Is the function \(f(x)=\sqrt{x}\) differentiable at x=0 and continuous over R?
Answers
Answer: No
Explanation:
Apply the derivative
\(f(x) = \sqrt{x}\\\\f(x) = x^{1/2}\\\\f'(x) = (1/2)x^{-1/2}\\\\f'(x) = \frac{1}{2x^{1/2}}\\\\f'(x) = \frac{1}{2\sqrt{x}}\\\\\)
Though we run into a problem since f ' (0) is undefined, due to the zero in the denominator.
Therefore, f(x) is not differentiable at x = 0.
The function is continuous, but only on the interval \(x \ge 0\) and not over the entire set of real numbers R.
Related Questions
write a function calculatenum that takes one integer parameter and returns the parameter minus 3. ex: calculatenum(3) returns 0.
Answers
The function `calculatenum` subtracts 3 from the input parameter `num` and returns the result.
What is an integer?Counting numbers (positive and negative), together with zero, are grouped together as integers because they may be written without a fractional component.
Here's a Python function called `calculatenum` that takes an integer parameter and subtracts 3 from it:
def calculatenum(num):
"""
Subtracts 3 from the given parameter.
Parameters:
num (int): The integer value to be subtracted from.
Returns:
int: The result of subtracting 3 from the given parameter.
"""
result = num - 3
return result
The calculatenum function takes one integer parameter called num and subtracts 3 from it. It then returns the result of the subtraction. For example, if you call calculatenum(3), it will return the value 0, since 3 - 3 equals 0.
The function `calculatenum` subtracts 3 from the input parameter `num` and returns the result.
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help this homework was due last month!!!!!!!!!
Answers
Option D is correct, a dilation by a scale factor of 2, centered at the origin, followed by the translation (x, y) --> (x + 5, y)
Dilate triangle ABC by a scale factor of 2, centered at the origin.
This will stretch the triangle by a factor of 2 in both the x and y directions.
Perform a translation of the dilated triangle by 5 units to the right (in the positive x-direction) and leave the y-coordinate unchanged.
This sequence of transformations will match the corresponding vertices of triangle ABC to triangle DEF, resulting in the desired transformation.
Hence, a dilation by a scale factor of 2, centered at the origin, followed by the translation (x, y) --> (x + 5, y)
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Find the 57th term of the following arithmetic sequence. 13, 20, 27, 34
Answers
Answer:
\({ \tt{n _{th} = a + (n - 1)d}} \\ { \tt{n _{57} = 13 + (57 - 1) \times 7}} \\ { \tt{n _{57} = 405}}\)
10^2 x 10^6 x 10 using single exponent
Answers
Step-by-step explanation:
10^2 + 10^6 + 10^1 = 10 ^(2+6+1) = 10 ^9
The fastest car on earth can travel 500 miles in
50 minutes. What is the average velocity and
speed, in mph, of this car if it was entered in the
Indy 500 and never had to use a pit stop?
Answers
The required both the average velocity and speed of the car would be 600 mph
How to find the average Velocity?To find the average velocity of the car, we need to know the distance it covers and the time it takes. In the given scenario, the car covers a distance of 500 miles in a time of 50 minutes.
To convert the time to hours, we can divide it by 60, which gives us:
50 minutes ÷ 60 minutes/hour
= 0.8333 hours
So, the average velocity of the car is:
Average velocity = Distance ÷ Time = 500 miles ÷ 0.8333 hours
= 600 mph
To find the speed of the car, we simply need to divide the distance covered by the time taken, without considering direction. So, the speed of the car is:
Speed = Distance ÷ Time = 500 miles ÷ 0.8333 hours
= 600 mph
Therefore, both the average velocity and speed of the car would be 600 mph if it was entered in the Indy 500 and never had to use a pit stop.
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The cost of one scooter is Rs.52,136. What is the cost of 34 scooters?
