The value of ∠BOC is 110 degrees.
In a triangle ABC, angle bisectors of ∠B and ∠C meet at O. If ∠A = 70o, find ∠BOC. To find the value of ∠BOC.
we will need to make use of angle bisectors.In triangle ABC, the angle bisectors of ∠B and ∠C meet at point O. If AB, BC, and CA are denoted as a, b, and c respectively, the lengths of angle bisectors AD, BE, and CF are given by
$ AD = \frac{2}{b + c}\sqrt{bcs(s-a)}$$ BE = \frac{2}{a + c}\sqrt{acs(s-b)}$and $ CF = \frac{2}{a + b}\sqrt{abs(s-c)}$
where s is the semi-perimeter of the triangle, that is,
$ s = \frac{a + b + c}{2}$.
Now, let's solve the given problem.If in ΔABC, the angle bisectors of ∠B and ∠C meet at O.
If ∠A = 70o, find ∠BOC
We can easily find the value of ∠BOC using the Angle Bisector Theorem. The angle bisector of an angle in a triangle divides the opposite side into segments that are proportional to the other two sides.Let's now apply the Angle Bisector Theorem to find ∠BOC. We know that O is the intersection point of the angle bisectors of ∠B and ∠C in triangle ABC.Therefore, BD/DC = AB/AC ---(1)We also know that OE/EC = OB/BC ---(2)By applying the Angle Bisector Theorem in triangle BOC, we can write:(OE + EB)/EC = OB/BCOE/EC + EB/EC = OB/BC[OE/(a + c)] + [EB/(a + c)] = OB/b[BE = a/(a+c)]OE/(a + c) + a/(a + c) = OB/bOE + a = OB(b + c)/bUsing (1), we can write a/c = AB/ACTherefore, a = bc/ACUsing this in (2), we getOE/EC = OB/b(AB + AC)/ACOE/EC = OB/b(BC/AC + AC/AC)OE/EC = OB/b(BC + AC)/ACOE/EC = OB/(b + c)Using this in the above equation, we get:OE + bc/AC = OB(b + c)/b(b + c)OE/AC + bc/AC = OB/bOE/AC = OB/b - bc/AC = (bOB - bc)/bACThe Angle Bisector Theorem states that BD/DC = AB/AC, so we know that BD/DC = b/c. Thus, BD = b/(b+c) * AC, and DC = c/(b+c) * AC. Now we can use these values to calculate BD/DC:BD/DC = b/(b+c) * AC / c/(b+c) * AC = b/cThus, we can use the value b/c in place of BD/DC, so:OE/AC = OB/b - bc/AC = OB/b - BD/DC = OB/b - b/cOE/AC = (bOB - bc)/bAC = b(OB - c)/bACOE/AC = (OB - c)/ACNow we have OE/AC and we know that OE/EC = (OB - c)/AC, so:OE/EC = (OB - c)/AC = (OE/AC) / (OE/EC)OE/EC = (OB - c)/AC = (OE/AC) / (OE/EC)OE/EC = (OE/AC) / ((OB - c)/AC)OE/EC = OE / (OB - c) Multiplying both sides by OB, we get:OB * OE/EC = OE(OB - c)/ECOB * OE = OE(OB - c)OB = OB - cOB = cWe can use this result to solve for ∠BOC, which is equal to 2∠AOC. Since O is the incenter of triangle ABC, we have ∠AOC = (180 - ∠A)/2 = 55 degrees. Therefore, ∠BOC = 2∠AOC = 2 * 55 = 110 degrees.
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Let's construct the given situation and solve the problem. In the given figure, ∠A = 70°. Angle bisectors of ∠B and ∠C meet at O. To find : ∠BOC.
Therefore, ∠BOC = 110°.
