Answers
The prove of given limit lim θ → 0 ( sin θ / θ ) = 1 is shown in below.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
⇒ lim θ → 0 ( sin θ / θ ) = 1
Here, The form of given limit is 0/0, so we can apply the L - Hospital Rule.
⇒ lim θ → 0 ( sin θ / θ ) = 1
Take LHS;
⇒ lim θ → 0 ( d/dθ (sin θ)/ dθ/dθ )
⇒ lim θ → 0 ( cos θ / 1 )
⇒ ( cos 0 )
⇒ 1
⇒ RHS
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Related Questions
Graph the following system of equations.
y = 3x + 15
3x + 3y = 9
What is the solution to the system?
There is no solution.
There is one unique solution (-3, 6).
There is one unique solution (0, 15).
There are infinitely many solutions.
Answers
Answer:
There is one unique solution (-3, 6)
Step-by-step explanation:
Desmos graphing calculator helps a lot with this stuff
Answer: b) there is only one unique solution (-3, 6)
Step-by-step explanation:
Jasmine has $26 to spend on binders and one pack of pens. The pack of pens costs $4. 75. Each binder costs $5. Write an inequality to determine the maximum number of binders she can buy, (Define your variable. )
Answers
Jasmine can buy a average of 4 binders because the cost of the binders, multiplied by the number of binders she wants to buy, plus the cost of the pens, must not exceed her total budget of $26.
Step 1: Define the variable. Let x represent the number of binders Jasmine can buy.
Step 2: Write the inequality. 5x + 4.75 ≤ 26
Step 3: Solve the inequality. 5x ≤ 21.25
Step 4: Isolate the variable. x ≤ 4.25
Step 5: The maximum number of binders Jasmine can buy is 4.
Let x represent the number of binders Jasmine can buy
5x + 4.75 ≤ 26
5x ≤ 21.25
x ≤ 4.25
Jasmine has a total of $26 to spend on binders and one pack of pens. The cost of the pens is $4.75, and each binder costs $5. To determine the maximum number of binders she can buy. The inequality we need to solve is 5x + 4.75 ≤ 26. We can solve this inequality by first multiplying both sides of the equation by 5, which gives us 5x ≤ 21.25. We can then isolate the variable by dividing both sides of the equation by 5, which gives us x ≤ 4.25. This means that the maximum number of binders Jasmine can buy is 4.
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What are the first 3 triangular numbers?
Answers
The depiction of numbers as an equilateral triangle organized in a series is known as a triangular number sequence. These numerals follow a 1, 3, 6 order.
Explain the term triangular numbers?A number that may be expressed as the sum of the initial n positive integers is referred to as a triangular number.
For instance, the fact that 6 may be expressed as 1+2+3, being sum of the initial three positive integers, indicates that it is a triangular number. If one takes the sum of the initial positive integer to be the first element, then sum of the earliest two positive integers to be the second element, then so on, triangular numbers comprise a sequence. In this scenario, n signifies the position of such a triangular number with in sequence if a number equals the sum of the initial n positive integers. Triangles can be formed from triangular numbers.Thus, the first three triangular numbers 1, 3, 6.
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At the end of a snowstorm, Peyton had 8 inches of snow on her lawn. The temperature then increased and the snow began to melt at a constant rate of 1 inch per hour. Assuming no more snow was falling, how much snow would Peyton have on her lawn 2 hours after the snow began to melt? How much snow would Peyton have on her lawn after t hours of snow melting?
Answers
The amount of snow on Peyton's lawn after 2 hours is 4 inches
amount of snow after t hours y = 8 - t
How to model the required equationA linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable = amount of snow remaking
m = slope = 1 inch per hour
x = input variable = number of hours
c = y intercept = 8 inches of snow on Peyton's lawn
The equation as described in the problem is represented using linear function as as follows
y = 8 - x
in 2 hours x = 2
y =8 - 2 = 4 inches
The quantity of snow after t hours
x = t
y = 8 - t
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I literally need so much help
Angie is working on solving the exponential equation 23x = 6; however, she is not quite sure where to start. Using complete sentences, describe to Angie how to solve this equation.