----------------------------------------------------------------------------------------------------------------------------
Rs.17,72,624
Rs.1,77,26,204
Rs.1,24,56,658
Answers
Answer:
Rs.1772624
Step-by-step explanation:
Multiply 52,236 by 34
this is similar to section 4.2 problem 30: determine the indefinite integral. use capital c for the free constant. ( −1 x4 − 2 x ) dx = incorrect: your answer is incorrect. .
Answers
The correct indefinite integral of (-1x^4 - 2x) dx is -1/5 * x^5 - 2x + C, where C represents the constant of integration.
Based on the given information, the problem is to determine the indefinite integral of the expression (-1x^4 - 2x) dx, using capital C for the free constant.
It appears that the previous answer given for this problem was incorrect.
To solve this problem, we need to use the rules of integration, which include the power rule, constant multiple rule, and sum/difference rule.
The power rule states that the integral of x^n is (x^(n+1))/(n+1), where n is any real number except -1.
The constant multiple rules state that the integral of k*f(x) is k times the integral of f(x), where k is any constant. The sum/difference rule states that the integral of (f(x) + g(x)) is the integral of f(x) plus the integral of g(x), and the same goes for subtraction.
Using these rules, we can break down the given expression (-1x^4 - 2x) dx into two separate integrals: (-1x^4) dx and (-2x) dx.
Starting with (-1x^4) dx, we can use the power rule to integrate: (-1x^4) dx = (-1 * 1/5 * x^5) + C1, where C1 is the constant of integration for this integral.
Next, we can integrate (-2x) dx using the constant multiple rule: (-2x) dx = -2 * (x^1/1) + C2 = -2x + C2, where C2 is the constant of integration for this integral.
To get the final answer, we can combine the two integrals: (-1x^4 - 2x) dx = (-1 * 1/5 * x^5) + C1 - 2x + C2 = -1/5 * x^5 - 2x + C, where C is the combined constant of integration (C = C1 + C2).
We can simplify this expression by using capital C to represent the combined constant of integration, giving us:
(-1x^4 - 2x) dx = -1/5 * x^5 - 2x + C
Therefore, the correct indefinite integral of (-1x^4 - 2x) dx is -1/5 * x^5 - 2x + C, where C represents the constant of integration.
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How do you find the height of a triangle when you know the base and area?
Answers
We can determine the height of a triangle when we know the base and area of the triangle using the area formula of triangle in base and height, that is
A = 1/2 × b × h
A triangle is a three sided polygon. The height of the triangle is the perpendicular distance of the not-included vertex to the considered base.
The formula to determine area of a triangle of base b and height h is
A = 1/2 × b × h
Therefore to determine the height of a triangle when base and area is given, we substitute the given values in appropriate units in the formula.
h = 2×A/ b
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Question 17
In a bag of trail mix, there is a ratio of 3 scoops of granola, 2 scoops of chocolate chips, and 1 scoop of pean
How many scoops of chocolate chips and peanuts will he need to keep the ratio equivalent?
A
17 scoops of chocolate chips and 16 scoops of peanuts
B
12 scoops of chocolate chips and 6 scoops of peanuts
с
8 scoops of chocolate chips and 7 scoops of peanuts
D
2 scoops of chocolate chips and 1 scoop of peanuts
Answers
Answer:
12 scoops of chocolate chips and 6 scoops of peanuts
Step-by-step explanation:
(5.8 × 105)(6.4 × 102)
Answers
scenario 2, continued next, you prepare for the question-and-answer session that will follow your presentation. what methods help you consider any limitations of your data? select all that apply. 1 point look at the context eliminate the outliers critically analyze the correlations understand the strengths and weaknesses of the tools
Answers
The concept is Data Analysis, which is the process of totally applying statistical tools to dissect data. The answer is options B, C, and D.
To help you consider data limitations, critically dissect correlations, examine the environment, and understand tool strengths and sins. Data analysis applies statistical and/ or logical ways to describe, illustrate, epitomize, and estimate data.
