why f is not differentiable at x = 0 , where f(x) is x ^1/3
Therefore the f is continuous on R , i.e. real numbers and f is not differentiable at 0 ,Option A and D is the correct answer.
What is a Function ?A function is a mathematical statement which find relation between independent variable and dependent variable.
It always comes with a defined range and domain.
It is given that :
[tex]\rm f(x) = x^{1/3}\\\\LHD (at\; x = 0) = RHD (at \; x = 0)\\\\\= \lim_{x\rightarrow 0}\dfrac{f(x)-f(0)}{x-0}\\\\=\lim_{h\rightarrow 0}\dfrac{f(0-h)-f(0)}{0-h-0}[/tex]
[tex]=\lim_{h\rightarrow 0}\dfrac{f(0-h)-f(0)}{0-h-0} \\\\= \lim_{h\rightarrow 0}\dfrac{(-h)^{1/3}}{-h}\\\\\lim_{h\rightarrow 0}\dfrac{(-1)^{1/3}(h)^{1/3}}{-1*h}\\\\\lim_{h\rightarrow 0} (-1)^{-2/3}h^{-2/3}[/tex]
if we substitute h = 0 ,
Here, LHD and RHD does not exist at x = 0 So, f(x) is not differentiable at x = 0 .
Therefore the f is continuous on R , i.e. real numbers
and f is not differentiable at 0
Option A and D is the correct answer.
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Two parallel lines are intersected by a third line so that angles 1 and 5 are congruent.
2 parallel horizontal lines are intersected by a third line. On the first horizontal line where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 1, 2, 4, 3. On the second horizontal line, where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 5, 6, blank, blank.
Which statement is true about angles 3 and 5?
They are acute.
They are congruent.
They are complementary.
They are supplementary.Two parallel lines are intersected by a third line so that angles 1 and 5 are congruent.
2 parallel horizontal lines are intersected by a third line. On the first horizontal line where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 1, 2, 4, 3. On the second horizontal line, where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 5, 6, blank, blank.
Which statement is true about angles 3 and 5?
They are acute.
They are congruent.
They are complementary.
They are supplementary.
Answer:
4. They are supplementary
Answer:
4 they are supplemental
Triangle U S T is shown. Angle U S T is 100 degrees. The length of U S is 9, the length of S T is 10, and the length of U T is s.
Which equation correctly uses the law of cosines to solve for the length s?
92 = s2 + 102 – 2(s)(10)cos(100°)
9 = s + 10 – 2(s)(10)cos(100°)
102 = s2 + 100 – 2(s)(10)cos(100°)
s2 = 92 + 102 – 2(9)(10)cos(100°)
By solving through law of cosines the length s can be written as [tex]s^{2} =9^{2} +10^{2} -2*9*10cos(100)[/tex].
Given the length of US is 9, the length of ST is 10 and the length of UT is s and the angle UST is 100 degrees.
According to law of cosines a length can be written as [tex]c^{2} =a^{2} +b^{2} -2abcos g[/tex]
where c is the side opposite to the given angle and a and b are other sides , g is the angle given.
[tex]s^{2} =9^{2} +10^{2} -2*9*10cos(100)[/tex]
where s is the length of the side opposite to the angle given, the length of other sides are 9 and 10 where the angle is 100.
Hence the fourth option is correct which is s^{2} =9^{2} +10^{2} -2*9*10cos(100).
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Answer:
its D
Step-by-step explanation: ed 2023
A concert manager counted 600 ticket receipts the day after a concert. The price for a student ticket was $13.50, and the price for an adult ticket was $17.00. The register confirms that $9,587.50 was taken in. How many student tickets and adult tickets were sold?
The number of student tickets is 175 and the number of adult tickets is 425.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that:-
A concert manager counted 600 ticket receipts the day after a concert. The price for a student ticket was $13.50, and the price for an adult ticket was $17.00. The register confirms that $9,587.50 was taken inSuppose the number of the student ticket is St and adult are At.
