When the expression inside the logarithm becomes zero, the natural logarithm is undefined and approaches negative infinity. In (c), as x approaches 9 from the left, the denominator becomes zero, resulting in the natural logarithm approaching infinity. In (d), as x approaches infinity, the expression 8/x approaches zero, and the natural logarithm of zero is negative infinity.
(a) To evaluate the limit lim ln(x^2 - 25) as x approaches 5+, we substitute x = 5 into the function:
lim ln(x^2 - 25) = ln((5^2) - 25) = ln(0) = -INFINITY
(b) To evaluate the limit lim ln(x^2 - 49) as x approaches -7-, we substitute x = -7 into the function:
lim ln(x^2 - 49) = ln((-7^2) - 49) = ln(0) = -INFINITY
(c) To evaluate the limit lim ln(1/(9 - x)) as x approaches 9-, we substitute x = 9 into the function:
lim ln(1/(9 - x)) = ln(1/(9 - 9)) = ln(1/0) = INFINITY
(d) To evaluate the limit lim ln(8/x) as x approaches infinity, we substitute x = infinity into the function:
lim ln(8/x) = ln(8/infinity) = ln(0) = -INFINITY
Note: In (a) and (b), when the expression inside the logarithm becomes zero, the natural logarithm is undefined and approaches negative infinity. In (c), as x approaches 9 from the left, the denominator becomes zero, resulting in the natural logarithm approaching infinity. In (d), as x approaches infinity, the expression 8/x approaches zero, and the natural logarithm of zero is negative infinity.
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Allen built these figures using triangular tiles. What would
be the perimeter of the tenth figure?
10 units
12 units
21 units
30 units
Answer:
The first one 10 units would be the perimenter of the tenth figure.
Alba is Saving for a big overseas trip she hopes to take her senior year in college , which is four years away . She plans to deposit 10,000 at the end of each quarter in an account earning 8% annual interest , compounded quarterly . How much money will alba have for trip after 20 years ?
Answer:
FV= $1,937,719.58
Step-by-step explanation:
Giving the following information:
Quarter deposit= $10,000
Number of periods= 20*4= 80
Interest rate? 0.08/4= 0.02
To calculate the future value, we need to use the following formula:
FV= {A*[(1+i)^n-1]}/i
A= quarter deposit
FV= {10,000*[(1.02^80) - 1]} / 0.02
FV= $1,937,719.58
A boat traveled 27 miles in 2 hours. At this rate, how many miles will the boat travel in 1/2 hour? PLEASE HELP!!
Answer:
6.75
Step-by-step explanation:
take 27 and divide by hours to get miles per hour rate
27/2= 13.5 mph
take this new rate and multiply by time. So
13.5m/h* (0.5 h)= 6.75 miles
The hours cancel and you are left with your answer in miles
Which linear function represents a slope of 1/4?
Answer:
a
Step-by-step explanation:
THE ANSWER IS B!!!!
Step-by-step explanation: I just did it on edge
2) Suppose the probability distribution for the one-period return of some asset is as follows: Return Probability 0.27 0.25* 0.18 0.25* 0.10 0.30 p.04 0.20+ a. What is this asset's expected one-period
The expected one-period return for the asset is given by the expression 0.0675 + 0.045 + 0.03 + 0.04p + 0.04, where 'p' represents an unknown probability.
The given probability distribution represents the one-period return for an asset, with corresponding probabilities assigned to each return value. To find the expected one-period return, we need to calculate the weighted average of the returns, where the weights are the probabilities.
Let's calculate the expected one-period return step by step:
1. Multiply each return value by its corresponding probability:
0.27 * 0.25 = 0.0675
0.18 * 0.25 = 0.045
0.10 * 0.30 = 0.03
p * 0.04 = 0.04p
0.20 * 0.20 = 0.04
2. Sum up the products calculated in step 1:
0.0675 + 0.045 + 0.03 + 0.04p + 0.04
3. Set the sum equal to the expected one-period return, denoted as E(R):
E(R) = 0.0675 + 0.045 + 0.03 + 0.04p + 0.04
Therefore, the expected one-period return of the asset is 0.0675 + 0.045 + 0.03 + 0.04p + 0.04.
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Write the ratio of corresponding sides for the similar triangles and reduce the ratio to lowest terms.
a.
10
d.
4 5
b. 4 5
I
s 100
10
4
8
--
8 10
415
이
00
I
C. 10 85
815
I
10
I
2/5
I
211
552
415
Mark this and return
Next
Submit
The ratio of corresponding sides for the given similar triangles is 2/5.
