Use an appropriate local linear approximation to estimate the value of √10. Recall that f '(a) [f(a+h)-f(a)] + h when his very small.
Answers
Answer:
\(\sqrt{10}\approx3.17\)
Step-by-step explanation:
We'll use \(x=9\) to get a local linear approximation of \(\sqrt{10}\):
\(f(x)=\sqrt{x}\\\displaystyle f'(x)=\frac{1}{2\sqrt{x}}\\f'(9)=\frac{1}{2\sqrt{9}}\\f'(9)=\frac{1}{2(3)}\\f'(9)=\frac{1}{6}\)
\(\displaystyle y-y_1=m(x-x_1)\\y-3=\frac{1}{6}(x-9)\\\\y-3=\frac{1}{6}x-\frac{9}{6}\\\\y=\frac{1}{6}x+\frac{3}{2}\)
Now that we have the local linear approximation for \(f(x)=\sqrt{x}\), we can plug in \(x=10\) to estimate the value of \(\sqrt{10}\):
\(\displaystyle y=\frac{1}{6}(10)+\frac{3}{2}\\\\y=\frac{10}{6}+\frac{9}{6}\\\\y=\frac{19}{6}\\ \\y\approx3.17\)
Note that the actual value of \(\sqrt{10}\) is 3.16227766, so this is pretty close to our estimate
Therefore, Using local linear approximation, √10 can be estimated to be approximately 3.1667.
To estimate the value of √10 using local linear approximation, we need to choose a value of a such that f(a) = √a is easy to calculate and f'(a) = 1/(2√a) is finite. Let's choose a = 9, then f(a) = √9 = 3 and f'(a) = 1/(2√9) = 1/6. Using the formula for local linear approximation, we have
√10 ≈ f(9) + f'(9)(10-9) = 3 + (1/6)(1) = 3.1667
Therefore, an appropriate local linear approximation estimates the value of √10 to be approximately 3.1667.
Therefore, Using local linear approximation, √10 can be estimated to be approximately 3.1667.
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Related Questions
hey can someone help me? thanks
Select the correct answer.
Function ris a continuous rational function with a horizontal asymptote at y = -8.
Which statement describes the key features of s(t) = (x +2) – 12
A. Function s is continuous and has a horizontal asymptote at y = -1.
В. Function shas a point of discontinuity at I = -2 and a horizontal asymptote at y= -9.
C. Function s has a point of discontinuity at r = -2 and a horizontal asymptote at y = -1.
D. Function sis continuous and has a horizontal asymptote at y = -9.
Answers
s(x) is continuous and has a horizontal asymptote at y = -9
We know that we have a function r(x) that has a horizontal asymptote at y = -8
Then, what can we say about the function s(x) = r(x + 2) - 1 ?
Ok, first remember that a horizontal asymptote means that as x, the variable, increases (or decreases), the function eventually tends to a given value, but never actually reaches it.
So as x tends to infinity, we should see an almost horizontal line that tends to y = -8.
So if that happens when x tends to infinity, the same thing will happen when x + 2 tends to infinity, because that "+2" does not add a lot.
Then is easy to conclude that:
r(x + 2) also has a horizontal asymptote at y = -8
And our function is:
s(x) = r(x + 2) - 1
So we are subtracting one, then that horizontal asymptote will be at:
y = -8 - 1 = -9
The function s(x) has a horizontal asymptote at y = -9
And because r(x) is continuous, then:
s(x) = r(x + 2) - 1
is also continuos, as there is nothing added that could change the continuity (we do not have any zero in the denominator or something like that)
Then the correct option is D.
"s(x) is continuous and has a horizontal asymptote at y = -9"
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Consider a male restroom design with minimum plumbing requirements of 12 water closets and 13 lavatories, which one of the following is closest to the minimum space required with considering urinal substitution? Select one: O a. 222 b. 219 c. 237 d. 249
Answers
none of the provided options (a, b, c, d) appear to be accurate or close to the minimum space required.
To determine the minimum space required for a male restroom design with the given plumbing requirements, we need to consider the minimum space required for water closets and lavatories.
The minimum space required for water closets is typically around 30-36 inches per unit, and for lavatories, it is around 24-30 inches per unit.
