Answers
The statement that is true about the function is D. it is discontinuous and non-differentiable at x = 3.
How to determine which statement is true?To determine which statement is true, we need to know the conditions for continuity and differentiablity of a function.
Conditions for continuity and differentiablity of a function.For a function f(x) to be continuous at a point x = a, then both the left hand limit of f(x) and the right hand limit of f(x) as x → a must be equal. That is [tex]\lim_{x \to a^{-} } f(x) = \lim_{x \to a^{+} } f(x)[/tex]. So, [tex]\lim_{x \to a^{} } f(x)[/tex] must exist since [tex]\lim_{x \to a^{-} } f(x) = \lim_{x \to a^{+} } f(x) = \lim_{x \to a^{} } f(x)[/tex]Also, for a function to be differentiable at a point x = a, it must also exist at x = a
So, since f(x) = {x² - 1 if -1 ≤ x ≤ 3 and x²/3 if 3 < x ≤ 8}
From the equality on the first condition,we see that f(x) is exists at x = 3 but is not continuous since f(x) changes to another function when x > 3. So,left hand limit of f(x) and the right hand limit of f(x) as x → 3 are not equal.
That is [tex]\lim_{x \to 3^{-} } f(x) \neq \lim_{x \to 3^{+} } f(x)[/tex] . Thus, the function is discontinuous at x = 3.
For differentiability, both conditions must be met. Since only one condition is met, it is non-differentiable.
So, the function is discontinuous and non-differentiable at x = 3.
So, the statement that is true about the function is D. it is discontinuous and non-differentiable at x = 3.
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Related Questions
Urve revolves around the x-axis. if you cannot evaluate the integral exactly, use your calculator to approximate it. (round your answer to four decimal places. ) y = 16 − x2 from x = −1 to x = 1
Answers
The value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1 is 94/3.
Given the equation y=16-[tex]x^{2}[/tex] and the limit of the integral be x=-1,x=1.
We are required to find the value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1.
Equation is relationship between two or more variables that are expressed in equal to form.Equation of two variables look like ax+by=c.It may be linear equation, quadratic equation, or many more depending on the power of variable.
Integration is basically opposite of differentiation.
y=16-[tex]x^{2}[/tex]
Find the integration of 16-[tex]x^{2}[/tex].
=16x-[tex]x^{3}/3[/tex]
Now find the value of integration from x=-1 to x=1.
=16(1)-[tex](1)^{3}/3[/tex]-16(-1)-[tex](-1)^{3}/3[/tex]
=16(1)-1/3+16-1/3
=32-2/3
=(96-2)/3
=94/3
Hence the value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1 is 94/3.
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Match the key features of functions terms to their corresponding definitions.
Answers
The key features of the above given functions are correctly matched to their corresponding definition.
Definition of termsNegative sections of the graph: They are the parts where the graph is below the x-axis. That is option C.End behaviour: This is what happens to the graph on the far left or far right. That is option E.Positive sections of the graph: This is the parts where the graph is above the x-axis. That is option D.Intercepts: This is the points where the graph crosses an axis. That is option BRelative extrema: This is the points of relative minimum or maximum in a graph. That is option A.Learn more about graphs here:
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A bag contains 4 blue marbles and 7 red marbles. Two marbles are randomly drawn without replacement. Find the probability of the event ""the first marble is red and the second marble is blue""?
Answers
Answer:
8/11
Step-by-step explanation:
In the given scenario was cannot calculate P(B) directly. As it depends on what happened first, by itself we don’t know what was drawn first. Thus it becomes a conditional probability question:
P( B | A ) ← reads as the probability of “B” happening “given that” “A” has already happened — in this case the probability that the second marble drawn is a blue marble given that the first was a red marble.
Can someone please help me with this?
Answers
Answer:
-2
Step-by-step explanation:
See attachment
Someone please explain.50 points available.Thankyou so much!
Answers
Answers:
a) 49 square tiles - did the work on paper.
b) 83 circular tiles - did the work on paper.
c) C: could be even or odd - all patterns had both even and odd amounts of square and circular tiles.
Step-by-step explanation:
I did all the work on paper it took a while to do it. pls mark brainliest
Identify ER rounded to the nearest tenth. The Figure shows right triangle M E R with right angle E. The length of hypotenuse M R is equal to 37 units. Angle R measures 61 degrees.
