let gx(−1,6,5)=−3 , gy(−1,6,5)=7, and gz(−1,6,5)=1.find the equation of the tangent plane to g(x,y,z)=0 at the point (−1,6,5)
Answers
The equation of the tangent plane is -3x + 7y + z - 56 = 0.
To find the equation of the tangent plane to the surface g(x,y,z) = 0 at the point (-1,6,5), we need to first find the gradient vector of g at this point, which will be perpendicular to the tangent plane. Then we can use the point-normal form of the equation of a plane to write the equation of the tangent plane.
The gradient vector of g(x,y,z) is given by:
∇g = ( ∂g/∂x , ∂g/∂y , ∂g/∂z )
We are not given the equation for g, but we are given the values of its partial derivatives at the point (-1,6,5):
∂g/∂x = gx(-1,6,5) = -3
∂g/∂y = gy(-1,6,5) = 7
∂g/∂z = gz(-1,6,5) = 1
Therefore, the gradient vector at (-1,6,5) is:
∇g(-1,6,5) = (-3, 7, 1)
Now we can use the point-normal form of the equation of a plane, which is:
a(x - x0) + b(y - y0) + c(z - z0) = 0
where (x0, y0, z0) is the point on the plane and (a, b, c) is the normal vector to the plane. In our case, we have the point (-1,6,5) on the plane, and we know that the normal vector is ∇g(-1,6,5) = (-3, 7, 1).
Therefore, the equation of the tangent plane to g(x,y,z) = 0 at (-1,6,5) is:
-3(x + 1) + 7(y - 6) + (z - 5) = 0
Simplifying this equation, we get:
-3x + 7y + z - 56 = 0
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Related Questions
Find the distance between these two points on the graph.
A. 2
B. 5.8
C. 3
D. 3.2
Answers
Answer:
B) 5.8
Step-by-step explanation:
5^2 + 3^2 = x^2 ( By Pythagoras theorem )
25 + 9 = x^2
34 = x^2
x = 5.8
Answer:
5.83 units
Step-by-step explanation:
By counting the squares and using Pythagoras theorem:
D^2 = 3^2 + 5^2 = 34
D = √34
= 5.83.
two times p plus five is greater than or equal to three times p minus ten
Answers
Answer:
2p + 5 ≥ 3p - 10
Step-by-step explanation:
Answer: 2p+5 ≥ 3p-10
The digits 0 through 9 are written on slips of paper (both O and 9 are included). An experiment consists of randomly selecting one numbered slip of paper. Event A: obtaining a prime number Event B: obtaining an even number Determine the probability P(A or B). A. 3/5
B. 4/5 C. 9/10 D. 7/10 E. 1
Answers
P(A or B) = 7/10. (Probability of obtaining a prime number or an even number is 7 out of 10 possible numbers.)
To calculate the probability of Event A or Event B occurring, we add the probabilities of Event A and Event B and subtract the probability of their intersection.
Event A is obtaining a prime number, with 4 out of 10 possibilities.
Event B is obtaining an even number, with 5 out of 10 possibilities. The intersection of A and B is the number 2, which satisfies both conditions.
Therefore, P(A or B) = P(A) + P(B) - P(A and B) = 4/10 + 5/10 - 1/10 = 7/10. Hence, the probability of Event A or Event B is 7/10.
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Find a point-slope form for the line with slope 1/5 and passing through the point (-2,-5)
The equation of the line in point-slope form is what?
Answers
The equation of the line in point-slope form is written as: y + 5 = 1/5(x + 2).
How to Find the Equation of a Line?We can write the equation of a line in point-slope form by substituting the value of the slope of the line, m, and the value of the coordinates of a point on the line, (a, b) into the equation y - b = m(x - a).
Given the variables below:
A point on the line (a, b) = (-2, -5)
Slope (m) = 1/5.
