To ascertain points of discontinuity, evaluate where functions are undefined or have limits that do not exist, often due to division by zero or undefined behavior in their basic components. For example, f(x) = 1/ sin x is discontinuous where sin x equals zero.
To find out where a function is discontinuous, we must examine points where the function is not defined or its limit does not exist. For a function defined by building blocks of continuous functions, it will generally remain continuous except at points where it involves division by zero or at points where its simpler components are not continuous.
For example, the function f(x) = 1/ sin x can be seen as the composition of the functions g(x) = 1/x and h(x) = sin x. We know that for a sine function, namely h(x), it is continuous everywhere, but the function g(x) is discontinuous at 0. Hence, f(x) will be discontinuous at points where sin x = 0, which occur at integer multiples of π.
More generally, to check continuity, ask yourself these questions about the function:
Does the function cross zero or involve division by a variable that may be zero?Is the function defined for all values of its independent variables?Is the function graph a single unbroken curve without jumps?If you answer 'no' to any of these, the function might be discontinuous at some points, and hence, it would also be nondifferentiable at those points.
You are making cookies for a bake sale and need to make enough cookies to fill 24 boxes containing 6 cookies each. How many dozen cookies do you need to make?
To make enough cookies to fill 24 boxes containing 6 cookies each, you need to make 12 dozen cookies.
Explanation:To find out how many dozen cookies you need to make, you need to divide the total number of cookies by 12.
In this case, there are 24 boxes with 6 cookies each, so the total number of cookies is 24 x 6 = 144.
Dividing 144 by 12 gives us 12 dozen cookies.
A carpenter has 16 1/2 m of wood. He cuts the wood into pieces that are each 2 3/4 m long. How many pieces of wood does the carpenter cut? please help ill mark brainliest
Answer:
the answer is 1/2
i think
Step-by-step explanation:
in each case are the 2 events dependent or independent toss a dime and then toss a quarter pick a card from a deck of cards keep the card and pick another one
Final answer:
Tossing a dime and then tossing a quarter are independent events because one toss does not affect the other. Picking a card from a deck, keeping it, and picking another is a dependent event because the first pick changes the composition of the deck for the second pick.
Explanation:
To determine whether the two events mentioned are dependent or independent, we can use the definition of statistical independence. If the outcome of the first event does not affect the outcome of the second event, then the events are independent. If the outcome of the first event influences the outcome of the second event, then the events are dependent.
For the first scenario, tossing a dime and then tossing a quarter are independent events. This is because the result of tossing the dime has no effect on the result of tossing the quarter, much like having a nickel and a dime in your pocket and pulling one out, replacing it, and pulling one out again with probabilities being independent.
For the second scenario, when you pick a card from a deck of cards, keep the card, and then pick another one, the events are dependent. This is because the first card you draw and keep affects the composition of the deck from which the second card is drawn. It's like not replacing the first coin before pulling out the second one; your chances change based on the first outcome.
Using the concept of compound events and the law of the probability of compound events, we can see that independent events allow us to calculate the probability of any outcome when combining two independent events. Conversely, with dependent events, the probability of the subsequent event is influenced by the outcome of the preceding one.
Solve w = t(r1 + r2) for t.
Answer:
The solution for t is [tex]\frac{w}{(r_1+r_2)}[/tex]
Step-by-step explanation:
The given expression is [tex]w = t(r_1+r_2)[/tex]
We need to solve for the 't' ,
To solve for t, divide [tex]w = t(r_1+r_2)[/tex] by [tex](r_1+r_2)[/tex]
[tex]\frac{w}{(r_1+r_2)} = t[/tex]
Hence, The solution for t is [tex]\frac{w}{(r_1+r_2)}[/tex]
At the restaurant, the cost of the meal before tax was $40. The tax is 8.5%, and Sheri wants to leave at least an 18% tip. Explain how to approximate the total cost of the meal.