Answers;
a) ER ≈ 66.7
b) ER ≈ 32.4
c) ER ≈ 17.9
d) ER ≈ 22.3
Please give an explanation! :)
Answers
The value of length ER rounded to the nearest tenth is 17.9 units (Option C)
Trigonometric ratiosThe trigonometric ratios which has been proven as regarding right angle triangles are given below:
Sine θ = Opposite / Hypothenus
Cos θ = Adjacent / Hypothenus
Tan θ = Opposite / Adjacent
With above information in mind, we can easily determine the length of ER in the question. This is illustrated below:
How to determine the length of ERFrom the question given above, which is summarized in the diagram (see attached photo) the following data were obtained:
Hypothenus (MR) = 37 unitsAngle R = 61 °Adjacent (ER) = ?Since we looking for the Adjacent (ER), the best trig ratio to use is the Cos θ ratio. This can be obtained as illustrated below:
Cos θ = Adjacent / Hypothenus
Cos 61 = ER / 37
Cross multiply
ER = 37 × Cos 61
ER = 37 × 0.4848
ER = 17.9 units
Thus, the length of ER to the nearest tenth is 17.9 units
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Someone help me please
30-60-90 triangles
Answers
Answer:
Short leg = 10
Longer leg = 10[tex]\sqrt{3}[/tex]
Hypotenuse = 20
Step-by-step explanation:
The given is a special right triangle, its angle measures are as follows:
30-60-90 and the side lengths will follow as:
x, x[tex]\sqrt{3}[/tex], 2x respectively.
The length of hypotenuse (sees angle measure 90) is represented with 2x and it's given as 20
We can conclude x = 10 from this
So the length of short leg is 10
Then the length of longer leg is 10[tex]\sqrt{3}[/tex]
The length of hypotenuse is already given as 20
A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. if a marble is randomly selected from the bag, what is the probability that it is blue?
Answers
3/12, or 1/4 is the probability that it is blue.
What is probability?
Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .Probability = number of successes / total number of outcomes
Total marbels in bag = 4+ 3 + 5 = 12
A total of 12 marbles are in the bag.
3 blue marbles are in the bag.
Therefore, the probability of picking a blue is 3/12, or 1/4.
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HELP! A city pays a manufacturing company to produce more stop signs for the city due to an increase in traffic incidents at intersections. After doing some research, the company manager reads that a standard stop sign is a regular octagon that is 30 inches wide and 30 inches tall.
Answers
The apothem is 15 inches, the perimeter is calculated to be 99.41 while the area is given as 745.59
How to solve for the octagonThe side of the octagon is given by x inches
the interior side of the angles can be gotten by:
8-2 * 180 / 8 sides
= 135
We have to find the value of the angles
<abc = 180 - 135 = 45 degree
<acb = 180 - 135 = 45 degrees
x² = 2AB²
AB = x/√2
30 = x/√2 + x + x/√2
x = 30 / 1 + √2
The apothem = 30 / 2
= 15
perimeter = 8x
= 8(30 / 1 + √2)
= 99.4 inches
area = 0.5 x 15 x 99.4
= 745.59
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HELP PLEASE
if a function representing distance (feet) as a function of time (minutes), what does f(30) represent in terms of the situation?
Answers
We know
In a function
y=f(x)x represents the input and y represents output
So
f(30)x is time
So
f(30) represents distance traveled in 30mins
The area of a circle is 9pi cm². Find its radius.
Please do this question with full solution:)
Answers
Answer:
3 cm
Step-by-step explanation:
The formula for the area of a circle is:
[tex]A = \pi r^2[/tex]
Where "r" represents the radius of the circle. We can substitute the given value for Area into the equation to solve for the radius.
Solve for Radius[tex]A=\pi r^2\\9\pi = \pi r^2[/tex]
Divide both sides by π
[tex]9=r^2[/tex]
Take the square root of both sides
[tex]\sqrt9=\sqrt {r^2}\\r=3[/tex]
The radius of the circle is 3 cm.
Which system of measurement uses the minim as the basic unit of liquid measure?
Answers
The apothecary system uses the minim as the basic unit of liquid measure and the grain as the basic unit of solid measure.
What is apothecary measurement?
The apothecary system was once a system of weights and measurements used for drug prescription and dispensing. A pound was divided into 12 ounces in the English version, which also divided an ounce into eight drams or drachms and a dram into three scruples, or 60 grains.What are the units of the apothecary system?