Since the design requires a minimum of 12 water closets and 13 lavatories, we can estimate the minimum space required as follows:
Minimum space required for water closets = 12 water closets * 30 inches = 360 inches
Minimum space required for lavatories = 13 lavatories * 24 inches = 312 inches
Adding these two values together, we get a total minimum space requirement of 672 inches.
Among the given options, the closest value to 672 inches is option d) 249. However, this value seems significantly lower than the expected minimum space requirement.
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What is the factor of x³ 3x² 9x 5?
Answers
(x+1) & (x-5) are the factors of given equation.
The given Equation is,
x3- \(3x^{3}\) - 9
Substitute - Substitute means to put something in the place of another and in mathematics substitution means putting numbers in the place of letters. It is used to calculate the value of an expression.Here, If we substitute x =5, in the given equation, then we find
(5)3 - 3(5)3 - 9*5 -5 = 0
x-5 is factor of given equation to find another factor dividing given equation by x-5
we will get =(x2+2x+1) after dividing the equation by x - 5
Hence x3- \(3x^{3}\) - 9 =(x2+2x+1) (x-5)
=(x+2)2 (x-5)
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Can someone please help?
Answers
Answer:
1: The highest score is 98, the lowest score is 74.
2: 55% of the scores are greater than 84
Step-by-step explanation:
Solution 1-1:
Starting from the top left and going from left to right row by row we compare the largest number we come across with the current number we are inspecting.
Starting with 92 then we look at 88, 92 is greater than 88 so we keep 92, next is 95, 95 is greater than 92 so we keep 95, next is 74, 95 is greater than 74 so we keep 95 and so on until we have compared all of the numbers. We are left with 98
Solution 1-2:
Using a similar method to finding the greatest number we go through the list of numbers in search of the smallest number. Starting with 92 we then look at 88, 88 is less than 92 so we keep 88. Next is 95, 88 is less than 95 so we keep 88. Then 74, 74 is less than 88 so we keep 74 and so on. We are left with 74
Solution 2:
There is a total of 20 numbers in the table. By comparing the numbers in the table to 84, we can determine that 11 numbers are greater than 84.
By dividing 11 by 20 we get 0.55 which is equal to 55%
This recipe makes 4 pancakes.
Sanjay follows the recipe but wants to make 24 pancakes.
How much of each ingredient does he need?
Recipe: Makes 4
135 g flour
1 teaspoon (tsp) baking powder
2 tablespoons (tbsps) sugar
130 ml milk
1 egg
2 tablespoons (tbsps) oil
Answers
Answer:
810 g flour
6 teaspoon (tsp) baking powder
12 tablespoons (tbsps) sugar
780 ml milk
6 egg
12 tablespoons (tbsps) oil
Step-by-step explanation:
24/4=6, so you need to multiply everything by six
in an isosceles triangle,the vertex angle is twice the base angle let the base angle be b in degrees remember that the sum of the angles of a triasngle is 180 degrees
Answers
The vertex angle is 90 degrees and the base angle is 45 degrees.
In an isosceles triangle, the vertex angle is twice the base angle. Let the base angle be b in degrees. Remember that the sum of the angles of a triangle is 180 degrees. In order to solve this problem, we need to use the property of angles of an isosceles triangle that tells us that the base angles are equal. Let's call the vertex angle V, and the two base angles B. Since the vertex angle is twice the base angle, we can write an equation: V = 2BWe also know that the sum of the angles of a triangle is 180 degrees.
So we can write another equation: V + B + B = 180 degrees Simplifying this equation, we get: V + 2B = 180 degrees Now we can substitute V = 2B into this equation and solve for B: 2B + 2B = 180 degrees 4B = 180 degrees B = 45 degrees So the base angle is 45 degrees. Using V = 2B, we can find the vertex angle: V = 2(45 degrees)V = 90 degrees Therefore, the vertex angle is 90 degrees and the base angle is 45 degrees.
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the bayley scales of infant development yield scores on two indices-the psychomotor development index (pdi) and the mental development index (mdi)- which can be used to assess a child's level of functioning in each of these areas at approximately one year of age. among normal healthy infants, both indices have a mean value of 100. as part of a study assessing the development and neurologic status of children who have undergone reparative heart surgery during the first three months of life, the bayley scales were administered to a sample of one-year-old infants born with congenital heart disease
Answers
As the test's p-value above the 0.05 level of significance, we cannot reject the hypothesis.
