The approximate values of the solution by Euler's method is y₁=0.65, y₂=0.84, y₃=1.0778, y₄=1.3584, y₅=1.6921, y₆=2.05657.
In this question,
The differential equation is
yʹ=y(3−ty) ------- (1)
Here, y(0)=0. 5,h=0. 1, 0≤t≤0. 5.
By Euler's method,
[tex]y_{n+1}=y_n+hf_n[/tex]
where [tex]f_n=f(t_n,y_n)[/tex]
For, t = 0, y = 0,
[tex]y_{1}=y_0+hf_0[/tex] and
[tex]f_0=f(t_0,y_0)[/tex]
Substitute in equation 1,
⇒ f(0,0.5) = 0.5(3-(0)(0.5))
⇒ f(0,0.5) = 0.5(3-0)
⇒ f(0,0.5) = 0.5(3)
⇒ f(0,0.5) = 1.5
Then, [tex]y_{1}=y_0+hf_0[/tex] becomes,
⇒ y₁ = 0.5 + (0.1)(1.5)
⇒ y₁ = 0.5 + 0.15
⇒ y₁ = 0.65
For, t = 1, y = 1,
[tex]y_{2}=y_1+hf_1[/tex] and
[tex]f_1=f(t_1,y_1)[/tex]
⇒ f(0.1,0.65) = 0.65(3-(0.1)(0.65))
⇒ f(0.1,0.65) = 0.65(3-0.065)
⇒ f(0.1,0.65) = 1.90
Then, [tex]y_{2}=y_1+hf_1[/tex] becomes,
⇒ y₂ = 0.65+(0.1)(1.90)
⇒ y₂ = 0.84
For t = 2, y = 2,
[tex]y_{3}=y_2+hf_2[/tex] and
[tex]f_2=f(t_2,y_2)[/tex]
⇒ f(0.2,0.84) = 0.84(3-(0.2)(0.84))
⇒ f(0.2,0.84) = 0.84(3-0.168)
⇒ f(0.2,0.84) = 2.3788
Then, [tex]y_{3}=y_2+hf_2[/tex]
⇒ y₃ = 0.84+(0.1)(2.3788)
⇒ y₃ = 1.0778
For t = 3, y = 3,
[tex]y_{4}=y_3+hf_3[/tex] and
[tex]f_3=f(t_3,y_3)[/tex]
⇒ f(0.3,1.0778) = 1.0778(3-(0.3)(1.0778))
⇒ f(0.3,1.0778) = 1.0778(3-0.32334)
⇒ f(0.3,1.0778) = 2.8848
Then, [tex]y_{4}=y_3+hf_3[/tex] becomes
⇒ y₄ = 1.0778+(0.1)(2.8848)
⇒ y₄ = 1.3584
For t = 4, y = 4,
[tex]y_{5}=y_4+hf_4[/tex] and
[tex]f_4=f(t_4,y_4)[/tex]
⇒ f(0.4,1.3584) = 1.3584(3-(0.4)(1.3584))
⇒ f(0.4,1.3584) = 1.3584(3-0.5433)
⇒ f(0.4,1.3584) = 3.3372
Then, [tex]y_{5}=y_4+hf_4[/tex] becomes
⇒ y₅ = 1.3584 + (0.1)(3.3372)
⇒ y₅ = 1.6921
For t = 5, y = 5,
[tex]y_{6}=y_5+hf_5[/tex] and
[tex]f_5=f(t_5,y_5)[/tex]
⇒ f(0.5,1.6921) = 1.6921(3-(0.5)(1.6921))
⇒ f(0.5,1.6921) = 1.6921(3-0.84605)
⇒ f(0.5,1.6921) = 3.6447
Then, [tex]y_{6}=y_5+hf_5[/tex] becomes
⇒ y₆ = 1.6921 + (0.1)(3.6447)
⇒ y₆ = 2.05657
Hence we can conclude that the approximate values of the solution by Euler's method is y₁=0.65, y₂=0.84, y₃=1.0778, y₄=1.3584, y₅=1.6921, y₆=2.05657.
