The Hyperbolic Sine (sinh(x)) and Hyperbolic Cosine (cosh(x)) functions are defined as such: sin h(x) = e^x - e^-x/2 cosh(x) = e^x + e^-x/2 Compute the y-Intercept of both functions Then Determine the end behavior of these two functions by analyzing the limit as x goes to positive infinity and as x goes to negative infinity
Answers
Answer:
y-incercepts:
sinh(x):0, cosh(x)=1
Limits:
positive infinity: sinh(x): infinity, cosh(x): infinity
negative infinity: sinh(x): - infinity, cosh(x): infinity
Step-by-step explanation:
We are given that
\(\sinh(x)=\frac{e^{x}-e^{-x}}{2}\)
\(\cosh(x)=\frac{e^{x}+e^{-x}}{2}\)
To find out the y-incerpt of a function, we just need to replace x by 0. Recall that \(e^{0}=1\). Then,
\(\sinh(0) = \frac{1-1}{2}=0\)
\(\cosh(0) = \frac{1+1}{2}=1 \)
For the end behavior, recall the following:
\(\lim_{x\to \infty}e^{x} = \infty, \lim_{x\to \infty}e^{-x} = 0\)
\(\lim_{x\to -\infty}e^{x} = 0, \lim_{x\to -\infty}e^{-x} = \infty\)
Using the properties of limits, we have that
\(\lim_{x\to \infty} \sinh(x) =\frac{1}{2}(\lim_{x\to \infty}e^{x}-\lim_{x\to \infty}e^{-x})=(\infty -0) = \infty\)
\(\lim_{x\to \infty} \cosh(x) =\frac{1}{2}(\lim_{x\to \infty}e^{x}+\lim_{x\to \infty}e^{-x}) =(\infty -0)= \infty\)
\(\lim_{x\to -\infty} \sinh(x) =\frac{1}{2}(\lim_{x\to -\infty}e^{x}-\lim_{x\to -\infty}e^{-x}) = (0-\infty)=-\infty\)
\(\lim_{x\to -\infty} \cosh(x) =\frac{1}{2}(\lim_{x\to -\infty}e^{x}+\lim_{x\to -\infty}e^{-x}) =(0+\infty)= \infty\)
Related Questions
Find x when () = 2. Please explain step by step
Answers
Answer: Ans is 990. First such a number is 5×0 +2=2, then 5×1 +2=7, like that in all 20 numbers are there from 2 to 97 in A.P.with common difference of 5.
Step-by-step explanation:
factor 1/8 out of 1/8x-49/8
Answers
Answer:
1/8(x - 49)
Step-by-step explanation:
When we factor out something, we are basically finding common factors from multiple terms to take out. Example:
ab + ac; factored out: a(b + c)
If we want to factor out 1/8 from 1/8x - 49/8, we simply divide the two terms by 1/8.
\(\frac{1/8}{1/8x}\) The 1/8 cancel out giving us x so:
1/8(x - __)
The next term,
\(\frac{49/8}{1/8}\)
When two fractions divide, you flip the bottom one and multiply them both,
\(\frac{49}{8} *\frac{8}{1}\)
giving us 49.
The answer is: 1/8(x - 49)
The results of a coin toss are shown.
What is P(heads)?
H T H H H T H T T H H T H T T T H H T H T T H H H H T H T T
A. 8/15. B.7/17. C.1/2. D3/5
Answers
Answer:
A is the answer!
Because that's reduced of 16/30
count and divide from 16/30 to 8/15!
The sum of three consecutive even numbers is 120. What is the smallest of the three numbers?
Answers
Answer:
Step-by-step explanation:
the consecutive are 39,40,41 and the smallest here is 39
Hope this helped
Are these lines parallel, perpendicular, or neither?