In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:
a. 10
This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.
b. 4/5
This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.
To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.
Dividing 4 and 5 by 1, we get:
4 ÷ 1 = 4
5 ÷ 1 = 5
Therefore, the simplified ratio is 4/5.
c. 10/85
This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.
Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.
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The figure below was made with a scale of 1 unit =9 m. You can place your figure anywhere on the grid on the right.
Answer & Step-by-step explanation:
I can't draw the image, but I can explain it to you.
Since 1 unit was 3 units and now it's 9, you would have to divide each side by 3. So, the width would be 1 unit and the length would be 2 units.
I hope this helped!!!
The scale of 1 unit = 9 m
The rectangle 1 unit = 3 m is similar to 1 unit = 9 m
Since the unit of the scale is reduced the image size will be smaller than the given diagram.
What is supposed by similarity in math?In Euclidean geometry, objects are comparable if they have an identical shape, or if one has the same form because they reflect a photograph of the other. more precisely, one can be obtained from the opposite by using uniformly scaling (enlarging or lowering), probably with extra translation, rotation and reflection.
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A 52 foot ladder is set against the side of a house so that it reaches up 48 feet. If Jevonte grabs the ladder at its base and pulls it 3 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 45 ft.) Round to the nearest tenth of a foot.
After Jevonte pulls the ladder 3 feet farther from the house, the ladder will reach approximately 10.15 feet up the Side of the house.
We can solve this problem using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the ladder forms a right triangle with the side of the house and the ground. The ladder acts as the hypotenuse, and we know its length is 52 feet. The height of the ladder on the house is 48 feet.
Using the Pythagorean theorem, we can calculate the distance of the ladder from the house after it is pulled 3 feet farther. Let's denote this distance as x.
We have:
(48 + 3)^2 + x^2 = 52^2
Simplifying:
51^2 + x^2 = 2704
2601 + x^2 = 2704
x^2 = 2704 - 2601
x^2 = 103
x = √103
Rounding to the nearest tenth of a foot, we have x ≈ 10.15 feet.
Therefore, after Jevonte pulls the ladder 3 feet farther from the house, the ladder will reach approximately 10.15 feet up the side of the house.
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a box has 10 disks numbered 1 through 10. a disk is drawn at random 50 times with replacement. the disk numbered 7 was drawn 6 times. what is the relative frequency of getting the disk numbered 7 on the next draw?
The relative frequency of getting the disk numbered 7 on the next draw is 0.12 or 12%.
To find the relative frequency of getting the disk numbered 7 on the next draw, we need to analyze the data provided.
In this scenario, a disk is drawn at random from a box containing 10 disks numbered 1 through 10. The draws are made with replacement, meaning that after each draw, the disk is returned to the box, and the next draw is independent of the previous ones.
We are given that the disk numbered 7 was drawn 6 times out of the 50 draws. To find the relative frequency of getting the disk numbered 7 on the next draw, we need to determine the proportion of times it appeared relative to the total number of draws.
The relative frequency can be calculated by dividing the number of times the desired outcome occurs (in this case, drawing disk 7) by the total number of trials (draws).
In this case, the number of times disk 7 was drawn is 6, and the total number of draws is 50. Therefore, the relative frequency is:
Relative frequency = (Number of times disk 7 was drawn) / (Total number of draws)
= 6 / 50
= 0.12
Hence, the relative frequency of getting the disk numbered 7 on the next draw is 0.12 or 12%.
This means that if we were to continue drawing disks with replacement, the probability of drawing disk 7 on the next draw would be approximately 12%. However, it's important to note that since the draws are made with replacement, the probability of drawing any specific disk remains the same for each draw, regardless of the previous outcomes.
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is √125 rational or irrational
Answer:
Irrational
Step-by-step explanation:
Answer: it is an irrational number
8 divided by 5/6 i need help
Answer:
9.6
Step-by-step explanation:
SHOW YOU WORK TO BE MARKED BRAINLIEST!!!
Answer: x=65
Step-by-step explanation:
Set (2x + 2) equal to (3x-63) because they are the same angle.
(2x+2)=(3x-63)
Subtract 2x from 3x which gives u 1x or just x
Now u have 2=x-63
Add 63 to both sides so now u have x =65
Lemme know if u need help
Question 5: (2+4+3+3 Marks) 4 Let B be a fixed n x n invertible matrix. Define T: Man Man by T(A)=B-¹AB. Find T(I) and T(B). i) ii) Show that T is a linear transformation. III) iv) Show that ker(7)= (0). What is nullity(7)?