18% + 8.5% = 26.5% which is close to 25%
25% of 40 is 10, 40 +10 = 50
so the total bill would be just over $50
real cost:
40*0.085 = 3.40 = 40 + 3.40 = 43.40
43.40 *0.18 = 7.81, 43.40 + 7.81 = 51.21
Answer:
The gratuity is about 20% of $40, which is $8. The tax is about 10% of $40, which is $4. So, the total cost is about $40 + $8 + $4 = $52.
A woman is 43 years old, and her daughter is 15 years old. How many years will it be before the woman’s age is just twice her daughter’s?
43 +x = 2(15+x)=
43 + x = 30 +2x
43 = 30 +x
13 =x
13 years
43+13 = 56
15 +13 = 28 ( 28*2 = 56)
Jose heard a song on the radio as he was flipping between stations. He immediately remembered that his brother, Juan, played that piece on his guitar. Jose's response was _____ .emotional physical intellectual none of the above
Answer:
Option C, Intellectual Response
Step-by-step explanation:
Intellectual response comes after intellectual thinking which includes deep , intensive and focused thinking in a certain direction. In this case, Jose after hearing a song on radio remembers that his brother used to play the same song on guitar. This is an intellectual response as after listening the song Jose's brain must have evaluated the past interactions associated with this song and hence after the evaluation he comes to know that he had heard the same song in past when his brother played it on his guitar.
Thus, option C is correct.
Jose wants to put a fence around his rectangular garden. His garden measures 31 feet by 33 feet. The garden has a path around it that is 3 feet wide. How much fencing material does Jose need to enclose the garden and path?
What is the value of x in the equation 3x – 1/9y = 18, when y = 27?
A. 5
B. 7
C. 45
D. 63
The answer is x=7, because if you use PEMDAS you will come up with x=7.
Solve the equation by factoring. 9 xsquared +21x -8= 0
suppose you deposit $500 into an account earning 7.8% interest compound annually. what will your balance be after 5 years?
What is the x value in the solution to this system of linear equations?
2x-y=11
x+3y=-5
a.-3
b.-1
c.2
d.4
Answer with Step-by-step explanation:
We have to determine the value of x on solving the system of linear equations:
2x-y = 11
x+3y = -5
2x-y=11
Adding y on both sides and subtracting by 11 on both sides, we get
y=2x-11
Putting value of y in x+3y = -5
x+3(2x-11) = -5
x+6x-33 = -5
7x -33 = -5
adding 33 on both sides, we get
7x= 28
Dividing by 7 on both sides, we get
x=4
Hence, Correct option is:
d. 4
An Internet service company earned $770 in set-up fees for new homes in a neighborhood. They charged $35 for each new set-up. How many new set-ups did they perform? A.19 B.22 C.25 D.26
An Internet service company earned $770 in set-up fees for new homes in a neighborhood. For each new set-up they charged $35. Then they performed 22 new set ups. So option B is correct.
What is equation?Two expressions with an equal sign is called equation.
An Internet service company earned $770 in set-up fees for new homes in a neighborhood. They charged $35 for each new set-up, then number of new setups we have to find,
Internet service company earned =$770
For each new set-up they charged $35
Number of set ups they perform = x
35x=770
x=770/35
x=22
Therefore 22 new setups are performed.
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The probability that Shania is on time for school is 1/2. Find the probability that Shania arrives on time for school for the next 5 days. Express your answer as a percent, to the nearest tenth of a percent. A. 50% B. 15.6% C. 11.4% D. 3.1%
Answer: 3.1 %
Step-by-step explanation:
Given : The probability that Shania is on time for school is [tex]\dfrac{1}{2}[/tex]
Since the each day is independent of other.
