The radius of convergence of series (cn dn)xn is 14.
The radius of convergence of a power series (cn xn) is the distance from the origin to the point beyond which the series no longer converges. It is denoted by R and it's calculated by using the formula:
R = 1/lim sup|cn|^(1/n)
The radius of convergence of a product of two series (cn xn) and (dn xn) is the minimum of the radius of convergence of the individual series.
So, in this case, since the radius of convergence of the series cn xn is 14 and the radius of convergence of the series dn xn is 15, the radius of convergence of the product series (cn dn)xn is
min(14, 15) = 14
Therefore, the radius of convergence of the product series (cn dn)xn is 14.
To know more on radius of convergence of series
https://brainly.com/question/30167798
#SPJ4
Find Z and X in each diagram below using the given area under the curve
The values of Z and X, considering the normal curve, are given as follows:
Z = -1.175.X = 115.3.How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution, which is the area to the left under the normal curve.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 120, \sigma = 4[/tex]
The p-value is of 0.12, hence the z-score is given as follows:
-1.175.
Then the value of X is obtained as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
-1.175 = (X - 120)/4
X - 120 = -1.175 x 4
X = 115.3.
More can be learned about the normal distribution at https://brainly.com/question/25800303
#SPJ1
To win the game, eitan has to roll a sum of 11 or more using two six-sided number cubes. asher has a better probability of winning than eitan has. which could be the outcome that asher needs to win the game? check all that apply.
The outcome Asher needs to win the game are 2, 3, 4, 5, 6, 7, 8, 9, 10.
We get the above answer following the given method.
We have been given the information that there are 2 six-sided number cubes and Eitan needs to roll a sum of 11 or more.
The possible outcomes for rolling two six-sided number cubes are the integers from 2 to 12. In order for Asher to have a better probability of winning than Eitan, Asher's winning outcome must be a lower number than Eitan's winning outcome of 11. The possible winning outcomes for Asher are therefore 2, 3, 4, 5, 6, 7, 8, 9, 10. So the possible outcomes that Asher needs to win the game are 2, 3, 4, 5, 6, 7, 8, 9, 10.
Read more about Probability from:
https://brainly.com/question/11034287
#SPJ4
joel is planning to paint the outside of his house. he wants a green paint that requires 3 parts blue paint to 2 parts yellow paint. if he needs a total of 10 gallons to paint the whole house, how many gallons of blue paint does he need?
Joel needs 1.5 gallons of blue paint.
Joel needs a total of 10 gallons of paint to paint the outside of his house. Since the ratio is 3 parts blue paint to 2 parts yellow paint, we can use proportions to solve for the amount of blue paint needed.
We can set up the proportion like this:
3/2 = x/10
We can solve for x (the amount of blue paint) by cross-multiplying:
3*10 = 2*x
3*10 = 20x
20x = 30
x = 30/20
x = 1.5
Joel needs 1.5 gallons of blue paint.
Learn more about proportion here:
https://brainly.com/question/7096655
#SPJ4
1) a man flies a kite at a height of 120 m. the wind carries the kite horizontally away from him at a rate of 6 m/sec. how fast is the distance between the man and the kite changing when the kite is 130 m away from him?
So, on solving the provided question, we can say that, here by differential equations So, 2(400)(25) = 2(500)(dy/dt) => [tex]dy/dt = 20 ft/sec[/tex]
What is differential equation?
Sequences in which the difference between succeeding terms is constant are known as arithmetic progressions. For instance, an arithmetic progression with a tolerance of 2 is the sequence 5, 7, 9, 11, 13, and so on. An arithmetic progression (A.P.) is a progression where the tolerance between two succeeding numbers is always the same.
Let x be the girl's distance from the kite at time t and y be the length of the string at that same moment.
The right triangle at time t has a hypotenuse of length y, a hypotenuse of length 300, and a hypotenuse of length x.
[tex]dx/dt = 25[/tex]
By the Pythagorean Theorem,
[tex]x2 + 3002 = y2[/tex]
[tex]2x(dx/dt) = 2y(dy/dt)[/tex]
Since [tex]x2 + 3002 = y2 and y = 500, x = 400[/tex]
So, 2(400)(25) = 2(500)(dy/dt)
[tex]dy/dt = 20 ft/sec[/tex]
To know more about differential equations visit:
brainly.com/question/28099315
#SPJ4
the number of inches in the perimeter of an equilateral triangle equals the number of square inches in the area of its circumscribed circle. what is the radius, in inches, of the circle? express your answer in terms of pi and in simplest radical form.