In question 5, we are asked to find T(I) and T(B) for a given linear transformation T, show that T is a linear transformation, prove that the kernel of T is {0}, and determine the nullity of T.
To find T(I), we substitute I (the identity matrix) into the definition of T: T(I) = B⁻¹IB = B⁻¹B = I. Similarly, for T(B), we substitute B into the definition of T: T(B) = B⁻¹BB = B⁻¹B² = B.
To show that T is a linear transformation, we need to demonstrate that it preserves vector addition and scalar multiplication. Let A₁ and A₂ be matrices and c be a scalar. We have T(A₁ + A₂) = B⁻¹(A₁ + A₂)B = B⁻¹A₁B + B⁻¹A₂B = T(A₁) + T(A₂), showing preservation of vector addition. Similarly, T(cA) = B⁻¹(cA)B = c(B⁻¹AB) = cT(A), demonstrating preservation of scalar multiplication.
To prove that the kernel (null space) of T is {0}, we need to show that the only solution to the equation T(A) = 0 is A = 0. By substituting 0 into the definition of T, we get B⁻¹0B = 0, which implies that A = 0.
The nullity of T is the dimension of the kernel, which in this case is 0 since the kernel only contains the zero matrix. Therefore, the nullity of T is 0.
In conclusion, T(I) = I, T(B) = B, T is a linear transformation, the kernel of T is {0}, and the nullity of T is 0.
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Leo just bought a guitar signed by Gene Simmons. The shape of the body is a triangle with a base of
14 inches and a height of 18 inches. The neck of the guitar is 3 inches X 21 inches.
What is the total area of Leo's new guitar?
Answer:
[tex]189in^2[/tex]
Step-by-step explanation:
[tex]\frac{14*18}{2}=\frac{252}{2}=126[/tex]
[tex]3*21=63[/tex]
[tex]126+63=189[/tex]
(03.06 LC)
Choose the equation below that represents the line that passes through the point (2, 4) and
has a slope of 3. (5 points)
O y + 2 - 3(x + 4)
Oy+4= 3(x + 2)
Oy - 4 - 3(x - 2)
Oy - 2 - 3(x - 4)
Answer:
i think B
Step-by-step explanation:
but im not sure
either way, Hope it helps
A person is starting a retirement fund. The person will add to the fund on a yearly basis. Each year, they will increase the amount added to the fund the previous year by 10%. In the first year, the person will add $2000. Which expression represents the total amount the person will add in the first 5 years?
A. 2000(1−1.1)^5/1−1.1
B. 2000(1−1.1^5)/1−1.1
C. 2000(1−.1)^5/.1
D. 2000(.1)^5/.1
The correct Retirement Fund expression is B. [tex]2000(1−1.1^5)/1−1.1.[/tex]
The expression that represents the total amount the person will add in the first 5 years is:
B. [tex]2000(1−1.1^5)/1−1.1[/tex]
Let's break down the expression to understand why it is the correct choice.
The person adds $2000 in the first year. Each subsequent year, they increase the amount added by 10% compared to the previous year. This means that in the second year, they will add 10% more than $2000, in the third year 10% more than what they added in the second year, and so on.
To calculate the total amount added in the first 5 years, we can use the formula for the sum of a geometric series:
S = a * [tex](1 - r^n)[/tex] / (1 - r)
where:
S is the sum of the series,
a is the first term,
r is the common ratio, and
n is the number of terms.
In this case, the first term a is $2000, the common ratio r is 1.1 (since each year's amount is 10% more than the previous year), and the number of terms n is 5 (since we want to calculate the total amount for the first 5 years).
Plugging these values into the formula, we get:
S = [tex]2000 * (1 - 1.1^5) / (1 - 1.1)[/tex]
Simplifying further, we get:
S = 2000 * (1 - 1.61051...) / (-0.1)
The approximate value of 1.61051... is obtained by evaluating 1.1^5.
This expression is equivalent to the expression in option B, [tex]2000(1−1.1^5)/1−1.1.[/tex]
Therefore, the correct Retirement Fund expression is B. [tex]2000(1−1.1^5)/1−1.1.[/tex]
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-2(x+1)+6x<-14
I need help
Answer:
x<-3
Step-by-step explanation:
-2(x+1)+6x<-14
Distribute
-2x-2 + 6x < -14
Combine like terms
4x -2 < -14
Add 2 to each side
4x-2+2 < -14+2
4x < -12
Divide by 4
4x/4 < -12/4
x<-3
A stadium can seat 46,000 people for a baseball game. One day, 49,442 people attended a game. How many people had to stand because they did not have a seat?
