Answers
Answer:
The rate of change of elevation tends to a constant value.
Explanation:
The average rate of change of e(x) on the interval [a, b] defined as
[tex]m_{\text{avg}}=\frac{e(b)-e(a)}{b-a}[/tex]which explicitly we can write as
[tex]m_{\text{avg}}=\frac{\sqrt[]{b-10}-\sqrt[]{a-10}}{b-a}[/tex]Now, the question is, what happens to m_avg as we increase b while keeping a fixed?
As b becomes large then √b -10 becomes √b and b - a becomes b (since a is comparatively small); therefore, m_avg becomes
[tex]m_{\text{avg}}=\frac{\sqrt[]{b-10}-\sqrt[]{a-10}}{b-a}\Rightarrow\frac{\sqrt[]{b}-\sqrt[]{a-10}}{b}\Rightarrow\frac{\sqrt[]{b}}{b}[/tex][tex]\Rightarrow m_{\text{avg}}=\frac{\sqrt[]{b}}{b}[/tex]which for any fixed value of b is a constant.
The same behaviour can be extrapolated by looking at the graph of e(x).
As can be seen from the graph, as x increases, the slope of the function becomes flatter and flatter, meaning it tends to be a constant. In other words, for large values of x, you can approximate the slope of the function by a straight line.
Related Questions
How do I find the missing angles marked by letters in this parallelogram
Answers
In a parallelogram,
i) Opposite angles are equal i.e
[tex]\begin{gathered} d=f \\ e=110^0^{} \end{gathered}[/tex]ii) Consecutive angles are supplementary i.e
[tex]110^0+f=180^0\text{ (Consecutive angles of a parallelogram are equal)}[/tex]To find f, collect like terms
[tex]\begin{gathered} 110^0+f=180^0 \\ f=180^0-110^0=70^0 \\ f=70^0 \end{gathered}[/tex]Since, d = f,
Thus,
[tex]\begin{gathered} d=f=70^0 \\ d=70^0 \end{gathered}[/tex]Hence, the missing angles are d = f = 70° and e = 110°
I need help with this practice problem solving I will send two additional pictures that go with this, one is the rest of the question and the other is the answer options
Answers
Given:
[tex]\frac{\sec x\sin x}{\tan x+\cot x}=\sin^2x[/tex]Find-: Prove the trigonometric identity.
Sol:
Use some trigonometric formula:
[tex]\begin{gathered} \sec x=\frac{1}{\cos x} \\ \\ \tan x=\frac{\sin x}{\cos x} \\ \\ \cot x=\frac{\cos x}{\sin x} \end{gathered}[/tex]So,
[tex]\begin{gathered} \frac{\sec x\sin x}{\tan x+\cot x}=\sin^2x \\ \\ \frac{\frac{1}{\cos x}\cdot\sin x}{\frac{\sin x}{\cos x}+\frac{\cos x}{\sin x}}.................\text{ First option } \end{gathered}[/tex]Then,
[tex]=\frac{\frac{\sin x}{\cos x}}{\frac{\sin^2x}{\sin x\cos x}+\frac{\cos^2x}{\sin x\cos}}................................(\text{ Second option\rparen}[/tex][tex]=\frac{\frac{\sin x}{\cos x}}{\frac{\sin^2x+\cos^2x}{\sin x\cos x}}...........................(\text{ Third option\rparen}[/tex]Solve the identity then,
[tex]=\frac{\frac{\sin x}{\cos x}}{\frac{1}{\sin x\cos x}}..................(\text{ Fourth option\rparen}[/tex]Here, use the formula:
[tex]\sin^2x+\cos^2x=1[/tex]Then,
[tex]\begin{gathered} =\frac{\sin x}{\cos x}\sin x\cos x..........(\text{ Fifth option\rparen} \\ \\ =\sin^2x \end{gathered}[/tex]Cann you prove the two triangles below to be congruent, if so which postulate did you use to prove them congruent
Answers
The angles shown in each triangle are congruent. Then, by SAS postulate, the triangles are congruent
An object is traveling at a steady speed of 9 9/10 mi/h. How long will it take the object to travel 2 1/10 miles? First round to the nearest integer to find the estimated answer. Then find the exact answer.