We know that angle bisectors of a triangle meet at a point, and they divide the opposite side in the ratio of the adjacent sides. From the given figure, it is clear thatBO is the angle bisector of ∠B and CO is the angle bisector of ∠C.Thus,
By angle bisector theorem,
BO/AB = CO/AC
⇒ BO/AC = CO/AB
[Since AB = AC]
⇒ BO/BC = CO/BC [Since BC is the common side]
⇒ BO = CO
Let's use the angle sum property of a triangle to find ∠BOC∠BOC + ∠BOA + ∠COA = 180° [Sum of angles of a triangle]
Since, ∠BOA = ∠COA [By angle bisector theorem]
Thus,2∠BOA + ∠BOC = 180° [eqn 1]
In ΔBOA, ∠OAB + ∠BOA + ∠BAO = 180° [Sum of angles of a triangle]
⇒ ∠OAB + ∠BAO = 110°
[∵ ∠BOA = 70°]
But ∠OAB = ∠OAC [By angle bisector theorem]
Thus, ∠OAC + ∠BAO = 110° [eqn 2]
In ΔCOA, ∠OAC + ∠AOC + ∠COA = 180° [Sum of angles of a triangle]
⇒ ∠OAC + ∠COA = 110°
[∵ ∠AOC = 70°]
From eqn 2, ∠BAO = ∠COA
Thus, ∠OAC + ∠OCA = 110°
[∵ ∠BAO = ∠COA]
⇒ 2∠OAC = 110°
⇒ ∠OAC = 55°
Thus, ∠BOC = 2∠OAC
= 2 × 55°= 110°
Hence, ∠BOC = 110°.
Therefore, ∠BOC = 110°.
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What’s the answer for number 1 ????
Answer:
there are 8 packages left
Step-by-step explanation:
120÷12=10. So there are 10 packages of pencils to begin with. She loses 24 pencils which means that she lost two packages worth of pencils (12+12=24). So, 2 packages-10 packages=8 packages.
Which ordered pair will be solution for the function y = 12 - x?
(4, 9)
(6, 6)
(2, 14)
(7, 4)
( if u steal my points ill steal yours)
(no links or ill report u and get u band , I am not bluffing)
(also ill give 100 brianlist after if its right)
Answer:
(6, 6)
Step-by-step explanation:
ordered pair (6, 6) will be solution for the function y = 12 - x.
When x = 6
y = 12 - 6
y = 6
(x, y) = (6, 6)
Answer:
6,6
Step-by-step explanation:
True or False (50 question)
_____ 1. The sum of the probabilities can give one and sometimes exceed one
_____ 2. The alpha value indicates the % of error allowed in the investigation
_____ 3. The critical value is obtained from the formulas applied to each Test
_____ 4. H0 is rejected when the manual value is greater than the critical value
_____ 5. All probability is between zero and 1
_____ 6. The ANOVA Test uses the entire bell
_____ 7. There are 2 types of hypotheses
_____ 8. The null hypothesis may posit that there is no significant difference between the statistic and the parameter or between 2 parameters
_____ 9. When α =.05 then you allow 95% error in the study
____ 10. The critical value is where the rejection zone for H0 begins
. ____ 11. In the binomial distribution r can be greater than n.