The grain, scruple (20 grains), dram (3 scruples), ounce (8 drams), and pound—a ancient scale of weight used in the British Isles for measuring and distributing pharmacological goods (12 ounces).
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Complete the steps to solve this linear equation: 2x 9(x – 1) = 8(2x 2) – 5 1.apply the distributive property: 2x 9x– 9 = 16x 16 – 5 2.combine like terms on each side: 11x – 9 = 16x 11 3.use the subtraction property of equality to isolate the variable term: –9 = 5x 11 use the subtraction property of equality to isolate the constant: –20 = 5x 4. use the division property of equality to solve: = x
Answers
Answer:
x= 5/2
Step-by-step explanation:
Answer:
-4 =x
Step-by-step explanation:
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Identify the equation that describes the line in slope-intercept form slope = 3/4 point (2, 2) is on the line
Answers
Answer:
y = (3/4)x + 1/2
Step-by-step explanation:
the slope-intercept form is in general
y = ax + b
with a being the slope, and b the y-intercept (the y-value when x = 0).
because we got the slope and a point we can start with the point-slope form and then transform the equation.
the point-slope form is in general
y - y1 = a(x - x1)
a is again the slope (the same value), and (x1, y1) is a point on the line.
so,
y - 2 = 3/4 × (x - 2) = (3/4)x - 3/2
y = (3/4)x - 3/2 + 2 = (3/4)x - 3/2 + 4/2 = (3/4)x + 1/2
Write the algebraic expression that represents the following: Forty more than a number
Answers
Answer:
x+40
Step-by-step explanation:
Let's say the the "number" is x.
"Forty more than a number" would be x+40
[tex]\Large\texttt{Answer}[/tex]
[tex]\bold{40+n}[/tex]
[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]
[tex]\Large\texttt{Process}[/tex]
⇨ Letting n be the number
[tex]\bold n[/tex]
⇨ Add 40 to n (40 more)
[tex]\bold{40+n}[/tex] (or n+40; you can swap these numbers, they'll still add up to the same amount)
Hope that helped
What is the exponent of x in in the expression -4x^3y^2 + 6
Answers
Answer:
3
Step-by-step explanation:
- 4x³y² + 6
the x is raised to the power of 3 , that is exponent of x is 3
Find the radius of convergence of the power series. (if you need to use or –, enter infinity or –infinity, respectively. ) [infinity] (−1)n xn 2n n = 0
Answers
For given power series [tex]\sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}[/tex] the radius of convergence is 2.
For given question,
We have been given a power series [tex]\sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}[/tex]
We need to find the radius of convergence of the power series.
We use ratio test to find the radius of convergence of the power series.
Let [tex]a_n=\frac{(-1)^nx^n}{2^n}[/tex]
[tex]\Rightarrow a_{n+1}=\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}[/tex]
Consider,
[tex]\lim_{n \to \infty}|\frac{a_{n+1}}{a_n} |\\\\= \lim_{n \to \infty} |\frac{\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}}{ \frac{(-1)^nx^n}{2^n} } |\\\\=\lim_{n \to \infty} |\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}\times \frac{2^n}{(-1)^nx^n} |\\\\=\lim_{n \to \infty} |\frac{(-1)x}{2} |\\\\=\lim_{n \to \infty}|\frac{-x}{2} |\\\\=\frac{x}{2}[/tex]
By Ratio test, given power series converges at [tex]|\frac{x}{2} | < 1[/tex]
⇒ |x| < 2
So, the radius of convergence is 2.
Therefore, for given power series [tex]\sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}[/tex] the radius of convergence is 2.
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n January 1989, the temperature in Nome, Alaska dropped to −49° F. Would the gas in the driver's truck have remained in liquid form so he could have driven on this day? Why or why not?
Answers
Answer: The gas would not have remained liquid
Step-by-step explanation:
Since the freezing point of gasoline starts at -40°F, and the temperature that day was -49°F, we can conclude that the gasoline would not have remained liquid
Veronica's trail-mix package says there are 7 peanuts for every 3 cashews. Casey's trail-
mix package says there are 63 peanuts and 27 cashews. Are these ratios proportional?
If not, how many peanuts should there have been to make it proportional?
Answers
Answer:
Yes, they are proportional.