The radius of the circle, in inches, is (2√6)/π.
The perimeter of an equilateral triangle is equal to 3 times its side length. We know that the area of a circle is equal to πr2, where r is the radius of the circle. Therefore, the radius of the circle, in inches, is equal to the square root of (3*s2)/π, where s is the length of the side of the triangle.
For example, if the length of the side of the triangle is 8 inches, then the radius of the circle is equal to the square root of [(3*82)/π] = (24/π) inches. Simplifying this into simplest radical form, we get (2√6)/π inches. Thus, the radius of the circle, in inches, is (2√6)/π.
Learn more about equilateral triangle here:
https://brainly.com/question/3461022
#SPJ4
please help me answer this question
Check the picture below.
notice, times where he stops, is time where distance is not added however time elapses, meaning we get a straight line, when chatting with his friend, it went from 10 minutes to 15 minutes over the same 800 meters, in other words, he never moved, time kept on going for 5 minutes. When he gets back home, distance goes from 2000 meters to 0 meters, 0 meters because he's back at 0 distance after 90 minutes.
2. A flagpole stands in the center of a square, and the distance from the base of the
pole to each corner of the square is 8 feet. How tall is the flagpole?
This is the answer above mentioned
The annual profits for a company are given in the following table, where x represents the number of years since 2006, and y represents the profit in thousands of dollars. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the projected profit (in thousands of dollars) for 2015, rounded to the nearest thousand dollars.
Regression equation:
Final answer in thousand dollars:
Answer: Hello how are you doing today?
Step-by-step explanation: How may I help you?
Ellen has a pencil 2x + 1/5cm long. Tom has a pencil 5x + 2/5cm long. How much longer is Tom's pencil than Ellen's?
The difference of length of Tom's pencil from Ellen's pencil is given by the equation A = 3x + 1/5 cm
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the difference of length be represented as A
Now , the equation will be
The length of Ellen's pencil is p = 2x + 1/5 cm
The length of Tom's pencil is q = 5x + 2/5 cm
Now , the difference of length A = q - p
Substituting the values in the equation , we get
The difference of length A = 5x + 2/5 cm - 2x + 1/5 cm
On simplifying the equation , we get
The difference of length A = ( 5x - 2x ) + ( 2/5 - 1/5 ) cm
The difference of length A = 3x + 1/5 cm
Therefore , Tom's pencil is longer than Ellen's pencil by 3x + 1/5 cm
Hence , the equation is A = 3x + 1/5 cm
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
Find two rael numbers whose is sum 12 and whose product is 36
Sry I thought I knew the answer and posted it, and do not know how to delete it so I leave u with this.
Which two numbers below will you set the inside of the absolute value to in the beginning of your work?
|3x-8|=4
A. 4 and -4
B. 2 and -2
C. 3 and -4
D. 8 and -8
Answer:
I think the answer is A. I hope this is helpful
Multiply. x^2-1/5xy * x^2y/1+x
The required expression is x(x - 1)/5 which is determined by multiplication.
The expression is given in the question, as follows:
(x² - 1)/5xy × x²y/(1 + x)
We have to determine the solution to the given expression by multiplication.
As per the given expression, we have
⇒ (x² - 1)/5xy × x²y/(1 + x)
Cancel out the equivalent terms in the above expression,
⇒ (x - 1)(x + 1)/5 × x/(1 + x)
Reduce the same in the above expression,
⇒ x(x - 1)/5
The required expression is x(x - 1)/5.
Learn more about Expressions here :
brainly.com/question/21751419
#SPJ1
A school of salmon was swimming in the river 5 feet below the surface. To escape a hungry bear, they went down another 3 feet.
What is the position of the salmon now relative to the surface?
Using the addition operation, the position of the salmon currently relative to the surface is 8 feet below the surface.
What is the addition operation?The addition operation is one of the four basic mathematical operations, including subtraction, division, and multiplication.
The addition operation involves adding two or more addends to get a result known as the sum or total, using the equal symbol (=) and the addition operand (+).