To write the equation of the line in point-slope form, substitute a = -2, b = -5 and m = 1/5 into y - b = m(x - a):
y - (-5) = 1/5(x - (-2))
y + 5 = 1/5(x + 2)
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a chemical company produces a substance composed of 98% cracked corn particles and 2% zinc phosphide for use in controlling rat populations in sugarcane fields. production must be carefully controlled to maintain the 2% zinc phosphide, because too much zinc phosphide will cause damage to the sugarcane and too little will be ineffective in controlling the rat population. records from past production indicate that the distribution of the actual percentage of zinc phosphide present in the substance is approximately mound shaped, with a mean of 2.0% and a standard deviation of .08%. suppose one batch chosen randomly actually contains 1.80% zinc phosphide. does this indicate that there is too little zinc phosphide in this production? explain your reasoning
Answers
Based on the results of the hypothesis test, we can say that a batch containing 1.80% zinc phosphide indicates that there is too little zinc phosphide in this production.
Based on the information provided, the chemical company produces a substance that contains 2% zinc phosphide for controlling rat populations in sugarcane fields. The production must be carefully controlled to ensure that the substance contains exactly 2% zinc phosphide. Records from past production indicate that the actual percentage of zinc phosphide present in the substance is approximately mound-shaped with a mean of 2.0% and a standard deviation of .08%.
Suppose one batch chosen randomly actually contains 1.80% zinc phosphide. This may or may not indicate that there is too little zinc phosphide in this production. To determine whether the batch contains too little zinc phosphide, we can perform a hypothesis test.
The null hypothesis in this case is that the batch contains exactly 2% zinc phosphide, and the alternative hypothesis is that the batch contains less than 2% zinc phosphide. We can use a one-tailed z-test to test this hypothesis.
Calculating the z-score for a batch with 1.80% zinc phosphide, we get:
z = (1.80 - 2.00) / 0.08 = -2.5
Using a standard normal distribution table, we can find that the probability of getting a z-score of -2.5 or lower is approximately 0.006. This means that if the batch truly contains 2% zinc phosphide, there is only a 0.006 probability of getting a sample with 1.80% zinc phosphide or less. Assuming a significance level of 0.05, we reject the null hypothesis if the p-value is less than 0.05. Since the p-value in this case is less than 0.05, we can reject the null hypothesis and conclude that there is evidence that the batch contains less than 2% zinc phosphide.
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Use mathematical induction (and the proof of Proposition as a model) to show that any amount of money of at least 14c can be made up using 3¢ and 8¢ coins.
Proposition
For all integers n ≥ 8, n¢ can be obtained using 3¢ and ¢ coins.
Proof (by mathematical induction):
Let the property P(n) be the sentence
n¢ can be obtained using 3¢ and 5¢coins. ← P(n)
Show that P(8) is true:
P(8) is true because 8¢can be obtained using one 3¢coin and one 5¢ coin.
Show that for all integers k≥ 8, if P(k) is true then P(k+1) is also true:
[Suppose that P(k) is true for a particular but arbitrarily chosen integer k ≥ 8. That is:]
Suppose that k is any integer with k ≥ 8 such that
k¢ can be obtained using 3¢ and 5¢ coins. ← P(k) inductive hypothesis
[We must show that P(k + 1) is true. That is:] We must show that
(k + 1)¢can be obtained using 3¢ and 5¢ coins. ← P(k + 1)
Case 1 (There is a 5¢ coin among those used to make up the k¢.): In this case replace the 5¢ coin by two 3¢ coins; the result will be (k + 1) ¢.
Case 2 (There is not a 5¢ coin among those used to make up the k¢.): In this case, because k ≥ 8, at least three 3¢ coins must have been used. So remove three 3¢ coins and replace them by two 5¢ coins; the result will be (k + 1) ¢.
Thus in either case (k + 1) ¢ can be obtained using 3¢ and 5¢ coins [as was to be shown].
[Since we have proved the basis step and the inductive step, we conclude that the proposition is true.]
Answers
Given statement is mathematical induction using 3¢ and 8¢ coins P(n) is true for all integers n ≥ 14.
The f is incorrect because it uses 5¢ coins instead of 8¢ coins as stated in the problem. A corrected proof using mathematical induction:
Proposition:
For all integers n ≥ 14, n¢ can be obtained using 3¢ and 8¢ coins.
Proof (by mathematical induction):
Let the property P(n) be the sentence "n¢ obtained using 3¢ and 8¢ coins."
Step 1: Show that P(14) is true.
To make 14¢, one 8¢ coin and two 3¢ coins. Therefore, P(14) is true.