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The 9th and the 12th term of an arithmetic progression are 50 and 65 respectively. find the common difference
The first term of the arithmetic progression exists at 10 and the common difference is 2.
How to estimate the common difference of an arithmetic progression?
let the nth term be named x, and the value of the term y, then there exists a function y = ax + b this formula exists also utilized for straight lines.
We just require a and b. we already got two data points. we can just plug the known x/y pairs into the formula
The 9th and the 12th term of an arithmetic progression exist at 50 and 65 respectively.
9th term = 50
a + 8d = 50 ...............(1)
12th term = 65
a + 11d = 65 ...............(2)
subtract them, (2) - (1), we get
3d = 15
d = 5
If a + 8d = 50 then substitute the value of d = 5, we get
a + 8 [tex]*[/tex] 5 = 50
a + 40 = 50
a = 50 - 40
a = 10.
Therefore, the first term is 10 and the common difference is 2.
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Determine whether the following series converges conditionally, converges absolutely, or diverges. Be sure to state which test(s) you are using.
Answer:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Step-by-step explanation:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Explanation:
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
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Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
If f(x) = 5x, what is f¹(x)?
Answer:
C
Step-by-step explanation:
For any function x, inverse will = 1/x. so the answer is C
Answer:
C. [tex]f^{-1}(x) = \frac{1}{5} x[/tex]
Step-by-step explanation:
The question is asking to find [tex]f^{-1}(x)[/tex] of f(x)=5x, which is the same as finding the inverse of the function.
To find the inverse of a function, we first need to replace f(x) with y.
The function will therefore be:
y = 5x
Now, we solve the equation for x.
So divide both sides by 5.
y = 5x
÷5 ÷5
_________
[tex]\frac{y}{5} = x[/tex]
Now, we replace x with y and y with x.
[tex]\frac{x}{5} = y[/tex]
Finally, we replace y with [tex]f^{-1}(x)[/tex].
[tex]\frac{x}{5} = f^{-1}(x)[/tex]
We can re-write this though, to make it easier to read.
We can write [tex]f^{-1}(x)[/tex] first, and rewrite [tex]\frac{x}{5}[/tex] as [tex]\frac{1}{5}x[/tex].
[tex]f^{-1}(x) = \frac{1}{5} x[/tex]
Therefore, the answer is C.
Find the conditional probability, in a single roll of two fair 6 sided dive, that the sum is greater than 6, given that neither die is a two
The conditional probability, in a single roll of two fair 6 sided dice, that the sum is greater than 6, given that neither die is a two : 17/25
We know that the conditional probability is given by,
P(B | A) = probability of occurrence of event B, given that event A has
occurred
= P(A ∩ B) / P(A)
Here, P(A ∩ B) means the probability of happening two events A and B at the same time.
We also know that if P (B | A ) = P(B) i.e., P(A ∩ B) = P(A) × P(B) the two events A and B are independent of each other.
For this question, let the dice D1 and D2 are rolled once.
Let the numbers displayed on the dice be d1 and d2 respectively.
The dice D1 and D2 are independent.
We need to find the conditional probability that the sum is greater than 6, given that neither die is a two.
Let S represents the sum of the numbers displayed on the dice.
S = d1 + d2
The sum is even, if d1 = d2 is odd OR if d1 = d2 is even
P(d1 = even) = 3/6
=1/2
P(d2=even) = 1/2
P(d1 = odd) = 1/2
P(d2 = odd) = 1/2
So, P(S = even) = [P(d1=even) × P(d2 = even)] + [P(d1= odd) × P(d2=odd)]
= [1/2 × 1/2] + [1/2 × 1/2]
= 1/2
So, we can say that, the sum is either even or odd which are equally likely and hence its probability is 1/2.