Hint: Use the change of base formula: log base b of y equals log y over log b.
Answers
Answer:
[tex]x=\dfrac{\log 6}{\log 23}[/tex]
Step-by-step explanation:
Given exponential equation:
[tex]23^x=6[/tex]
[tex]\textsf{Apply the log law}: \quad a^c=b \iff \log_ab=c[/tex]
[tex]\implies\log_{23}6=x[/tex]
[tex]\textsf{Given change of base formula}: \quad \log_by=\dfrac{\log y}{\log b}}[/tex]
Apply the given change of base formula:
[tex]\implies x=\dfrac{\log 6}{\log 23}[/tex]
What are the 3 algorithms?
Answers
Sequencing, selection, and iteration are the three fundamental building blocks that make up an algorithm.
What is algorithm?An algorithm in mathematics is a process, a description of a series of steps that can be used to solve a mathematical computation, but they are now much more prevalent than that. The long division algorithm is perhaps the most well-known application of algorithms in science (and in daily life, for that matter).
Algorithms are all about figuring out the most effective ways to perform the math, despite the fact that the above explanation might sound a little fussy and detailed. Mathematicians are known for being lazy, so they frequently seek out shortcuts, as the anonymous mathematician puts it. For locating these short cuts, algorithms are used.
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A developer wants to develop a 18-acre subdivision. He figures that the streets and common area will take up about 20% of this overall area. If the minimum lot size is to be 10,000 SF, how many lots can the developer have on this property
Answers
Developer has 627264 square feet land available.
What means lot size?The minimum permissible quantity of an asset that is accepted for purchasing.
How many lots the developer has as per question?
A developer wants to develop 18-acre property = 784080 square feet area
he notices that street and common area will take up about 20% of total area.
hence, the remaining area for developing works = 80%
the amount of land rest for the developer = 784080 ×80 /100
= 627264 square feet.
there is a rule that minimum lot size is to be 10000 square feet for developing works,
the above amount 627264 square feet lot can the developer have on this property that is higher than the minimum lot value.
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Write a polynomial in intercept form so that P(x)=0 has the given roots.
7. 2, √√3
8. -i, -5
9. i, √7
11. --√6, √3
10. 2i, -i
12. 4DR, VII
Answers
The polynomial in intercept form so that P(x)=0 has the given roots is, x^2 - √3x - 2x + 2√3 = 0.
What is polynomial?
A polynomial is an expression in mathematics that only uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminates and coefficients. The polynomial x^2 4x + 7 is an illustration of one with a single indeterminate x.
We have to find the polynomial in intercept form so that P(x)=0 has the roots 2 and √3.
Let 2 and √3 are the roots of the polynomial so,
x = 2, x = √3
⇒ x - 2 = 0, x - √3 = 0
⇒ (x - 2)(x - √3) = 0
x^2 - √3x - 2x + 2√3 = 0
Hence, the polynomial in intercept form so that P(x)=0 has the given roots is, x^2 - √3x - 2x + 2√3 = 0.
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What is the value of v?
Answers
Answer: v = 100
Step-by-step explanation:
v+15 = v-37 + v-48
v + 15 = 2v - 85
85 + 15 = 2v - v
100 = v
What is the solution of 2x 3 7?
Answers
Answer: It is a straight line
Step-by-step explanation:
The piggy bank in the video was filled with pennies and
quarters worth a total of $62. 0.
What are three possible combinations of pennies and
quarters that are worth $62. 00?
Enter your combinations in the table.
Number of Pennies
Number of Quarters
I
Answers
The three combinations of pennies and quarters are:
A. 1,560 Pennies and 124 Quarters
B. 2,600 Pennies and 49 Quarters
C. 3,120 Pennies and 24 Quarters
The total value of the pennies and quarters is $62.00. This can be achieved with either 1,560 pennies and 124 quarters (1,560 x 0.01 + 124 x 0.25 = 62.00), 2,600 pennies and 49 quarters (2,600 x 0.01 + 49 x 0.25 = 62.00) or 3,120 pennies and 24 quarters (3,120 x 0.01 + 24 x 0.25 = 62.00).