Y = -4x +5 and y = -1/4x + 3
Answers
Answer:
neither
Step-by-step explanation:
Help its due today and I'm stuck on this question
Convert 75 gram per cm 3 to pounds per cubic inch (round to nearest tenth) [ 1 pound = 0.4536 kg] [ 1 cm = 0.3937 in] [ 1 kg = 1000g] (Show your work)
2.07 pounds/in 3
1.7 pounds/in 3
2.7 pounds/in 3
3.2 pounds/in 3
Answers
Answer:
It’s 2.07 pounds/in 3
Step-by-step explanation:
1 kilogram = 2.2 × pounds, so,2.07 × 1 kilogram = 2.07 × 2.2 pounds (rounded), or2.07 kilograms = 4.554 pounds.Step 2: Convert the decimal part in pounds to ouncesAn answer like "4.554 pounds" might not mean much to you because you may want to express the decimal part, which is in pounds, in ounces which is a smaller unit.So, take everything after the decimal point (0.55), then multiply that by 16 to turn it into ounces. This works because one pound equals 16 ounces. Thus,4.55 pounds = 4 + 0.55 pounds = 4 pounds + 0.55 × 16 ounces = 4 pounds + 8.8 ounces. So, 4.55 pounds = 4 pounds and 8 ounces (when rounded). Obviously, this is equivalent to 2.07 kilograms. Step 3: Convert from decimal ounces to a usable fraction of ounceThe previous step gave you the answer in decimal ounces (8.8), but how to express it as a fraction? See below a procedure, which can also be made using a calculator, to convert the decimal ounces to the nearest usable fraction: a) Subtract 8, the number of whole ounces, from 8.8:8.8 - 8 = 0.8. This is the fractional part of the value in ounces.b) Multiply 0.8 times 16 (it could be 2, 4, 8, 16, 32, 64, ... depending on the exactness you want) to get the number of 16th's ounces:0.8 × 16 = 12.8.c) Take the integer part int(12.8) = 13. This is the number of 16th's of a pound and also the numerator of the fraction.Finalmente, 2.07 quilogramas = 4 pounds 8 3/4 ounces.A fração 12/16 não está simplificada, e ainda pode ser reduzida para 3/4 para que possamos expressar como a fração mais simples possível.In short:2.07 kg = 4 pounds 8 3/4 ounces
Need help with 34-40
Answers
Answer:
This is the answer and I hope it helps. have a great time.
I need some help with this
Answers
If all real numbers satisfy the inequality, select all real numbers. If no real numbers satisfies the inequality, select no solution.
how can you tell if it's all real numbers or if no real numbers.
Answers
The solution to the inequality is x >= -2 for inequality 3x-5≥-11
The given inequality is 3x-5≥-11
Three times of x greater than or equal to minus eleven
x is the variable
3x - 5≥ -11:
Adding 5 to both sides, we get:
3x ≥ -6
Dividing both sides by 3, we get:
solution is x≥-2
Therefore, the solution to the inequality is x >= -2.
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This year, the number of raffle tickets sold for a school's extracurricular activities fundraiser is 848. It is estimated that the number of raffle tickets sold will increase by 5% each year. Find the total number of raffle tickets sold at the end of 9 years.
Select the correct answer below:
9,158
9,351
9,818
10,666
Answers
This year, the number of raffle tickets sold for a school's extracurricular activities fundraiser is 848. It is estimated that the number of raffle tickets sold will increase by 5% each year.
The total number of raffle tickets sold at the end of 9 years is approximately 9,818.
To find the total number of raffle tickets sold at the end of 9 years, we need to calculate the number of tickets sold each year and sum them up.
Starting with the initial number of tickets sold, which is 848, we will increase this number by 5% each year for a total of 9 years.
Year 1: 848 + (5% of 848) = 848 + 42.4 = 890.4
Year 2: 890.4 + (5% of 890.4) = 890.4 + 44.52 = 934.92
Year 3: 934.92 + (5% of 934.92) = 934.92 + 46.746 = 981.666
Year 9: Ticket sales at the end of 9 years = Number of tickets sold in Year 8 + (5% of Year 8 sales)
Year 9: Total = 1,399.585 + 69.97925 = 1,469.56425 ≈ 1,469.56
The total number of raffle tickets sold at the end of 9 years is approximately 1,469.56.
The correct option is 9,818.