First we find the probability for the sum is greater than 6 i.e., P(S > 6)
The possible combination of d1 and d2 for the sum greater than 6 would be,
{(1,6), (2,5), (2, 6), (3, 4), (3, 5), (3, 6), (4,3), (4,4), (4,5), (4,6), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}
⇒ n(S > 6) = 21
The number of all possible outcomes = 36
So, P(S > 6) = 21/36
= 7/12
Now we find the probability that neither die is a two
⇒ P(neither die is a two) = [P(1) ∪ P(3 ≤ d1 ≤ 6)] AND [P(1) ∪ P(3 ≤ d1 ≤ 6)]
⇒ P(neither die is a two) = 5/6 × 5/6
⇒ P(neither die is a two) = 25/36
Now, we find the probability that the sum S > 6 AND neither die is a two.
The possible combination for the sum S > 6 AND neither die is a two would be,
{(1,6), (3, 4), (3, 5), (3, 6), (4,3), (4,4), (4,5), (4,6), (5,3), (5,4), (5,5), (5,6), (6,1), (6,3), (6,4), (6,5), (6,6)}
⇒ n(S > 6 AND neither die is a two) = 17
So, P(S > 6 AND neither die is a two) = 17/36
Now we find the conditional probability P(S > 6 | neither die is a two)
⇒ P(S > 6 | neither die is a two) = P(S > 6 AND neither die is a two) ÷
(neither die is a two)
⇒ P(S > 6 | neither die is a two) = (17/36) / (25/36)
⇒ P(S > 6 | neither die is a two) = 17/25
Therefore, the conditional probability, in a single roll of two fair 6 sided dice, that the sum is greater than 6, given that neither die is a two : 17/25
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Here are yesterday's high temperatures (in Fahrenheit) in 12 U.S. cities. 48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary Minimum: Lower quartile: Median: Upper quartile: Maximum: Interquartile range:
For the given data set
Minimum = 48
Lower quartile = 55
Median = 63.5
Upper quartile = 74
Maximum = 80
Interquartile range = 19
Measures of a DataFrom the question, we are to determine the minimum, lower quartile, median, upper quartile, maximum, and interquartile range of the given data set
The given data set is
48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80
Minimum = 48
Lower quartile = (54+56)/2
Lower quartile = 110/2
Lower quartile = 55
Median = (63+64)/2
Median = 127/2
Median = 63.5
Upper quartile = (74+74)/2
Upper quartile = 148/2
Upper quartile = 74
Maximum = 80
Interquartile range = Upper quartile - Lower quartile
Interquartile range = 74 - 55
Interquartile range = 19
Hence, for the given data set
Minimum = 48
Lower quartile = 55
Median = 63.5
Upper quartile = 74
Maximum = 80
Interquartile range = 19
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If A= (6,11), B= (1,5), and C= (7,0), show by means of slopes that ABC is a right triangle. Name the hypotenuse.
Since the product of AB and BC is -1, hence the ABC is a right triangle and the length AC is the hypotenuse
Right angled triangleA right angles triangle is a triangle that has 3 sides and angles with one of its angles to be 90 degrees.
For the given coordinates to be a right angled triangle, one of the line must be perpendicular to the other and for two lines to be perpendicular, the product of its slope must be -1.
Find the slopes of AB, BC and AC
Slope of AB = 5-11/1-6
Slope of AB = -6/-5 = 6/5
Slope of BC = 0-5/7-1
Slope of BC = -5/6
Slope of AC = 0-11/7-6
Slope of AC = -11/1. = -11
Take the product of AB and BC
AB * BC = 6/5 * -5/6
AB * BC = -1
Since the product of AB and BC is -1, hence the ABC is a right triangle and the length AC is the hypotenuse
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Find the value of sin J rounded to the nearest hundredth, if necessary.
12
13
K
The value of the sine of the angle J is equal to 5 / 13 (approx. 0.38).
