Answers
3) We have
[tex]f(x) = \sec\left(\dfrac{\pi x}2\right) = \dfrac1{\cos\left(\frac{\pi x}2\right)}[/tex]
which has vertical asymptotes (i.e. infinite discontinuities) whenever the denominator is zero. This happens for
[tex]\cos\left(\dfrac{\pi x}2\right) = 0[/tex]
[tex]\implies \dfrac{\pi x}2 = \cos^{-1}(0) + 2n\pi \text{ or } \dfrac{\pi x}2 = -\cos^{-1}(0) + 2n\pi[/tex]
(where [tex]n[/tex] is any integer)
[tex]\implies \dfrac{\pi x}2 = \dfrac\pi2 + 2n\pi \text{ or } \dfrac{\pi x}2 = -\dfrac\pi2 + 2n\pi[/tex]
[tex]\implies x = 1 + 4n \text{ or } x = -1 + 4n[/tex]
So the graph of [tex]f(x)[/tex] has vertical asymptotes whenever [tex]x=4n\pm1[/tex] and [tex]n\in\Bbb Z[/tex].
4) Given
[tex]h(t) = \begin{cases} t^3+1 & \text{if } t<1 \\ \frac12 (t+1) & \text{if } t\ge1 \end{cases}[/tex]
we have the one-sided limits
[tex]\displaystyle \lim_{t\to1^-} h(t) = \lim_{t\to1} (t^3+1) = 1^3+1 = 2[/tex]
and
[tex]\displaystyle \lim_{t\to1^+} h(t) = \lim_{h\to1} \frac{t+1}2 = \frac{1+1}2 = 1[/tex]
The one-sided limits don't match, so the two-sided limit [tex]L[/tex] does not exist. In other words, the limit does not exist at [tex]x=1[/tex] because the function approaches different values from the left and right side of [tex]x=1[/tex].
Related Questions
Jeff places a 13 ft ladder against a wall. The base of the ladder is 5 ft from the wall. How high on the wall does the ladder reach?
Answers
Work Shown:
[tex]a^2+b^2 = c^2\\\\5^2+b^2 = 13^2\\\\25+b^2 = 169\\\\b^2 = 169-25\\\\b^2 = 144\\\\b = \sqrt{144}\\\\b = 12\\\\[/tex]
I used the pythagorean theorem.
what is the constant of variation?
Answers
Answer:
constant (unchanged) ratio of two variable quantities
Step-by-step explanation:
y = k x ( or y = k x )
y = 15 when x = 24, find x when y = 25. find the constant of variation.
What was the percent increase of China's
population from 1970 to 1995?
56.25%
45%
156.25%
9.405%
China's Population
Population
(billions)
0.7
Year
1965
1970
1975
1980
1985
1990
1995
2000
0.8
0.92
0.98
1.08
1.14
1.25
1.26
Answers
The percentage increase China's population from 1970 to 1995 is: 56.25%.
How to Calculate Percentage Increase?Percentage increase = (Final Value - Original Value)/Original value × 100.
Given the following:
Original value = 0.8 billion
Final Value = 1.25 billion
Final Value - Original Value = 1.25 - 0.8
Final Value - Original Value = 0.45
Percentage increase = 0.45/0.8 × 100 = 56.25%.
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Evaluating an exponential function
Answers
Using the given exponential function, we have that:
The initial amount is of 523 grams.The amount after 50 years will be of 165 grams.What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex]
In which:
a is the initial value.b is the rate of change.In this problem, the function is:
[tex]A(t) = 523(0.5)^{\frac{t}{30}}[/tex]
Hence the initial amount is of 523 grams.
The amount after 50 years will be given by:
[tex]A(50) = 523(0.5)^{\frac{50}{30}} = 165[/tex]
The amount after 50 years will be of 165 grams.
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HELP ME ANSWER THIS PLEASE
Answers
Answer:
C , D , B
Step-by-step explanation:
Trigonometry is given by three formulas :
SOH - CAH - TOA
Sin x = Opp/HypSo Sine must be Option DCos x = Adj/Hyp
So Cosine must be Option C Tan x = Opp/Adj
So tangent must be Option B
Hope this helped and have a good day
A printer designs a tag in the shape of a circle with a smaller circle cut out. She cuts her prototype from a 5 in. by a 7 in. index card. The cut edges of the tag will be printed with gold leaf. What is the approximate amount of gold leaf on a tag?
The circumference of the larger circle is about ____ inches. The circumference of the smaller circle is about ____ inches. So, the total length of gold leaf on a tag is approximately
____ inches.
Answers
The circumference of the larger circle is about 12.57 inches. The circumference of the smaller circle is about 3.14 inches. So, the total length of gold leaf on a tag is approximately 15.71 inches.
