if f(x) = 4x² - 2, find(f⁻¹)'(-2)
Answers
Division by zero is undefined, (f⁻¹)'(-2) does not exist.
To find the derivative of the inverse of a function at a given point, we can use the formula:
(f⁻¹)'(y) = 1 / f'(x)
where y = f(x) and x = f⁻¹(y).
In this case, we are given the function f(x) = 4x² - 2 and asked to find (f⁻¹)'(-2). To do this, we need to first find the value of x for which f(x) = -2. In other words, we need to solve the equation:
4x² - 2 = -2
Simplifying, we get:
4x² = 0
x = 0
So, f⁻¹(-2) = 0.
Next, we need to find f'(x), the derivative of f(x), which is:
f'(x) = 8x
To find f'(0), we substitute x = 0 into this expression:
f'(0) = 8(0) = 0
Now, we can substitute these values into the formula for (f⁻¹)'(-2):
(f⁻¹)'(-2) = 1 / f'(f⁻¹(-2)) = 1 / f'(0) = 1 / 0
Since division by zero is undefined, (f⁻¹)'(-2) does not exist.
Therefore, we cannot find the derivative of the inverse of f at the point -2. This is because f(x) = 4x² - 2 is not invertible at x = 0, since it fails the horizontal line test. In other words, multiple inputs (x values) can produce the same output (y value), so there is not a unique inverse function at x = 0. As a result, the derivative of the inverse function is undefined at this point.
To learn more about function visit: https://brainly.com/question/12431044
#SPJ11
Related Questions
Amir posts a video trailer
Answers
Step-by-step explanation:
He gets five positive reviews
Divide B by 3 then triple the results
Answers
Answer:
It is B
Step-by-step explanation:
B:3=b
bx3=B
2x + 4y = 16
3x - 2y = 8
Solve using substitution method
100 POINTS PLS ANSWER
Answers
Answer:
(4,2) or x=4, y=2
Step-by-step explanation:
As your question asks, we'll solve the system of equations by substitution, where we'll solve for the value of one variable and than substitute that value into the other equation and solve for the two variables
we're given the system:
2x+4y=16
3x-2y=8
Let's take the first equation:
you can isolate either x or y, but I'll do x for this problem
2x+4y=16
subtract 4y from both sides
2x=-4y+16
divide both sides by 2
x=-2y+8
now take the second equation (3x-2y=8) and substitute -2y+8 as x
3(-2y+8)-2y=8
do the distributive property
-6y+24-2y=8
combine like terms
-8y+24=8
subtract 24 from both sides
-8y=-16
divide by -8
y=2
we found the value of y. However, we also need to find the value of x
above, we said that x=-2y+8; since we found the value of y, we can substitute that value into the equation and find x
so:
x=-2(2)+8
x=-4+8
x=4
the answer is x=4, y=2. If you need it as a coordinate point, it's (4,2)
Hope this helps!
In a certain Algebra 2 class of 29 students, 13 of them play basketball and 14 of them play baseball. There are 11 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Answers
P(A and B) = P(A) + P(B) - P(A or B)
where A represents playing basketball, B represents playing baseball, and P(A or B) represents the probability of playing at least one of the sports.
From the given information, we can calculate:
P(A) = 13/29
P(B) = 14/29
P(A or B) = 1 - P(neither) = 1 - 11/29 = 18/29
Substituting these values into the formula, we get:
P(A and B) = 13/29 + 14/29 - 18/29
P(A and B) = 9/29
Therefore, the probability that a student chosen randomly from the class plays both basketball and baseball is 9/29.
A right triangle has a hypotenuse of 26 units. If one leg is 4 more than twice the other, what is the sum of the lengths of the legs, in units
Answers
After solving the quadratic equation, the sum of the lengths of the legs is 11 + (2 x 11 + 4) = 11 + 26 = 37 units.
Let's assume that one leg of the right triangle is x units. According to the problem, the other leg is 4 more than twice the length of x, which can be represented as 2x + 4 units.