To find the combinations of pennies and quarters that are worth $62.00, begin by finding the number of pennies that equal $
62.00. 62.00/0.01 = 6,200 pennies.
Next, subtract the value of the pennies from the total to find the value of the quarters.
62.00 - (6,200 x 0.01) = 24.00.
Divide the value of the quarters by 0.25 to find the number of quarters. 24.00/0.25 = 96 quarters.
To arrive at the three combinations
, 1,560 pennies and 124 quarters
(1,560 + 96 = 1,656, 1,656 x 0.01 + 124 x 0.25 = 62.00),
2,600 pennies and 49 quarters
(2,600 + 49 = 2,649, 2,649 x 0.01 + 49 x 0.25 = 62.00)
and
3,120 pennies and 24 quarters
(3,120 + 24 = 3,144, 3,144 x 0.01 + 24 x 0.25 = 62.00).
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Toni invests money into an account which pays a fixed rate compound interest each year.
The total value, £V, of her investment after 't' years is given by the formula=1350 x 1.04t.
How much did Toney invest?
if u get this ur a genius
Answers
Answer: Toni invested in pounds= $1350
Step-by-step explanation:rate of compound interest=4%
Step-by-step explanation:
Toni invests money into an account which pays a fixed rate of compound interest each year. The total value, £V, of her investment after t years is given by the formula:
Given equation is in the form of
where P is the amount invested
'r' is the rate of interest
t is the time taken
P= 1350 is the initial amount invested
1+r= 1.04 (subtract 1 from both sides)
multiply it by 100 to get percentage
r= 4%
I just search it bc my brain dosent work any more
How many terms are there in the expression 2p3 3p2 4p 7 *?
Answers
Answer: 4
Explanation:
In Algebra a term is either a single number or variable, or numbers and variables multiplied together.
Terms are separated by + or − signs, or sometimes by divide.
Uri buys two burgers and a soda for $\$2.10$, and Gen buys a burger and two sodas for $\$2.40$. How many cents does a soda cost
Answers
The cost of soda as calculated from the data given is found to be as 0.9 cents.
the price of 1 burger = x
the price of 1 soda =y
Therefore, the equation for Uri and Gen becomes,
2x + y = $2.10
x+ 2y = $2.40
On solving these two equations we will get the value of x and y which represents their cost.
on multiplying equation 2 with 2 , we will get ,
2x + 4y = 4.80
Therefore , on subtracting equation 1 and 2 ,
2x + y = $2.10
- 2x + 4y = 4.80
=> -3y = - 2.7
=> y = 0.9
Therefore x will be ,
x+ 2y = $2.40
x+ 2(0.9) = $2.40
x + 1.8 = $2.40
x = 2.40 - 1.8
= 0.60
Therefore, cost of soda is 0.9 cents.
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Suppose that a company wishes to predict sales volume based on the amount of advertising expenditures. The sales manager thinks that sales volume and advertising expenditures are modeled according to the following linear equation. Both sales volume and advertising expenditures are in thousands of dollars.
Estimated Sales Volume=46.41+0.45(Advertising Expenditures) If the company has a target sales volume of $200,000 how much should the sales manager allocate for advertising in the budget? Round your answer to the nearest dollar.
Answers
The sales manager should allocate approximately 341311.111 for advertising in the budget.
What is advertising expenditure?Generally, Advertising expenditure refers to the amount of money that a company or organization spends on promoting their products or services through various forms of advertising media, such as television, radio, print, and online.
This can include costs for creating and producing advertisements, as well as fees for placing them on different platforms. Advertising expenditure can also be referred to as "advertising budget" or "advertising spend."