Answers
Answer:
See below
Step-by-step explanation:
Distance / rate = time
2 1/10 mi / 9 9/10 mi/hr
21/10 / 99/10 = 21/99 hr = 12.73 minutes
ZERO hr if rounded to nearest integer hr
= 13 minutes as nearest integer minutes
exact is 21/99 hr = 7/33 hr
what is 2(9n-1)+7n+6= -60
Answers
n = -2.56
Explanation:2(9n-1)+7n+6= -60
The first thing we do is expand the parenthesis:
2× 9n - 2×1 + 7n + 6 = -60
18n -2 + 7n + 6 = -60
collect like terms:
18n + 7n -2 + 6 = -60
25n + 4 = -60
Subtract 4 from both sides:
25n + 4 -4 = -60 - 4
25n + 0 = -64
25n = -64
divide both sides by 25:
25n/25 = -64/25
n = -2.56
Find the greatest common factor.6m, 2mWrite your answer as a constant times a product of single variables raised to exponents.
Answers
For 6m and 2m the comun factor corresponds to 2m, because 2 can divide 6 and 2 and m appears on both expressions with the same exponent.
Suppose that the function g is defined, for all real numbers, as follows.
Find g (-2), g (1), and g (4).
Answers
The values of the functions, when g is defined for all real numbers is as follows:
g(-2) = -3
g(1) = 3
g(4) = 0
Given, the function g is defined for all real numbers.
g(x) = { 1x²/4 - 4 if x≠1
3 if x=1 }
g(-2):
here, x = -2
where x ≠ 1
therefore, g(-2) = 1x²/4 - 4
substitute x as -2
g(-2) = 1(-2)²/4 - 4
g(-2) = 4/4 - 4
g(-2) = 1 - 4
g(-2) = -3
g(1):
here, x = 1
where x = 1
therefore, g(1) = 3
g(4):
here, x = 4
where x ≠ 1
therefore, g(4) = 1x²/4 - 4
substitute x as 4
g(4) = 1(4)²/4 - 4
g(-2) = 16/4 - 4
g(-2) = 4 - 4
g(-2) = 0
Hence we get the values of g(-2), g(1) and g(4) as -3,3 and 0 respectively.
Learn more about Functions here:
brainly.com/question/25638609
#SPJ1
Morgan had $1,679 in her savings account. After one year, her balance increases by 26. How much does Morgan have in her account now?
Answers
Morgan had $1,679 in her savings account. After one year, her balance increases by 2%. How much does Morgan have in her account now?
Remember that
100%+2%=102%=102/100=1.02
so
Multiply the original amount by the factor 1.02
1,679*(1.02)=$1,712.58
answer is
$1,712.58Commute Time to Work The average commute to work (one way) is 25 minutes according to the 2005 American Community Survey. If we assume thatcommuting times are normally distributed and that the standard deviation is 6.1 minutes, find the probabilities. (b) The selected commuter spends less than 11 minutes commuting one way.P (x<11) =
Answers
mean: 25 minutes
standard deviation: 6.1 minutes
A 11 minutes commute time is 2.30 standard deviations away from the mean. In this case, we have, for a normal distribution:
[tex]P(x<11)=P(x<\mu-2.3\sigma)=0.0107[/tex]Give a Θ estimate of the number of addition operations that the following algorithm will execute: i←1 t←0 while (i≤n) t←t+i i←i+
Answers
The estimate of the number of addition operations that the algorithm will execute is:
Θ(2n).
What is the complexity of the given algorithm?The complexity of the given algorithm is an estimate of the number of operations that the algorithm will execute.