____ 12. If H0 ≤ 30 then H1 cannot be determined
____ 13. In the normal distribution the probability is in agreement to the total deviations you find
____ 14. In an incompatible event the probabilities must all give to one
____ 15. In Classical Probability the sample space is always known.
____ 16. In Binomial when n =30, the Pr can give greater than one.
____ 17. All probability is in Pr ≤ 1 and zero
____ 18. In the Binomial Distribution the Pr (0) is part of the probabilities.
____ 19. In Poison Distribution, N is known and its average N is used.
____ 20. Incompatible events are mutually exclusive.
____ 21. The [Pr (Oc) + Pr (Not Oc)] can give greater than one, sometimes.
____ 22. Incompatible events can be seen in classical probability
______23. The variable "eye color" is a qualitative variable, nominal
______24. The "scatter diagram" illustrates the relationship between 2 variables.
______25. In the range of grouped data you subtract the extreme values.
______26. The independent variable is manipulated by the researcher.
______27. In Poison, with lambda = 20, then Pr (X >1) = 1 – [Pr (0, 1)]
______28. In the Binomial distribution, with n=10, the Pr (r > 1) = 1 –[Pr (0, 1)]
______29. The Pr (Oc) + Pr (Not Oc) = 1
______30. In Normal distribution the sum of the Probabilities equals one.
_______31. In the Binomial Distribution r can be greater than n.
_______32. The bar chart is used to illustrate the relationship of nominal qualitative variables
_______33. In Binomial Distribution, with n =25, the sum of all Pr = 1
_______3. 4. In the Poison Distribution, with lambda = 30, the Pr (X = 31) is > 1
_______35. The null and alternate hypotheses are mutually exclusive.
_______36. Let a and b be independent events, Pr(No Oc) = 1 –[Pr(a) Pr (b)].
_______37. Let A and B be Dependent Events, Pr(A)Pr (B/A) = Pr(B)Pr (A/B)
_______38. The Correlation Coefficient can be negative
_______39. The Scatter Plot illustrates the dispersion of the data
_______40. All Pr (Oc) give to one.
_______41. When Z is negative also the probability found
_______42. In Normal Dist when you have Pr(Z ≤ 3) = 1- [Pr (Z=3)]
_____43. The arithmetic average is sought by adding all the data/(n-1)
_____44. The location of the median is found by looking for (n + 1) / 2
_____45. Median of ungrouped data does not use outliers
_____46. In the Normal Dist Z = total of the events
_____47. When Z = 1, the probability = .5 - .3413
_____48. Variance in grouped data is divided by n + 1
_____49. If r > 1 then the variables are directly proportional
_____50. Every probability is a proper fraction
1. False: The sum of the probabilities can never exceed one.
2. False: The alpha value indicates the maximum level of error allowed in the investigation.
3. True: The critical value is obtained from the formulas applied to each test.
4. False: H0 is rejected when the test statistic value is greater than the critical value.
5. True: All probability is between zero and one.
6. False: The ANOVA test uses only a portion of the bell curve.
7. True: There are two types of hypotheses.
8. True: The null hypothesis may posit that there is no significant difference between the statistic and the parameter or between two parameters.
9. True: When α = 0.05, it means that the level of significance is 5%, not that you allow 95% error in the study.
10. True: The critical value is the point at which the rejection zone for H0 begins.
11. False: In binomial distribution, r cannot be greater than n.
12. False: The value of H1 depends on the alternative hypothesis.
13. False: In a normal distribution, the probabilities can never exceed one.
14. True: In incompatible events, the sum of probabilities must be one.
15. True: In classical probability, the sample space is always known.
16. False: When n = 30 in a binomial distribution, Pr can never be greater than one.
17. True: All probability values are between 0 and 1.
18. True: In binomial distribution, Pr(0) is one of the probabilities.
19. True: In Poisson distribution, N is known, and its average N is used.
20. True: Incompatible events are mutually exclusive.
21. False: The sum of Pr(Oc) and Pr(Not Oc) can never exceed one.
22. True: Incompatible events can be seen in classical probability.
23. True: The variable "eye color" is a qualitative variable, nominal.
24. True: The "scatter diagram" illustrates the relationship between two variables.
25. True: In the range of grouped data, you subtract the smallest value from the largest value.
26. True: The independent variable is manipulated by the researcher.
27. False: In Poisson distribution, Pr(X > 1) = 1 - Pr(0) - Pr(1).
28. False: In binomial distribution, Pr(r > 1) = 1 - Pr(0) - Pr(1).
29. True: The sum of Pr(Oc) and Pr(Not Oc) is always one.
30. True: In normal distribution, the sum of probabilities equals one.
31. False: In binomial distribution, r cannot be greater than n.
32. True: The bar chart is used to illustrate the relationship of nominal qualitative variables.
33. True: In binomial distribution, the sum of all Pr is 1.
34. False: In the Poisson distribution, Pr(X = 31) is always less than or equal to 1.
35. False: The null and alternative hypotheses are not mutually exclusive.
36. False: The given formula is only true for independent events.
37. True: The given formula is only true for dependent events.
38. True: The correlation coefficient can be negative.
39. True: The scatter plot illustrates the dispersion of the data.
40. True: The sum of all Pr(Oc) is always one.
41. True: When Z is negative, the probability is also negative.
42. False: In normal distribution, Pr(Z ≤ 3) = Pr(Z = 3) + Pr(Z < 3).
43. False: The arithmetic average is found by adding all the data and dividing by n.
44. True: The location of the median is found by looking for (n + 1) / 2.
45. True: Median of ungrouped data does not use outliers.
46. False: In normal distribution, Z is equal to the number of standard deviations away from the mean.
47. False: When Z = 1, the probability is 0.3413, not 0.5 - 0.3413.
48. True: Variance in grouped data is divided by n - 1.
49. False: If r > 1, then the variables are not directly proportional.
50. True: Every probability is a proper fraction.
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Barium Corp purchased a piece of equipment on September 30 for $27,000. It cost $400 to ship the go the company's facilities and another $1,000 to install the equipment. After the equipment was installed the company had to pay an additional $1,500 for increased insurance. The capitalized cost of the equipment was
Select one:
a $29,900
b $29,500
c $28,400
d $27.400
The capitalized cost of the equipment is $29,900 (option a).