The initial position of the school of salmon below the surface = 5 feet
The depth they went down further to escape the bear = 3 feet
The current position = 8 feet (5 + 3) below the surface.
Thus, based on the addition operation, the school of salmon can be located 8 feet below the surface as they attempted to escape the hungry bear.
Learn more about mathematical operations at https://brainly.com/question/4721701
#SPJ1
evaluate the indefinite integral as an infinite series. integral cos(x) − 1/ x dx
∑[infinity]n=1+C
The infinite series for the given indefinite integral will be as [tex]\int\ {\frac{cos(x) - 1}{x} } \, dx[/tex] Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n}}{(2n)} . \frac{1}{(2n)!} + C[/tex].
We know that the infinite series also called as Maclaurin series
the Maclaurin series for cos(x)
cos(x) = Σ[infinity]n=0 [tex](-1)^n \frac{x^{2n}}{(2n)!}[/tex]
cos(x) = [tex]1 - \frac{x^2}{2!} + \frac{x^4}{4!} - .. + (-1)^n \frac{x^{2n}}{(2n)!}[/tex]
cos(x) - 1 = Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n}}{(2n)!}[/tex]
Now, divide both sides by x
cos(x) -1/x = Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n-1}}{(2n)!}[/tex]
[tex]\int\ {\frac{cos(x) - 1}{x} } \, dx =[/tex] [tex]\int { } \,[/tex] Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n-1}}{(2n)!} dx[/tex]
or [tex]\int\ {\frac{cos(x) - 1}{x} } \, dx =[/tex] Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n}}{(2n)} . \frac{1}{(2n)!} + C[/tex]
Therefore, [tex]\int\ {\frac{cos(x) - 1}{x} } \, dx =[/tex] Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n}}{(2n)} . \frac{1}{(2n)!} + C[/tex]
To learn more about the Maclaurin series:
https://brainly.com/question/27946299
#SPJ4
Evaluate the function.
p(x) = 3x^3 -x^2; Find p(2)
Answer:
20
Step-by-step explanation:
Given the function:
[tex]p(x)=3x^3-x^2[/tex]
We need to find p(2)
This means we need to find the value of the function when x is 2
[tex]p(2)=3*2^3-2^2=3*8-4=24-4=20[/tex]
Hope this helps :)
Have a great day!
Observational data that contains a numerical value or amount is called: _________
Observational data that contains a numerical value or amount is called Quantitative observation.
What is observational data?
An observational study draws conclusions from a sample to a population in disciplines like epidemiology, social sciences, psychology, and statistics when the independent variable is not under the researcher's control due to ethical considerations or logistical limitations.
Observational data in market research refers to information gathered without the research subject (such as a specific client, patient, employee, etc.) having to be explicitly involved in documenting what they are doing.
An objective collection of data, quantitative observation refers to "associated to, of or depicted in terms of a quantity" and is primarily focused on numbers and values.
Methods of statistical and numerical analysis are used to derive the results of quantitative observation.
Hence, observational data that contains a numerical value or amount is called Quantitative observation.
To know more about observational data, click on the link
https://brainly.com/question/14393640
#SPJ4
a financial analyst wants to estimate the difference in the mean growth for all large- and small-cap stocks for the last 60 days. he selects a random sample of 30 large-cap stocks and 30 small-cap stocks from the large populations of large- and small-cap stocks. are the conditions for constructing a 90% confidence interval for the difference in the true mean growth of all large- and small-cap stocks for the last 60 days met? random: 10%: normal/large sample:
Yes, the conditions for constructing a 90% confidence interval for the difference in the true mean growth of all large- and small-cap stocks for the last 60 days are met.
Shares of businesses having a market value between $300 million and $2 billion are considered small-cap stocks. Small-cap firms have the potential for rapid development, which makes them attractive investment targets even if their stocks may be more volatile and carry greater risks for buyers.
Large-cap stocks, commonly referred to as large caps, are stocks that are traded for businesses with a market value of at least $10 billion. Because investors gravitate toward quality and stability and become more risk-averse during challenging markets, large-cap companies often exhibit lower volatility.
Thus, the conditions for constructing a 90% confidence interval for the difference in the true mean growth of all large- and small-cap stocks for the last 60 days are met.