Step 2: Show that for all integers k ≥ 14, if P(k) is true, then P(k + 1) is also true.
Assume that P(k) is true for a particular but arbitrarily chosen integer k ≥ That is, assume k¢ can be obtained using 3¢ and 8¢ coins to show that (k + 1)¢ can be obtained using 3¢ and 8¢ coins.
There are two cases to consider:
Case 1: There is 8¢ coin among those used to make up the k¢ replace one 8¢ coin with a five 3¢ coins. The result will be (k + 1)¢, and it can be obtained using 3¢ and 8¢ coins.
Case 2: There is no 8¢ coin among those used to make up the k¢.
In k ≥ 14, that at least five 3¢ coins must have been used. Remove five 3¢ coins and replace them with two 8¢ coins. The result will be (k + 1)¢, and it can be obtained using 3¢ and 8¢ coins.
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pleaee solve this problem!!
Answers
Answer:
RHS=tanA/2
Step-by-step explanation:
LHS=1+sinA-cosA/1+sinA+cosA
=(1-cosA)+sinA/(1+cos A)+sinA
=2sin^2A/2+2sinA/2*cosA/2
_____________________
2cos^2A/2+22sinA/2*cosA/2
=2sinA/2(sinA/2+cosA/2)
___________________
2cosA/2(sinA/2+cosA/2)
sinA/2
=_____
cosA/2
= tanA/2 proved.
Answer: see proof below
Step-by-step explanation:
Use the following Double Angle Identities:
sin 2A = 2cos A · sin A
cos 2A = 2 cos²A - 1
Use the following Quotient Identity: tan A = (sin A)/(cos A)
Use the following Pythagorean Identity:
cos²A + sin²A = 1 --> sin²A = 1 - cos²A
Proof LHS → RHS
Given: \(\dfrac{1+sin\theta - cos \theta}{1+sin \theta +cos \theta}\)
Let Ф = 2A: \(\dfrac{1+sin2A - cos 2A}{1+sin2A +cos2A}\)
Un-factor: \(\dfrac{\bigg(\dfrac{1- cos^2\ 2A}{1+cos\ 2A}\bigg)+sin\ 2A }{1+sin\ 2A +cos\ 2A}\)
Pythagorean Identity: \(\dfrac{\bigg(\dfrac{sin^2\ 2A}{1+cos\ 2A}\bigg)+sin\ 2A }{1+cos\ 2A +sin\ 2A}\)
Simplify: \(\dfrac{sin\ 2A}{1+cos\ 2A}\)
Double Angle Identity: \(\dfrac{2sin\ A\cdot cos\ A}{1+(2cos^2 A-1)}\)
Simplify: \(\dfrac{2sin\ A\cdot cos\ A}{2cos^2\ A}\)
\(=\dfrac{2sin\ A\cdot cos\ A}{2cos^2\ A}\)
\(=\dfrac{sin\ A}{cos\ A}\)
Quotient Identity: tan A
\(\text{Substitute} A = \dfrac{\theta}{2}}:\qquad tan\dfrac{\theta}{2}\)
\(tan\dfrac{\theta}{2} = tan\dfrac{\theta}{2}\quad \checkmark\)
express the followinf percentage as a fraction
a) 6 3/5%
Answers
Answer:
6.6/100 or 3.3/5
Step-by-step explanation:
6.6% or 6 3/5% now since those are all out of 100 (since percentages) you just put #/100 and get your fraction
the median can also be described as: question 9 options: the middle observation when the data values are arranged in ascending order the second quartile the 50th percentile all of the above
Answers
Median can described as -
the middle observation when the data values are arranged in ascending order; the second quartile; and 50th percentile all.
Hence the correct option is (D).
Median of a data observations set is the middle point or middle value of the data set arranged in ascending or descending order.
Hence point (A) is correct.
50th percentile means the middle observation or the observation, after or before which equal number of observations lie.
So the point (B) is also correct.
A quartile means = 25 percentile
second quartile stands for = 25*2 = 50 percentile.
Hence point (C) is also correct.
Hence the best suited option is (D) all of the above.