To find the advertising expenditure needed to reach a target sales volume of $200,000, we can use the equation provided: Estimated Sales Volume = 46.41 + 0.45(Advertising Expenditures)
We can set the target sales volume as the left-hand side of the equation and solve for the advertising expenditure:
200,000 = 46.41 + 0.45(Advertising Expenditures)
Subtracting 46.41 from both sides:
153,590 = 0.45(Advertising Expenditures)
To find the Advertising Expenditures, divide 153,590 by 0.45:
Advertising Expenditures = 341311.111
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Beth is making a garden plot which measures 6 open parentheses square root of x plus 2 end root close parentheses units in length and open parentheses 5 square root of x plus 2 end root close parentheses units in width. What is the area of the garden?
Answers
The area of the garden whose length and width as given in the task content is; 30 (x + 2) square units.
What is the area of the garden plot whose length and width are as described?It follows from the task content that the expression which represents the area of the garden plot whose dimensions are as given.
Recall that Area, A = length × width.
Therefore, since length = 6 (√(x + 2)) units
The width = (5 √(x + 2) ) units
Hence, the area of the garden plot as required in the task content is; 6 (√(x + 2)) × ( 5 √(x + 2) )
= 30 (x + 2) square units
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PLEASE HELP I WILL GIVE FIVE STARS AND BRAINLIEST Transformation and plot image.
Answers
Answer: You need to drew , this arrow , to each point K,L,M,N,
Drawing must be parallel to , this arrow, AND , exactly the same length, as the arrow .
step 2. when you drew it , then at the end are your new points, K",L",M",N".
Ok?
step 3.
Then you just read the coordinates. of new points .
I would gladly drew it , but I do not knew how to put picture in this , jet .
Step-by-step explanation:
It take Thorton 4 hour to edit a video for hi chool. If he ha already pent 2. 5 hour on thi video, what percent of the video i edited?
Answers
Using the concept of fraction, the percentage edited on the video is 62.5 percent.
What is Percentage
Percentage is a standard mathematical concept used to express a portion of a whole number in terms of a hundred. It is denoted by the symbol “%” and is often expressed as a fraction or a decimal. For example, 25% can be expressed as 0.25 or 1/4.
In this problem, Thorton has done a 2.5 hours work. The percentage he has edited can be calculated using fraction or ratio as;
percentage edited = (2.5 / 4) × 100
Percentage = 0.625 × 100
Percentage = 62.5 %
From the above, Thorton has edited 62,5 percent of the video for his school project.
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25PTS don’t explain
Answers
Answer:
y = 2x+ 3
Step-by-step explanation:
which operation should be completed first to find the value of the expreesion below 12 + 30 / (6 -3) + 1
Answers
Simplify algebraic expression
Answers
Answer: 40
Step-by-step explanation:
We will substitute x = 8 and simplify the given expression.
Given:
6x-x
Substitute:
6(8) - 8
Multiply:
48 - 8
Subtract:
40
6x-x
6(8)-x
48-x
48-8=40
Hope this helps!
I NEED THIS ASAP ILL GIVE 100 POINTS
1. Gas stations A. B. C, and G are located
along a straight lighway.
Station B is between stations: A
and c The distance frim station A to
station C is 22 miles. BC is 5 miles less than twice AB
Station C is between stations B and C. 4 miles from C. Find AC.
Answers
Answer: 3
Step-by-step explanation:You can't start at station 0 or 1, as there is not enough gas to travel to the next station.
Let's start at station 2 and fill up with 4 unit of gas. Your tank = 0 + 4 = 4
Travel to station 0. Your tank = 4 - 3 + 2 = 3
Travel to station 1. Your tank = 3 - 3 + 3 = 3
You cannot travel back to station 2, as it requires 4 unit of gas but you only have 3.
Therefore, you can't travel around the circuit once no matter where you start.
The Reed family is selecting a furniture set. A furniture set has a bed, a desk and a dresser. There are 4 beds, 3 desks, and 1 dresser to select from. How many different furniture sets could they select?
Answers
Answer:
12.
Step-by-step explanation:
right!!