St + At = 600
St = 600 - At
Another expression for the total amount will be given as:-
13.5St + 17At = 9587.50
Put the value of St in the equation to find the value of At.
13.5( 600 - At) + 17At = 9587.50
8100 - 13.5At +17At = 9587.5
17At - 13.5 At = 9587. 5 - 8100
3.5 At = 1487.5
At = 425
St + At = 600
St = 600 - At = 600 - 425 = 175
Therefore the number of student tickets is 175 and the number of adult tickets is 425.
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(3x + 2y = 7
(7x-2y = 3
pls help with thisc...................................
Answer:
D
598*47+38=
28106+38=
28134
The number of wrecks at a certain intersection varies directly as the number of cars that travel through the intersection. If there are 31 wrecks when 1,085 cars have traveled through the intersection, how many cars have passed through the intersection after 7 wrecks?
The number of cars that have passed through the intersection after 7 wrecks is 1/5 cars
Direct variationNumber of wrecks = wNumber of cars = cw = k × c
31 = k × 1,085
31 = 1,085k
k = 1085/31
k = 35
If w = 7
w = k × c
7 = 35 × c
7 = 35c
c = 7/35
c = 1/5 car
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Please answer all four of the questions please I will mark u brainliest
Answer:
1: 8 ft
2: 10 cm
3: c is approximately 127.2 or exactly equal to 90 * sqrt(2)
4: sqrt(133)
Step-by-step explanation:
(1) Kevin tries to climb a wall with a ladder. The length of a ladder is 17 feet and it reaches only 15 feet up the wall. What is the distance between the base of the ladder and the wall? :
Here you can use the Pythagorean Theorem to find the length of the base.
the equation is a^2 + b^2 = c^2 where c is the hypotenuse. In this case 17 is the hypotenuse which is c, 15 is a or b it doesn't really matter where you put it.
a^2 + (15)^2 = 17^2
a^2 + 225= 289
a^2 = 64
a = 8
(2) In a right triangle, if the length of one leg is 8 cm and the length of the other leg is 5 cm, what is the length of the hypotenuse? :
The same formula can be used except you don't have to move anything around.
8^2 + 6^2 = c^2
64 + 36 = c^2
100 = c^2
10 = c
10 cm
A baseball field is a square with sides of length 90 feet. What is the shortest distance between the first base and the third base?:
So if you look at the image provided, the shortest distance is just a straight line, but more specifically that straight line forms two triangles with the same lengths, That line is the hypotenuse so you can use the same equation as the previous equations
90^2 + 90^2 = c^2
16,200 = c^2
c is approximately 127.2 or exactly equal to 90 * sqrt(2)
(4) How far up a wall will a 13-meter ladder reach, if the foot of the ladder is 6 meters away from the base of the wall?:
6^2 + b^2 = 13^2
36 + b^2 = 169
b^2 = 133
b = sqrt(133)
Change a Relation to Make It a Function The relation R is shown below as a list of ordered pairs. R = { (1, 4), (1, 3), (-1, 3), (2, 15) } Which ordered pairs prevent this relation from being a function? (1, 4) and (1, 3), because they have the same x-value (1, 3) and (–1, 3), because they have the same y-value
Answer: (1,4) and (1,3) because the have the same x-value
Step-by-step explanation:
A function is defined so that for each input (known as the domain), there is no more than one output (known as the range).
Karen runs 7 miles in 50 minutes. At the same rate, how many miles would she run in 75 minutes?
Answer :
10.5 miles
Given :
7 miles in 50 mins
Step-by-step explanation :
Calculate how many miles in 1 minute :
Divide both by 50 :
7/50 miles in 1 minute
To work out 75 minutes we multiply both by 75 :
75 × 7/50 =
10.5
Therefore our final answer is 10.5 miles
Hope this helped and have a good day
What is the reason for statement 7 in the given proof? A. definition of midpoint B. definition of slope C. Parallel lines have equal slopes. D. using point-slope formula
The reason is using point slope formula.