Data analysis helps individualities and associations make sense of data. Data analysts typically analyze raw data for insights and trends.
Limitations include:
Lack of alignment within teamsLack of commitment and patienceLow quality of dataPrivacy concernsComplexity & BiasQuestion
You're preparing a question-and-answer session that will follow your donation. Which styles help you to consider data limitations? elect everything that suits you.
A) exclude the outliers
B) Understand the strengths and sins of the tools
C) Critically dissect the correlations
D) Look at the environment
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if the work required to stretch a spring 3 ft beyond its natural length is 12 ft-lb, how much work (in ft-lb) is needed to stretch it 9 in. beyond its natural length?
Answers
The answer is 3 ft-lb.
What is the natural length of a spring?The spring's length without any attached mass is its natural length. Assuming the spring abides with Hooke's law The spring exerts a force Fs=kL if its length is altered by an amount L from its normal length, where k is a positive quantity known as the spring constant.W = 12kx2 is the amount of work required to stretch a spring x distances from its equilibrium point. Calculation information: (a) The formula is as follows: F = mg = (4 kg)(9.8 m/s2) = 39.2 N. x = 0.025 m.The spring's length at equilibrium is the length it has when no external forces are exerting any force on it. This is how spring naturally exists.
Beyond its natural length:
Work done to strech the spring to a lentgh x = 0.5 * k * x^2
Now;
12 = 0.5 * k * 9
k = 8/3 = 2.667
9 in = 1.5 ft
Work needed to stretch it 9 in. beyond its natural length = 0.5 * 2.667 * 1.5*1.5 = 3 ft-lb
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solve the following system of equations
Answers
-10x+12y=6
x=9
-81+12y=15
12y=96
y=8
Answer: x = 9 y = 8
The Smith Family is buying a house for $350,000 with a down payment of $70,000 for a 15-year loan, $66 per month insurance, property tax is $230 per month and HOA is $600 per year. Calculate their total monthly payment
Answers
Using monthly payment formula, the Smith Family's total monthly payment is approximately $2,360.99.
What is the Monthly Payment?To calculate the total monthly payment for the Smith Family, we need to consider the mortgage payment, insurance, property tax, and HOA fees.
1. Mortgage Payment:
The loan amount is the house price minus the down payment:
$350,000 - $70,000 = $280,000.
To calculate the monthly mortgage payment, we need to determine the interest rate and loan term. Since you mentioned it's a 15-year loan, we'll assume an interest rate of 4% (which can vary depending on market conditions and the borrower's credit).
We can use a mortgage calculator formula to calculate the monthly payment:
M = P [i(1 + i)ⁿ] / [(1 + i)ⁿ⁻¹]
Where:
M = Monthly mortgage payment
P = Loan amount
i = Monthly interest rate
n = Number of months
The monthly interest rate is the annual interest rate divided by 12, and the loan term is 15 years, which is 180 months.
i = 4% / 12 = 0.00333 (monthly interest rate)
n = 180 (loan term in months)
Plugging in the values into the formula:
M = $280,000 [0.00333(1 + 0.00333)¹⁸⁰] / [(1 + 0.00333)¹⁸⁰⁻¹]
Using a calculator, the monthly mortgage payment comes out to be approximately $2,014.99.
2. Insurance:
The monthly insurance payment is given as $66.
3. Property Tax:
The monthly property tax payment is given as $230.
4. HOA Fees:
The HOA fees are stated as $600 per year. To convert this to a monthly payment, we divide by 12 (months in a year): $600 / 12 = $50 per month.
Now, let's add up all these expenses:
Mortgage payment: $2,014.99
Insurance: $66
Property tax: $230
HOA fees: $50
Total monthly payment = Mortgage payment + Insurance + Property tax + HOA fees
Total monthly payment = $2,014.99 + $66 + $230 + $50
Total monthly payment = $2,360.99
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half-life of Po-210 is 140 days. If the initial mass of the sample is 5
kg, how much will remain after 420 days.