Using the Pythagorean theorem, we can set up the equation:
\(x^2 + (2x + 4)^2 = 26^2\)
Expanding and simplifying the equation:
\(x^2 + 4x^2 + 16x + 16 = 676\)
\(5x^2 + 16x - 660 = 0\)
We can now solve this quadratic equation to find the value of x. By summing the lengths of the legs (x + 2x + 4), we can determine the final answer.
After solving the quadratic equation, we find two possible solutions: x = 11 and x = -12. Since the lengths of the sides cannot be negative, we consider x = 11 as the valid solution.
Therefore, the sum of the lengths of the legs is 11 + (2 x 11 + 4) = 11 + 26 = 37 units.
learn more about quadratic equation here:
https://brainly.com/question/30098550
#SPJ11
scarlett is younger than nasim. their ages are consecutive integers. find scarlett's age if the sum of scarlett's age and 5 times nasim's age is 185.
Answers
Given ages represent the consecutive integers and sum of Scarlett's age and five times Nasim age is 185 , then Scarlett age is equal to 30 years.
As given in the question,
Age represents the consecutive integers and Scarlett age is less than Nasim's age.
Let 'x' represent the age of Scarlett
And ' x + 1' represents the age of Nasim
As per the given condition of their ages we have,
x + 5 ( x + 1 ) = 185
⇒ x + 5x + 5 = 185
⇒ 6x + 5 = 185
⇒ 6x = 185 - 5
⇒ 6x = 180
⇒ x = 180 / 6
⇒ x = 30 years
Therefore, for the given ages represent the consecutive integers and sum of Scarlett's age and five times Nasim age is 185 , then Scarlett age is equal to 30 years.
Learn more about consecutive integers here
brainly.com/question/1767889
#SPJ4
problem 3: for the function f (w3, w2, w1) = m1 + m3 + m4 + m6, show how the function f can be implemented using a 3-to-8 binary decoder and what is the truth table of your decoder?
Answers
To implement the function f(w1,w2,w3) = Σ m(0, 2, 4, 5, 7) using a 3 to 8 binary decoder and an OR gate, we can connect the input lines w1, w2, and w3 to the A, B, and C inputs of the decoder, respectively.
To implement the given function f(w1,w2,w3) = Σ m(0, 2, 4, 5, 7), we first need to convert it into a truth table as follows:
w1 w2 w3 f
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 0
1 1 0 1
1 1 1 1
Here, the binary values of w1, w2, and w3 are listed in the first three columns, and the corresponding value of f is listed in the fourth column. The expression Σ m(0, 2, 4, 5, 7) indicates that the function f should be equal to 1 for the minterms 0, 2, 4, 5, and 7.
We can use a 3 to 8 binary decoder to implement this function as follows:
The input lines of the decoder are w1, w2, and w3.
The outputs of the decoder are eight lines labeled Y0, Y1, Y2, Y3, Y4, Y5, Y6, and Y7, each corresponding to one of the possible input combinations of w1, w2, and w3.
The output line corresponding to each minterm that evaluates to 1 is connected to the input of an OR gate.
The output of the OR gate is the output of the function f.
Specifically, we can connect the input lines w1, w2, and w3 to the decoder as follows:
w1 is connected to the A input of the decoder.
w2 is connected to the B input of the decoder.
w3 is connected to the C input of the decoder.
The eight outputs of the decoder are connected to the inputs of an OR gate as follows:
Y0 is not connected to the OR gate since it corresponds to the input combination 000, which is not a minterm in the function.
Y1 is connected to one input of the OR gate since it corresponds to the input combination 001, which is a minterm in the function.
Y2 is not connected to the OR gate since it corresponds to the input combination 010, which is not a minterm in the function.
Y3 is connected to one input of the OR gate since it corresponds to the input combination 011, which is a minterm in the function.
Y4 is connected to one input of the OR gate since it corresponds to the input combination 100, which is a minterm in the function.
Y5 is connected to one input of the OR gate since it corresponds to the input combination 101, which is a minterm in the function.
Y6 is not connected to the OR gate since it corresponds to the input combination 110, which is not a minterm in the function.
Y7 is connected to one input of the OR gate since it corresponds to the input combination 111, which is a minterm in the function.
The other input of the OR gate is connected to ground (or logic 0).