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The question is incomplete. The complete question will be -
Use synthetic division to find the quotient and remainder when - 3x + 10x? - 6x + 9 is divided by x-3 by completing the parts below. (a) Complete this synthetic division table. 3) -3 10-6 9 х ? D D D
Answers
The quotient when -3x^3 + 10x^2 - 6x + 9 is divided by x - 3 is -3x^2 + x - 3. The remainder is 0.
To perform synthetic division, we set up the table as follows:
3 | -3 10 -6 9
| -9 3 -9
-------------------
-3 1 -3 0
The numbers in the first row of the table are the coefficients of the polynomial, starting from the highest power of x and going down to the constant term. We divide each coefficient by the divisor, which in this case is x - 3, and write the results in the second row. The first number in the second row is the constant term.
To calculate the values in the second row, we multiply the divisor (x - 3) by each number in the first row, and subtract the result from the corresponding number in the first row. The first number in the second row is obtained by multiplying 3 by -3 and subtracting it from -3. This process is repeated for each term in the polynomial.
The numbers in the second row represent the coefficients of the quotient. Therefore, the quotient is -3x^2 + x - 3. Since the remainder (the last number in the second row) is 0, we can conclude that -3x^3 + 10x^2 - 6x + 9 is evenly divisible by x - 3.
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In pensacola in june, high tide was at noon. the water level at high tide was 12 feet and 2 feet at low tide. assuming the next high tide is exactly 12 hours later and that the height of the water can be modeled by a cosine curve, find an equation for water level in june for pensacola as a function of time (t). f(t) = 12 cospi over 2t 5 f(t) = 5 cospi over 2t 12 f(t) = 5 cospi over 6t 7 f(t) = 7 cospi over 6t 12
Answers
An equation for water level in june for pensacola as a function of time (t) is f(t) = 5 cos pi/6 t + 7.
Which equation of cos show period amplitude ?
The equation given below show aplitude and period
\(y = A cos bx + c\)
where A = amplitude,
b = 2 pi/Period,
Period = 12 hrs,
c = midline,
x = t and y = f(t)
We have to find the amplitude
What is the formula for the amplitude?
\(A = 1/2 (Xmax - Xmin)\)
\(12 - 2 / 2 = 10/2 = 5\)
\(b = 2 pi / 12 = pi/6\)
\(c = 1/2 (Xmax + Xmin)\)
\(12+2/2 = 7\)
Therefore, the an equation for water level in june for pensacola as a function of time (t)
\(f(t) = 5 cos pi/6 t + 7\)
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The _______ of a probability experiment is the collection of all possible outcomes. a. outcome b. sample space c. event d. unusual event e. experiment
Answers
Answer:B.Sample space
Step-by-step explanation:
What is the value of X?
3
4
6
8
Answers
Answer:
The answer is 4
Step-by-step explanation:
What is the smallest possible difference between two different nine-digit integers, each of which includes all of the digits 1 to 9?
Answers
Answer:
Step-by-step explanation:
To find the smallest possible difference between two different nine-digit integers that include all the digits 1 to 9, we can start by arranging the digits in ascending order to form the smaller number and in descending order to form the larger number.
The smallest possible nine-digit integer that includes all the digits 1 to 9 is 123456789, and the largest possible nine-digit integer is 987654321.
To calculate the difference, we subtract the smaller number from the larger number is
987654321 - 123456789 = 864197532
Therefore, the smallest possible difference between two different nine-digit integers, each of which includes all the digits 1 to 9, is 864,197,532
In number theory, the smallest possible difference between two different nine-digit integers, each of which includes all of the digits from 1 to 9, is 1.
Explanation:The subject matter of this question belongs to Mathematics, specifically, number theory. The smallest possible difference between two different nine-digit integers, each of which includes all of the digits 1 to 9, is 1. For instance, consider the two numbers
123456789
and
123456790
. Both numbers use each of the digits 1 to 9 once. The difference between these two numbers is 123456790 - 123456789 = 1. This is the smallest difference that can be achieved under the given conditions.
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Find the radius of convergence and the interval of convergence
for the following
series.
∑[infinity] (x − 2)n
nn n=1
Problem 2 Find the radius of convergence and the interval of convergence for the following series. [infinity] n=1 (x − 2)n nn
Answers
the radius of convergence is 1 and the interval of convergence is (1, 3) in terms of x-values.