How to illustrate the circle?The circumference will be:
= 2πr
= 2 × 3.14 × 2
= 12.57 inches.
The circumference of the smaller circle will be:
= 2πr
= 2 × 3.14 × 0.5
= 3.14
The total length will be:
= 12.57 + 3.14
= 15.71 inches.
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Explain what the slope and y-intercept of the equation represents in this situation y=14x+9
Answers
Answer:
slope: 14
y intercept: (0,9)
Step-by-step explanation:
in the form y = mx + b, the slope is m: 14
to solve for the y intercept, we set x as 0: 14 * 0 + 9 = y interecept is 9.
-5(-1) ≤ 55
and
8-y< 12
Step 2 of 4: Solve the second inequality and express your answer in interval notation. Use decimal form for numerical values.
Answers
The solution to the inequality is (-4, ∞)
How to solve the inequality?The second inequality is given as:
8 - y < 12
Subtract 8 from both sides
-y < 4
Rewrite as:
y > -4
In interval form, we have:
y = (-4, ∞)
Hence, the solution to the inequality is (-4, ∞)
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if the following data were linearized using logarithms, what would be the equation of the regression line? Round the slope and y-intercept of the regression line to three decimal places.
x y
2 73
3 77
4 85
5 101
6 133
A. log(y) =-1.706x + 0.064
B. log(y) =-0.064x + 1.706
C. log(y) = 1.706x + 0.064
D. log(y) = 0.064x + 1.706
Answers
The regression equation is (d) log(y) = 0.064x + 1.706
How to determine the regression equation?The table of values is given as:
x 2 3 4 5 6
y 73 77 85 101 133
Calculate the logarithm of the y values.
So, we have:
x 2 3 4 5 6
log(y) 1.86 1.89 1.93 2 2.12
Next, we enter the above values in a regression calculator.
From the calculator, we have the following summary:
Sum of X = 20Sum of Y = 9.8Mean X = 4Mean Y = 1.96Sum of squares (SSX) = 10Sum of products (SP) = 0.63The regression equation is then represented as:
log(y) = bx + a
Where:
b = SP/SSX = 0.64/10 = 0.064
a = MY - bMX = 1.96 - (0.064*4) = 1.706
So, we have:
log(y) = 0.064x + 1.706
Hence, the regression equation is (d) log(y) = 0.064x + 1.706
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Answer: D. log(y) = 0.064x + 1.706
Step-by-step explanation: I got it right on my test
3. Which graph represents the solution to 13k-21> 7?
Answers
Answer: Option (2)
Step-by-step explanation:
[tex]|3k-2| > 7[/tex] means [tex]3k-2 < -7[/tex] or [tex]3k-2 > 7[/tex].
Solving each of these cases gives [tex]k < -\frac{5}{3}[/tex] or [tex]k > 3[/tex].
So, the answer is Option (2).
A bank loaned out $19,500, part of it at the rate of 11% annual interest, and the rest at 7% annual interest. The total interest earned for both loans was $1,485.00. How much was loaned at each rate?
____ was loaned at 11% and
____was loaned at 7%.
Answers
The amount loaned at the interest rate of 11% is $3000.
The amount loaned at the interest rate of 7% is $16,500
What are the linear equations that represent the question?a + b = 19500 equation 1
0.11a + 0.07b = 1485 equation 2
Where:
a = amount loaned at the interest rate of 11%
b = = amount loaned at the interest rate of 7%
How much was loaned at 11% and 7%In order to determine how much was loaned at 7%, take the following steps:
Multiply equation 1 by 0.11:
.11a + 0.11b = 2145 equation 3
Subtract equation 2 from equation 3:
0.04b = 660
Divide both sides by 0.04:
b = 16,500
Subtract 16,500 from 19,500 :
19,500 - 16,500 = $3000
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here is a gauge for the fuel tank of a car the fuel tank hols 52 litres of fuel when the tank is full the tank is 1/4 full of fuel
work out how many more litres of fuel are needed to fill the tank
Answers
Ibsan want to buy a chicken from one of two supermarkets around his house. the two supermarkets contain 20 local and 25 imported chickens respectively. how many possible chickens are there to choose from
Answers
Answer:
Since there are 20 chickens in one supermarket, and 25 chickens in the other supermarket, there are 45 chickens to choose from.
Elsa sold 24 drawings for $12 each at the art fair. She is going to use ‡ of the money to buy books. The rest of the money is going into her savings account. How much money will she put into her savings account?
Answers
The amount going to her savings accounts is $192
How to determine the amount saved?The given parameters are:
Drawings = 24
Rate = $12
The total amount earned from selling the drawings is:
Total = 24 * $12
Evaluate
Total = $288
She buys books with 1/3.