Answers
Answer:
\(0.625kg\)
Step-by-step explanation:
we are given half-life of PO-210 and the initial mass
we want to figure out the remaining mass after 420 days
in order to solve so we can consider the half-life formula given by
\( \displaystyle f(t) = a {0.5}^{t/T} \)
where:
f(t) is the remaining quantity of a substance after time t has elapsed.a is the initial quantity of this substance.T is the half-lifesince it halves every 140 days our T is 140 and t is 420. as the initial mass of the sample is 5 our a is 5
thus substitute:
\(\displaystyle f(420)=5\cdot{0.5}^{420/140}\)
reduce fraction:
\(\displaystyle f(420)=5\cdot{0.5}^{3}\)
By using calculator we acquire:
\(\displaystyle f(420)=0.625\)
hence, the remaining sample after 420 days is 0.625 kg
DECIDE!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Step-by-step explanation:
DA,DG,DC are tangents of the circles so have the same length.
NB: F is the orthocenter of triangle HDF
1. Simplify (3x² + 5x) + (6x-6x² + 2).
A. 10x³
B. -3x² + 11x + 2
C. 10x²
D. 3x² - 1x + 2
Answers
Answer:
so ans is ((b)-3x^2+11x+2
Step-by-step explanation:3x^2 +5x+6x-6x^2+2
rearrange expression
3x^2-6x^2+5x+6x+2
-3x^2+11x+2
Answer:
B. -3x² + 11x + 2
Step-by-step explanation:
Got it right on my test
the loft in casa batlló in barcelona, contains a series of sixty catenary arches which closely resemble parabolas. the left side of the arch is close to parabolic in shape all the way to the floor. on the right side of the arch, it is parabolic in shape until 2.06 meters from the floor. then the arch drops vertically at this point. the equation of the parabola that closely models these arches is − 19 100 ⋅ ( y − 3 )
Answers
The equation −19/100 * (y - 3) models the shape of the arches in the loft, closely resembling parabolic curves.
The equation of the parabola that closely models the arches in the loft of Casa Batlló in Barcelona is −19/100 * (y - 3).
To understand the equation, let's break it down step by step:
1. The equation represents a parabola that closely resembles the shape of the arches.
2. The term "−19/100" is the coefficient that determines the steepness of the parabola. A negative value indicates that the parabola opens downwards.
3. The term "(y - 3)" represents the vertical displacement of the parabola. It indicates that the vertex of the parabola is at the point (0, 3).
So, the equation −19/100 * (y - 3) models the shape of the arches in the loft, closely resembling parabolic curves.
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Janelle spent:
Harper and Dean raced each other in
gym class. Harper ran 100 m in 14. 56
seconds. Dean ran the same distance in
15. 12 seconds. How much faster was
Harper than Dean?
Number model:
Estimate:
Answers
Harper and Dean raced each other in gym class. Harper ran 100 m in 14. 56
seconds. Dean ran the same distance in 15. 12 seconds. Therefore, Harper 0.56 second faster than Dean.
Distance:
Distance is a numerical or sometimes qualitative measurement of the distance between objects or points. In physics or common usage, distance can refer to a physical length or an estimate based on other criteria. Since spatial cognition is a rich source of conceptual metaphors in human thought, the term is also often used metaphorically to refer to a measure of the amount of difference between two similar objects (such as statistical distance or distance between changing probability distributions) text strings) or some degree of separation (like the distance between people in a social network). Most of these concepts of distance, whether physical or metaphorical, are formalized in mathematics using the concept of metric spaces.
In the social sciences, distance can refer to qualitative measures of separation, such as social or psychological distance.
Given that:
Harper ran 100 m in 14. 56 seconds. Dean ran the same distance in 15. 12 seconds.
Now, The faster Harper ran than dean is:
15.12- 14.56 = 0.56 seconds.