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Given that the coefficient of x⁵ in the expansion of (1+kx)⁵ is -672 find the value of k
Answers
The value of k that satisfies the given condition is approximately 0.4041.
In the expansion of (1+kx)⁵, the coefficient of x⁵ is given by the term:
C(5,k) * (kx)⁵ = k⁵ * C(5,k) * x⁵
where C(5,k) is the binomial coefficient or the number of ways to choose 5 items out of k.
So, we have the equation:
k⁵ * C(5,k) = -672
We can use a table of binomial coefficients to find C(5,k) for different values of k, but this can be time-consuming. Alternatively, we can use the fact that C(5,k) = C(5,5-k) and rewrite the equation as:
k⁵ * C(5,5-k) = -672
Expanding C(5,5-k), we get:
k⁵ * C(5,5-k) = k⁵ * C(5,k) = -672
Now, we can use trial and error to solve for k. Using this method, we can find that k = -4 or k ≈ 0.4041. However, since k must be positive (since it appears as a factor in the expansion), the only valid solution is k ≈ 0.4041.
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a researcher computes a 90% confidence interval for the mean weight (in lbs) of widgets produced in a factory. the interval is (7.2, 8.9). which of these is a correct interpretation of this interval?
Answers
(A) There's a 90% chance the population value is between 7.2 and 8.9 oz.
What is confidence interval?You should know that In frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used
The confidence interval is the probability that the population value would fall within a range of values for a number of times. The confidence interval are calculated by adding and subtracting the margin of error to/from the mean.
A 90% confidence interval of (7.2, 8.9) means that their is a 90% confidence or chance that the population value is between 7.2 and 8.9 oz
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Solve the system of equations.
5x - 4y = -10
- 4x + 5y = 8
y =
Answers
Answer:
x= -2
y= 0
Step-by-step explanation:
check answer
5(-2)-4(0)= -10
-10-0= -10 (TRUE)
-4(-2)+5(0)= 8
8+0= 8 (TRUE)
Answer: 5x−4y=−10;−4x+5y=8
Step-by-step explanation:
the long run, the mean number of candies handed out is 1.7, with standard deviation of 0.781. a) In one half hour 5 trick or treaters visit Raul's house. What is the probability that each trick or treater gets exactly 2 pieces of candy
Answers
The probability that each trick or treater gets exactly 2 pieces of candy is approximately 0.6517 or 65.17%.
We may use the normal distribution along with the characteristics of the mean and standard deviation given to determine the likelihood that each trick-or-treater receives exactly 2 pieces of candy.
In the long term, the average number of candies distributed is 1.7, with a standard deviation of 0.781, according to our knowledge. Raul's home will be visited by 5 trick-or-treaters, thus we can use the normal distribution to determine the likelihood that each child will receive exactly 2 pieces of candy.
The distribution must first be standardized by finding the z-score for the value of 2:
z = (2 - 1.7) / 0.781 = 0.384
Then, we calculate or utilize a conventional normal distribution table to determine the likelihood of obtaining a z-score of 0.384 or below, which is equivalent to the likelihood that each trick-or-treater will receive precisely 2 pieces of candy:
P(Z ≤ 0.384) = 0.6517
Hence, there is an about 0.6517 or 65.17% probability that each trick-or-treater will receive exactly 2 pieces of candy.
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which expressions are equivalent to 1/81? check all that apply.