To determine the radius of convergence, we can use the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1 as n approaches infinity, then the series converges. Applying the ratio test to the given series, we have:
lim(n->∞) |((x - 2)^(n+1)/(n+1)) / ((x - 2)^n/n)| < 1
Simplifying the expression, we get:
lim(n->∞) |(x - 2)n+1 / (n+1)(x - 2)^n| < 1
Taking the absolute value and rearranging, we have:
lim(n->∞) |x - 2| < 1
This implies that the series converges when |x - 2| < 1, which gives us the interval of convergence. The radius of convergence is the distance between the center of the series (x = 2) and the nearest point where the series diverges, which in this case is 1.
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A math test has 12 multiplication problems and 24 division problems.
What is the ratio value of division problems to multiplication problems?
Type your answer as a fraction in simplest form
Answers
Answer: 2:1
Step-by-step explanation:
hi there! since there are 24 division problems and 12 division problems, you need to divide by the gcf of 24 and 12, which gives you 2:1.
hope it helps!
lovelymoonlight
Answer: 2:1 is the ratio of division problems to multiplication problems.
Step-by-step explanation:
12 is half as small as 24, so the ratio of division problems to multiplication problems is 2:1.
Chebyshev's theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the mean is?
Answers
Chebyshev's theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the mean is 1 - 1/k².
What do you mean by standard deviation?In statistics, Standard deviation is a measure of the variation of a set of values.
σ = standard deviation of population
N = number of observation of population
X = mean
μ = population mean
We know that Chebyshev's theorem states that for a large class of distributions, no more than 1/k² of the distribution will be k standard deviations away from the mean.
This means that 1 - 1/k² of the distribution will be within k standard deviations from the mean.
Lets k = 1.8, the amount of the distribution that is within 1.8 standard deviations from the mean is;
1 - 1/1.8² = 0.6914
= 69.14%
Hence, Chebyshev's theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the mean is 1 - 1/k².
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What is the surface area of a cube with a side length of 5 yards?
Answers
Answer:270
Step-by-step explanation:
5*5=25
25*6=270
6 because that’s the side of a cube
What is the average rate of change of f(x) from x1=−5.7 to x2=−1.6 ? Please write your answer rounded to the nearest hundredth
f(x)=−7x−1
Answers
The average rate of change of f(x) from x1 = -5.7 to x2 = -1.6 is approximately -7.00. To find the average rate of change of the function f(x) = -7x - 1 from x1 = -5.7 to x2 = -1.6, we need to calculate the difference in the function values divided by the difference in the x-values.
First, let's calculate f(x1) and f(x2):
f(x1) = -7(-5.7) - 1 = 39.9 - 1 = 38.9
f(x2) = -7(-1.6) - 1 = 11.2 - 1 = 10.2
Next, let's calculate the difference in the function values and the difference in the x-values:
Δf = f(x2) - f(x1) = 10.2 - 38.9 = -28.7
Δx = x2 - x1 = -1.6 - (-5.7) = -1.6 + 5.7 = 4.1
Finally, we can calculate the average rate of change:
Average rate of change = Δf / Δx = -28.7 / 4.1 ≈ -7.00
Therefore, the average rate of change of f(x) from x1 = -5.7 to x2 = -1.6 is approximately -7.00.
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a. What is the nth fraction in the following sequence? 2
1
, 4
1
, 8
1
, 16
1
, 32
1
,… b. What is the sum of the first n of those fractions? To what number is the sum getting closer and closer? Two forces, A=80 N and B=44 N, act in opposite directions on a box, as shown in the diagram. What is the mass of the box (in kg ) if its acceleration is 4 m/s 2
?
Answers
A)an = 2*2^(n-1)`. B) `The sum of the first n fractions is `2*(2^n - 1)`.
a. The sequence is a geometric sequence with the first term `a1 = 2` and common ratio `r = 2`.Therefore, the nth term `an` is given by:`an = a1*r^(n-1)`
Substituting `a1 = 2` and `r = 2`, we have:`an = 2*2^(n-1)`
b. To find the sum of the first n terms, we use the formula for the sum of a geometric series:`S_n = a1*(1 - r^n)/(1 - r)
`Substituting `a1 = 2` and `r = 2`, we have:`S_n = 2*(1 - 2^n)/(1 - 2)
`Simplifying:`S_n = 2*(2^n - 1)
`The sum of the first n fractions is `2*(2^n - 1)`.As `n` gets larger and larger, the sum approaches `infinity`.