X=97.77 is the mean on the PDI.
a )
The population standard deviation of the PDI:S = 14-69
The PDI sample size is n=70.
The test statistic value is
=X -μ/б-√n
97.77 - 100/14.69√70
Z = - 1.27
The test's p-value is 1.
Value of p = 2p (z - 1.27).
=2 ( = NORMSDIST (-1.27) )
= - 2 (0.1020 )
p-value = 0.2041
Since , the p -value of the test is greater the the 0.05 level of significance, so we fail to reject hypothesis
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2r2 + 3r – 1=0
solve using the quadratic equation
Answers
Answer:
r^1 = -3-square root21/4
r^2 = -3+square root21/4
Step-by-step explanation:
Test 43,785 for divisibility by 2, 3, 5, 9, and 10.
3 and 5
5
3, 5, and 9
3 and 9
Answers
Answer:
Step-by-step explanation:
43,785 is not even so it is not divisible by 2
when we add its digits 4+3+7+8+5 = 27 and it is divisile by 3
43,785 ends with 5 so it is divisible by 5
43,785's sum of digits are 27 and it is divisible by 9
43,785 does not end with a zero so it is not divisible by 10
2. -7 +5m3 + 9m - 3m^2
Answers
Answer:
\(5m^3-3m^2+9m-7\)
Step-by-step explanation:
Solve for c round your answer to the nearest tenth
Answers
Answer:
C = 7.72 ~ 7.7
Step-by-step explanation:
So when you solve this equetion you must 1st find x then c
we can find x by using cos(60)
cos(60) = x/14
x = cos(60) × 14
x = 1/2 ×14
x = 7
so after we find x we are going to solve c by using cos (25)
cos (25) = X/C = 7/c
cos(25) × C = 7
C = 7/cos (25)
C = 7.72 ~ 7.7
so the solution is 7.7
Abc car share inc. offers car sharing for a $199 yearly fee plus $14/hr for the
use of its car share. what is the total cost for a person who purchases a car
share and uses it for 72 hours total time?
Answers
The total cost for a person who purchases a car share and uses it for 72 hours is $1207.
What is the total cost?The total cost is a function of the yearly fee and the cost per hour.
Total cost = yearly fee + (total hours the car was used for x cost per hour)
$199 + (72 x $14)
$199 + $1008 = $1207
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Write an equation that you could use to solve for X.
Answers
THE CORRECT EQUATION IS..
(8X+3)°=(7X+12)°
[BEING VERTICALLY OPPOSITE ANGLES ARE ALWAYS EQUAL ]
HOPE THIS HELPS YOU...
Answer:
8x + 3 = 7x + 12
8x -7x= 12-3
x=9
Solving Equations with Variables on Both Sides
Answers
Answer: x=-9
Step-by-step explanation: First, combine like terms. 3x+4-2x=-5
Then x+4 = -5
x=-9
What is the answer?
-3 (-7 + 2)
Answers
Hope this helps :D
Answer:
15
Step-by-step explanation:
-3(-7+2)
21 - 6
15
five hamburgers cost 5.25 at this rate what is the cost of 8 hamburgers
Answers
Answer: 8.4
Step-by-step explanation: 5.25 divided by 5 is 1.05. So 1.05 x 8 is 8.4
2. Price of 1 is 1.05
3. 1.05 multiply by 8 is 8.40
ANSWER: $8.40 for 8
Systolic blood pressure for a group of women is normally distributed, with a mean of 121 and a standard deviation of 9. Find the probability that a woman selected at random has the following blood pressures. (Round your answers to four decimal places.) (a) greater than 136 (b) less than 114 (c) between 114 and 128
Answers
the probability that a woman selected at random has a blood pressure between 114 and 128 is 0.5588.
What is a Z-table?A z-table also known as the standard normal distribution table, helps us to know the percentage of values that are below (or to the left of the Distribution) a z-score in the standard normal distribution.
Given the mean is 121 while the standard deviation of the women is 9. Therefore, Using the z-table, the probability can be found.
(a) The probability that a woman selected at random has blood pressures greater than 136.