Answers
Answer: here are some examples :
8-1 9^
-2 9^
8/9^
4 9^
8/9^
10 9^
-6 x 9^
3 9^5 x 9^-7
Step-by-step explanation: pls mark branliest
Find the measure of 3x-46+14=90
Answers
Answer:
Step-by-step explanation:
3x = 90 + 46 - 14
3x = 122
x=\(\frac{122}{3}\)≈40,7
Answer: 40.6 repeated
Step-by-step explanation: combine -46 and 14 which is -32. then add 32 to 90. then divide 3 on both sides. 122/3 is 40.6 repeated
xpress 8/(1 - 2x)2 as a power series by differentiating the equation below. What is the radius of convergence? 4 (1 - 2x) = 4(1 + 2x + 4x2 + 8x3 + ...) = 4 [infinity] Σ n=0 (2x)n SOLUTION Differentiating each side of the equation, we get 8 (1 - 2x)2 = 4(2 + Correct: Your answer is correct. + 24x2 + ...) = 4 [infinity] Σ n=1 Incorrect: Your answer is incorrect. If we wish, we can replace
Answers
Recall that for |x| < 1, we have
\(\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n\)
Replace x with 2x, multiply 4, and call this function f :
\(f(x)=\dfrac4{1-2x}=\displaystyle4\sum_{n=0}^\infty(2x)^n\)
Take the derivative:
\(f'(x)=\dfrac8{(1-2x)^2}=\displaystyle8\sum_{n=0}^\infty n(2x)^{n-1}=\boxed{8\sum_{n=0}^\infty (n+1)(2x)^n}\)
By the ratio test, the series converges for
\(\displaystyle\lim_{n\to\infty}\left|\frac{(n+2)(2x)^{n+1}}{(n+1)(2x)^n}\right|=|2x|\lim_{n\to\infty}\frac{n+2}{n+1}=|2x|<1\)
or |x| < 1/2, so the radius of convergence is 1/2.
George eat 3/8 a pizza and 1/4 of pizza
What fraction of pizza has George eaten
Answers
Answer: 5/8
Step-by-step explanation:
Answer:
5/8
Step-by-step explanation:
1/4=2/8
2/8+3/8=5/8
What is the range of possible sizes for side 3.2 5.5 x?
Answers
Answer:
the range is :
10 , 74 , 78 , 102
3 , 4 , 4 , 5 , 17
1.2, 1.2 , 3.2 , 3.5 , 3.6 , 6.5 , 8.2 , 9.2
Step-by-step explanation:
10% of the library books in the fiction section are worn and need replacement. 20% of the nonfiction holdings are worn. The library's holdings are 60% fiction and 40% nonfiction. The probability to get a worn book is?
Answers
Answer: 14%
Step-by-step explanation:
Let's assume that there are 100 books in total.
So there are 60 fiction books and 40 nonfiction books.
10% of 60 is 6.
20% of 40 is 8.
So there are 14 books out of 100 that are worn.
This is 14%
if x-y = 8 and xy=5 , find x^2 + y^2
Answers
Answer:
x² + y² = 74
Step-by-step explanation:
given
(x - y) = 8 ( square both sides )
(x - y)² = 8² ← expand left side using FOIL
x² - 2xy + y² = 64 ← substitute xy = 5
x² - 2(5) + y² = 64
x² - 10 + y² = 64 ( add 10 to both sides )
x² + y² = 74
The function f(x)= 2x +4x^-1 has one local minimum and one local maximum.
This function has a local maximum at x=?
with value ?
and a local minimum at x=?
with value ?
Answers
The requried, local minimum and maxium for the given function is √2 and -√2.
We need to find the local maximum and local minimum of the function \(f(x) = 2x + 4x^{(-1)}.\)
First, we find the derivative of f(x):
\(f'(x) = 2 - 4x^{(-2)} = 2 - 4/x^2\)
Setting f'(x) = 0 to find the critical points:
\(2 - 4/x^2 = 0\)
Solving for x, we get:
x = ±√2
To determine whether these critical points are local maxima or minima, we need to examine the sign of the second derivative:
\(f''(x) = 8x^{(-3)}\)
When x = √2, f''(√2) = 8/(√2)³ = 8√2 > 0, so x = √2 is a local minimum.
When x = -√2, f''(-√2) = 8/(-√2)³ = -8√2 < 0, so x = -√2 is a local maximum.
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Find the axis of symmetry.
f(x) = -(x - 2)(x + 4)
a) x = 2
b) y = -1
c) y = 8
d) x = -1
Answers
The axis of symmetry of the given quadratic function f(x) = -(x - 2)(x + 4) is x = -1.