Thus, the sum is getting closer and closer to infinity.
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Given g(x) = 4x - 7, find g(-9)
Answers
Answer:
g(- 9) = - 43
Step-by-step explanation:
substitute x = - 9 into g(x) , that is
g(- 9) = 4(- 9) - 7 = - 36 - 7 = - 43
I roll a fair die twice and obtain two numbers: X 1
= result of the first roll, X 2
= result of the second roll. a. Find the probability that X 2
=4. b. Find the probability that X 1
+X 2
=7. c. Find the probability that X 1
=2 and X 2
≥4. Four teams A,B,C, and D compete in a tournament, and exactly one of them will win the tournament. Teams A and B have the same chance of winning the tournament. Team C is twice as likely to win the tournament as team D. The probability that either team A or team C wins the tournament is 0.6. Find the probabilities of each team winning the tournament.
Answers
a) The probability that X2 equals 4 is 1/6, or approximately 0.1667.
b) The probability that X1 + X2 equals 7 is 1/6, or approximately 0.1667.
c) The probability that X1 is not equal to 2 and X2 is greater than or equal to 4 is 2/6, or approximately 0.3333.
For the tournament, the probabilities of teams A, B, C, and D winning are 0.3, 0.3, 0.4, and 0, respectively.
a) Since the die is fair, each roll has an equal probability of 1/6 of landing on the number 4. Therefore, the probability that X2 equals 4 is 1/6.
b) To calculate the probability that X1 + X2 equals 7, we need to determine the number of favorable outcomes. The pairs of rolls that sum to 7 are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). Since there are six favorable outcomes out of a total of 36 possible outcomes (6 choices for the first roll and 6 choices for the second roll), the probability is 6/36, which simplifies to 1/6.
c) The probability that X1 is not equal to 2 is 5/6, as there are five other outcomes out of six possibilities. The probability that X2 is greater than or equal to 4 is 3/6, as there are three favorable outcomes out of six possibilities. Multiplying these probabilities together gives (5/6) * (3/6) = 15/36, which simplifies to 5/12 or approximately 0.4167. However, the question asks for the probability that X1 is not equal to 2 and X2 is greater than or equal to 4, so we subtract this probability from 1 to get 1 - 5/12 = 7/12 or approximately 0.5833.
For the tournament, let's denote the probability of team A winning as PA, team B winning as PB, team C winning as PC, and team D winning as PD. We are given that PA = PB, PC = 2PD, and PA + PC = 0.6. From this information, we can deduce that PD = 0 (since the sum of all probabilities must equal 1) and PC = 0.4. Substituting this into PA + PC = 0.6, we find PA = 0.2. Since PA = PB, we have PB = 0.2. Thus, the probabilities of teams A, B, C, and D winning the tournament are 0.2, 0.2, 0.4, and 0, respectively.
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we have f '(x) = 2 cos x − 2 sin x, so
Answers
We have f '(x) = 2 cos x − 2 sin x, so f"(x) = -2 sin(x) – 2 cos(x) which equals 0 when tan(x) = -1 . Hence, in the interval \(0\leq x\leq 2\pi\), f"(x) = 0 when X = \(\frac{3\pi }{4}\) and x = \(\frac{7\pi }{4}\)
To find when f"(x) = 0 with the given f"(x) = -2 sin(x) - 2 cos(x), we need to solve the equation:
-2 sin(x) - 2 cos(x) = 0
First, divide both sides of the equation by -2 to simplify:
sin(x) + cos(x) = 0
Now, we want to find when tan(x) is equal to a certain value. Recall that tan(x) = sin(x) / cos(x). To do this, we can rearrange the equation:
sin(x) = -cos(x)
Then, divide both sides by cos(x):
sin(x) / cos(x) = -1
Now, we have:
tan(x) = -1
In the given interval 0 ≤ x ≤ 2π, tan(x) = -1 at:
x = 3π/4 and x = 7π/4.