To know more about sample visit: brainly.com/question/11045407
#SPJ4
you record the number x of runs scored by the winning team and the number y of runs scored by the losing team for each softball game in a team's season. does the relation necessarily represent a function? explain.
No the relation doesn't necessarily represent a function.
The term function is known as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Here we have given that you record the number x of runs scored by the winning team and the number y of runs scored by the losing team for each softball game in a team's season.
As we all know that in any two games here we have given that if the winning teams had the same numbers of runs while the losing teams had different numbers of runs then the given relation is not a function.
Here we have to remember that for a relationship to be a function then it must be fulfilled and it is possible for every input value there must be only one output value
To know more about function here
https://brainly.com/question/28193995
#SPJ4
Round off 987 416 to the nearest 5
round off 987 416 to the nearest 5 mean the 6 turns into 5 so the answer is 987 415.If the 6 was 2 the 2 will turn into 0 and if the 6 was 9 the 9 will turn into 10
Which is closest to the volume of Mike's cup?
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=7 \end{cases}\implies V=\cfrac{\pi (3)^2(7)}{3} \\\\\\ V=21\pi \implies {\Large \begin{array}{llll} V\approx 65.97 \end{array}} ~in^3 ~~ \approx 66~in^3[/tex]
the diameter of a wheel of a car is 50 cm. if the car travels at an average speed of 36 km per hour, what is the number of revolutions made by the wheel per minute? (use
The number of revolutions per minute made by the wheel of a car with a diameter of 50 cm travelling at an average speed of 36 km/hr is 226.7 revolutions per minute.
Number of revolutions per minute = (36 x 1000) / (50 x 3.14) = 226.7 revolutions per minute
1. Convert the speed from kilometers to meters per hour
36 km/hr = 36 x 1000 m/hr
2. Calculate the circumference of the wheel
Circumference of wheel = Diameter x π
Circumference of wheel = 50 cm x 3.14 = 157 cm
3. Calculate the number of revolutions per minute
Number of revolutions per minute = (Speed in m/hr) / (Circumference of wheel in cm)
Number of revolutions per minute = (36 x 1000) / (50 x 3.14) = 226.7 revolutions per minute
The number of revolutions per minute made by the wheel of a car with a diameter of 50 cm travelling at an average speed of 36 km/hr is 226.7 revolutions per minute.
Learn more about average here
https://brainly.com/question/24057012
#SPJ4
Factorise the following.
x^2-4
Answer:
(x - 2)(x + 2)
Step-by-step explanation:
x² - 4 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , then
x² - 4
= x² - 2²
= (x - 2)(x + 2) ← in factored form
In the given figure, triangle QPS = triangle SRQ.Find each value.
(a) x (b)angle PQS (c)angle PSR
In the given figure, where triangle QPS = triangle SRQ, the value of
a. x = 47°
b. ∠PQS = 32°
c. ∠PSR = 74°
What is a triangle?A triangle is a 3-sided polygon that is occasionally (though not very frequently) referred to as the trigon. Every triangle has three sides and three angles, some of which might be the same.
In a right triangle, the two sides opposite the right angle are referred to as the hypotenuse, and the other two sides are referred to as the legs. All triangles are bicentric and convex. The triangle's interior is that part of the plane it encloses; the exterior is the rest.
Given that ∆QPS ≈ ∆SRQ
a) ∠QPS = ∠QRS
106° = 2x + 12
106° - 12 = 2x
2x = 94°
x = 47°
b) ∠RSQ = ∠PQS
∠SQR + ∠SRQ + ∠RSQ = 180°
42° + 2(47°) + 12 + ∠RSQ = 180°
148 + ∠RSQ = 180°
∠RSQ = 180° - 148°
∠RSQ = 32°
∠PQS = 32°
c) ∠PSR = ∠PSQ + ∠RSQ
[ ∠PSQ = 42° = ∠SQR ; ∠RSQ = 32°]
∠PSR = 42° + 32°
∠PSR = 74°
Thus, In the given figure, where triangle QPS = triangle SRQ, the value of x = 47°, ∠PQS = 32°, ∠PSR = 74°.
Learn more about triangle
https://brainly.com/question/2773823
#SPJ1
Using f(x) = 2x-3 and g(x) = 5, find f(g(3)).