Learn more about 3-to-8 binary decoder here
brainly.com/question/28945040
#SPJ4
Find the greatest common factor of 28 and 63
Answers
Answer:
The Greatest Common Factor (GCF) for 28 and 63, notation CGF(28,63), is 7.
Step-by-step explanation:
The factors of 28 are 1,2,4,7,14,28;
The factors of 63 are 1,3,7,9,21,63.
So, as we can see, the Greatest Common Factor or Divisor is 7, because it is the greatest number that divides evenly into all of them.
Brainlist maybe? :)
In march 2015, the public policy institute of california (ppic) surveyed 7525 likely voters living in california. Ppic researchers find that 68 out of 200 central valley residents approve of the california legislature and that 156 out of 300 bay area residents approve of the california legislature. Ppic is interested in the difference between the proportion of central valley and bay area residents who approve of the california legislature. Ppic researchers calculate that the standard error for the proportion of central valley residents who approve of the california legislature minus bay area residents who approve of the california legislature is about 0. 44. Find the 95% confidence interval to estimate the difference between the proportion of central valley and bay area residents who approve of the california legislature. Responses
Answers
The null hypothesis get rejected comparing the 95% confidence interval to the proportion of the given central valley residents and bay area residents .
As given in the question,
Total number of voters in California = 7525
x₁ = Number of voters of central valley residents approved California legislature
= 68
n₁ = Total number of voters of central valley residents
= 200
x₂ = Number of voters of bay area residents approved California legislature
= 156
n₂= Total number of voters of bay area residents
= 300
p₁ = proportion of voters of central valley
p₂= proportion of voters of bay area
p₁ = x₁/ n₁
= 68/200
= 0.34
p₂ = x₂/n₂
= 156/300
= 0.52
Standard error = √p₁(1 -p₁) / n₁ + p₂( 1- p₂)/n₂
= √0.34(1-0.34) / 200 + 0.52(1-0.52)/ 300
= √0.001122 + 0.000832
= 0.044
\(p_{w}\) = (68 + 156 )/ (200 + 300)
= 0.448
\(q_{w} = 1- p_{w}\)
= 1 - 0.448
= 0.552
null hypothesis p₁ - p₂ = 0
z = ( 0.52 - 0.34 ) - 0/ √(0.448)(0.552)( 1/200 + 1/300)
= 4
Tabular value for confidence interval 95% = 1.96
4 > 1.96
We reject the null hypothesis.
Therefore, the difference of proportion of central valley residents and the bay area residents rejection of null hypothesis as per given 95% confidence interval.
Learn more about confidence interval here
brainly.com/question/24131141
#SPJ4
Let yn be a sequence of constants tending to oo. Let fn(x) be the sequence of functions defined as follows: fn (1/2)=0, Ynin the interval [1/2-1/n,1/2], let fn(x)=-Yn in the interval (1/2,1/2 +1/n and let fn(x) = 0 elsewhere. Show that: (a) fn(x) --> 0 pointwise(b) The convergence is not uniform. (c) fn (x) → 0 in the L^2 sense if Yn= n^1/3 (d) fn(x) does not converge in the L^2 sense if Yn= n
Answers
a) fn(x) → 0 pointwise.
b) The convergence cannot be uniform since there exists a sequence of x values for which the sequence fn(x) does not approach 0 uniformly.
c) ||fn||_2 → 0 as n → ∞. Therefore, fn(x) → 0 in the L^2 sense.
d) ||fn||_2 → ∞ as n → ∞. Therefore, fn(x) does not converge in the L^2 sense.
(a) To show that fn(x) → 0 pointwise, we need to show that for any given x, the sequence fn(x) approaches 0 as n tends to infinity. We consider two cases:
Case 1: x ≤ 1/2 - 1/n for some n. Then fn(x) = 0, so fn(x) → 0 as n → ∞.
Case 2: x > 1/2 - 1/n for all n. Then x ≥ 1/2, so fn(x) = 0 for all n. Hence, fn(x) → 0 as n → ∞.
Therefore, fn(x) → 0 pointwise.
(b) To show that the convergence is not uniform, we need to find an ε > 0 and a sequence of x values such that |fn(x)| > ε for all n sufficiently large.