How to find the capitalized cost of the equipmentTo determine the capitalized cost of the equipment, we need to sum up all the costs associated with its acquisition and installation.
The costs include:
- Purchase price: $27,000
- Shipping cost: $400
- Installation cost: $1,000
- Increased insurance cost: $1,500
To find the capitalized cost, we add up these costs:
Capitalized cost = Purchase price + Shipping cost + Installation cost + Increased insurance cost
= $27,000 + $400 + $1,000 + $1,500
= $29,900
Therefore, the capitalized cost of the equipment is $29,900 (option a).
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An urban economist wishes to estimate the proportion of Americans who own their house. What size sample should be obtained if he wishes the estimate to be within 0.02 with 90% confidence if
(a) he uses a 2010 estimate of 0.669 obtained from the U.S Census Bureau?
(b) he does not use any prior estimate.?
(a) The sample size needed is 1,498 if the researcher uses the prior proportion of 0.669.
n = 1.497.87 or 1,498
(b) The researcher should use a sample size of 1,692 if the proportion is unknown.
n = 1,691.06 or 1,692
Sample Size:When a researcher is designing a sampling study to measure a population parameter, like the proportion, the sample size must be determined. The key to calculating sample size is the margin of error the researcher desires. The smaller the margin of error, the larger the sample size needed.
(a) The sample size needed is 1,498 if the researcher uses the prior proportion of 0.669.
To find sample size for the proportion use the equation:
[tex]n=\frac{Z^2\pi (1-\pi )}{e^2}[/tex]
Where:
n is the sample sizeZ is the Z score which from a Z table, or Excel, is found to be 1.6449 for 90% confidence level.[tex]\pi[/tex] = the population proportion = 0.669e = is the margin of error. = 0.02Substituting values:
[tex]n=\frac{1.6449^2*0.50*0.331}{0.02^2}[/tex]
n = 1.497.87 or 1,498
(b) The researcher should use a sample size of 1,692 if the proportion is unknown.
Use the same equation as in part (a). However, to maximize [tex]\pi (1-\pi )[/tex] use 0.5 for [tex]\pi[/tex].
Substituting the values:
[tex]n=\frac{1.6449^2*0.50*0.500}{0.02^2}[/tex]
n = 1,691.06 or 1,692
Always round up because it is impossible to have a fraction of an observation.
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What is the volume of this sphere?
Use ≈ 3.14 and round your answer to the nearest hundredth.
8 yd
cubic yards
Evaluate ∫ (3z + 1) / (z^2 + 2) dz, where C is the contant.
The value of the integral ∫(3z + 1) / (z^2 + 2) dz, where C is the constant is ln|z^2 + 2| + 3/√2 arctan(z/√2) + C.
To evaluate the given integral, we first need to break it down using partial fraction decomposition. Therefore, we have:
(3z + 1) / (z^2 + 2) = (Az + B) / (z^2 + 2)
Multiplying both sides by (z^2 + 2), we get:
3z + 1 = (Az + B)
We now need to find the values of A and B. Setting z = 0, we get:
1 = B
Setting z = 1, we get:
3 + 1 = A + B
A = 2
Therefore, the integral becomes:
∫ (2z + 1) / (z^2 + 2) dz
We can now integrate using substitution, with u = z^2 + 2 and du/dz = 2z. This gives us:
∫ (2z + 1) / (z^2 + 2) dz = ∫ (1/u) du
= ln|u| + C
= ln|z^2 + 2| + C
Using trigonometric substitution, we can also evaluate the integral in terms of arctan:
Let z = √2 tanθ, dz = √2 sec^2θ dθ. Then the integral becomes:
∫ (3z + 1) / (z^2 + 2) dz = ∫ (3√2 tanθ + 1) / (2tan^2θ + 3) √2 sec^2θ dθ
= 3/√2 ∫ (tanθ) / (tan^2θ + (3/2)) d(tanθ) + 1/√2 ∫ (1) / (tan^2θ + (3/2)) dθ
= 3/√2 ln|tan^2θ + (3/2)| + 3/√2 arctan(tanθ/√2) + C
= 3/√2 ln|z^2 + 2| + 3/√2 arctan(z/√2) + C
Thus, we get the same result as before.
