartile (highest 25%) and lower quartile (lowest 25%) points of a data set.
From the figure, we can find:
The interquartile range of the bus driver is: 20 -10 = 10
The interquartile range of the teacher is: 30 -15 = 15
Therefore,
the interval interquartile distance is bus The driver's distance was 5 miles less than the interquartile range of the teacher's distance.
Complete Question:
A principal gathered data about the distance in miles that his teachers and bus drivers live from the school .The box plots below show these data.
(1) The inter Quartile range of the distances for the bus driver is twice the interquartile range of the distances for the teachers.
(2) The range of the distances for the teachers is twice the range of the distances for the bus drivers.
(3) the interquartile range of the distances for the bus drivers in 5 miles less than the interquartile range of the distance for the teacher.
(4) The range of the distances for the teachers is 5 miles less than the range of the distances for the bus driver.
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Answer: C. The interquartile range of the distances for the bus drivers is 5 miles less than the interquartile range of the distances for the teachers.
Amina was given 25% trade discount on an article listed 0.75p she sold it with a cash discount of 5% find Amina's percentage profit
Answers
Amina's percentage profit is 25%, as the percentage profit must be rounded down to the nearest whole number.
What is profit?Profit is an important concept in economics and finance, referring to the difference between the cost of production and the revenue generated from the sale of goods and services. It is a measure of success and financial performance and is used to analyze the profitability of a business. Profit is generally expressed as a percentage of revenue or as a dollar amount.
To calculate this, first find the cost of the article after the trade discount:
Article Cost = 0.75p - (0.75p * 0.25) = 0.75p * 0.75 = 0.5625p
Next, find the cost of the article after the cash discount:
Article Cost = 0.5625p - (0.5625p * 0.05) = 0.5625p * 0.95 = 0.5343p
Finally, calculate the percentage profit:
Percentage Profit = (0.75p - 0.5343p) / 0.75p * 100 = 0.2167 / 0.75 * 100 = 28.89%
Amina's percentage profit is 25%, as the percentage profit must be rounded down to the nearest whole number.
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the combined score on this test ranges from 400 to 1600. if you were to randomly draw five numbers from a 400-1600 number set, what is the probability that the medium score of the actual 2022 sat results is contained in between the highest and lowest value of these five random numbers?
Answers
The combined score on the 2022 SAT test ranges from 400 to 1600. If you were to randomly draw five numbers from a 400-1600 number set, the probability that the medium score of the actual 2022 SAT results is contained in between the highest and lowest value of these five random numbers is approximately 0.004%
How do we find the probability?To find the probability that the medium score of the actual 2022 SAT results is contained in between the highest and lowest value of these five random numbers, we need to find the probability of the following event: “the three other random numbers drawn lie between the highest and lowest values.
The probability of choosing one of the five numbers that falls within the range is (1600 – 400)/1201 = 1/2.25.
The first number can be any number within the 400-1600 range, so the probability is 1.The second number must lie within the range created by the highest and lowest values of the first number, which has a width of 1201. Thus, the probability is 1201/3201.
The third number must lie within the range created by the highest and lowest values of the first two numbers, which has a width of 801. Thus, the probability is 801/2401.The fourth and fifth numbers must lie within the range created by the highest and lowest values of the first three numbers, which has a width of 401.
Thus, the probability is 401/1601.Therefore, the probability of the medium score of the actual 2022 SAT results being between the highest and lowest values of these five random numbers is (1/2.25) * (1201/3201) * (801/2401) * (401/1601) * 1 = 0.000038 or approximately 0.004%.
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A triangle is shown on the coordinate plane below.
1 unit
H
y
(-1,9) of
-(-1, 2)
7
6
5
-3
3 d
(7,2)
-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7
-11
-2
What is the area of the triangle?
Il unit
X
Answers
You answer would be mate it would be x=66
Bernie helped design a magician costume for a school play. He used 5.75 feet of ribbon for the magician's wand. He used 11.75 feet of the same ribbon to decorate the magician's robe. If Bernie used $10.50 of ribbon in all, how much did the ribbon cost per foot?
The best solution gets brainlist
Answers
The ribbon cost $0.60 per foot.
Solution:[tex]\text{Total number of ribbon used} = (5.75 + 11.75) = 17.50 \ \text{feet}[/tex]
[tex]\text{17.50 feet of ribbon cost} = \$10.50[/tex]
[tex]\text{1 foot of ribbon cost = x}[/tex]
Cross Multiply[tex]17.50 \times x = 1 \ foot \times \$10.50[/tex]
[tex]x = 1 \ foot \times 10.50\div17.50[/tex]
[tex]x = \$0.60[/tex]
Therefore, The ribbon cost per foot $0.60 per foot.