The photo attached given below:
what is point slope formula?The equation of a straight line in the form y − y1 = m(x − x1) where m is the slope of the line and (x1, y1) are the coordinates of a given point on the line — compare slope-intercept form.
Now, we have to find the slope of AE, BF and CD.
We have to done this with help of coordinates.
So, we have to use point slope formula to find the slope of AE, BF and CD.
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A variable is normally distributed with mean 6 and standard 2 deviation .
a. Find the percentage of all possible values of the variable that lie between 5 and 9.
b. Find the percentage of all possible values of the variable that exceed 1.
c. Find the percentage of all possible values of the variable that are less than 4.
The normal distribution is also known as the Gaussian distribution. The percentage of all possible values of the variable that are less than 4 is 15.87%.
What is a normal distribution?
The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.
A.) The percentage of all possible values of the variable that lie between 5 and 9.
P(5<X<9) = P(X<9) - P(5<X)
= P(z<1.5) - P(-0.5<z)
= 0.9332 - 0.3085
= 0.6247
= 62.47%
B.) The percentage of all possible values of the variable that exceed 1.
P(X>1) = 1 - P(X<-2.5)
= 1-0.0062
= 0.9938
= 99.38%
C.) The percentage of all possible values of the variable that are less than 4.
P(X<4) = P(X <4)
= P(z<-1)
= 0.1587
= 15.87%
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A candle burns down at the rate of 0.5 inches per hour. The original height of the candle was 8 inches.
Part A: Write a list of 6 ordered pairs to show the height of the candle in inches (y) as a function of time in hours (x) from the first hour after it started burning. For example, the point (0, 8) would represent a height of 8 inches after 0 hours. Explain how you obtained the ordered pairs. (5 points)
Part B: Is this relation a function? Justify your answer using the list of ordered pairs you created in Part A. (2 points)
Part C: If the rate at which the candle burned was 0.4 inches per hour instead of 0.5 inches per hour, would the relation be a function? Explain your answer using input and output values. (3 points)
The ordered pairs are (0,8), (1, 7.5), (2, 7), (3,6.5), (4, 6) and (5, 5.5)
How to determine the ordered pairs?The given parameters are:
Initial height, h = 8 inches
Rate = 0.5 inches per hour
The height of the candle at x hour is:
y = Initial - rate * x
This gives
y = 8 - 0.5x
Set x = 0 to 5
y = 8 - 0.5(0) = 8
y = 8 - 0.5(1) = 7.5
y = 8 - 0.5(2) = 7
y = 8 - 0.5(3) = 6.5
y = 8 - 0.5(4) = 6
y = 8 - 0.5(5) = 5.5
So, the ordered pairs are (0,8), (1, 7.5), (2, 7), (3,6.5), (4, 6) and (5, 5.5)
Is the relation a function?In (a), we have:
y = 8 - 0.5x
The above is a linear relation.
All linear relations are functions
Hence, the relation is a function.
Would a new relation be a function?
We have
Initial height, h = 8 inches
New rate = 0.4 inches per hour
The height of the candle at x hour is:
y = Initial - rate * x
This gives
y = 8 - 0.4x
The above is a linear relation.
All linear relations are functions
Hence, the new relation is also a function.
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Help me with this question please!! :)
Answer: 20/63
Step-by-step explanation:
The probability that the first marble is red is 16/28.The probability that the second marble is red is 15/27.Multiplying these probabilities, we get (16/28)(15/27) = 20/63
The graph of the quadratic function f(x) = - 1/2 x ^ 2 + 3 is shown. Describe the end behavior of the function.
Turkey sandwiches cost $2.50 and veggie wraps cost $3.50 at a snack stand. Ben has sold no more than $30 worth of turkey sandwiches and veggie wraps in the first hour of business. Let x represent the number of turkey sandwiches and y represent the number of veggie wraps. The inequality 2.50x+3.50y30 represents the food sales in the first hour.