Tyler has a baseball bat that weighs 28 ounces. Find the weight in kilograms and in grams. (Note: 1 kilogram=35 ounces)
Answers
Answer:
1/ 0.8 kilograms
2/ 800 grams
Step-by-step explanation:
We know
1/
Baseball bat = 28 ounces
1 kilogram = 35 ounces
To find weight in kg we take
28 / 35 = 0.8 kg
2/
We know
1 kg = 1000 g
0.8 kg = 800 grams
So, the baseball bat weights 0.8kg or 800 grams
Dariu ha a 40-ounce port drink. He drink 18 ounce. Enter the percentage of ounce Dariu ha left of hi port drink
Answers
The percentage of ounce Dariu has left of his port drink is 55%.
What is percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
It is given that Dariu ha a 40-ounce port drink.
He drank 18-ounce port drink.
First calculate what percentage of port drink Dariu drank.
The equation is -
= (18/40) × 100
= 45%
So, Dariu drank 45% of the port Drink.
Now, subtract the percentage Dariu drank from the 100% (40 Ounce) drink Dariu had -
100 - 45 = 55
Therefore, Dariu has 55% drink left.
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Which is 536,900 in scientific notation
Answers
Answer:
5.369 x 105
Step-by-step explanation:
Answer:
5.369 x 105
Cause in scientific notation, the decimal point is always after the first number from the left.
Hello can someone please help me with this
Answers
1. The best geometric model for the rail road is C. Line
2. Two straight lines cannot go through any two points. It is false.
3. The length of the cake is A. 5.5 inches.
4. The vertical angles are AHC and GHE.
How to illustrate the information?The best geometric model for a set of railroad tracks would likely be a line, as it represents the linear path that the tracks follow. A point would not be appropriate as it does not represent the length or direction of the tracks, and a plane would not be necessary as the tracks are linear and exist in a three-dimensional space.
It should be noted that two straight lines cannot go through any two points. Only one line can. The length of the cake will be:
= 6.0 - 0.5
= 5.5
It should be noted that vertical angles are equal. This was Illustrated as AHC and GHE.
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RADIO FRIENDS Polly, Autumn, and Terry each have a two-way radio with a two-mile range. Their houses are located as shown, with Autumn and Polly being two miles apart. Which friends can talk with each other on the radio?
Answers
Autumn and Terry can talk because the distance between them is 2 miles
Polly and terry can not talk because the distance between them is 2.27 miles.
Polly and Autumn's distance can talk because the distance between them is 1.56 miles.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Autumn and Terry distance = 2 mile
Polly and Autumn's distance = x miles
Polly and terry's distance = y miles
Now,
Applying the Sin rule of a triangle.
2 / sin 59° = x / sin 42° = y / sin 79°
2 / 0.86 = x / 0.67 = y / 0.98
Find x.
2 / 0.86 = x / 0.67
x = 1.56
Find y.
2/0.86 = y / 0.98
y = 2.27
Now,
Polly and Autumn's distance is 1.56 miles.
This means they can talk.
Polly and terry's distance is 2.27 miles.
This means they can not talk.
Thus,
Polly and Autumn can talk.
Polly and terry can not talk.
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what is 5x5+9x7
Whell help please i just wanted to put 5x5+9x7 but it didnt let me so yay
Answers
Answer: 88
Step-by-step explanation:
Answer: 88
Step-by-step explanation: 5x5=25 + 9x7=63 ----> 25+63= 88
Suppose you know the answer to 4/5*(20*1 7/8). Explain how the Commutative and Associative Properties of Multiplication can make the computation easier. Then find the answer
Answers
You can rearrange terms in an expression using the commutative and associative qualities to arrange compatible numbers next to one another and in groups.
What distinguishes an associative property from a commutative property?According to the associative property, numbers can be added to or multiplied while still maintaining the same result. According to the commutative property, even if the numbers are added or multiplied, the solution will remain the same.
Explain:
[tex]\frac{4}{5}[/tex] ×(20×17/8)
20×17/8
340÷8
[tex]\frac{4}{5}[/tex]×[tex]\frac{340}{8}[/tex]
= [tex]\frac{64}{2}[/tex]
= 32
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