So, in the interval 0 ≤ x ≤ 2π, f"(x) = 0 when x = 3π/4 and x = 7π/4.
The complete question is:-
we have f '(x) = 2 cos x − 2 sin x, so f"(x) = -2 sin(x) – 2 cos(x) which equals 0 when tan(x) = __ . Hence, in the interval \(0\leq x\leq 2\pi\), f"(x) = 0 when X = \(\frac{3\pi }{4}\) and x = \(\frac{7\pi }{4}\)
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how would I graph the line, 3x+4y= -4
Answers
Given the equation:
3x + 4y = -4
Let's graph the line that represents the equation above.
To grah the line, rewrite the equation in slope-intercet form:
y = mx + b
Where m is the slope and b is the y-intercept.
Rerite the equation for y:
3x + 4y = -4
Subtract 3x from both sides:
3x - 3x + 4y = -3x - 4
4y = -3x - 4
Divide all terms by 4:
\(\begin{gathered} \frac{4y}{4}=-\frac{3x}{4}-\frac{4}{4} \\ \\ y=-\frac{3}{4}x-1 \end{gathered}\)The slope of the line is -3/4, while the y-intercept is at (0, -1).
Now, let's graph the line using 3 points.
• When x = -4:
Substitute -4 for x and solve for y
\(\begin{gathered} y=-\frac{3}{4}\ast(-4)-1 \\ \\ y=3-1 \\ \\ y=2 \end{gathered}\)• When x = 0:
Substitute 0 for x and solve for y
\(\begin{gathered} y=-\frac{3}{4}\ast(0)-1 \\ \\ y=-1 \end{gathered}\)• When x = 4:
Substitute 4 for x and solve for y
\(\begin{gathered} y=-\frac{3}{4}\ast4-1 \\ \\ y=-3-1 \\ \\ y=-4 \end{gathered}\)Therefore, we have the following points:
(-4, 2), (0, -1) and (4, -4)
Plot the three points on the graph, then connect all 3 points using a straight edge.
We have the graph attached below:
eport the Fama-MacBeth test statistic, i.e. sqrt(N)*avg(X)/stddev(x), where N is the number of observations (the number of months), and X is the monthly estimated slope coefficient on MarketCap when explaining Returns by MarketCap and CAPM-Beta (i.e. the slope coefficients from the previous regression). Round the value to two decimal digits, and use the dot to separate decimal from non-decimal digits, i.e. enter like: 12.23
Use all slope coefficients from 2010 (i.e. N=12).
Coefficient 0.00423 -4.02658E-10
T-stat 0.322949664 -0.84670755
Answers
The Fama-MacBeth test statistic for the monthly estimated slope coefficient on MarketCap when explaining Returns by MarketCap and CAPM-Beta using all slope coefficients from 2010 (N=12) is 0.16.
This was calculated by taking the average of the monthly estimated slope coefficient on MarketCap, multiplying it by the square root of the number of observations (12), and then dividing it by the standard deviation of the monthly estimated slope coefficient on MarketCap.
The resulting value was rounded to two decimal digits (0.16) and entered with a dot to separate decimal from non-decimal digits.
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1
What is the solution to the equation n-5
2 16
*+5 12 - 25?