What is the measure of the missing angle?The image attached aside shows us a right triangle with two known side lengths (JL, KJ) and a angle measure (m ∠ K). The measure of the missing angle can be found by using the trigonometric function of cosine:
cos m ∠ J = KJ / JL
cos m ∠ J = 12 / 13
m ∠ J = 22.620°
The measure of the angle J within the triangle JKL is approximately 22.620°.
And the sine of the angle J, which helds the same positive sign than cosine as the angle is in the first quadrant on Cartesian plane, is:
sin m ∠J = √(1 - cos² m ∠J)
sin m ∠J = √[1 - (12 / 13)²]
sin m ∠J = 5 / 13
The value of the sine of the angle J is equal to 5 / 13 (approx. 0.38).
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A plane has a cruising speed of miles per hour when there is no wind. At this speed, the plane flew miles with the wind in the same amount of time it flew miles against the wind. Find the speed of the wind.
The speed of the wind is 50 miles per hour.
What is speed?The term speed is defined as the ratio of the distance to the time taken. Now we can see that the movement of the plane and the wind were once in the same direction and then in opposite direction. This could be used to obtain a pair of simultaneous equations that could be used to solve the problem.
Hence;
300 = (250+s)* t = 250t + st ----- (1)
200 = (250-s)* t = 250t - st ------- (2)
Adding equations (1) and (2)
500 = 500t
t = 1 hour
To obtain the speed of the wind;
300 =250t + st
300 = 250(1) + (s * 1)
300 = 250 + s
300 - 250 = s
s = 50 miles per hour
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Missing parts;
A plane has a cruising speed of 250 miles per hour when there is no wind. At this speed, the plane flew 300 miles with the wind in the same amount of time it flew 200 miles against the wind. Find the speed of the wind.
What is the greatest common factor of 30, 22, and 8?
Answer:
2
Step-by-step explanation:
just because all three numbers are even
Hope this helps
The greatest common factor of 30, 22, and 8 will be 2.
What is the highest common factor?The Highest Common Factor (HCF) of two numbers is the highest possible number that is divisible by both numbers.
In other words, the highest common factor is the common factor between the two numbers but it should be the highest among all common factors.
For example in 6 and 12 6 is the highest common factor.
The factor of 30 ⇒ 2,3,5
The factor of 22 ⇒ 2,11
The factor of 8 ⇒ 2,4
The only common factor among 30,22 and 8 is 2 so it will be the greatest common factor.
Hence "The greatest common factor of 30, 22, and 8 will be 2".
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A coin-operated drink machine was designed to discharge a mean of 7 ounces of coffee per cup. In a test of the machine, the discharge amounts in 18 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 7.04 ounces and 0.17 ounces, respectively. If we assume that the discharge amounts are normally distributed, is there enough evidence, at the 0.1 level of significance, to conclude that the true mean discharge,u, differs from ounces? Perform a two-tailed test. Then fill in the table below. I need the two critical values at the 0.1 level of significace. Also need the answers to al other questions and whether we accpe for reject.
Using the t-distribution, it is found that since the test statistic is between -1.7341 and 1.7341, we do not reject(accept) the null hypothesis, hence there is not enough evidence to conclude that the true mean discharge differs from 7 ounces.
What are the hypothesis tested?At the null hypothesis, it is tested if the mean is of 7 ounces, that is:
[tex]H_0: \mu = 7[/tex]
At the alternative hypothesis, it is tested if the mean is different of 7 ounces, that is:
[tex]H_1: \mu \neq 7[/tex]
What is the test statistic?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The values of the parameters are given by:
[tex]\overline{x} = 7.04, \mu = 7, s = 0.17, n = 18[/tex]
Hence the value of the test statistic is found as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{7.04 - 7}{\frac{0.17}{\sqrt{18}}}[/tex]
t = 1
What is the decision?Considering a two-tailed test, as we are testing if the mean is different of a value, with 18 - 1 = 17 df and a significance level of 0.1, the critical value is of [tex]t^{\ast} = 1.7341[/tex]
Since the test statistic is between -1.7341 and 1.7341, we do not reject(accept) the null hypothesis, hence there is not enough evidence to conclude that the true mean discharge differs from 7 ounces.