For an algorithm bounded by a loop such as this one, due to the command while (i≤n), the length of the loop is bound of the complexity of the algorithm, hence we can begin the complexity equation as follows:
Θ(n).
Inside the loop, for each iteration of the loop, that is, each value of i, two addition operations are made, adding i to t and incrementing the count control variable i by 1.
Due to the two addition operations inside on each iteration of the loop, 2 is multiplied inside the complexity, hence the estimate of the number of addition operations that the algorithm will execute is:
Θ(2n).
More can be learned about complexity of algorithms at https://brainly.com/question/15363449
#SPJ1
Square meters of ceiling | Number of tiles 1 | 10.75 10 | X what is the value of X?
Answers
We can find the number of tiles, using the next proportion:
[tex]\frac{1\text{ square meter}}{10\text{ }square\text{ meters}}=\frac{10.75\text{ tiles}}{x\text{ tiles}}[/tex]Solving for x:
[tex]\begin{gathered} 1\cdot x=10.75\cdot10 \\ x=107.5\text{ tiles} \end{gathered}[/tex]A carton of eggs contains 12 eggs. Each carton of eggs costs $1.89.A function, f(x), is written to represent the cost of purchasing x cartons of eggs.What is the practical domain for the function f(x)?all whole numbersall real numbersall whole numbers that are multiples of 12all positive integers
Answers
Given the information on the problem, we have the following function:
[tex]f(x)=1.89x[/tex]where 'x' represents the numer of cartons of eggs.
Notice that this is a real function, but it can only take integer values. Therefore, the practical domain of the function f(x) is positive integers
You need to arrange five of your favorite books along a small shelf. How many different ways can you arrange the books, assuming that the order of the booksmakes a difference to you?
Answers
For the first place in the shlef you have 5 possibilities to choose, for the second place you have 4 possibilities, for the third you have three possibilities and so on. This means that we can find the number of ways to arrange the books with a factorial, that is:
[tex]5!=5\cdot4\cdot3\cdot2\cdot1=120[/tex]Therefore, there are 120 ways to arrange your books in the shelf.
The regression equation y= - 0.434x+72.21 approximates the percent of people in an audience who finish watching a documentary, y, given the length of the film in minutes, x.
What percentage is the best prediction for the percent of people in an audience who will finish watching a documentary that is 27 minutes long? Round your answer to the hundredths place
Answers
Using the regression equation we can estimate that 60.49% of people will finish the documentary.
Regression analysis is a group of statistical procedures used in statistical modelling to determine the associations between a regression model and one or more relationship between the independent variable.
Y is the variable (the variable that is plotted on the Y axis), X is the independent variable (i.e., it is displayed on the X axis), b is the slope of the line, and an is the y-intercept.The equation has the form Y= a + bX.The equation is given as Y= - 0.434X+72.21
At X=27 , the value of Y can be estimated as :
Y = -0.434 × 27 +72.21
or, Y = 60.492
or, Y ≈ 60.49
Therefore 60.49 % is the best prediction of people will watch the documentary completely.
To learn more about regression equation visit:
https://brainly.com/question/14184702
#SPJ1
Solve the equation. Justify each step using the word bank provided. *Properties may be used more than once! Given Addition Property of Equality Subtraction Property of Equality Multiplication Property of Equality Division Property of Equality Distributive Property Combine Like Terms 2(x − 4) − 9 = 3(2x + 1) + 4
Answers
The result of the equation 2(x-4)-9 = 3(2x+1)+4 is x= -6
The equation is
2(x-4)-9 = 3(2x+1)+4
The distributive property states that multiplying the sum of two or more variables by a number will produce the same result as multiplying each variables individually by the number and then adding the products together.