If Ben has sold 4 veggie wraps, what is the maximum number of turkey sandwiches Ben could have sold?
The maximum number of turkey sandwiches Ben sold is 6.
What is the maximum number of turkey sandwiches Ben sold?Given this equation : 2.50x + 3.50y ≤ $30
If y is 4, take the following steps in order to determine the value of x:
Substitute for y in the above equation:
2.50x + (3.50 x 4) ≤ $30
2.50x + 14 ≤ $30
2.50x ≤ $30 - 14
2.50x ≤ $16
x ≤ 6.4
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Answer:
6
Step-by-step explanation:
A student needed to find the measure of angle b. She incorrectly said mZb=118°. Find the correct measure of angle b. What mistake did she likely make?
Answer:
D
Step-by-step explanation:
To find angle B, you should subtract 62 from 90 since because a right angle is 90 degrees.
A polynomial-function has −5+√3 as a root. Which of the following must also be a root of the function?
O-5-√√3
0 -5+√√√31
05-√√√31
0 5+√√31
Answer:
First option.
Step-by-step explanation:
3x+7-6=(8/7)-0
Value of x?
Answer:
[tex]\boxed{\sf x = \dfrac{1}{21}}[/tex]
Explanation:
[tex]\rightarrow \sf 3x+7-6= \dfrac{8}{7} - 0[/tex]
simplify the following
[tex]\rightarrow \sf 3x+1= \dfrac{8}{7}[/tex]
subtract 1 from both sides
[tex]\rightarrow \sf 3x+ 1 -1= \dfrac{8}{7} - 1[/tex]
simplify the following
[tex]\rightarrow \sf 3x= \dfrac{1}{7}[/tex]
multiply both sides by 1/3
[tex]\rightarrow \sf 3x \cdot \dfrac{1}{3}= \dfrac{1}{7}\cdot \dfrac{1}{3}[/tex]
simplify the following
[tex]\rightarrow \sf x = \dfrac{1}{21}[/tex]
[tex]3x + 7 - 6 = \frac{8}{7} - 0 \\ \\ 3x + 1 = \frac{8}{7} \\ \\ 3x = \frac{8}{7} - 1 \\ \\ 3x = \frac{ 8 - 7}{7} \\ \\ 3x = \frac{1}{7} \\ \\ x = \frac{1}{7 \times 3} \\ \\ x = \frac{1}{21} .[/tex]
63, 58, 57, 71, 54, 60 Calculate the coefficient of variation for the following data
Answer:
The coefficient of variation (CV)= 9.83
Step-by-step explanation:
look at the attachment above ☝️
In ABC, m<2=70 and m
The measure of the third angle in the ΔABC is 70 degrees
Complete questionIn ΔABC, m∠2 = 70 and m∠1 = 40, find the measure of all third angle of ΔABC.
How to determine the third angle?The given parameters are:
m∠2 = 70
m∠1 = 40
The sum of angles in a triangle is:
m∠1 + m∠2 + m∠3 = 180
So, we have:
70 + 40 + m∠3 = 180
Subtract 110 from both sides
m∠3 = 70
Hence, the measure of the third angle in the ΔABC is 70 degrees
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Evaluate
3(x+4)(x+1)
HP for x = 4.
(x+2)(x-2)
Answer:
120
Step-by-step explanation:
3(x+4)(x+1)
3((4)+4) ((4)+1)
(12 + 12)(4+1)
(24)(5)
120
If you need the other function, here:
(4+2)(4-2)
6(2)
12
Answer:
below
Step-by-step explanation:
3×x=12
3×4=12
3(x+4)=12+12+12+3=39
HELP ME !!!!!!! Which of the following best describes a single fixed point that is the same
distance from the parabola as the directrix is from the parabola?
A. center
B. vertex
C. focus
D. locus
Answer:
C. Focus
.............
who is known as the father of computer
Answer:
Charles Babbage
Step-by-step explanation:
Answer: Hope this may help you
Charles Babbage, I think
Step-by-step explanation:
Charles Babbage is sometimes referred to as the father of computers.