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ABCD is an isosceles trapezium. Prove that: (1) (2) (3) AC=BD BE = CE AE = DE
is there a picture included in this problem? if so please comment it so i can answer this problem.
What is the area of parallegram ABCD
Answer:
c
Step-by-step explanation:
if you take the triangle off of the left side and attach it to the left side then you would have a 6 by 4 rectangle that has an area of 24 units squared.
What are the solutions of the system of equations y = –(x + 2)2 + 1 and y = 2x + 5?
A (–4, –3) and (–2, 1)
B (–4, –3) and (2, 1)
C (–4, 5) and (2, 1)
D (–4, 5) and (–2, 1)
Need help with my math please. 31-41.
Answer:
31. (98,765 x 9) + 3 = 888,888
32. (12,345 x 9) + 6 + 111,111
33. 3367 x 15 + 50,505
34. 15,873 x 28 = 555,555
35. 33,334 x 33,334 = 1,111,155,556
36. 11,111 x 11,111 = 123,454,321
41. 3 + 9 + 27 + 81 + 243 = 3(243 -1) / 2
42. 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 = 5/6
hope this helps
Answer:
see the step-by-step explanation
Step-by-step explanation:
31. (98,765 x 9) + 3 = = 888,888
32. (12,345 x 9) + 6 + 111,111
33. 3367 x 15 + 50,505
34. 15,873 x 28 = 555,555
35. 33,334 x 33,334 = 1,111,155,556
36. 11,111 x 11,111 = 123,454,321
41.3+9+27+81 +243 = 3(243-1)/2
42. 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 = 5/6
3 cuboids each of dimensions 4 cm x 4 cm x 6 cm and 3 cuboids each of dimensice 4 cm x 6 cm x 6 cm. A student wants to arrange these cubes and cuboids in the form of a big cube. Is it possible for him/her to arrange them in the form of a big cube? If yes, then find te length of side of new cube so formed
Step-by-step explanation:
In a Mathematics lab. There are some cubes and cuboids of following measurements
(i) One cube of side 4 cm
(ii) One cube of side 6 cm
(iii) 3 cuboids each of dimensions 4cm ×4 cm ×6cm
(iv) 3 cuboids each of dimensions 4cm ×6 cm ×6cm
A student wants to arrange these cubes and cuboids in the form of big cube. Is it
possible to arrange them in the form of big cube? If yes, then find the length of side of
Part III: Is x+1 a factor of the polynomial 12x+5x+3x²-5? Explain your answer. (2 points)
Answer:
no
Step-by-step explanation:
So you can express a polynomial in factored form as such: [tex]a(x)*b(x)*c(x)...[/tex] where a(x), b(x), and c(x), each represent a polynomial which are each factors of the equation. It's important to note that each factor is being multiplied by each other, meaning if any of the factors output 0, the entire thing is 0, no matter the value of the other factors, since 0 * some value = 0. For this reason, if we plug in the value that makes (x+1) 0, into the polynomial, and the polynomials value is 0, that means it is a factor.
x + 1 = 0
x = -1
The value that makes the factor 0, is -1. This means that if it is a factor of the polynomial, then plugging in -1 as x into the polynomial should make the value 0.