Which number has a 3 with a value 100 times greater than the three in 62,091.384
Answers
Answer:
You didn't give any options, but I'm guessing one of them has a 3 in the tens digits, which should be the right answer
Step-by-step explanation:
300?
To refresh your memory of 9th grade math read Chapter 12. Complete the following table of angle and side measurements. Right Angles Angle A B C a b c
1 40 __ 90 __ __ 55 2 __ 55 __ __ 77 __
3 35 __ __ __ 68 83
4 __ __ __ 50 70 __
Answers
To refresh your memory of 9th-grade math, read Chapter 12. Complete the following table of angle and side measurements.
Right AnglesAngleA B C a b c
1 40 50 90 50 40 552 35 55 90 55 35 77
3 35 55 90 55 35 684 30 60 90 60 30 855 60 30 90 60 30 906 45 45 90 45 45 63
The above given table represents the values of angles and sides of the right-angled triangles. In the right-angled triangle, one angle measures 90°, and this angle is known as the right angle.
Further, the sum of other two angles measures 90°.In the above table, a, b and c are sides, and angles A, B, and C are opposite angles of a, b, and c, respectively.
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a survey of 50 people were taken 30 like chocolate 20 like vanilla 10 like both how mnay like choclate
Answers
From the survey of 50 people 20 people like chocolate.
A survey was conducted with 50 people, out of which 30 liked chocolate, 20 liked vanilla, and 10 liked both. The question is asking how many people like chocolate.
To determine the number of people who like chocolate only, we subtract the number of people who like both flavors from the total number of people who like chocolate.
The number of people who like chocolate alone = total number of people who like chocolate - the number of people who like both
= 30 - 10= 20
This means that out of the 50 people surveyed, 20 individuals like chocolate, while 10 people enjoy both chocolate and vanilla.
Therefore, 20 people like chocolate.
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Which two angles in the triangles below are complementary?
I NEED HELPPPPPPPP
Answers
Answer:
∠ BAC and ∠ CAD
Step-by-step explanation:
• Complementary angles sum to 90°
∠ BCA and ∠ ACD are a linear pair and sum to 180°
∠ BCA + 110° = 180° ( subtract 110° from both sides )
∠ BCA = 70°
the sum of the 3 angles in a triangle = 180°
in Δ ABC
∠ BAC + 55° + 70° = 180°
∠ BAC + 125° = 180° ( subtract 125° from both sides )
∠ BAC = 55°
in Δ ACD
∠ CAD + 110° + 35° = 180°
∠ CAD + 145° = 180° ( subtract 145° from both sides )
∠ CAD = 35°
then
∠ BAC + ∠ CAD = 55° + 35° = 90°
∠ BAC and ∠ CAD are complementary
Answer:
(a) ∠BAC and ∠CAD
Step-by-step explanation:
You want to know which angles in the figure are complementary.
Complementary anglesTwo angles are complementary when the total of their measures is 90°. In the given figure, triangle ABD is a right triangle with the right angle at vertex A.
The two acute angles at vertices B and D will be complementary:
∠ABC and ∠CDA . . . . . not on the list of choices
Ray AC divides the right angle into two complementary parts:
∠BAC and ∠CAD . . . . . first choice on the list
__
Additional comment
The two smaller triangles are isosceles. Angles CDA and CAD are both 35°, so have a sum of 70°. Likewise, angles ABC and BAC are both 55°, with a sum of 110°.
Angles BCA and ACD are a linear pair, so have a sum of 180°. They are supplementary, not complementary.
Look at photo and let me know the answers to the three blanks ASAP! Thank you!
Answers
a) Heating cost for a month with 25°F is $67.10
b) Heating cost for a month with 0°F is $98.60
c) Decrease in the monthly heating cost is $1.26
Define the term graph?The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic. The vertical or dependent variable is represented by the y-axis, while the horizontal or independent variable is represented by the x-axis.
(a) To find the predicted heating cost for a month with an average temperature of 25°F, we can substitute x = 25 into the equation of the line of best fit:
y = -1.26x + 98.60
y = -1.26(25) + 98.60
y = 67.10
Hence, $67.10 is the estimated monthly heating expense for a month with an average temperature of 25°F.
(b) To find the predicted heating cost for a month with an average temperature of 0°F, we can substitute x = 0 into the equation of the line of best fit:
y = -1.26x + 98.60
y = -1.26(0) + 98.60
y = 98.60
Thus, $98.60 is the estimated monthly heating expense for a month with an average temperature of 0°F.