Let ε = 1/2 and consider the sequence of x values {x_n} where x_n = 1/2 + 1/(2n). For these values of x, we have fn(x_n) = -Y_n > 0. Moreover, fn(x) = 0 for all x outside the interval [1/2 - 1/n, 1/2 + 1/n].
Now, as n tends to infinity, we have Y_n → ∞, so fn(x_n) → -∞. Therefore, the convergence cannot be uniform since there exists a sequence of x values for which the sequence fn(x) does not approach 0 uniformly.
(c) We have Y_n = n^(1/3), so
∫ |fn(x)|^2 dx = ∫_{1/2 - 1/n}^{1/2 + 1/n} Y_n^2 dx
= 2Y_n^2/n
= 2n^(2/3)/n
= 2n^(-1/3)
Thus,
||fn||_2^2 = ∫ |fn(x)|^2 dx ≤ 2n^(-1/3)
So, ||fn||_2 → 0 as n → ∞. Therefore, fn(x) → 0 in the L^2 sense.
(d) We have Y_n = n, so
∫ |fn(x)|^2 dx = ∫_{1/2 - 1/n}^{1/2 + 1/n} n^2 dx
= 2n
Thus,
||fn||_2^2 = ∫ |fn(x)|^2 dx ≤ 2n
So, ||fn||_2 → ∞ as n → ∞. Therefore, fn(x) does not converge in the L^2 sense.
Learn more about converge here:
https://brainly.com/question/29258536
#SPJ11
Which of the following is not included in the cost of merchandise inventory? O Purchase discounts. O Purchase returns and allowances. O Purchase price of the inventory. O Freight costs paid by the seller. O Freight costs paid by the buyer. 4 pts 0 Question 2 Sunshine Cleaning purchased $3,500 worth of merchandise. The seller offered a 2% cash discount. Transportation costs for the buyer were an additional $310. The company returned $240 worth of merchandise and then paid the invoice within the discount period. The total cost of this merchandise is: O $3.570.00. O $3,500.00 O $3,332.00 O $3,430.00. $3,504.80 Question 5 A company has not sales of $759.300 and cost of goods sold of $548.300. Its not income is $10.280. The company's gross margin and operating expenses, respectively, are: O $211.000 and $230,750 $739.550 and $191,720 O $529,020 and $230.750 O $211.000 and $191,720 $230,750 and $529,020 4 pts D D Question 5 A company has not sales of $750,300 and cost of goods sold of $548,300. Its not income is $10.280 The company's groas margin and operating expenses, respectively, arm O $211,000 and $230,750 O $739,550 and $191,720 $529,020 and $230,750 O $211.000 and $191,720 O $230.750 and $529,020 Question 6 Sales less sales discounts, less sales returns and allowances equals: Cost of Goods Sold Net Income O Net Sales O Gross Profit 4 pts 4 pts Goods in transit are included in a purchaser's inventory: O At any time during transit. O After the half-way point between the buyer and seller, When the supplier is responsible for freight charges. When the goods are shipped FOB shipping point. OIf the goods are shipped FOB destination. Question 11 The inventory costing method that smooths out erratic changes in costs is: O LCM. O FIFO. OLIFO. O Specific Identification. O Weighted average. 4 t ne 0 Question 12 Krusty Krab has the following products in its ending inventory Compute lower of cost or market for inventory. applied separately to each product Inventory by Product Product Quantity Cost per Unit 500 $ 500 $ 30 600 Scuba Masks Scuba Sults O $265,000 O $290,000. O $250,000 $268,000 O $275,000. Question 13 Market per Unit $ 550 $ 25 If equity is $368,000 and liabilities are $186,000, then assets equal: O $554,000. $922,000. $368,000. $186,000. O $182,000. 2 pts
Answers
Question 1: The item not included in the cost of merchandise inventory is "Purchase discounts."
2: The total cost of the merchandise is $3,332.00.
5: The company's gross margin and operating expenses, are $211,000 and $191,720.
What is the cost of merchandise inventory?Merchandise inventory expenses normally consist of the price paid for the inventory, deductions from the purchase price resulting from purchase returns and allowances, and freight expenses paid by the purchaser.