\(P(x > 136) = 1 - P(x < 136)\\\\P(x > 136) = 1 - P(z < \dfrac{x-\mu}{\sigma})\)
\(=1 - P(z < \dfrac{136-121}{9})\\\\=1 - P(z < 1.667)\\\\=1-0.9515\\\\=0.0485\)
(b) The probability that a woman selected at random has a blood pressure less than 114.
\(P(x < 114)= P(z < \dfrac{114-121}{9})\\\\\)
\(= P(z < -0.77)\\\\= 0.2206\)
(c) The probability that a woman selected at random has a blood pressure between 114 and 128.
\(P(114 < x < 128)= P(\dfrac{114-121}{9} < z < \dfrac{128-121}{9})\\\\\)
\(= P(-0.77 < z < 0.77)\\\\= P(z < 0.77)-P(z < -0.77)\\\\= 0.7794 - 0.2206\\\\=0.5588\)
Hence, the probability that a woman selected at random has a blood pressure between 114 and 128 is 0.5588.
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Step by step answer please
Answers
Answer: 48°
Step-by-step explanation:
We know that the angles of a triangle are equal to 180 degrees when added together. Using this logic, we will create an equation to solve for x. Then we will substitute this value of x back into the expression for angle F.
Given:
E + D + F = 180°
Substitue:
(8x - 18)° + (6x - 4)° + (5x - 7)° = 180°
Reorder and combine like terms:
8x° + 6x° + 5x° - 18° - 4° - 7° = 180°
19x° - 29° = 180°
Add 29 to both sides of the equation:
19x° = 209°
Divide both sides of the equation by 19:
x = 11
Substitute this value of x into the expression for angle F:
(5x - 7)°
(5(11) - 7)°
(55 - 7)°
48°
The probability that the interval estimation procedure will generate an interval that contains the actual value of the population parameter being estimated is the _____.
Answers
The population parameter being estimated is the confidence coefficient.
What is a confidence coefficient?The confidence coefficient is the confidence level stated as a proportion, rather than as a percentage. For example, if you had a confidence level of 99%, the confidence coefficient would be . 99. In general, the higher the coefficient, the more certain you are that your results are accurate.
probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Hence, The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the confidence coefficient.
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Find the measure of the angles indicated
Answers
Both angles have a measure of 125°.
How to find the measure of the angles?
Assuming the two horizontal lines are parallel, we know that the measure of the two indicated angles must be the same one.
Then:
-1 + 14x = 12x + 17
Now we need to solve this for x:
14x - 12x = 17 + 1
2x = 18
x =18/2 = 9
Now that we know the value of x we can replace it in any of the expressions for the angles:
-1 + 14*9 = 125°
Both angles have a measure of 125°.
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Fantasia has a skirt that is 2 1/4 ft. long. If she cuts off 5 inches, how long will the skirt be?
Answers
Answer:
1 foot 10 inches
Step-by-step explanation:
A foot is 12 inches
So currently her skirt is 27 inches
If she cuts of 5 inches, her skirt will be 22 inches, or 1 ft 10 inches, or 1 10/12 ft or 1 5/6 ft
Answer:
1 ft and 10 inches
Step-by-step explanation:
ok so 2 1/4 ft is 27 inches so it's gonna be 22 inches if we subtract so it'll be 1 ft and 10 inches
You can infer causality from a correlational result, but only when the r value is greater than____a. 0 b. 0.5 c. 1
Answers
You can infer causality from a correlational result, but only when the r value is greater than b. 0.5
A correlation coefficient, generally denoted by the symbol "r," is a metric that evaluates the degree and direction of a linear relationship between two variables. r has a value between -1 and 1, with -1 indicating a strong negative correlation, +1 indicating a high positive correlation, and 0 indicating no connection.
A correlation value of 0.5 or above is regarded moderate or strong, and it might indicate that a causal link exists between the two variables. It is crucial to remember, however, that correlation does not imply causation, and that other factors such as confounding variables, spurious correlations, or reverse causality may be contributing to the apparent association.