(c) The slope of the line of best fit is -1.26, which means that for every increase of one degree Fahrenheit in the average monthly temperature, the predicted decrease in the monthly heating cost is $1.26.
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(5 points) For each of the following vector spaces, write down the zero vector. No justification required.a. (1 point) The vector space R 4 with the standard vector addition/scalar multiplication.b. (1 point) The vector space P3 with standard polynomial addition/scalar multiplication.c. (1 points) The vector space M22 with standard matrix addition/scalar multiplication.d. (2 points) The vector space M23 with standard matrix addition/scalar multiplication.
Answers
Here are the solutions:
a) R4 = {(a, b, c, d) | a, b, c, d ∈ R}
b) P3 = {a0 + a1x + a2x^2 + a3x^3 | a0, a1, a2, a3 ∈ R}
c) M22 = {(aij) | i, j = 1, 2}
d) M23 = {(aij) | i = 1, 2, j = 1, 2, 3}
For the given vector space R4 with the standard vector addition/scalar multiplication, the zero vector is the following: 0 = [0, 0, 0, 0].b) For the given vector space P3 with standard polynomial addition/scalar multiplication, the zero vector is the following: 0(x) = 0.c) For the given vector space M22 with standard matrix addition/scalar multiplication, the zero vector is the following:[0 0] [0 0]d) For the given vector space M23 with standard matrix addition/scalar multiplication, the zero vector is the following:[0 0 0][0 0 0].
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Please help me solve this
Answers
The ratio of the deposit to the total of the 12 equal payments is 3 : 5.
How to find the ratio of the deposit to the total of the 12 equal payments?The VAT on the van is calculated as follows:
VAT = 20% * £8500 = £1700
Total cost = £8500 + £1700 = £10200
Total amount paid in the 12 equal payments = 12 * £531.25 = £6375
Deposit = £10200 - £6375 = £3825
Deposit : Total of 12 equal payments = £3825 : £6375 = 3 : 5
Therefore, the ratio of the deposit Raya pays to the total of the 12 equal payments is 3 : 5.
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I need help please i will give you stars and 12 points
Answers
Answer:
5:3 = 5/3
Step-by-step explanation:
Given Sin∅ = 3/5
We know sin∅ = Perpendicular/Hypotenuse
And, By inverse relationship, we get
cosec∅ = Hypotenuse/Perpendicular = 1/sin∅
So, csc∅ = 5/3, 5:3
If 140 men working 10 hours a day can build a house in 16 days, find out how many men will build same kind of house in 12 days by working 13 hours a day?
Answers
We need 144 men to build the house in 12 days working 13 hours a day.
Let M be the number of men needed to build the house in 12 days working 13 hours a day.
140 x 10 x 16 = M x 13 x 12
Simplifying the equation, we get:
22400 = 156M
Dividing both sides by 156, we get:
M = 144.1
An equation in mathematics is a statement that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The expressions on either side can be numbers, variables, or combinations of both. The equation expresses that the values of the expressions on both sides are equivalent.
Equations play a fundamental role in many areas of mathematics and are used to model various real-world situations, such as physics, engineering, and finance. They can be solved using various techniques, such as substitution, elimination, or graphing, to find the values of the variables that satisfy the equation.
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What is the slope of the line passing through the points (4, -6) and (2, 3)?
Answers
Answer:
m = -9/2
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (4, -6) (2, 3)
We see the y increase by 9, and the x decrease by 2, so the slope is
m = -9/2
I need help I need to show my work please help
Answers
Answer: 19
Step-by-step explanation:
This is an isosceles trapezoid. Note that because this is an isosceles trapezoid, QN and MP are equal. Use the lengths given and solve:
3x + 1 + 6 = 6x - 5
3x = 12
x = 4
Plug x = 4 in 3x + 1 + 6, and we get 3(4) + 1 + 6 = 12 + 7 = 19
Hope this helps!
7) 99 was divided by some number, then added to 15. Next, this sum was
multiplied by 8, which gave a product of 48. Find this number.
Answers
Answer:
-11
Step-by-step explanation:
48 ÷8=6-15=-9
99÷-9=-11
Let A denote the balance at the end of Month n for each month where the balance is positive. To find a formula for An, we can do the following. For Month 1, note that A1 = 4000(1.015) - 100 For Month 2, note that A2 =[4000(1.015 ) – 100] (1.015) – 100
= 4000(1.015)^2 – 100 - 100(1.015) For Month 3, note that A3 = [4000(1.015)^2 - 100 - 100(1.015)] (1.015) - 100 = [4000(1.015)^3 - 100 - 100(1.015)] - 100(1.015)^2
B. (6 pts) (Formulas for An) i. Give a recursive formula for An. Make sure to show that the formula is consistent with the results for n= 1,2,3 on the previous page. ii. Give an explicit formula for An in summation notation that captures the pattern exhibited at the bottom of the previous page. Make sure to show that the formula is consistent with the results for n = 1,2,3 on the previous page.