I need a second degree equation that the solution is 7.10
This equation is a second degree equation that has a solution of 7.
To find a second degree equation with a solution of 7, we can use the fact that the solutions of a quadratic equation are given by the quadratic formula: x = (-b ± √(b^2 - 4ac))/(2a).
Since we want the solution to be 7, we can set x = 7 in the quadratic formula and solve for the other variables.
First, let's set x = 7 and simplify the equation: 7 = (-b ± √(b^2 - 4ac))/(2a).
Next, let's multiply both sides of the equation by 2a to eliminate the fraction: 14a = -b ± √(b^2 - 4ac).
Now, let's square both sides of the equation to get rid of the square root: (14a)^2 = (-b ± √(b^2 - 4ac))^2.
Expanding both sides of the equation gives: 196a^2 = b^2 ± 2b√(b^2 - 4ac) + (b^2 - 4ac).
Simplifying further, we have: 196a^2 = 2b^2 ± 2b√(b^2 - 4ac) - 4ac.
Now, we can rearrange the equation to have all terms on one side: 2b^2 ± 2b√(b^2 - 4ac) + 4ac - 196a^2 = 0.
In summary, the second degree equation that has a solution of 7 is 2b^2 ± 2b√(b^2 - 4ac) + 4ac - 196a^2 = 0.
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The sum of three consecutive integers is 267. What is the largest integer? (1 point)
Answer:
2=1
Step-by-step explanation:
without solving explain why the equations do not have solutions
We have 2 terms:
[tex]\sqrt{x+2}[/tex] and [tex]\sqrt{4x+1}[/tex]
For the sum of these to equal a negative number, in this case -3, one of these terms would have to be negative.
So what's the problem?The function [tex]\sqrt{x}[/tex] (square root of x) only returns positive values!
(See the attached image for a graph of [tex]\sqrt{x}[/tex])
Since neither of the terms can be negative, it can't be equal to -3. In other words, no matter what we put as [tex]x[/tex], we can't solve the solution, so we say that the equation does not have any solutions.
Which postulate or theorem can be used to determine the length of RT
Answer:
AAS Congruence Theorem
Step-by-step explanation:
The two triangles share the same vertex T. Therefore, both ∆s has the same measure of <T.
From the information made available in the diagram above, it shows that the non-included side of 170, and two given angles, <T and <S in ∆RST are congruent to the non-included side of 170, and two given angles, <T and <U in ∆VUT. Therefore, ∆RST and ∆VUT are both congruent to each other based on the AAS Congruence Theorem.
This invariably implies that the length of RT is congruent to the length of VT.
You invest $3,287 in a savings account with a fixed annual interest rate of 9% compounded monthly. What is the account balance after 4 years?
Answer: I’m pretty sure that it’s 14199.84
Step-by-step explanation:
.09 times 48 is 4.32
4.32 times 3287 is 14199.84
You get the 48 from 12 months per year for 4 years
Johnny has a computer repair businesss and he needs to make at least $475 a day to remain in business. He charges an initial fee of $100, and $75 for each hour he works. How many hours must he work each day to remain profitable?
Subtract the fee from the total he needs:
475 - 100 = 375
Now divide that by the hourly rate:
375 / 75 = 5
He needs to work 5 hours.
help, i need help for my test, you matter and i love you. <3
a gun has a muzzle speed of 90 meters per second. what angle of elevation should be used to hit an object 200 meters away? neglect air resistance and use g=9.8m/sec2 as the acceleration of gravity.
A gun has a muzzle velocity of 90 meters per second. If an object is 200 meters away, what angle of elevation should be used to hit it? We must first understand that this is a problem about projectile motion. When an object is launched, it follows a trajectory.
It is affected by gravity, air resistance, and other factors. A projectile's motion can be divided into two components: horizontal and vertical. The horizontal component of a projectile's motion is constant. The vertical component is influenced by gravity.Let's assume the angle of elevation to be ө, and the velocity of the gun is v₀.
The horizontal velocity of the projectile is v = v₀ cos(ө), and the vertical velocity is u = v₀ sin(ө) - gt, where g is acceleration due to gravity and t is time of flight. The formula for time of flight is t = 2u/g. The range R can be calculated as R = v t = v₀ cos(ө) t. The formula for maximum height is h = u²/2g. Therefore, the angle of elevation needed to hit an object 200 meters away is 30.2 degrees.