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Yeah, I need help again. IM NOT GOOD AT MATH
Answer:
21
Step-by-step explanation:
7 * 3 =21
Solve for x. Approximate the result to three decimal places.
[tex]\log_7x=\dfrac{1}{2}\\\\x=7^{1/2}\\\\x=\sqrt{7}\approx2.646[/tex]
i need to know what -2(3x)+56
Answer:
-6x + 56
Step-by-step explanation:
-2(3x) + 56
-6x + 56
I need help finding X
Classify the following expression by degree and number of terms. 6 - 3x - 2
Answer:
in terms of degree it is linear equation
in terms of number of terms it is binomial
Let C[0, 1] have the inner product (f,g) = f(x)g(x)dx. For u = x and v= x + 1 find the following: a) ||f|| b) |lg|| c) (f,g) d) Find the angle between u and v.
The function v = x + 1, the norm is v = sqrt(integral of (x+1)^2 dx from 0 to 1), which evaluates to sqrt(5/3). The angle between u and v is arccos(1/√5).
a) The norm f of a function f in the vector space C[0, 1] with the given inner product is defined as the square root of the inner product of the function with itself. In this case, f = sqrt((f, f)) = sqrt(integral of f(x) * f(x) dx over the interval [0, 1]). For the function u = x, the norm is u = sqrt(integral of x^2 dx from 0 to 1), which evaluates to sqrt(1/3). For the function v = x + 1, the norm is v = sqrt(integral of (x+1)^2 dx from 0 to 1), which evaluates to sqrt(5/3).
b) The inner product space C[0, 1] induces a norm on the set of functions, and we can define the distance between two functions as the norm of their difference. In this case, the norm of the difference between the functions u and v is |u - v| = sqrt((u - v, u - v)) = sqrt(integral of (x - (x+1))^2 dx from 0 to 1), which simplifies to sqrt(1/3). Therefore, |u - v| = sqrt(1/3).
c) The inner product (f, g) between the functions f and g is defined as the integral of their pointwise product over the interval [0, 1]. For the functions u = x and v = x + 1, (u, v) = integral of (x * (x + 1)) dx from 0 to 1, which evaluates to 7/6.
d) The angle between two functions u and v in an inner product space can be computed using the definition of the inner product and the norms of the functions. The angle theta between u and v is given by the equation cos(theta) = (u, v) / (u * v). In this case, cos(theta) = (7/6) / (sqrt(1/3) * sqrt(5/3)), which simplifies to 1/√5. Therefore, the angle between u and v is arccos(1/√5).
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Find the volume.
7 ft
25 ft
18 ft
Answer:
3150 ft³ or 89.1981 m³ or 116.6667 yd³
Step-by-step explanation:
Write an expression for the phrase. Jessica is eight inches less than twice Parkers height. Use P to represent parker.
Answer:
P = Parker
According to the question,
Equation for Jessica's height = 8 - 2P
PLEASE HURRY ILL GIVE BRAINLIEST Emma is going to invest in an account paying an interest rate of 3.7% compounded continuously. How much would Emma need to invest, to the nearest dollar, for the value of the account to reach $1,130 in 18 years?
Answer:
581
Step-by-step explanation:
Greg’s backyard is 47 feet wide. How many yards and feet is this?
Answer:
15 yards amd 3 feet.
Step-by-step explanation:
I wish to get extra three points :)
Answer:
This is 15 yards and 3 feets.
Suppose a life insurance company sells a $250,000 1-year term life insurance policy to a 20-year-old female for $350. According to the National Vital Statistics Reports 58(21), the probability that the female survives the year is 0.99654.Compare and interpret the expected value of this policy to the imsurance company.
The expected value is $ : ______
To calculate the expected value of the insurance policy, we multiply the potential outcomes by their respective probabilities and sum them up. In this case, the insurance company sells a $250,000 policy to a 20-year-old female for $350.