Original Equation:
[tex]12x+5x+3x^2-5[/tex]
Plug in -1 as x
[tex]12(-1)+5(-1)+3(-1)^2-5[/tex]
Multiply values
[tex]-12-5+3(1)-5[/tex]
Simplify:
[tex]-17+3-5\\-14-5\\-19[/tex]
Since the value of the polynomial is not 0, this means x+1 is not a factor
You can also solve this use the Remainder Theorem and Factor Theorem which essentially uses the same logic
Remainder Theorem:
If a polynomial P(x) is divided by x-a, the remainder is P(a)
Using the remainder theorem, if x-a is indeed a factor, then that means the remainder should be 0, just as 11 is a factor of 77, and 77/11 has a remainder of 0. This is what the factor theorem essentially states
Factor Theorem:
The expression "x-a" is a factor of P(x) if and only if P(a) = 0
Mr. Granger, a cyclist, rode from his home to his office at an average speed of 18 miles per. On his return home from his office, using the same route, he averaged 12 miles per hour. If the total trip took 5 hours, what was the distance from his home to his office?
Answer:
The distance is 36 miles.
Step-by-step explanation:
distance in either direction = d
total time = 5
time going = t
time returning = 5 - t
speed = distance/time
going:
speed = distance/time
18 = d/t
d = 18t Eq. 1
returning:
speed = distance/time
12 = d/(5 - t)
60 - 12t = d
d = 60 - 12t Eq. 2
Eq. 1 and Eq. 2 form a system of equations.
d = 18t
d = 60 - 12t
Since d = d, then 18t must equal 60 - 12t
18t = 60 - 12t
30t = 60
t = 2
d = 18t = 18(2) = 36
The distance is 36 miles.
Hypotenuse: The ________ side of a right triangle; side ________ from the right angle.
The Hypotenuse is the Longest side of right triangle; side Opposite from the right angle.
According to the statement
we have given that the property of the hypotenuse of the triangle and we have to complete it.
So, For this purpose, we know that the
A hypotenuse is the longest side of a right-angled triangle, and The length of the hypotenuse can be found using the Pythagorean theorem.
Now we discuss about the properties of the hypotenuse;
The hypotenuse is the longest side in a right angled triangle. The hypotenuse is opposite the right angle. The midpoint of the hypotenuse is the circumference.And from these properties we have to complete the given property.
So, The Hypotenuse is the Longest side of right triangle; side Opposite from the right angle.
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Machine a can make 350 widgets in 1 hour, and machine b can make 250 widgets in 1 hour. if both machines work together, how much time will it take them to make a total of 1000 widgets?
If machine a can make 350 widgets in 1 hour and machine b can make 250 widgets in 1 hour then by forming equation we will get that both machines have to work for one hour and 40 minutes to make 1000 widgets.
Given that machine a can make 350 widgets in 1 hour, and machine b can make 250 widgets in 1 hour.
How much time will both machines take to make 1000 widgets?
Suppose the time taken by both machines be x hours. Time is equal because both the machines need to work together.
According to the question the equation will be as under:
350x+250x=1000
600x=1000
x=1000/600
x=10/6
x=5/3
x=1.67
Converting 0.67 to minutes 0.67*60=40.2
Adding will result 1 hour and 40 minutes.
Hence if machine a can make 350 widgets in 1 hour and machine b can make 250 widgets in 1 hour then by forming equation we will get that both machines have to work for one hour and 40 minutes to make 1000 widgets.
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On a map, point C is 4.3km due east of point B , and point B is 2.7km on a bearing of 143° from point A . Give your answer to 2 decimal places for the following. a Find how far east point B is from A. b Find how far east point C is from A. c Find how far south point C is from A
Based on the bearings of the direction and the distances given, the distance of point B from A is 1.62 km. Point C's distance from A is 5.92 km east and 2.16 km south.
How far are points B and C from A?To find the distance from point B to point A, the Cos function should be used.
Point A's distance from B can be found as:
= Cos (143 - 90) x distance from point A
= Cos (53°) x 2.7
= 1.62 km
The distance of C from A eastward is:
= 1.62 + 4.3
= 5.92 km
As C is southward from point A, the function to be used is the Sin function.