When an object is fired from a gun, it is subject to projectile motion. There are two components to the projectile's motion: horizontal and vertical. The horizontal component is constant, whereas the vertical component is affected by gravity. Let's consider a gun with a muzzle velocity of 90 meters per second. Assume that an object is located 200 meters away. To hit the object, the angle of elevation must be determined.Assume the angle of elevation is ө and the velocity of the gun is v₀. The horizontal velocity of the projectile is v = v₀ cos(ө), while the vertical velocity is u = v₀ sin(ө) - gt. Here, g is acceleration due to gravity, and t is the time of flight. The formula for time of flight is t = 2u/g.The range R can be calculated as R = v t = v₀ cos(ө) t. The formula for maximum height is h = u²/2g. Therefore, the angle of elevation required to hit an object 200 meters away is 30.2 degrees.
A gun with a muzzle velocity of 90 meters per second is used to hit an object 200 meters away. This is a problem about projectile motion. When an object is launched, it follows a trajectory. The projectile motion can be split into two components: horizontal and vertical. The horizontal component of a projectile's motion is constant, whereas the vertical component is influenced by gravity. To hit an object 200 meters away, the angle of elevation must be determined. It has been determined that the angle of elevation required to hit an object 200 meters away is 30.2 degrees.
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What is the solution set for the equation 2|-3n| + 10 = 50
I
Answer:
[tex]n=-\frac{20}{3}\quad \mathrm{or}\quad \:n=\frac{20}{3}[/tex]
Step-by-step explanation:
[tex]2\left|-3n\right|+10=50\\\\\mathrm{Subtract\:}10\mathrm{\:from\:both\:sides}\\\\2\left|-3n\right|+10-10=50-10\\\\Simplify\\\\2\left|-3n\right|=40\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{2\left|-3n\right|}{2}=\frac{40}{2}\\\\Simplify\\\\\left|-3n\right|=20\\\\\mathrm{Apply\:absolute\:rule}:\\\quad \mathrm{If}\:|u|\:=\:a,\:a>0\:\mathrm{then}\:u\:=\:a\:\quad \mathrm{or}\quad \:u\:=\:-a\\[/tex]
[tex]-3n=-20\quad \mathrm{or}\quad \:-3n=20\\\\-3n=-20\quad :\quad n=\frac{20}{3}\\\\-3n=20\quad :\quad n=-\frac{20}{3}\\\\n=-\frac{20}{3}\quad \mathrm{or}\quad \:n=\frac{20}{3}[/tex]
how????
2 1/3 divided by 1/4
Answer:
9.3
Step-by-step explanation:
what's that 2 i just don't understand that buddy??
Solve the problems. Write the complete proof in your paper homework and for online (only) respond to questions or statements (if any) that are parts of your proof or related to it. Given: AB = AC m∠1=m∠2 AC = 15, DC = 5 Find: BD, AB
Answer:
AB=15 BD=18
Step-by-step explanation:
AB is 15 because AB=AC and AC is 15
BD:
Using the Pythagorean Theorem
10²+15²=√325
√325=18
10 is from AB-CD
15 is the height which is AC
Answer:
BD = 5, and AB = 15 :)
.The increasing sequence 2,3,5,6,7,10 consists of all positive integers which are not perfect powers. What is the sum of the squares of the digits of the 1000th number in this sequence?
The sum of the squares of the digits of the 1000th number in the sequence is 5.
How to determine the sum of the squares of the digits of the 1000th number in this sequenceTo find the 1000th number in the sequence 2, 3, 5, 6, 7, 10, we can observe the pattern of the sequence. It consists of all positive integers that are not perfect powers.
The sequence starts with the prime numbers (2, 3, 5, 7), followed by numbers that are products of two primes (6 = 2 * 3, 10 = 2 * 5).
After that, the sequence includes numbers that are products of three primes (30 = 2 * 3 * 5, 42 = 2 * 3 * 7, 70 = 2 * 5 * 7), and so on.
We can see that each number in the sequence is built by multiplying distinct primes together.
To find the 1000th number in the sequence, we need to continue this pattern until we reach the desired position.
Let's calculate the 1000th number:
We start with the prime numbers: 2, 3, 5, 7.
Next, we multiply them together: 2 * 3 * 5 * 7 = 210.
So, the 1000th number in the sequence is 210.
To find the sum of the squares of the digits of 210, we calculate:
[tex](2^2) + (1^2) + (0^2) = 4 + 1 + 0 = 5.[/tex]
Therefore, the sum of the squares of the digits of the 1000th number in the sequence is 5.
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