Oh=
11
3
Oh=5
O h=7
21
Oh=
2
Answers
\(\begin{aligned}\frac{1}{h-5}+\frac{2}{h+5}&=\frac{16}{h^2-25}\\\frac{(h+5)+2(h-5)}{(h-5)(h+5)}&=\frac{16}{h^2-25}\\\frac{h+2h+5-10}{h^2-25}&=\frac{16}{h^2-25}\\\frac{3h-5}{\cancel{h^2-25}}&=\frac{16}{\cancel{h^2-25}}\\3h-5&=16\\3h&=16+5\\3h&=21\\h&=\frac{21}{3}\\h&=7\end{aligned}\)
Hello this is the question
Answers
Answer:
A. 36/5
Step-by-step explanation:
cross multiply
6/5 = x/6
5x = 36
x = 36/5
Answer:
A) \(\frac{36}{5}\)
Step-by-step explanation:
\(\frac{6}{5}\) = \(\frac{x}{6}\) Cross multiply and solve for x
36 = 5x Divide both sides by 5
\(\frac{36}5}\) = \(\frac{5x}{5}\)
\(\frac{36}{5}\) = x
Consider the initial-value problem y′′+4y=g(x)y(0)=1,y′(0)=2 where g(x)={sinx00≤x≤π/2x>π/2 (a) Find a solution y1(x) to the differential equation over the interval 0≤x≤π/2. Use the initial conditions to determine the unknown constants c1 and c2. (b) Find a solution y2(x) to the differential equation over the interval x>π/2. (c) The goal is to combine the two solutions y1 and y2 into one solution y(x)={y1(x)y2(x)0≤x≤π/2x>π/2 'To ensure that y(x) meets the requirements to be a solution to a differential equation, it must be continuous and differentiable. Determine the values of the unknown constants in y2 that ensure y is continuous and differentiable.
Answers
The solution to the differential equation over the entire interval 0≤x≤π/2
Consider the initial-value problem y′′+4y=g(x)y(0)=1,y′(0)=2 where g(x)={sinx00≤x≤π/2x>π/2
(a) Find a solution y1(x) to the differential equation over the interval 0≤x≤π/2.
Use the initial conditions to determine the unknown constants c1 and c2.Solution: The given differential equation is y''+4y=g(x) ...[1]
Using the initial condition y(0)=1 and y'(0)=2, we get the following equation :y1(0)=c1....[2]and y1'(0)=c2-2sin(0)=-2c2...[3]
Therefore, the solution of the differential equation for 0≤x≤π/2 is given by, y1(x)=c1cos(2x)+c2sin(2x)+1 ...[4]
Differentiating the above equation, we get y1′(x)=−2c1sin(2x)+2c2cos(2x) ...[5]
Using equation [3] in the above equation, we get y1′(0)=2c2.Using the initial condition, we get 2c2=-2, which gives us c2=-1.
(b) Find a solution y2(x) to the differential equation over the interval x>π/2.
Given, g(x)=0 for x≤π/2 and g(x)=sinx for x>π/2.
The solution to the differential equation over the interval x>π/2 is y2(x)=kcos(2x)+ksin(2x), where k is an arbitrary constant.
Using the value of y2(x) in the differential equation, we getk=1/2.
(c) Determine the values of the unknown constants in y2 that ensure y is continuous and differentiable.
To ensure that y(x) is continuous, we have to make sure that y1(π/2) = y2(π/2), i.e.,c1 cos(π)+c2 sin(π) + 1 = k cos(π) + k sin(π),which reduces to 0=c1-k.
To ensure that y(x) is differentiable, we have to make sure that y1'(π/2) = y2'(π/2), i.e.,-2c1 sin(π) + 2c2 cos(π) = -2k sin(π) + 2k cos(π),which reduces to 2c2 = 2k.
Using the values of c2 and k, we getc2=k=−1/2, and y2(x)=−1/2(cos(2x)+sin(2x)).
Hence, the solution to the differential equation over the entire interval 0≤x≤π/2 is given by,y(x)=y1(x), for 0≤x≤π/2, and y(x)=y2(x), for x>π/2, y(x)={c1cos(2x)+c2sin(2x)+1, for 0≤x≤π/2,−1/2(cos(2x)+sin(2x)), for x>π/2.
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What is meant by the notations AE, AE, and AE
Answers
Answer:
æïœü
Step-by-step explanation:
æïœü æïœü æïœü æïœü
Watch help video Find the length of the third side. If necessary, write in simplest radical form. 7 4√2
Answers
In simplest radicle form, the length of the third side = 9 units.
Given,
Side A = 7 units.
Side B = 4√2 units.
To find Side C, we use the Pythagorean formula,
a² = b² + c²
7² = \(4\sqrt{2}^{2}\) + c²
c² = 49 + 32
c² = 81
√c² = √81
c = -9,9.
c ≠ -9 as negative values are not considered for dimensions.
Hence, the length of the third side is 9 units.
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Your question is incomplete. The complete question is:
With reference to the figure below, find the length of the third side. If necessary, write in the simplest radical form.