Although purchase discounts reduce the cost of merchandise inventory, they are not considered part of it. Instead, they are treated as a distinct discount in the accounting records.
Learn more about merchandise inventory from
https://brainly.com/question/27046371
#SPJ1
Find f(2) if f(x)=-x^2+2x-1
Answers
7 is the value of f(2) in the Linear equation
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
f(x)=-x²+2x-1
f(2) = 2² + 2 * 2 -1
= 4 + 4 - 1
= 8 - 1
= 7
Learn more about Linear equations
brainly.com/question/11897796
#SPJ1
A kite string is 35m long. The angle the string makes with the ground is 50o
.
How far from the person holding the string is a person directly under the kite?
Answers
Answer:
22.50m
Step-by-step explanation:
With the ground, the horizontal ground distance is the adjacent side, so by SOHCAHTOA, the ratio used is cosine, i.e.
Ground distance
= hypotenuse * cos(50°)
= 35 cos(50°)
= 35*0.64279
= 22.50m
I need help! I don't know how to do this
Answers
For the probability distribution of a discrete random variable x
, the sum of the probabilities of all values of x
must be:
a. In the range of zero to 1
.
b. equal to zero.
c. equal to 1
.
d. equal to 0.5
.
Answers
The sum of the probabilities of all values of x must be equal to 1, as this is the total probability of all possible outcomes.
The probability distribution of a discrete random variable x is a mathematical function that provides the probabilities of occurrence of different possible outcomes of x. In probability theory, the sum of the probabilities of all values of x must be equal to 1, since this is the total probability of all possible outcomes. This is because the value of 1 represents the certainty of the event occurring, and if the sum of the probabilities of all the possible outcomes is not equal to 1, the probability of any individual outcome cannot be known. The sum of the probabilities of all values of x must be equal to 1 or it cannot be used to calculate the probability of any individual outcome. The probability of any individual outcome is determined by multiplying the probability of each outcome by the sum of all probabilities.
Learn more about probability here
https://brainly.com/question/11234923
#SPJ4
All of the following expressions are equivalent except _____.
1.)x - 7
2.)7 + (- x)
3.)7 - x
4.)- x + 7
Answers
The normal annual rainfall at stations A, B, C, and D in a basin are
70.55, 57.59, 66.28 and 82.01 cm respectively. In the year 1980, the station D was inop-
erative and the stations A, B and C recorded annual precipitations of 86.11, 74.23 and
81.89 cm respectively, Estimate the rainfall at station D in that year.
Answers
The question asks to estimate the rainfall at station D in the year 1980 based on the rainfall data of other stations. The answer is that station D's rainfall in 1980 can be estimated by comparing the rainfall patterns of all stations in the basin.
To estimate the rainfall at station D in 1980, we can analyze the relationship between the rainfall at different stations. In this case, we can observe that there is a correlation between the annual rainfall at stations A, B, C, and D. By comparing the rainfall patterns of these stations, we can make an estimation for station D.
In the given data, station D is inoperative in 1980, but the rainfall data for stations A, B, and C are available. By analyzing the rainfall patterns in previous years and considering the correlation between the stations, we can estimate the rainfall at station D in 1980 based on the rainfall data of the other stations in the basin.
Learn more abut inoperative here: brainly.com/question/30889685
#SPJ11
A marine biologist compared two large pools that could be used for a new dolphin training arena. Pool A held 2×1010
gallons, and pool B held 2×108
gallons. How many times more gallons will the larger pool hold than the smaller pool?
Responses
4
20
100
200 Please help im really slow rn tbh giving 40 points thank you
Answers
\(\huge\mathcal{\fcolorbox{Aqua}{azure}{\red{➳Answer}}}\)
The larger pool will hold is 100 times more gallons than the smaller pool
From the question, we are to determine how many times more gallons the larger pool holds than the smaller pool.
From the given information,
Capacity of the larger pool = 2 × 10¹⁰ gallons
Capacity of the smaller pool = 2 × 10⁸ gallons
we will simply divide the capacity of the larger pool by the capacity of the smaller pool.