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2/3x+8<10 please help im so bad at math
Answers
Answer:
x < 3
Step-by-step explanation:
2/3 x + 8 < 10
2/3 x < 10 - 8
2/3 x < 2
x < 2*3/2
x < 3
Find the values of x and y if
Answers
Answer:
see explanation
Step-by-step explanation:
Since the triangles are congruent then corresponding sides are congruent, then
CA = NE , that is
4x + 3 = 11 ( subtract 3 from both sides )
4x = 8 ( divide both sides by 4 )
x = 2
----------------------------------------
AR = EW, that is
4y - 12 = 10 ( add 12 to both sides )
4y = 22 ( divide both sides by 4 )
y = 5.5
-------------------------------------------
NW = x + y = 2 + 5.5 = 7.5
CR = NW = 7.5
-3 √(36)
calculate the square root
Answers
2. -3•-6= 18
Cuz square root of 36 is + or - 6
The ratios from parts A and B are equivalent. Write an equation by setting the ratios equal to one another.
Answers
Answer:
the solution is 9/2 = X24
if on a scale drawing 15 ft are represented by 10 in then a scale of 1/10 in represents how many ft
Answers
Let be "x" the length in feet represented by a scale drawing of:
\(\frac{1}{10}in\)You can write the given fraction as a Decimal number. To do this, you only need to divide the numerator by the denominator. Then:
\(\frac{1}{10}in=0.1in\)Based on the information given in the exercise, you can set up the following proportion:
\(\frac{15}{10}=\frac{x}{0.1}\)Now you must solve for "x" in order to find its value. This is:
\(\begin{gathered} (0.1)(\frac{15}{10})=x \\ \\ \frac{1.5}{10}=x \\ \\ x=0.15 \end{gathered}\)The answer is:
\(0.15ft\)Printing Brochures The trade show is less than three weeks away. Your manager wants to be sure you have plenty of color brochures in time for the show. She said there will be nearly 4100 attendees, and that the brochures should cost no more than $1900. You were told to call Sofia for help ordering the brochures.
Step 1: Understand the Problem
What do you know?
11. List three criteria for the print order that you know are important to your manager. (6 points: 2 points for each piece of information)
Answers
Answer:
1. No extra fees unless we need out order sooner (2 weeks for an extra $50)
2 .orders of 1000 or more are 40 cents a piece orders of fewer thank 1000 are 60 cents a piece
3. The brochure will arrive in three weeks so we need to pay an extra $50 to get them before the show
Step-by-step explanation:
I’ve done this already but if you need me to explain lmk:)
The concept that you have just developed is called The Second Law of Probability. Write one sentence to describe the relationship between the chance of separate events occuring and the chance of combined events occuring.
Answers
The Second Law of Probability states that the chance of combined events occurring is determined by the product of the chances of each separate event occurring.
The Second Law of Probability, also known as the Multiplication Rule, describes the relationship between the probability of separate events and the probability of combined events. According to this rule, if we have two or more independent events, the probability of both events occurring together is found by multiplying the probabilities of each individual event. This can be extended to more than two events by continuing to multiply the probabilities.
For example, if we have Event A with a probability of P(A) and Event B with a probability of P(B), the probability of both events A and B occurring simultaneously is given by P(A and B) = P(A) * P(B). This rule applies to any number of independent events.
The Second Law of Probability allows us to calculate the probability of complex events by breaking them down into separate, independent components. It provides a fundamental principle for determining the likelihood of combined events based on the probabilities of their individual occurrences.
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Select all the expressions that are equivalent to 312 • 79. 33 • 34 • 49
(33)9 • (73)6
73 • (3–4)–3 • 76
(33 + 39) • (76 + 73)
320 • (73)3 • (34)–2
please help asap
Answers
The expressions that are equivalent to 312 • 79 are (33)9 • (73)6 and 320 • (73)3 • (34)–2.
To determine which expressions are equivalent to 312 • 79, we need to evaluate each option and compare the results.
First, let's consider (33)9 • (73)6. Here, (33)9 means raising 33 to the power of 9, and (73)6 means raising 73 to the power of 6. By evaluating these powers and multiplying the results, we obtain the product.
Next, let's examine 320 • (73)3 • (34)–2. Here, (73)3 means raising 73 to the power of 3, and (34)–2 means taking the reciprocal of 34 squared. By evaluating these values and multiplying them with 320, we obtain the product.
Expressions yield the same result as 312 • 79, confirming their equivalence. The other options listed do not produce the same value when evaluated, and thus are not equivalent to 312 • 79.
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