7
5
3
0
None of the choices are correct.
Answer: 7
Step-by-step explanation:
[tex]g(3)=5 \implies f(g(3))=f(5)=2(5)-3=7[/tex]
Describe each correlation value.
A. r = 0.921
B. r=-0.873
C. r = -0.281
D. r = 0.303
[Select]
[Select]
[Select]
[Select]
>
>
The correlation coefficient having -negative value means inverse correlation and +positive value means direct relationship.
What Is the Correlation Coefficient?An analytical way to gauge how strongly two variables are linearly related is to use the correlation coefficient. Anywhere between -1 and 1 can be its value. A correlation coefficient of -1 indicates a perfect negative, inverse, or inverse-correlation, where values in one series increase as those in the other decline and vice versa. An exact positive correlation or direct relationship is indicated by a coefficient of 1, or 1. In the absence of a linear relationship, a correlation coefficient of 0 indicates.
When evaluating the level of association between two variables, factors, or data sets, scientists and financiers alike use correlation coefficients. Assuming, for instance, that there is a strong positive correlation between oil prices and forward returns on oil stocks given that high oil prices are advantageous for crude producers
Now,
For
A. r = 0.921 -Direct relationship.
B. r= -0.873 -Inverse relationship.
C. r = -0.281 -Inverse relationship.
D. r = 0.303 -Direct relationship.
To know more about correlation coefficient visit the link
brainly.com/question/15577278
#SPJ1
Solve for X, Leave in simplest radical form.
Hope it helps.
If you have any query, feel free to ask.
Assume that the number of liters of water remaining in the bathtub varies
quadratically with the number of minutes which have elapsed since you
pulled the plug. a. If the tub has 38.4, 21.6, and 9.6 liters remaining at 1, 2, and 3 minutes,
respectively, since you pulled the plug, find a function V(t) expressing the
volume of water t minutes after you pulled the plug.
b. How much water was in the tub when you pulled the plug?
c. When will the tub be empty?d. In the real world, the number of liters of water in the tub can never be
negative. What does the model predict is the least amount of water in the
tub? Is this number reasonable?e. Draw a graph of the function in the appropriate domain. Use a dotted curve
for any portion of the graph that is outside the reasonable domain.f. What is the reasonable domain and range for this model?g. Why is a quadratic function more reasonable for this problem than a linear
function would be?
The function expressing the volume of water t minutes after the plug was pulled is V(t) = -2.4t^2 + 11.2t + 46,b)tub had 46 liters of water when the plug was pulled and will be empty at 2.16 minutes,c) the least amount of water predicted by the model is -52.6667 liters which is not reasonable as the volume of water can't be negative.
What is parabola ?
A parabola is a symmetric, U-shaped geometric shape.
a)V(1) = 38.4 = a(1)^2 + b(1) + c
V(2) = 21.6 = a(2)^2 + b(2) + c
V(3) = 9.6 = a(3)^2 + b(3) + c
Solving the system of equations, we get ,
a = -2.4 , b = 11.2 , c = 46 , V(t) = -2.4t^2 + 11.2t + 46.
b)We can find the initial volume of water in the tub by plugging in t = 0 into the function V(t) = -2.4t^2 + 11.2t + 46. This gives us V(0) = 46 liters, so the tub had 46 liters of water when the plug was pulled.
c)t = (-11.2 +/- sqrt(11.2^2 - 4*(-2.4)46))/(2(-2.4))
t = (11.2 +/- sqrt(124.48 + 552.8))/-4.8
t = (11.2 +/- sqrt(677.28))/-4.8 = (11.2 +/- 26.16)/-4.8 = -14.96 or 2.16
d)V(4.6667) = -2.4*(4.6667)^2 + 11.2*(4.6667) + 46 = -2.4*21.778 + 46.4 + 46 = -52.6667. So the least amount of water the model predict is -52.6667 liters. This number is not reasonable as the volume of water can't be negative.
e) The graph of the function V(t) = -2.4t^2 + 11.2t + 46 is a parabola that opens downward and has its vertex at (4.6667, -52.6667). Any portion of the graph for t < 0 or t > 2.
The function expressing the volume of water t minutes after the plug was pulled is V(t) = -2.4t^2 + 11.2t + 46,b)tub had 46 liters of water when the plug was pulled and will be empty at 2.16 minutes,c) the least amount of water predicted by the model is -52.6667 liters which is not reasonable as the volume of water can't be negative.