2(x-4)-9 = 3(2x+1)+4
Apply distributive property in the equation
2x-8-9 = 6x+3+4
Add the like terms in the equation
2x-17 = 6x+7
Rearrange the terms and combine the like terms in one terms
2x-6x = 7+17
Combine the like terms
-4x = 24
x = 24/-4
x = -6
Hence, the result of the equation 2(x-4)-9 = 3(2x+1)+4 is x= -6
Learn more about distributive property here
brainly.com/question/5637942
#SPJ1
A 2 1/2-pound box of frozen corn costs $1.65. How much does a 4-ounce serving cost?
Answers
Given data:
The given cost of 2 1/2 pound of box is $1.65.
The given expression can be written as,
[tex]\begin{gathered} 2\frac{1}{2}\text{ lb=1.65} \\ 2.5\text{ lb=1.65} \\ 1\text{ lb(}\frac{16\text{ ounce}}{1\text{ lb}})\text{ =0.66} \\ 16\text{ ounces=0.66} \\ \frac{1}{4}\times16\text{ ounces=}\frac{1}{4}\times\text{0.66} \\ 4\text{ ounces=0.165} \end{gathered}[/tex]Thus, the cost of 4 ounces is $0.165.
Pls help fast !!!!!!!!!!!
Answers
Answer: last one
Step-by-step explanation:
I'm not 100% sure but I would like to help you and I think it is. I say this because the 7 can't have a different outcome.
Jim earns $44,700 annually and pays 11 1/4 % for state and local taxes.How much tax does he pay annually?a. $39,671.25b. $49,728.75c. $5,028.75d. $5,014.31
Answers
The percentage paid as tax annually is 11 1/4 %. We would convert this perentage to decimal. It becomes 11.25%
Recall, percentage is expressed in terms of 100. If Jim earns $44,700 annually, then the amount of tax that he pays annually is
11.25/100 x 44700
= 5028.75
The correct option is C
All digits in a dropdown number are different and one of its digits is the average of all its digits. It has at least two digits. For example, 5021 is a dropdown number, but neither 4389 nor 6033 is a dropdown number.1. Find the smallest dropdown number2. What are the smallest and largest 4-digit dropdown numbers? Please provide working out for a and b. Thanks.
Answers
a) 102 is the smallest of the dropdown number
b) 1025 is the smallest dropdown number
c) 9874 is the largest 4-digit dropdown number
Explanation:Given:
All digits in a dropdown number are different and one of its digits is the average of all its digits.
It has at least two digits.
To find:
a) the smallest dropdown number
b) the smallest and largest 4-digit dropdown numbers
a) From the information given, the numbers are at least two digits. This means the smallest of the digits from the dropdown is 2
We can't have 0 as the starting number because it will reduce the digits by 1. The list will start from the smallest to the highest since we are looking for the smallest number.
For two digits: 12, 13, 14, etc
We can only have a 2-digit number whose average is part of digits if the numbers are the same digit.
As a result, we will move to 3 digits.
For 3 dgits: 102, 103, 104, 105, etc
We will check if any of the above will have one of its digits as average
102: 1 + 0 + 2 = 3
Average = 3/3 = 1
One of the digits of this number is the average of the number.
Hence, 102 is the smallest of the dropdown number
b) To get the smallest 4 digit dropdown number, we will list from smallest to highest
For 4 digits: 1023, 1024, 1025, 1026, 1027, ...
We will check if any of the above will have one of its digits as average
1023: 1+0+2+3 = 6
Average = 6/4 = 1.5
1024: 1+0+2+4 = 7
Average = 7/4 = 1.75
1025: 1+0+2+5 = 8
Average = 8/4 = 2
One of the digits of this number is the average of the number.
Hence, 1025 is the smallest dropdown number
To get the largest 4-digit dropdown number, we will list from largest to smallest
For 4 digits: 9876, 9875, 9874, 9873, 9872, etc
We will check if any of the above will have one of its digits as average
9876: 9+8+7+6 = 30
Average = 30/4 = 7.5
9875: 9+8+7+5 = 29
Average = 29/4 = 7.25
9874: 9+8+7+4 = 28
Average = 28/4 = 7
One of the digits of this number is the average of the number.