This means that she saved 2/3
So, we have:
Savings = 2/3 * $288
Evaluate
Savings = $192
Hence, the amount going to her savings accounts is $192
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help me help me help help help me
Answers
Answer:
b. 0
c. 4
d. 2
e. [tex]\frac{76}{35}[/tex]
Step-by-step explanation:
b.) When translated it will become this expression 10 - [(2x15)/3] = 0
c.) It will become [tex]\frac{4(12-7)}{5}[/tex]
d.) This will transform to [tex]\frac{(\frac{78-13}{5}) + 5}{9}[/tex]
e.) The first eq is [tex]\frac{4(7+3)}{8}[/tex], then after the changes it becomes [tex]\frac{4[\frac{(7+3)+9}{7}]}{5}[/tex]
The number of goals the Blue Jay hockey team scored in each game last year are: 3, 2, 1, 3, 0, 3, 1, 1, 2, 3, 3 What is the mode?
Answers
Answer:
3 is the mode
Step-by-step explanation:
Why is it most logical to let x represent Dianna’s current age?
Answers
Answer:
In 3 years, Dianna will be 4 times as old as she was 33 years ago. How old is Dianna now?
Choose the most logical value for the variable to represent.
x= Diana's age now
This question is impossible to fully answer without further context. (Who is Dianna? Why do we need her age?)
However, it can be noted that [tex]x[/tex] is easily the most common variable name whenever you have a missing value in an equation. Generally, it is understood by mathematicians that [tex]x[/tex] and most other letters denote an unknown value, something to either use in solving the equation or something to find on its own.
complete the flow chart to prove
someone pls help me pls pls asap
Answers
The attached figure represents the complete flowchart.
How to complete the flowchart?The given statement is:
∠1 ≅ ∠2
To prove
∠3 ≅ ∠4
By vertical angle theorem, we have:
∠2 ≅ ∠4
By transitive property of congruence, we have:
∠2 ≅ ∠3
By transitive property of congruence, we have:
∠1 ≅ ∠3
By vertical angle theorem, we have:
∠3 ≅ ∠4
See attachment for the complete flowchart.
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the diameter of a baseball is appromately 3 inches. What is its volume?Round your answer to the nearest whole number.
Answers
The volume of the baseball roundibg off to nearest whole number is 14 cube inches.
If radius of a sphere is r and the volume of that spherical figure is given by V then,
[tex]V=\frac{4}{3}\pi r^3[/tex]
So in the problem the object is a baseball which is a sphere for sure.
Given that the diameter of that baseball is 3 inches.
So the radius of that baseball is given by = 3/2 = 1.5 inches.
Hence the volume of that base ball is
[tex]=\frac{4}{3}\pi\times(1.5)^3 \approx 14.1372 \approx 14[/tex]
Thus the volume of the baseball rounding off to nearest whole number is given by 14 cube inches.
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San is currently three times Harry's age. Sam's age is also 10 more than twice Harry's age. the following systems of equation models this scenario. x=3y, x=10+2y
Answers
Step-by-step explanation:
so, what do we need to do ?
just solve these equations and find Sam's age (and Harry's) ?
x = 3y
x = 10 + 2y
so, we simply use the first equation in the second :
3y = 10 + 2y
y = 10
x = 3y = 3×10 = 30
Sam is currently 30 years old, Harry is 10.
What is the value of f(x) when x = 4 in the piecewise function f(x) =
2x² when x>4 …….. 4x when x < 4
Answers
The question asks the value of f(x) when x = 4 in the equation
x = 4 is less than or equal to 4, so we use the first equation in the piecewise functions => {4x when x≤4}
Solving for f(x):
4(4)=16
16 is the answer!
Hope it helps!
I need help asap. ive tired a lot and cant get it
Answers
Since the coordinates of point A are given along with coordinate of Midpoint. We can easily locate the coordinates for point B.
By using the equation:
M=(x1+x2)/2 , (y1+y2)/2
Substituting M value of (-2,2):
(-2,2) = (-5+x2)/2 , (7+y2)/2
We can now compute for x2 and y2 values via subject of the formula method:
-2 = (-5+x2)/2 multiply by 2 of left
-4 = (-5+x2) add +5 on left
1 = x2
2 = (7+y2)/2
4 = 7+y2
-3 = y2
Therefore: the coordinates for point B are (1,-3).
Justin‘s gas tank is 3/10 full after he buys 14 gallons of gas it is 4/5 full how many gallons can Justin‘s tank hold
Answers
Answer:
I can help, its 45
You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production of Les Misérables this year, and they need your help planning it.
Since the role of young Cosette is played by a child, the Main Street Theatre company must actually cast 3 girls in the role of young Cosette, and alternate girls from night to night. (This is because of restrictions on working hours for children.) You have received headshots and resumes from 25 girls who wish to audition for young Cosette.
Does order matter when casting the 3 young Cosettes? (In other words, are young Cosette 1, young Cosette 2, and young Cosette 3 different parts?)