If g(x) = 2^x were shifted 7 units to the right and 3 units down, what would be the new equation?
H(x) = 4(x - 7)^2 - 19
Hope you find it usefull
Which of the following is most likely the next step in the series?
⠀⠀
The next step in the series is choice D.
Answer:
D
Step-by-step explanation:
if we define the diagrams in terms of their rows and columns, then
1st : 2 by 1
2nd : 3 by 2
3rd : 4 by 3
note that the rows and columns both increase by 1
then the next likely diagram is
5 by 4 , that is diagram D
A bakery sold 27 mocha cupcakes in a day, which was 9% of the total number of
cupcakes sold that day. How many total cupcakes did the bakery sell that day?
Answer:
300 cupcakes
Step-by-step explanation:
[tex]27 = .09c[/tex]
[tex]c = \frac{27}{.09} = \frac{2700}{9} = 300[/tex]
In total, the bakery sold 300 cupcakes on a certain day.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, A bakery sold 27 mocha cupcakes in a day, which was 9% of the total number of cupcakes sold that day.
let, 'x' be the total number of cupcakes sold that day.
Therefore, 9% of 'x' is 27 which is,
(9/100)×x = 27.
0.09x = 27.
x = 27/0.09.
x = 300.
So, The number of cupcakes sold that day is 300.
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The Scooter Company manufactures and sells electric scooters. Each scooter cost $150 to produce, and the company has a fixed cost of $2,000. The Scooter Company earns a total revenue that can be determined by the function R(x) = 400x − 2x2, where x represents each electric scooter sold. Which of the following functions represents the Scooter Company's total profit?
−2x2 − 150x − 2,000
−2x2 + 250x − 2,000
−2x2 + 150x − 1,600
−300x3 − 4,000x2 + 60,000x + 800,000
The function that represents the Scooter Company's total profit is given by:
P(x) = -2x² + 250x - 2,000.
How to calculate the profit function?The profit function is calculated by the revenue function subtracted by the cost function, hence:
P(x) = R(x) - C(x).
In this problem, we have that:
The revenue function is: R(x) = 400x - 2x².The cost function is: X(x) = 150x + 2000.Hence the profit function is:
P(x) = R(x) - C(x).
P(x) = 400x - 2x² - (150x + 2000).
P(x) = -2x² + 250x - 2,000.
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Dan Barker, the chief engineer, told Ms. Silva that the company is currently making 150 units of Model Diamond per batch and 245 units of Model Gold per batch. He suggests doubling the batch sizes to cut the number of setups in half, thereby reducing the setup cost by 50 percent. Compute the cost per unit for each product if Ms. Silva adopts his suggestion.
The cost per unit for each product is given as:
x ≈ 0.0067; and
y ≈ 0.0041. See explanation below.
What is the cost per unit for each product?Given that the current production:
Model Diamond (Md) - 150 UnitsModel Gold (Mg) - 245 UnitsCurrent cost of production is given as:
Current Total Cost = 150y + 245x where;
if doubling the batch sizes will reduce the cost per unit by 50% then the new cost equation will be:
Thus, New Total Cost of production = (150 x 2) (y/2) + (245 x 2) (x/2)
= (300)(y/2) + (490) (x/2)
Since we are looking for the cost per unit of each product:
f(x) = 300 * (x/2)..........Unit cost of Model Gold
If we make x subject of the formula, then we arrive at:
1/300 = x/2
x = (1/300) * 2
x = 0.00666666666
x ≈ 0.0067
f(x) = 490* (x/2)
If we make y subject of the formula, then we arrive at:
i/490 = y/2
y = (1/490) * 2
y = 0.00408163265306122448979591836735
y ≈ 0.0041
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In the last three years Frederic’s basketball team win 40 more games than they lost
Answer:
Wht is the total matches they played?