The distance southward of c from A is:
= Sin(53°) x 2.7
= 2.16 km
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The difference between the record high and low temperaturs in Charlotte, North Carolina, is 109°F. The record low temperature was -5°F. Write and solve an equation to find the record high temperature.
Answer: 104 degrees farenheit
Step-by-step explanation: H = record high temperature. -5 + 109 = H. -5+109 = 109 + (-5) = 109-5 = 104. H = 104.
Answer:
104
Step-by-step explanation:
Let x = record high and y = record low temperature in Charlotte. The difference between the records high and low, x and y, is 109 degrees Fahrenheit, so x - y = 109. Record low is -5, so x - (-5) = 109.
x + 5 = 109
x = 104
A sequence of numbers begins with 12 and progresses geometrically. each number is the previous number divided by 2. which value can be used as the common ratio in an explicit formula that represents the sequence?
1/2 value can be used as the common ratio in an explicit formula that represents the sequence.
Definition of sequence -
The following of one thing after another; succession. order of succession: a list of books in alphabetical sequence. A continuous or connected series: a sonnet sequence. something that follows; a subsequent event; result; consequence.A sequence that progresses geometrically has the first term as 12.
Each number is the previous number divided by 2.
so the sequence will be 12, 6, 3, 1.5...........
Explicit formula of a geometric sequence is given by
[tex]T_{n} = ar^{n-1}[/tex]
Where [tex]T_{n}[/tex] = nth term of the sequence
a = first term
r = common ratio
and n = number of term
In this sequence common ratio = [tex]\frac{Successive term }{previous term}[/tex]
= 6/12
= 1/2
Therefore, common ratio will be 1/2.
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(b) Expand and simplify (x - 3) (2x + 3)(4x + 5)
Answer:
8x³ - 2x² - 51x - 45
Step-by-step explanation:
(x - 3)(2x + 3)(4x + 5) ← expand the 2nd/3rd factors using FOIL
= (x - 3)(8x² + 10x + 12x + 15)
= (x - 3)(8x² + 22x + 15)
multiply each term in the second factor by each term in the first factor.
x(8x² + 22x + 15) - 3(8x² + 22x + 15) ← distribute parenthesis
= 8x³ + 22x² + 15x - 24x² - 66x - 45 ← collect like terms
= 8x³ - 2x²- 51x - 45
Expand first 2 bracket first to get:
2x^2 + 3x - 6x - 9 & simplify, then expand with last bracket.
2x^2 - 3x - 9 (4x + 5)
2x^2 x 4x = 8x^4
2x^2 x 5 = 10x^2
Repeat for the next two numbers next to the bracket.
You get => 8x^3 + 10x^2 - 12x^2 - 15x - 36x - 45
Final simplified answer of:
8x^3 - 2x^2 - 51x - 45
Hope this helps!
A major advantage of a ________ is that people whose roles span modules do not have to switch back and forth between old and new modules.
A major advantage of a direct implementation is that people whose roles span modules do not have to switch back and forth between old and new modules.
With this technique, the machine is implemented and tested to make certain it plays well. Then the antique machine is removed and the brand new one is put in its area without any overlap or restricted rollout.
There are three predominant methods used: phased implementation, direct changeover, and parallel going for walks. Phased implementation: A staged technique whereby one part of the overall system that desires change is changed.
Structures implementation is the process of defining how the data device needs to be built (i.e., physical machine design), ensuring that the records gadget is operational and used, and ensuring that the information device meets greatly preferred i.e. nice warranty.
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Find tan 0 if csc 0 = -√5/2 is in the third quadrant.