No, all three girls will play the same part.
Yes, even though they will all be playing the same part, it will be on different nights.
No, all three girls will get paid the same amount.
Yes, young Cosette 1, young Cosette 2, and young Cosette 3 are all different parts.
Answers
The inference based on the information about ordering is that D. Yes, young Cosette 1, young Cosette 2, and young Cosette 3 are all different parts.
What is an inference?It should be noted that a inference simply means the conclusion that can be deduced based on the information given.
In this case, the Main Street Theatre company must actually cast 3 girls in the role of young Cosette.
Hence, young Cosette 1, young Cosette 2, and young Cosette 3 are all different parts. Therefore, ordering matters.
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Super confused new topic please help
Answers
Answer:
1960cm squared
Step-by-step explanation:
in case you're still confused ask where you're still confused and I'll offer my assistance.good day.
Currently, professional men’s basketball players score an average of 18.2 points per game with a standard deviation of 4.5 points. the current top-scoring professional basketball player scores an average of 36.2 points per game. in one season in the 1990s, professional basketball players averaged 13.2 points per game with a standard deviation of 3.7 points. the top-scoring professional basketball player averaged 30.1 points per game. which player did better relative to his peers? the 1990s basketball player did better than the current basketball player because his z-score is higher. the current basketball player did better than the 1990s basketball player because his z-score is higher. the 1990s basketball player did better than the current basketball player because his z-score is closer to the mean. the current basketball player did better than the 1990s basketball player because his z-score is closer to the mean.
Answers
Hence, the correct option is "The 1990s basketball player did better than the current basketball player because his z-score is higher."
What is an expression?expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.). This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)
How to solve?the correct option is "The 1990s basketball player did better than the current basketball player because his z-score is higher."
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In a catalog, movies are identified by an ID number—2 letters followed by 3 digits.Repetitions are permitted. How many catalog numbers can be made?What is the probability that the ID number is divisible by 5? (Include the 2 letters in the ID number.)
Answers
Using the Fundamental Counting Theorem, it is found that:
676,000 catalog numbers can be made.There is a 0.2 = 20% probability that the ID number is divisible by 5.What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For the 2 letters(26 outcomes each), and 3 numbers(10 outcomes each), we have that the parameters are:
[tex]n_1 = 26, n_2 = 26, n_3 = 10, n_4 = 10, n_5 = 10[/tex]
Hence the number of catalog numbers is:
[tex]N = 26^2 \times 10^3 = 676000[/tex]
The ID number is divisible by 5 if the last digit is either 5 or 0, hence [tex]n_5 = 0[/tex] and the probability is:
[tex]p = \frac{26^2 \times 10^2 \times 2}{26^2 \times 10^3} = 0.2[/tex]
There is a 0.2 = 20% probability that the ID number is divisible by 5.
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A large washer has an outer radius of 10mm and a hole with a diameter of 14mm. What is the area of the washer? (Use π =3.14)
Answers
Answer:
160.14 mm^2
Step-by-step explanation:
Area of a circle = pi r^2
subtract the area of the smaller circle from the larger
note that the smaller radius = 7 mm
pi ( 10^2 - 7^2 ) =
3.14 ( 51) = 160.14 mm^2
The area of the washer is approximately 160.14 square millimeters.
Use the concept of the circle defined as:
A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.
The line of reflection symmetry is formed by all lines that traverse the circle.
Additionally, every angle possesses rotational symmetry around the center.
Given that,
The outer radius of the washer: 10mm
Diameter of the hole: 14mm
π value to be used: 3.14
To find the area of the washer:
Subtract the area of the hole from the area of the outer circle.
The area of a circle is given by the formula A = πr²,
Where r is the radius.
For the outer circle:
The radius is 10mm, so the area of the outer circle = 10²π.
The area of the outer circle = 100π mm²
For the hole,
The diameter is 14mm,
So the radius of the hole = 7 mm.
The area of the hole = 7²π
The area of the hole = 49π mm²
To find the area of the washer,
Subtract the area of the hole from the area of the outer circle:
Area of washer = Area of the outer circle - Area of hole
Area of washer = (100π - 49π) mm²
Area of washer = 51π mm²
Area of washer ≈ 160.14 mm²
Hence,
The area of the washer is approximately 160.14 square millimeters.
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please solve it?
1. 3q4 × 2q5 ÷q3
2. 4-²
3. 16^1/2
4.4°
Answers
(3.125) + (-3.9) - (2.46)
Answers
Answer:
-3.235Step-by-step explanation:
First, let's start by removing the parentheses and simplifying the expression.
3.125 + - 3.9 - 2.46
Adding a negative number is the same as subtracting it, so we can remove the + sign.
3.125 - 3.9 - 2.46
From there, we can do simple subtraction and get:
-3.235