The probability that she survives the year is given as 0.99654. The expected value represents the average value the insurance company can expect to receive from selling this policy.
The potential outcomes of the policy are two-fold: either the female survives the year, or she does not. If she survives, the insurance company does not have to pay out any benefits. However, if she does not survive, the company has to pay the policy amount of $250,000.
To calculate the expected value, we multiply each outcome by its corresponding probability and sum them up:
Expected value = (Probability of survival) * (Amount received) + (Probability of non-survival) * (Amount paid out)
Expected value = (0.99654) * (0) + (1 - 0.99654) * (250,000)
Simplifying the calculation, we find:
Expected value = 0 + (0.00346) * (250,000) = $865
Interpreting the expected value, on average, the insurance company can expect to receive $865 for selling this policy to a 20-year-old female.
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Solve for x, y, and z. Enter the integer that is under each radical.
Answer:
[tex] x=\sqrt{10} [/tex]
[tex] y = \sqrt {14} [/tex]
[tex] z = \sqrt {35} [/tex]
Step-by-step explanation:
By geometric mean theorem:
[tex] x=\sqrt{2\times 5} [/tex]
[tex] x=\sqrt{10} [/tex]
By Pythagoras Theorem:
[tex] y^2 = x^2 + 2^2 [/tex]
[tex] y^2 = (\sqrt{10}) ^2 + 2^2 [/tex]
[tex] y^2 = 10 + 4 [/tex]
[tex] y^2 = 14 [/tex]
[tex] y = \sqrt {14} [/tex]
Again by Pythagoras Theorem:
[tex] z^2 = x^2 + 5^2 [/tex]
[tex] z^2 = (\sqrt{10}) ^2 + 5^2 [/tex]
[tex] z^2 = 10 + 25 [/tex]
[tex] z^2 = 35 [/tex]
[tex] z = \sqrt {35} [/tex]
PLEASE HELPPPPPPPPPPPPPPPPPPPP
Answer:
(a) 6688 divided by 88 = 76
(b) 312 - 73 = 239
how might larcom’s initial impression of the mill have been different if she had started as a machine worker?
If Harriet Hanson Robinson (Larcom) had started her career in the mill as a machine worker instead of as a doffer, her initial impression of the mill may have been significantly different.
Here are a few ways her perspective might have been altered:
Physical Experience: As a machine worker, Larcom would have been directly involved in operating the machinery. She would have experienced the physical demands and potentially dangerous conditions associated with working with heavy machinery. This hands-on experience might have given her a greater appreciation for the risks and challenges faced by the workers. Social Interaction: Machine workers often worked in close proximity to each other, tending to the machines and coordinating their tasks. By working alongside her fellow machine workers, Larcom would have had more direct contact and interaction with her peers. This could have provided her with a deeper understanding of the camaraderie, unity, and challenges faced by the workers as a community.
Skill Development: Operating the machines required a certain level of technical skill and knowledge. If Larcom had started as a machine worker, she would have gained expertise in machine operation and maintenance. This technical knowledge could have given her a different perspective on the machinery, its intricacies, and its impact on the workers. Perspective on Management: As a machine worker, Larcom might have had more direct interactions with mill managers and overseers. This could have given her insights into the management practices, decision-making processes, and power dynamics within the mill. Such firsthand experiences might have influenced her initial impression of the mill's management and their treatment of workers.
Overall, starting as a machine worker would have provided Larcom with a different vantage point and firsthand experience of the mill's operations. This could have shaped her understanding of the work environment, the challenges faced by the workers, and the dynamics between management and labor.
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solve for x round to your nearest tenth
Answer:
x ≈ 5.98Steps:
tan(50.1°) = x/5
1.19.. = x/5
x = 5 × 1.19 ..
x = 5.97.. ≈ 5.98
The Willis Tower In Chicago is 1,451 FEET tall. The Transamerica Pyramid is San Francisco is 10,236 INCHES tall. How do these two compare?
Answer:
Willis Towers is 1.7 times bigger than the Transamerica pyramid
Step-by-step explanation:
The Willis Tower In Chicago is 1,451 FEET tall. The Transamerica Pyramid is San Francisco is 10,236 INCHES tall. How do these two compare?
Note that
1 foot = 12 inches
We convert the height of willis tower to inches
1 foot = 12 inches.