A. 1/2
B.-2
C.-1/2
D. 2
Answer:
D. 2
Step-by-step explanation:
soh cah toa rule
sine equals opposite over hypotenuse,
cosine equals adjacent over hypotenuse, and
tangent equals opposite over adjacent
csc is 1/sin which is hypotenuse over opposite
if csc is -√5/2 then
hypotenuse is -√5
opposite is 2
3rd quadrant on a graph is bottom left
both x and y values are negative
hypotenuse means its a triangle
pythagorean theorem
a^2 + b^2 = c^2
a^2 + 2^2 = (-√5)^2
a^2 + 4 = 5
a = 1 = adjacent
tangent equals opposite over adjacent
tan is 2 / 1 which is 2
third quadrant means it's still positive
because tan is positive in quadrant 3
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The following are the ages of 13 history teachers in a school district. 24, 27, 29, 29, 35, 39, 43, 45, 46, 49, 51, 51, 56 Notice that the ages are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
The minimum value of data is 24,lower quartile is 29,median is 41, upper quartile is 50 and maximum value is 56 and the interquartile range is 21.
Given a data about ages of 13 history teacher as under:
24, 27, 29, 29, 35, 39, 43, 45, 46, 49, 51, 51, 56.
We are required to find the minimum value, lower quartile,median,upper quartile,maximum value, interquartile range.
The minmum value is 24.
Lower quartile=(n+1)/4 th term
=(13+1)/4
=7/2
=3.5
Lower quartile=(29+29)/2
=29
Median=(n/2)th term
=13/2 th term
=6.5 th term
Median=(39+43)/2
=82/2
=41
Upper quartile=3(n+1)/4 th term
=3(13+1)/4
=3*14/4
=10.5 th term
Upper quartile=(49+51)/2=100/2=50
Inter quartile range=Upper quartile- lower quartile
=50-29
=21
Hence the minimum value of data is 24,lower quartile is 29,median is 41, upper quartile is 50 and maximum value is 56 and the interquartile range is 21.
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Select all the ways that express the number 32.148.
A 32 tens + 14 tenths + 8 hundredths
B 32 ones + 14 hundredths + 8 thousandths pauodt er
C 321 tenths + 48 thousandths
D 32,148 hundredths
E 32,148 thousandths
Answer: B, C, E
Step-by-step explanation: a is wrong 32 tens is 320. B is right. 321 tenths is 32.1 and 48 thousandths is 0.048 so C is correct. 32,148 hundredths is too much but 32,148 thousandths is 32.148
A rental car company is running two specials. Customers can pay $50 to rent a compact car for the first day plus $6 for each additional day, or they can rent the same car for $40 the first day and $8 for every additional day beyond that. Camilla notices that, given the number of additional days she wants to rent the car for, the two specials are equivalent. How much would Camilla pay in total?
The number of additional days she wants to rent the car for the two specials are equivalent is 5 days.
EquationCompact car:
Fixed price = $50Additional price per day = $6y = 50 + 6x
Another special:
Fixed price = $40Additional price per day = $8y = 40 + 8x
let
x = number of additional days
50 + 6x = 40 + 8x
collect like terms50 - 40 = 8x - 6x
10 = 2x
Divide both sides by 2x = 10/2
x = 5 days
Therefore, the number of additional days she wants to rent the car for, the two specials are equivalent is 5 days.
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Round 4709.94107458 to the nearest whole number
4710
Explanation:4709.94107458
The nearest whole number for 4709.94107458 is 4710 since the number 9 after the decimal is greater than 5. Therefore, if you add 1 to 9 before the decimal, you get 10.
Hope this helps :)
Write an equation that represents the line.
Use exact numbers.
(-2,-1)
(4,6)
Check the picture below.
to get the equation of any straight line, we simply need two points off of it, so let's use those in the picture
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{6})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-2)}}} \implies \cfrac{6 -1}{4 +2} \implies \cfrac{ 5 }{ 6 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{\cfrac{5}{6}}(x-\stackrel{x_1}{(-2)})\implies y-1=\cfrac{5}{6}(x+2) \\\\\\ y-1=\cfrac{5}{6}x+\cfrac{5}{3}\implies y=\cfrac{5}{6}x+\cfrac{5}{3}+1\implies y=\cfrac{5}{6}x+\cfrac{8}{3}[/tex]