Then , the probability that Shania arrives on time for school for the next 5 days will be :_
[tex]=(\dfrac{1}{2})^5=\dfrac{1}{32}=0.03125\approx3.125\%\approx3.1\%[/tex]
Hence, the probability that Shania arrives on time for school for the next 5 days. = 3.1 %
write a system of linear equations with -3,9 as its solution
Final answer:
To create a system of linear equations with the solution (-3, 9), we need to construct two equations that intersect at this point, for example, y = -3x + 18 and y = 2x + 15.
Explanation:
To write a system of linear equations with the solution (-3, 9), we can create two separate equations that intersect at this point. Using the equation provided, y = 9 + 3x, we can see that the point (-3, 9) satisfies this equation since plugging in x = -3 gives us y = 9 + 3(-3) = 9 - 9 = 0, which is incorrect. We must correct the mistake and ensure that the solution (-3, 9) satisfies both equations in our system.
A correct form of the first equation would be y = -3x + 9 (not y = 9 + 3x as provided), since plugging x = -3 yields y = -3(-3) + 9 = 9 + 9 = 18, which is also incorrect. Therefore, we need to be careful in constructing our equations.
Let's construct two new equations correctly:
First, we start with the equation y = -3x + 18, which does satisfy the condition when x = -3 and y = 9. Next, we can create a different equation with the same solution. For instance, if we want another equation, we might use the slope-intercept form, y = mx + b. We can choose a different slope (m), for example, m = 2, and find b such that when x = -3, y = 9:
y = mx + b
9 = 2(-3) + b
9 = -6 + b
b = 15
So, the second equation is y = 2x + 15. The system of linear equations with the solution (-3, 9) is:
1. y = -3x + 18
2. y = 2x + 15
A point on the terminal side of an angle is given. find the exact value of the indicated trigonometric function of
An earthquake registered 7.4 on the Richter scale. If the reference intensity of this quake was 2.0 × 1011, what was its intensity?
Answer:
The intensity was [tex]5.02377\times 10^{18}[/tex]
Step-by-step explanation:
We are given
An earthquake registered 7.4 on the Richter scale
so, RC=7.4
the reference intensity of this quake was 2.0 × 10^11
so,
[tex]I_r=2.0\times 10^{11}[/tex]
now, we can use formula
[tex]RS=log(\frac{I}{I_r} )[/tex]
now, we can plug values
[tex]7.4=log(\frac{I}{2.0\times 10^{11}} )[/tex]
now, we can solve for I
[tex]10^{7.4}=\frac{I}{2.0\times 10^{11}}[/tex]
[tex]I=10^{7.4}\times 2.0\times 10^{11}[/tex]
[tex]I=5.02377\times 10^{18}[/tex]
To find the intensity of an earthquake registered on the Richter scale, use the formula based on the magnitude difference and energy ratio.
The intensity of the earthquake can be calculated using the Richter scale formula, which relates the magnitude difference to the energy ratio.
Given that one step on the Richter scale corresponds to a factor of 100 in energy, a difference of 7.4 - 2.0 = 5.4 on the Richter scale results in a ratio of 100^5.4.Therefore, the intensity of the earthquake can be calculated as (100^5.4) * (2.0 x 10^11), which simplifies to approximately 2.52 x 10^17.Line segment YV of rectangle YVWX measures 24 units. What is the length of line segment YX? 8 units units 12 units units
The length of the line segment YX in rectangle YVWX is [tex]\rm 8\sqrt{3} \; units[/tex] and it can be determine by using the trignometric properties and properties of rectangle.
Given :
YV = XW = 24 units[tex]\rm \angle VXW = 30^\circ[/tex][tex]\rm \angle XWV = 90^\circ[/tex][tex]\rm \angle XVW = 60^\circ[/tex]The length of the line segment YX in rectangle YVWX can be determine by using the trignometric properties.
[tex]\rm tan \theta = \dfrac{Perpendicular}{Base}[/tex]
[tex]\rm tan 60 = \dfrac{24}{VW}[/tex]
[tex]\rm \sqrt{3} = \dfrac{24}{VW}[/tex]
[tex]\rm VW =8\sqrt{3}\;units[/tex]
In rectangle opposite sides are equal. Therefore, [tex]\rm VW=YX = 8\sqrt{3}\;units[/tex].