Therefore, Harper 0.56 second faster than Dean.
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Spot the anomalies in the data sets below
Need help and can someone please explain what an anomaly is?
Answers
Answer:
For the bottom one it would be 43 in the second column i think.
Step-by-step explanation:
An anomaly is a number that stands out to the rest, so if i had the numbers 2,4,6 and 80 the anomaly would be 80 because of how different it is to the rest
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gold is sold by the troy ounce (31.103 g). what is the volume (in cm3) of 2 troy ounces of pure gold?
Answers
1.62 is the volume (in cm3) of 2 troy ounces of pure gold .
What is full answer for density?
A material substance's density is defined as its mass per unit volume. Density is defined as d = M/V, where M stands for mass, and V for volume. The unit of density that is most frequently used is grams per cubic centimeter.We determine the volume, V, corresponding to the given amount of gold. We do this by dividing the given mass, m, by the density, d, such that
V = m/d
m = 31.03 g
d = 19.3 g/ml
We proceed with the solution
V = m/d
= 31.03/19.3
≈ 1.62 ml
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which scatter diagram accurately represents the data? - select your answer - does the scatter diagram indicate any influential observations? - select your answer - b. compute the standardized residuals for these data (to decimals, if necessary). enter negative values as negative numbers. observation 1 observation 2 observation 3 observation 4
Answers
The options for scatter diagram that accurately represents the data are yes, yes and yes
What is called a graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
What is a graph example?A graph is a type of non-linear data structure composed of nodes, also known as vertices and edges. Any two nodes, often referred to as vertices, in a network are connected by edges. The vertex numbers in this graph are 1, 2, 3, and 5, while the edge numbers are 1, 2, 1, 3, 2, 4, and 5, respectively.
The estimate aa of the intercept \alphaα is the average of yy decreased by the product of the estimate of the slope and the average of xx.
Because the point close to the residual plot's right edge is substantially farther to the right than the other points, the plot exhibits an outlier.
Furthermore, this outlier has a significant impact because the pattern in the points to the left clearly slopes upwards, suggesting that the regression model does not adequately account for the vast majority of the data.
Hence the correct options are
yes, yes, and yes.
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Think carefully about the angle relationship the following represents.
What is the value of ∠ZXY?
Answers
Answer:
55°
Step-by-step explanation:
Since ∠WXY has a square on ∠X, ∠WXY is a 90° angle. This means that the angles in between ∠WXY also sum up to 90°.
⇒ 35 + 4x + 7 = 90
⇒ 4x = 90 - 35 - 7
⇒ 4x = 48
⇒ x = 48/4 = 12
Substitute the value of x into the expression "4x + 7"
⇒ ∠ZXY = 4x + 7 = 4(12) + 7 = 48 + 7 = 55°
Answer:
We know that this is a 90° Angle.
We already have 35° so we subtract that from 90
90-35=55
So the value of ∠ZXY = 55°
Also, the value of X is equal to 12
Hope this helps!
Today the population of a city is 250,000 and is growing at a rate
of 4% per year. When or how many years will the population reach
850,000
Answers
Step-by-step explanation:
Principal = 250,000
Rate = 4%
Simple interest = 850,000
Time = ?
\(t = \frac{100 \times interest}{principal \times rate} \\ t = \frac{100 \times 850000}{250000 \times 4} \\ t = \frac{100 \times 85}{25 \times 4} \\ t = \frac{8500}{100} \\ t = 85years\)
The graph shows one of the linear equations for a system of equations. Which equation represents the second linear equation for the system of equations that has the solution which corresponds to a point at (2,0)?
A) -x - 3y = 2
B) x + 3y = -2
C) 5x + y/2 = 10
D) 5x + y/2 = -10
Answers
Write an algebraic expression for the word expression: 14 more than the difference of r and s.