To learn more about parabola visit : brainly.com/question/21685473
#SPJ4
Examine the composite figure formed by placing a triangular prism on top of a rectangular prism. All of the measurements have centimeters as their units.
The triangular base has height 12, base 14 & 2 other sides 13 & 15. The prism height is 20. The rectangular prism is 8 by 14 by 20. The prisms share a face that is 14 by 20.
© 2018 StrongMind
To find the surface area, Brad splits the figure into two pieces, the rectangular prism and the triangular prism.
He finds the total surface area of the rectangular prism by finding the area of each face to get 1,104 cm2.
He then finds the total surface area of the triangular prism by finding the area of each face to get 1,008 cm2.
Finally, he adds the surface areas together to get 2,112 cm2.
Is Brad's solution correct? Why or why not?
Answer:
Step-by-step explanation:
Brad's solution to find the surface area of the composite figure is not correct.
In his solution, Brad adds the surface areas of the triangular prism and the rectangular prism separately,
but it's not taking into account that the two prisms share a face that is 14 by 20.
When finding the surface area of a composite figure, it's important to take into account any shared faces.
Since the two prisms share a face that is 14 by 20, Brad should subtract this area from one of the prisms,
otherwise he will be counting it twice in the final result.
The correct method would be:
Rectangular prism: (2 * 8 * 14) + (2 * 14 * 20) + (2 * 8 * 20) = 1,104 cm^2
Triangular prism: (1/2 * 14 * 12) + (1/2 * 13 * 15) + (3 * 14 * 20) = 1,008 cm^2
Subtracting shared area: 1,104 cm^2 + 1,008 cm^2 - (14 * 20) = 2,096 cm^2.
So Brad's solution is incorrect, the correct surface area of the composite figure is 2,096 cm^2.
Answer:90x567
Step-by-step explanation:
Element X decays radioactively with half life of 6 minutes. If there are 220 grams of
Element X, how long,
decay to 26 grams?
to the nearest tenth of a minute, would it take the element to decay 26 grams?
The element X will take 7.3 minutes to decay to 26 grams.
What is radioactive radiation?Radioactive radiations are the radiations that an atom nucleus releases.
It is a sequence of numbers that have common differences.
The decaying acts like an arithmetic progression in which a=670,d=-30.45 (per minute decaying), and n we have to find with the value of 26 grams.
So, the formula of the nth term of an arithmetic progression is
nth term=a+(n-1)d
26=220+(n-1) x (-30.45)
-194=-30.45n+30.45
-224.45 =-30.45n
n=7.3 (after rounding off)
Hence the element X would take 22.10 minutes to decay to 26 grams.
Learn more about arithmetic progression at brainly.com/question/6561461
#SPJ1
Find the gradient vector field ∇f of f and sketch it.
f(x, y) = 7 x2 + y2
∇f(x, y) =
The gradient vector field ∇f of f(x, y) = 7 x2 + y2 is ∇f(x, y) = <14x, 2y>.
The gradient vector field ∇f of a scalar function f(x, y) is given by the vector function
∇f(x, y) = <∂f/∂x, ∂f/∂y>.
In this case, the function f(x, y) = 7x^2 + y^2 and we can find the gradient vector field as follows:
∇f(x, y) = <∂f/∂x, ∂f/∂y> = <14x, 2y>
This vector field points in the direction of steepest ascent at each point in the xy-plane, and its magnitude at each point is equal to the rate of change of f in that direction.
To sketch the gradient vector field, we can plot the vector <14x, 2y> at various points in the xy-plane. The direction of the vector at each point will be the direction of steepest ascent of the function f, and the length of the vector will indicate the rate of change of f in that direction.
We can notice that for the function f(x,y) = 7x^2+y^2, the function is always increasing as we move along the direction of the vector <14x,2y> and the vectors are always pointing away from the origin, which means that the origin is a local minimum of the function.
It's important to note that this is a paraboloid. The direction of steepest ascent is the direction of the tangent of the paraboloid at any point, which is pointing upwards from the vertex of the paraboloid.
To know more on gradient vector field
https://brainly.com/question/29815461
#SPJ4