Step-by-step explanation:
The ratio for Veronica's trail mix is 3:7
The ratio for Casey's trail mix is 27:63 <--- Simplify this number
27:63 simplified is 3:7, which means these ratios are proportional.
hope this helps :)
PLEASE HELP ME !!!
The height of the pyramid in the diagram is three times the radius of the cone. The base area of the pyramid is the same as the base area of the
cone. What is the expression for the volume of the pyramid in terms of the radius r of the cone?
base area for cone= B
base area for pyramid= B, 3r heigh
A. V = pi r³
B. V = 1/3 pi r²
C. V = 2 pi r²
D. V = 1/9 pi r³
E. V = 3 pi r³
Answers
Answer:
The answer is A. V=pi r³
Step-by-step explanation:
:)
The expression for the volume of the pyramid in terms of the radius r of the cone is [tex]\pi r^3[/tex]. So, option A is correct.
The cone is a three-dimensional figure with a vertex and a flat base.
The volume of a pyramid is given by the formula:
[tex]V = \dfrac{1}{3} \times base\ area \times height.[/tex]
Given that:
The base area of the pyramid = B
The height is 3r
The base area of the pyramid is the same as that of the cone.
The base of the cone = [tex]\pi r^2[/tex]
The volume of the pyramid is calculated as:
[tex]V = \dfrac{1}{3} \times \pi r^2 \times 3r[/tex]
V =[tex]\pi r^3[/tex]
Therefore, the volume of the pyramid is [tex]\pi r^3[/tex]. So, option A is correct.
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PLEASE ASAP - Drag each tile to the correct box. Arrange the figures from least to greatest according to their volumes. Assume the variable h has the same value for each figure.
Answers
Assuming that the variable h is the same for each figure, the figures from the least to the greatest is:
Cone with radius of 3 units Cylinder with radius of 3 units Cone with radius of 6 units Cylinder with radius of 6 unitsWhat are the volumes of these shapes?The value of h is the same for all the shape so assume the value of h is 2 units.
The volume of a cylinder is:
= πr²h
First cylinder area:
= 22/7 x 3 x 2
= 56.54867 units
The second cylinder area:
= 22/7 x 6 x 2
= 226.19467 units
The volume of a cone is:
= πr²h/3
First cone volume:
= 22/7 x 3 x 2/3
= 18.84956 units
Second cone volume:
= 22/7 x 6 x 2/3
= 75.39822 units
The order is therefore:
Cone with radius of 3 units < Cylinder with radius of 3 units < Cone with radius of 6 units < Cylinder with radius of 6 units
In conclusion, the shapes with the larger radius of 6 units will have more volume.
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QUICK!!!HELP!!!!!!!!!!!!!!!!!!
Answers
Using the normal distribution, the probability that a worker selected at random makes between $500 and $550 is: 2.15%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean mu and standard deviation sigma is given by:
Z = (X - mu)/sigma
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given as follows:
mu = 400, sigma = 50
The probability is the p-value of Z when X = 550 subtracted by the p-value of Z when X = 500, hence:
X = 550:
Z = (X - mu)/sigma
Z = (550 - 400)/50
Z = 3
Z = 3 has a p-value of 0.9987.
X = 500:
Z = (X - mu)/sigma
Z = (500 - 400)/50
Z = 2
Z = 2 has a p-value of 0.9772.
0.9987 - 0.9772 = 0.0215 = 2.15% probability.
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MN =7. Find AB.
3.5
10.5
14
Answers
The length of line segment AB by observation if the diagram in the task content is; 14.
What is the length of line segment AB?It follows from the task content that the line segment MN can be considered as parallel to line segment AB. This follows from the fact that the vertices of triangle MNO are midpoints of the line segments of triangle ABC.
Consequently, it can be concluded that line segment AB is twice the length of line segment MN and hence, BC = 2 × 7 = 14.
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When calculating a nation’s digital power, what term is used to refer to the demonstrated capabilities of a nation-state in cyber offense or defense?
Answers
When calculating a nation’s digital power, the term that is used to refer to the demonstrated capabilities of a nation-state in cyber offense or defense is Cyberwarfare.
What is Cyberwarfare?Cyberwarfare can be regarded as the use of cyber attacks against a nation-state so as to produce significant harm.
It should be noted that Cyber Warfare is set of actions which is been carried out by nation or organization so as to be able to launch an attack on institutions' computer network systems.