Answers
(a) The recursive formula for An is: An = (1.015)An-1 - 100.
(b) The explicit formula for An in summation notation is: An = 4000(1.015)^n - 100[1 + (1.015) + (1.015)^2 + ... + (1.015)^(n-1)].
(a) This formula says that to find the balance for month n, we take the balance for month n-1, multiply it by 1.015 (to account for the interest rate), and subtract 100 (to account for the withdrawal). This formula is consistent with the results for n=1,2,3 on the previous page.
(b) The explicit formula for An in summation notation is: An = 4000(1.015)^n - 100[1 + (1.015) + (1.015)^2 + ... + (1.015)^(n-1)].
This formula says that to find the balance for month n, we take the starting balance of 4000 multiplied by the interest rate raised to the power of n, and then subtract the sum of 100 multiplied by the geometric series (1 + r + r^2 + ... + r^(n-1)), where r = 1.015. This formula is consistent with the results for n=1,2,3 on the previous page.
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A 17-ft ladder is leaning against the side of a house. The top of the ladder is sliding down the house at rate of 5 ft/sec. a) Determine how fast the bottom of the ladder is sliding away when the top of the ladder is 8 feet from the ground. b) At what rate is the angle o between the ladder and the ground is changing then.
Answers
a) d/dt [√(289 - 8²)] = d/dt [√(255)] = d/dt [√(5²*17)] = 5/2√17 m/s.
b) The required value is the rate of change of x when the top of the ladder is 8 feet from the ground, then y = 15 feet.
a) Determine how fast the bottom of the ladder is sliding away when the top of the ladder is 8 feet from the ground. As the ladder leans against the side of the house, it makes a right angle with the ground. Using Pythagorean Theorem, the length of the ladder is given by.
Ladder length = √(hypotenuse)² - (height)²= √(17² - height²) meters. Taking the derivative of both sides of this equation, we get: dL/dt = [d/dt √(289 - h²)] meters/sec. Let h = 8 feet, dL/dt = -5 feet/sec.
Thus, the rate of change of the bottom of the ladder is d/dt [√(289 - h²)] meters/sec when the top of the ladder is 8 feet from the ground, and the bottom of the ladder is sliding away at a rate of 5 feet/sec.
b) At what rate is the angle o between the ladder and the ground changing then. Let y be the height of the ladder and the angle it makes with the ground be x. From the given values, y = 17 cos x.
Taking the derivative of both sides with respect to time: dy/dt = -17 sin x (dx/dt)In the given problem, dx/dt = -5/17sin x. Then, dy/dt = 5 sin x cos x= (5/2) sin 2x.
Solving this value of sin x by Pythagorean Theorem, sin x = 8/17. Substituting the value in the equation for the derivative, we get: dy/dt = (5/2) * sin 2x= (5/2) * sin 2(arc sin(8/17))= (5/2) * (2*8/17 * 15/17)= (600/289) ft/sec.
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Barbara is going to buy a shirt for 15.00$ and a pair of pants for 25.00$. She has to also pay 7% sales tax. If Barbara pays with a 50$ bill, how much change will she get back?
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Barbara will get $7.20 back in change.
What exactly is a sales tax?A sales tax that is typically added to the selling price by the seller.
Without tax, the total cost of the shirt and pants is:
$15.00 + $25.00 = $40.00
The sales tax is 7% of $40.00, which is as follows:
0.07 x $40.00 = $2.80
So, with tax, the total cost of the shirt and pants is:
$40.00 + $2.80 = $42.80
If Barbara pays with a $50 bill, she will receive the following change:
$50.00 - $42.80 = $7.20
As a result, Barbara will receive $7.20 in change.
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If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is A(x) p(x) * (a) Find A'(x). Why does the company want to hire more workers if A'(x) > 0? (b) Show that A'(x) > 0 if p'(x) is greater than the average productivity.
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The average productivity of the workforce, A(x), is given by
A(x) = p(x)/x,
where p(x) is the total value of the production when there are x workers in the plant.
A'(x) is the derivative of A(x) with respect to x.
A'(x) = (p(x)/x)' = (p'(x)x - p(x))/x^2.
The company wants to hire more workers if A'(x) > 0 because it means that the average productivity of the workforce is increasing with additional workers.
A'(x) > 0 if p'(x) is greater than the average productivity, which is p(x)/x.
Therefore, A'(x) > 0 if p'(x) > p(x)/x.
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