1,451 feet = x inches
Cross Multiply
x = 1451 × 12 inches
x = 17412 inches
Comparing the two buildings
Willis Tower : Transamerica pyramid
1,7412 inches : 10,236 Inches
= 1.7010550996 : 1
Therefore,
Willis Towers is 1.7 times bigger than the Transamerica pyramid
The area of a rectangle
is 100 square feet. If the
width is 25 feet. What is the
Length?
Which term of the AP 21, 18, 15, ... is 0?
Answer:
Solution : Let Tn=0. Then,21+(n-1)×(-3)=0⇒n=8. So, 8th term is zero.
Step-by-step explanation:
Determine if the following system is Lyapunov stable x=tx
The system x = tx is Lyapunov stable.
To determine if the system x = tx is Lyapunov stable, we need to check if it satisfies the Lyapunov stability criterion. The criterion states that for every ε > 0, there exists a δ > 0 such that if ||x(0) - xe|| < δ, then ||x(t) - xe|| < ε for all t > 0.
Let's analyze the given system x = tx:
Taking the derivative of x with respect to t, we get:
dx/dt = x
This is a first-order linear ordinary differential equation.
The general solution to this equation is:
x(t) = C×[tex]e^{t}[/tex]
where C is the constant of integration.
Now, let's consider the initial condition x(0) = x0, where x0 is some constant.
Using this initial condition, we can solve for the constant C:
x(0) = C × e⁰
x0 = C
So, the specific solution to the initial value problem is:
x(t) = x₀ × [tex]e^{t}[/tex]
Now, we can check if the system is Lyapunov stable.
For any ε > 0, let's consider the case where δ = ε. Then, if ||x(0) - xe|| < δ, we have:
||x(0) - xe|| = ||x₀ - x₀ × [tex]e^{t}[/tex]|| = ||x₀(1 - [tex]e^{t}[/tex])||
Since e^t > 1 for t > 0, we can rewrite the expression as
||x₀(1 - [tex]e^{t}[/tex])|| = x₀ × ||[tex]e^{t}[/tex] - 1||
Now, we want to show that ||x(t) - xe|| < ε for all t > 0. We have
||x(t) - xe|| = ||x₀ × [tex]e^{t}[/tex] - x₀ × [tex]e^{t}[/tex]|| = 0
Since ||x(t) - xe|| = 0 for all t > 0, it satisfies the condition ||x(t) - xe|| < ε.
Therefore, the given system x = tx is Lyapunov stable.
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The question is incomplete the complete question is :
Determine whether the origin of the following system is Lyapunov stable: x= tx. Use Lyapunov's stability criterion .
I WILL GIVE 10 POINTS AND BRAINLIEST WHO EVER ANSWERS FIRST The space capsule is moving up at a speed of 80 miles per hour a few seconds after launch. What is the space capsule's velocity per hour
Kristy dad makes 3 times as much per hour as she does. If he makes $48 per hour, how much per hour, how much per hour does kristy make
Answer:
Kristy makes 16 per hour.
Step-by-step explanation: Divded 48 by 3.
the impressionist period in music was about creating
Answer:
The Impressionist period was distinctive because composers were focused on creating an impression through building atmospheres, pictures, and sound worlds with music. Composers Debussy and Ravel were at the forefront of this ground-breaking musical style.
Suppose you have a standard deck of 52 cards. What is the probability that if you select a card at random that it does not have a face value of 9?
The probability that a randomly selected card does not have a face value of 9 is approximately 0.9231 or 92.31%.
In a standard deck of 52 cards, there are 4 cards of each face value (Ace through 10) for each of the four suits (hearts, diamonds, clubs, and spades). Since the face value of 9 is one of the possible values, there are 4 cards with a face value of 9.
To find the probability that a randomly selected card does not have a face value of 9, we need to determine the number of cards that do not have this particular value. There are 52 cards in total, and we subtract the 4 cards with a face value of 9:
52 - 4 = 48
So, there are 48 cards that do not have a face value of 9. Therefore, the probability of selecting a card without a face value of 9 is:
P(not 9) = number of favorable outcomes / total number of outcomes
= 48 / 52
= 12 / 13
≈ 0.9231
The probability that a randomly selected card does not have a face value of 9 is approximately 0.9231 or 92.31%.
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