Hence, 9874 is the largest 4-digit dropdown number
In Ron's neighborhood, 5 out of every 6 families get a newspaper. Currently, 75 of the families get a newspaper. How many families are in Ron's neighborhood?
Answers
To solve this question we use the following ratio
[tex]\frac{No\text{of families that have newspaper}}{\text{Total number of families}}[/tex]No of families with newspaper = 5
No of families in the neighbourhood = 6
If the number of families currently with newspaper = 75 then,
[tex]\frac{5}{6}=\frac{75}{\text{total number of families in the neighbourood}}[/tex]12 Bernadette has recently opened her own soup store. It costs her $360 a month plus $2.50 for each bowl of soup she makes. Bernadette brings in $5.50 on each bowl of soup she sells. How many bowls of soup would Bernadette need to sell to make money each month? Explain.
Answers
Answer:
So, to make money each month, Bernadette would need to sell at least 121 bowls of soup.
Step-by-step explanation:
Cost function:
Has a fixed cost($360), and a variable cost($2.5 per bowl). So the cost of each making b bowls is given by:
C(b) = 360 + 2.5b
Profit function:
She earns $5.5 for each bowl of soup she sells. So the earnings of selling b bowls are given by:
P(b) = 5.5b
How many bowls of soup would Bernadette need to sell to make money each month?
Bernadette will make money if the profit is higher than the cost, that is:
P(b) > C(b)
Then
5.5b > 360 + 2.5b
5.5b - 2.5b > 360
3b > 360
b > 360/3
b > 120
So, to make money each month, Bernadette would need to sell at least 121 bowls of soup.
What is a formula for the nth term of the given sequence? Also how do I find it with further questions
Answers
option (D) aₙ = 300 (5 / 3)¹⁻ⁿ is a formula for the nth term of the given sequence.
The sequence given is:
300, 180, 108
The initial term = a = 300
We will first calculate the common ratio between the terms:
Common ratio = r
r = 180 / 300
r = 18 / 30
r = 3 / 5
Also,
108 / 180 = 3 / 5
Now, the formula for the nth term is given by:
aₙ = a rⁿ⁻¹
Substitute the values:
aₙ = 300 (3 / 5)ⁿ⁻¹
which can also be written as:
aₙ = 300 (5 / 3)¹⁻ⁿ
Therefore, we get that, option (D) aₙ = 300 (5 / 3)¹⁻ⁿ is a formula for the nth term of the given sequence.
Learn more about sequence here:
https://brainly.com/question/6561461
#SPJ9
Write the FOLLOWING algebraic expression in words1/3 a to the 3rd power
Answers
From the question we are to express the algebraic expression in words
[tex]\frac{1}{3}a^3[/tex]The algebraic expression can be written as
The product of one-third and the cube of a certain number, a
or
The cube of a certain number, a divided by 3
Hello! I'm stuck here. I've tried solving it and I'm not getting any of the answers.
Answers
We have the cost function C(d) and the revenue function R(d) as:
[tex]C(d)=10500+3.9d[/tex][tex]\begin{gathered} R(d)=d(14.5-0.00003d) \\ R(d)=14.5d-0.00003d^2 \end{gathered}[/tex]The profit can be defined as the difference between the revenue and the cost, so we can express it as:
[tex]\begin{gathered} P(d)=R(d)-C(d) \\ P(d)=(14.5d-0.00003d^2)-(10500+3.9d) \\ P(d)=-0.00003d^2+14.5d-3.9d-10500 \\ P(d)=-0.00003d+10.6d-10500 \end{gathered}[/tex]We can now evaluate it for d = 30,000 as:
[tex]\begin{gathered} P=-0.00003\cdot(30,000)^2+10.6(30,000)-10,500 \\ P=-0.00003\cdot900,000,000+318,000-10,500 \\ P=-27,000+318,000-10,500 \\ P=280,500 \end{gathered}[/tex]Answer: the profit for 30,000 units is $280,500 [Fourth option].