That is,
2×10^10÷2×10^8
=10^2
=100
Thus, the answer is 100 times
Hope it helps you
Mark the above user as brainliest
\(\red{\rule{200pt}{5pt}}\)
\(\bold{Thank~you~:)}\)
What does the Harby-Weinberg equation?
Answers
The equation is represented as follows:
p^2 + 2pq + q^2 = 1
The Hardy-Weinberg equation is a mathematical formula used in genetics to predict the frequency of genetic traits in a population. The equation is named after the scientists G. H. Hardy and W. Weinberg, who independently developed it in 1908 and 1909, respectively.
The equation states that the frequency of a genetic trait in a population will remain constant over time as long as certain conditions are met. These conditions are:
No mutations occur in the gene responsible for the trait
There is no natural selection for or against the trait
There is random mating within the population
The population size is large
The Hardy-Weinberg equation can be used to calculate the frequency of the dominant and recessive alleles (versions of a gene) in a population, and the probability of different genotypes (the combination of alleles an individual has) and phenotypes (the physical expression of the trait) within that population.
Where p is the frequency of the dominant allele, q is the frequency of the recessive allele, and p^2 represents the proportion of homozygous dominant individuals, 2pq represents the proportion of heterozygous individuals and q^2 represents the proportion of homozygous recessive individuals.
The Hardy-Weinberg equation is a useful tool for understanding how genetic traits are inherited and how they change over time. It is widely used in population genetics, evolutionary biology and medical genetics.
It is also important to notice that the Hardy-Weinberg equilibrium is a theoretical concept that is rarely met in real populations due to the existence of genetic drift, migration, mutation, nonrandom mating and natural selection.
to know more about equation refer here
https://brainly.com/question/29657992#
#SPJ11
Derrick is outside playing basketball with his friend Bryce. Derrick is óft tall and at this time of day is casting a 13ft shadow. The basketball hoop is 10ft tall. How long is the basketball hoop's shadow? * Your answer
Answers
Answer:
21ft
Step-by-step explanation:
The probability of randomly hitting a bullseye on a dartboard with radius 12 inches depends on the size of the bullseye Thus the probability is a function of the size If this function is called PS?
Answers
If we denote the probability of hitting a bullseye on a dartboard with radius 12 inches as a function of the size of the bullseye, we can refer to this function as PS.
The function PS represents the probability of hitting the bullseye and is dependent on the size of the bullseye. The larger the bullseye, the higher the probability of hitting it, and vice versa. By adjusting the size of the bullseye, we can determine the corresponding probability of hitting it using the function PS.
It's important to note that without specific information about the relationship between the bullseye size and the probability, it's not possible to provide a specific mathematical expression or further details about the PS function. The function would need to be defined or provided to calculate the probability accurately.
learn more about "probability ":- https://brainly.com/question/25839839
#SPJ11
how do you multiply a square root by a square root and a whole number?
for example, the square root of 5 times (4 times the square root of 5) is 20, but i don’t understand how rob solve for this thanks!
Answers
To multiply a square root by a square root and a whole number, you can use the distributive property of multiplication
Given data ,
Let the numbers be represented by the expression A
Now , the value of A is
A = √2 × 3√5
First, you can simplify each square root:
√2 = 1.4142 (rounded to 4 decimal places)
3√5 = 5.1962 (rounded to 4 decimal places)
Next, you can multiply the two simplified square roots and the whole number:
√2 × 3√5 = 1.4142 × 5.1962 × 3
= 22.3607 × 3
= 67.0821
Hence , the expression is A = √2 × 3√5 = 67.0821
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
In 1972 a Honda Civic went for $2000, today a Honda civic sells for around $25000. The rate of inflation is %
Answers
Answer:
5.1%
Step-by-step explanation:
You want the rate of inflation if the price of a Honda Civic increase from $2000 in 1972 to $25000 in 2023.
InflationThe rate of inflation can be computed from ...
r = (p1/p0)^(1/t) -1
r = (25000/2000)^(1/51) -1 ≈ 0.05077 ≈ 5.1%
The rate of inflation is about 5.1%.