I really dont know
Answers
A. Name the smallest angle and the largest angle of the following triangles: F 6 S 5 1. A J 5.03 7 5 G B H 5.1 2. D 4 3 E
Answers
Answer:
(smallest, largest) = (B, C), (D, E), (G, J)
Step-by-step explanation:
Side lengths of a triangle are proportional to the sine of the opposite angle. In a triangle, a larger angle will always have a larger sine. That means the smallest angle is opposite the shortest side, and the largest angle is opposite the longest side.
__
ΔABCThe shortest side is 5 units, opposite angle B. The longest side is 7 units, opposite angle C.
smallest angle: Blargest angle: CΔDEFThe shortest side is 3 units, opposite angle D. The longest side is 5 units, opposite angle E.
smallest angle: Dlargest angle: EΔGHJThe shortest side is 5 units, opposite angle G. The longest side is 5.1 units, opposite angle J.
smallest angle: Glargest angle: J_____
Additional comment
Angles in a triangle may exceed 90°. The sine function actually is decreasing for angles above 90°. However, since the total of angles of a triangle must be exactly 180°, there cannot be two angles in a triangle such that the smaller angle has the larger sine.
An advertising company is purchasing a new industrial-sized color printer. The company has been approved for a $75,000 loan at two different
banks. The terms of each loan are:
Offer 1: 4.99% annual simple interest, with a total account balance of $91,529.38 after a 53-month term
Offer 2: 3.5% annual interest compounded monthly for a 62-month term
Assuming no payments are made, what is the difference in the account balances at the end of the loan terms. Round your answer to the nearest
penny.
O $1,624.49
$1,686.87
$1,894.02
O $2,207.67
Answers
The difference in the account balances at the end of the loan terms is given as follows:
$1,686.87.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for the offer 2 are given as follows:
P = 75000, r = 0.035, n = 12, t = 62/12.
Hence the balance of the offer 2 is given as follows:
B = 75000 x (1 + 0.035/12)^(12 x 62/12)
B = $89,842.51.
The balance of Offer 1 is of $91,529.38, hence the difference in the balances is given as follows:
91529.38 - 89842.51 = $1,686.87.
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A regular polygon has it exterior angles all equal to 2°.
Find the number of sides of the polygon.
Answers
Divide 360 by the amount of the exterior angle to also find the number of sides of the polygon.
Step-by-step explanation:
360/2 = 180
therfore it has 180 sides
3. A man earns # 140 000 per annum. He is allowed a tax free pay of # 30 000. If he pays 25 kobo in the naira as tax on his taxable income, how much has he left as disposable income?
4. A discount of 15% is allowed on an article. If a customer received N600.00, find the actual amount paid on the article.
Answers
the man has #112,500 left as disposable income after paying taxes.
the actual amount paid on the article after the 15% discount is N600.00.
How to calculate the disposable income?To calculate the disposable income of the man, we first need to determine his taxable income.
Taxable income = Annual income - Tax-free pay
Taxable income = #140,000 - #30,000 = #110,000
Next, we need to calculate the tax he has to pay on his taxable income.
Tax = Tax rate x Taxable income
Note that the tax rate is given in kobo, so we need to convert it to naira.
1 naira = 100 kobo, so 25 kobo = 0.25 naira
Tax = 0.25 x #110,000 = #27,500
Finally, we can calculate the disposable income by subtracting the tax from the annual income.
Disposable income = Annual income - Tax
Disposable income = #140,000 - #27,500 = #112,500
Therefore, the man has #112,500 left as disposable income after paying taxes.
4.If the discount allowed on an article is 15%, it means that the customer will pay only 85% of the original price of the article after the discount is applied.
Let the original price of the article be P.
Then, the amount paid by the customer after the 15% discount is 85% of the original price:
Amount paid = 0.85P
We know that the customer received N600.00.
So, we can set up an equation:
0.85P = N600.00
Solving for P, we get:
P = N600.00 / 0.85
P = N705.88 (rounded to two decimal places)
Therefore, the actual amount paid on the article after the 15% discount is N600.00.
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