The interests or reasons for cyberwarfares based on the Cybersecurity as well as Infrastructure Security Agency are;
To weaken the system of another country.To disrupt or destroy the sytem of another nation.In order to achieve the goals behind the cyberwarfare programs, it is usually designed to focus on spectrum of objectives which will bring harm to national interests.
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Find the Area Of each circle.
Answers
The area of the circle A and B is 86.54 inches and 124.62 mm
According to the statement
we have given that the radius of the circle A and b and we have to find the area of the given circle.
So, we know that the
The area enclosed by a circle of radius r is πr².
So, For area of the circle
For condition A :
diameter = 10.5 inches
then radius = 5.25
Area = πr²
Area = 3.14*27.56
Area = 86.54 inches
Now, For condition B :
radius = 6.3 mm
Area = πr²
Area = 3.14*39.69
Area = 124.62mm
So, The area of the circle A and B is 86.54 inches and 124.62 mm
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Bob needs to send out a mailing for his company. Working alone, it will take him 10 hours to get the job done. Ellen can do the job in 8 hours by herself. They work together for 2 hours, and then Ellen finishes the job by herself. Which choice is the best estimate for how long the job will take in all?
Answers
Answer:
6 2/5 hrs or 6.4 hours total
Step-by-step explanation:
In two hours, Bob completes 2/10 = 1/5 of the job
Ellen completes 2/ 8 = 1/4
Find amount left
1 - 1/5 -1/4 = 1 - 4/20 - 5/20 = 11/20 left
Ellen will need 8hrs * 11/20 = 88/20 = 4 2/5 hours to finish the job
2 hours to start + 4 2/5 hours to finish = 6 2/5 hours total
The triathletes were offered water as they rode by the volunteer station. The volunteers handed them cones with the dimensions shown. If each triathlete sloshed 1/3 of the water out before they drank it, how many cubic cm of water did they slosh out? Round to the nearest tenth. (PLEASE ANSWER)
Answers
Answer:
29.9 cm³
Step-by-step explanation:
You want to know the volume represented by 1/3 of a cone that is 7 cm high and has a radius of 3.5 cm.
ConeThe volume of a cone is given by ...
V = 1/3πr²h
The volume of the cone of interest is ...
V = 1/3π(3.5 cm)²(7 cm) ≈ 89.797 cm³
Slosh1/3 of the volume is the amount of water that sloshed out of the cone. That volume is ...
1/3(89.797 cm³) ≈ 29.9 cm³
They sloshed out about 29.9 cm³ before they drank the water.
<95141404393>
If BD = 16 yd and the area of rhombus ABCD is 72 yd^2, what is AC?
Answers
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Given:▪ [tex] \sf{Area\text{ ABCD=}\frac{1}{2}\times AC\times BD}[/tex]
▪ [tex] \sf{Area = 72 yd^2}[/tex]
▪ [tex] \sf{BD = 6yd}[/tex]
[tex]\leadsto[/tex] Substitute the values:
[tex]\longrightarrow \sf{72 = \dfrac{1}{2} \times AC \times 16}[/tex]
[tex]\leadsto[/tex] Solve for AC:
[tex]\longrightarrow \sf{72=8\times AC}[/tex]
[tex]\longrightarrow \sf{ \dfrac{72}{8}=\dfrac{8\times AC}{8}}[/tex]
[tex]\longrightarrow \sf{AC=9}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex]\large \bm{AC= \: 9 yd}[/tex]
BD = 16 yd
Area of ABCD = 72 yd²
AC = ?
Area of rhombus, using diagonal:
[tex] \frac{1}{2} \times d1 \times d2[/tex]
Therefore:
[tex] \frac{1}{2} \times 16 \times ac = 72[/tex]
Then:
[tex] \frac{16ac}{2} = 72[/tex]
Cross multiply the above into:
[tex]16ac \times 1 = 72 \times 2 = 144 \\ 16ac = 144[/tex]
Divide by the coefficient of AC:
[tex] \frac{16ac}{16} = \frac{144}{16} [/tex]
Final answer is 9 yd
Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed.
Cos C
C
21
B
35
28
A
Answers
=0.6
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Halfway through the season, the USF Bulls football team had the highest average final score. What was the USF Bulls' average score if their final
scores were 31, 36, 28, 52, and 27
Answers
Answer:
D 34.8
Step-by-step explanation:
[tex]\frac{31+36+28+52+27}{5}[/tex]