What is the axis of symmetry of the function?Given the function in the question:
f(x) = -(x - 2)(x + 4)
To find the axis of symmetry, first expand quadratic function f(x) = -(x - 2)(x + 4).
f(x) = -(x - 2)(x + 4)
f(x) = (-x + 2)(x + 4)
f(x) = -x(x + 4) + 2( x + 4 )
f(x) = -x² - 4x + 2x + 8
Collect and add like terms
f(x) = -x² - 2x + 8
To find the axis of symmetry, we can use the formula:
x = -b/2a
Where a = -1 and b = -2.
Substituting these values, we get:
x = -(-2) / 2(-1)
Simplify
x = 2 / -2
x = -1
Therefore, the the axis of symmetry is x = -1.
Option D) x = -1 is the correct answer.
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Aaron ate 1/2 of a blueberry pie and 2/3 of an apple pie how much pie did she eat
Answers
Answer:
7/6pie. i think
Step-by-step explanation:
1/2 + 2/3 = 3/6 + 4/6 = 7/6 = 1 1/6
Answer:
1 and 1/6
Step-by-step explanation:
1/2 + 2/3 = 3/6 +4/6= 1 1/6
Johnny uses a wheelbarrow to move planting soil to a delivery truck. The volume of planting soil that fits in the wheelbarrow measures
2
2 feet by
3
3 feet by
1.5
1.5 feet. The delivery truck measures
11
11 feet by
8
8 feet and is
6
6 feet tall. Johnny puts planting soil in the delivery truck until the truck is
70
70% full.
What is the minimum number of times Johnny needs to use the wheelbarrow until the delivery truck is
70
70% full?
Answers
The minimum number of times Johnny needs to use to the wheelbarrow until the delivery truck is filled up to 70%, whereby the shape of the truck is a rectangular prism is about 41 times
What is a rectangular prism?A rectangular prism is a three dimensional geometric figure with three pairs of parallel facing sides, and perpendicular adjacent faces.
Whereby the wheelbarrow and the truck are rectangular prisms, we get;
The dimensions of the wheel barrow are;
2 feet by 3 feet by 1.5 feet
The dimensions of the truck are;
11 feet by 8 feet by 6 feet
The amount of soil John puts in the truck = 70% of the volume of the truck
Therefore;
The amount of soil John puts in the truck = 11 feet × 8 feet × 6 feet × 70%
11 feet × 8 feet × 6 feet × 70% = 528 ft³ × 70% = 369.6 ft³
The number of times to use the wheelbarrow, n, is therefore;
n = 369.6 ft³ ÷ (2 ft × 3 ft × 1.5 ft) ≈ 41.0
The minimum number of times Johnny needs to use the wheelbarrow until the delivery truck is 70% filled is therefore 41 = 41 times
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EXPLANATION:
Complete the equations to find the
length of the side of the square that
is 49 cm2.
2
А
cm 2
S=
cm
Help please
Answers
Answer:
S = 7cm
Step-by-step explanation:
A = 49cm² = 7 × 7 (Square root of 49 as Area = s²)
S = 7cm
Mark wants to be a chef someday and would like to start learning to grow his own
ingredients in a garden. His mom gives him 12 square feet of space in the back yard to plant
a garden. He marks off % of it to save for a tomato plant and has the rest to use for onions.
Each onion bulb needs square feet of room to grow. How many onion bulbs can he
plant?
Answers
The area of the space available for onions is:n12 square feet - 0.12x square feet. number of onion bulbs Mark can plant is: (12 - 0.12x) / y
What is percentage?
Percentage is a way of expressing a number or proportion as a fraction of 100. It is represented by the symbol "%".
Mark has marked off a certain percentage of the 12 square feet to save for a tomato plant, which means the remaining space will be used for onions.
Let's say Mark marks off x% of the space for the tomato plant. That means he will have (100-x)% of the space for onions.
The area of the space reserved for the tomato plant is:
12 square feet x (x/100) = 0.12x square feet
The area of the space available for onions is:
12 square feet - 0.12x square feet
Let's say each onion bulb needs y square feet of room to grow. Mark can plant as many onion bulbs as can fit in the remaining space, which is:
(12 square feet - 0.12x square feet) / y
So the number of onion bulbs Mark can plant is:
(12 - 0.12x) / y.