Complete the following using all of the numbers
1, 2, 3, 4, 5, 6
to find the smallest even number
Must be in the format
____ - ____ (3 digit numbers only)
Answers
Answer:
Step-by-step explanation:
hdhdhdhdh
Answer:
The answer is
[tex]465 - 321[/tex]
Or;
[tex]456 - 312[/tex]
Question 1
A student went to the gas station to buy gasoline and a bag of potato chips. Gasoline was $2.31 per
gallon and potato chips were $1.25.
Part 1. Write a linear equation to model the total amount the student spent at the gas station,
where g represents the number of gallons of gasoline, and t represents the total amount of money
spent. Assume there is no tax.
Part 2. Suppose the student bought 16 gallons of gas. Find the total amount the student spent at
the gas station
Answers
Part 1. The linear equation is 2.31g + 1.25t = 0
Part 2. Total amount student spent at the gas station is $36.96
What is linear equation?
An equation between two variables that, when plotted on a graph, produces a straight line or say first degree equation is known as linear equation.
Part 1.
Here in question of part 1 it stated that
g = the number of gallons of gasoline
t = the total amount of money
So according to question, the linear equation will be
2.31g + 1.25t = 0
Part 2.
Given, 1g = $2.31
then, 16g = 16 * 2.31
= $36.96
Therefore, for Part 1. The linear equation is 2.31g + 1.25t = 0 and,
for part 2. Total amount student spent at the gas station is $36.96
To read more about the Linear equation
https://brainly.in/question/24318520
#SPJ9
EM bisects ZDEF and mZDEF = 83.6°. Find mZDEM and mZMEF. mZDEM mZMEF
Answers
Answer:
[tex]\begin{gathered} m\angle DEM=41.8^{\circ} \\ m\angle MEF=41.8^{\circ} \end{gathered}[/tex]Explanation:
See the below image;
From the above image, we can see that line EM is the bisector of angle DEF and we know that an angle bisector always splits an angle into two equal angles.
Given m[tex]\begin{gathered} m\angle DEM=\frac{83.6}{2}=41.8^{\circ} \\ m\angle MEF=\frac{83.6}{2}=41.8^{\circ} \end{gathered}[/tex]
The ratio of students who play video games to those who don't play video games if 7:2. If a class has 126 students that play video games, how many students do not play video games?
Answers
Answer:
98 students play videogames
28 students dont play videogames
Step-by-step explanation:
we have to make n equation using 7:2=126 so we are going to intaduce x witch will give us 7x+2x=126
9x=126 then we divide it with 9 witch gives us x=14 then we multiply x by 7 and agen x by 2
I got 190m but I need someone to check pls
Answers
Step 1: Write out the formula for the volume V of a rectangular based pyramid with height h base length l and base width w:
[tex]V=l\cdot w\cdot h[/tex]Step 2: Write out the given values and substitue them into the formula to find the volume:
From the image, we can see that:
[tex]l=12m,w=5m,h=9.5m[/tex]Therefore,
[tex]V=(12)\cdot(5)\cdot(9.5)=570m^3[/tex]Hence the volume of the pyramid is 570m³
Answer:
190 m^3
Step-by-step explanation:
the volume of a pyramid is b * h * 1/3
the base is the bottom
5 * 12
that is 60
60 * the height * 1/3
60 * 9.5 * 1/3
we can first do 60 * 1/3
that is 20
20 * 9.5 = 190
that is the answer
youre correct!
Kathleen and ednardo both ran from the park entrance along the loop Kathleen started walking from the park entrance and gets a five mile Head Start of aarona the graph shows how far they have both traveled
Answers
Answer:
75
Step-by-step explanation:
They meet up when their distance traveled is the same (in other words, when the graphs intersect).
The graphs intersect x=75.