__
Additional comment
The question refers to "today," but we don't know exactly what is intended by that. The year at the time of this writing has been used. The required answer may vary, depending on the intended number of years.
<95141404393>
I need help ASAP!! If you know what you’re doing go ahead and answer but if you don’t, don’t even bother thanks
Answers
Answer:
133.97 cm³
Step-by-step explanation:
The volume of a cone is given by:
\(V = \frac13 \pi r^2h\)
r is half the diameter, so 4 cm
h is 8 cm
So:
V= 1/3 * 3.14 * 16 * 8 ≈ 133.97 cm³
Solution: 3.14*r^2 *h/3
r: 8
h:3
3.14*8^2*8/3
Plot the vector field F(x,y)=(xy,x+y^2) Calculate divF.
Determine where divF>0 and where divF<0.
Answers
The divergence of the vector field F is positive for y > -1/3 and negative for y < -1/3.
To plot the vector field F(x, y) = (xy, x + y^2), we can first visualize the vectors at various points in the xy-plane. Let's choose a range of values for x and y and calculate the corresponding vectors. We'll use a step size of 1 for simplicity.
Here is a sample grid of points and their corresponding vectors:
(x, y) = (-2, -2) -> F(-2, -2) = (4, 2)
(x, y) = (-1, -2) -> F(-1, -2) = (2, 2)
(x, y) = (0, -2) -> F(0, -2) = (0, 2)
(x, y) = (1, -2) -> F(1, -2) = (0, 2)
(x, y) = (2, -2) -> F(2, -2) = (4, 2)
(x, y) = (-2, -1) -> F(-2, -1) = (2, 1)
(x, y) = (-1, -1) -> F(-1, -1) = (1, 1)
(x, y) = (0, -1) -> F(0, -1) = (0, 1)
(x, y) = (1, -1) -> F(1, -1) = (0, 1)
(x, y) = (2, -1) -> F(2, -1) = (2, 1)
... and so on for other values of y and for positive values of y.
To calculate the divergence (divF) of the vector field, we need to find the partial derivatives of the components of F with respect to x and y. Then we sum these partial derivatives.
F(x, y) = (xy, x + y^2)
∂F/∂x = y
∂F/∂y = 1 + 2y
divF = ∂F/∂x + ∂F/∂y = y + (1 + 2y) = 3y + 1
Now, we can analyze where the divergence is positive (divF > 0) and where it is negative (divF < 0).
For divF > 0:
If y > -1/3, then divF > 0.
For divF < 0:
If y < -1/3, then divF < 0.
Know more about vector field here;
https://brainly.com/question/102477
#SPJ11
Simple question
Find the measure of the angle indicated.
Answers
help if you have time !
Answers
Answer:
72 Bricks would be needed.
Step-by-step explanation:
24 * 2 = 48
12 * 2 = 24
48 + 24 = 72
change 7/8 as a fraction in simplest form
Answers
Answer:
It's already it in it's simplest form. You can find the simplest form by dividing the fraction by two ( 4/8 for example, you can divide 4 by two, giving you 2, and divided 8 by two, giving you 4, which makes 2/4, and do it once more, giving you 1/2.
Ava sells pottery at a market. Each piece of pottery costs $4.50 to make. Ava marks up the pottery by 250%. She then decides to have a sale of 30% off the retail price. What is the discounted price of each piece of pottery?
Answers
Thus, the discounted price on the retail price of each piece of pottery is found to be: Discounted price = $11.025.
Explain about the discounted price?The interest rate that is adjusted to the projected cash flows of either an investment to determine its present value is referred to as the discount rate. The expected rate of return on investment that businesses or investors anticipate. The viability of an investment can be determined by computing the net present value via discounting.
Cost price = $4.50
Percentage increase = 250%.
Marked price = 4.50 + 2.5*4.50
Marked price = $15.75
Discount = 30%
Discounted price = 15.75 - 0.30*15.75
Discounted price = $11.025
Thus, the discounted price on the retail price of each piece of pottery is found to be: Discounted price = $11.025.
Know more about the discounted price
https://brainly.com/question/23865811
#SPJ1
Please help this is due in ten minutes!!!!!!!!!!!!
Use the figure to find the measures of <1 and <2.