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The cost of a week long vacation in a city has a mean of 1000 and a variance of 1200. The city imposes a tax which will raise all tourism related costs by 10%. Find the coefficient of variation for the cost of a week long vacation in this city after the tax is imposed.
Answers
Answer:
The coefficient of variation after the tax is imposed is 0.033
Step-by-step explanation:
Given
\(\mu =1000\) --- mean
\(\sigma^2 = 1200\) --- variance
\(tax = 10\%\)
Required
The coefficient of variation
The coefficient of variation is calculated using:
\(CV = \frac{\sqrt{\sigma^2}}{\mu}\)
After the tax, the new mean is:
\(\mu_{new} = \mu * (1 + tax)\)
\(\mu_{new} = 1000 * (1 + 10\%)\)
\(\mu_{new} = 1100\)
And the new variance is:
\(\sigma^2_{new} = \sigma^2 * (1 + tax)\)
\(\sigma^2_{new} = 1200 * (1 + 10\%)\)
\(\sigma^2_{new} = 1320\)
So, we have:
\(CV = \frac{\sqrt{\sigma^2}}{\mu}\)
\(CV = \frac{\sqrt{1320}}{1100}\)
\(CV = \frac{36.33}{1100}\)
\(CV = 0.033\)
classifying paralelagrams
Answers
a. Length of GK = \(\sqrt{34}\) and Length of adjacent to GK = \(\sqrt{34}\)
b. Slope of GK = \(\frac{5}{3}\) and Slope of adjacent to RS = \(-\frac{3}{5}\)
c. The parallelogram GHJK is Square.
Define the term parallelogram?A quadrilateral with two sets of parallel sides is referred to as a parallelogram. As a result, a parallelogram's opposite sides are parallel and congruent in length, and its opposite angles are similarly congruent.
Given in figure GHJK, the vertices are G(-3, 6), H(2, 3), J(-1, -2), K(-6, 1)
a. Length of line = \(\sqrt{({x_{2}-x_{1})^{2} } + ({y_{2}-y_{1})^{2}}\)
for points G(-3, 6) and K(-6, 1)
Length of GK = \(\sqrt{(-6+3)^{2} + (1-6)^{2} }\) = \(\sqrt{34}\)
Length of GK = \(\sqrt{34}\)
Length of adjacent side (GH, KJ) to GK = \(\sqrt{(2+3)^{2} + (3-6)^{2} }\) = \(\sqrt{34}\)
Length of adjacent to GK = \(\sqrt{34}\)
b. \(Slope = \frac{(y_{2} -y_{1})}{(x_{2} -x_{1})}\)
Slope of GK = \(\frac{(1 - 6)}{(-6 + 3)}\) = \(\frac{5}{3}\)
Slope of GK = \(\frac{5}{3}\)
Slope of adjacent side to GK = \(\frac{3-6}{2+3}\) = \(-\frac{3}{5}\)
Slope of adjacent to RS = \(-\frac{3}{5}\)
c. All sides are equals to \(\sqrt{34}\)
So, length of diagonal GJ = \(\sqrt{({-3+1))^{2} } + ({6+2})^{2}} = \sqrt{68}\)
and length of diagonal HK = \(\sqrt{({2+6))^{2} } + ({3-1})^{2}} = \sqrt{68}\)
All sides and diagonals are equal then parallelogram GHJK is Square.
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What is the difference between Independent and dependent events?
Choose the correct answer below.
O A Two events are independent when the occurrence of one event does not affect the probability of the occurrence of the other event. Two events are dependent when the occurrence of one event affects the probability
of the occurrence of the other event.
OB. Two events are independent if only one of the two events can occur. Two events are dependent if they can occur at the same time.
OC. Two events are independent when the occurrence of one event affects the probability of the occurrence of the other event. Two events are dependent when the occurrence of one event does not affect the probability
of the occurrence of the other event
OD. Two events are independent if they can occur at the same time. Two events are dependent if only one of the two events can occur.
Answers
Answer: A
Step-by-step explanation:
It is the definition of independent and dependent events