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[tex]\rm VW=YX = 8\sqrt(3)\;units.[/tex]
The length of the line segment YX in rectangle YVWX is \rm 8√(3) \; units and it can be determine by using the trignometric properties and properties of rectangle.
Given :
YV = XW = 24 units
[tex]\rm \angle VXW = 30^\circ\\\rm \angle XWV = 90^\circ\\\rm \angle XVW = 60^\circ[/tex]
The length of the line segment YX in rectangle YVWX can be determine by using the trignometric properties.
[tex]\rm tan \theta = (Perpendicular)/(Base)\rm tan 60 = (24)/(VW)\rm √(3) = (24)/(VW)\rm VW =8√(3)\;units[/tex]
In rectangle opposite sides are equal. Therefore, [tex]\rm VW=YX = 8√(3)\;units[/tex].
What are the zeros of the polynomial function f(x) = x3 − x2 − 20x?
The other two zeros, which are x = 5 and x = -4.
To find the zeros of the polynomial f(x) = x³ − x² − 20x, we need to set the polynomial equal to zero and solve for x. This can be done by factoring out the common term x from each term of the polynomial:
f(x) = x(x² - x - 20) = 0
The zeros of the polynomial will be the values of x for which the product is zero. Since we already have x as one factor, one zero is x = 0. We then need to factor the quadratic, which is:
x² - x - 20
We can factor this quadratic to
(x - 5)(x + 4)
Thus, the other two zeros of the polynomial are x = 5 and x = -4.
Given: f(x) =x^3 and g(x)= 4x+3
Find: g(f(3))
Zoe and Hannah share tips in the ratio 3:7 Last week , Zoe received £24. how much did Hannah receive Last week?
Answer:
£56 did Hannah receive Last week
Step-by-step explanation:
Let the number be x.
As per the statement:
Zoe and Hannah share tips in the ratio 3:7.
Then;
Total Zoe share = 3x
Total Hannah share = 7x
It is also given that Last week , Zoe received £24.
⇒3x = 24
Divide both sides by 3 we have;
x = 8
Hannah receive Last week = 7x = 7(8) = £56
Therefore, £56 did Hannah receive Last week
30 packages a minute are unloaded from a truck that has 2700 packages. How long would it take to unload the truck?
It would take 90 minutes to unload a truck containing 2700 packages at a rate of 30 packages per minute.
Explanation:This problem involves performing a simple division operation. Given that 30 packages are unloaded from a truck each minute and there are a total of 2700 packages on the truck, we find the time it would take to unload the truck by dividing the total number of packages by the number of packages that can be unloaded each minute.
Solution:
We solve the problem as follows:
First, state the number of packages in the truck, which is 2700 packages. Next, note the rate at which packages are being unloaded per minute, which is 30 packages a minute. Then, we simply divide the total number of packages by the number of packages that can be unloaded per minute. This gives us the total time required to unload the entire truck, which is 2700⁄30 = 90 minutes.Therefore, it would take 90 minutes to unload the entire truck.
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A scientist is measuring the temperature change and a chemical compound the temperature dropped 11 Fahrenheit per hour from the original temperature after four hours the temperature was 90°F find the compounds original temperature
Answer: 134°F
Step-by-step explanation:
Given : A scientist is measuring the temperature change and a chemical compound the temperature dropped 11° Fahrenheit per hour from the original temperature .
Let x be the original temperature.
Then , the compound temperature after t hours is given by :_
[tex]y=x-11t[/tex]
At t= 4 hours and x= 90°F, we have
[tex]90=x-11(4)\\\\\Rightarrow\ x-44=90\\\\\Rightarrow\ x=90+44=134[/tex]
Hence , the compounds original temperature = 134°F
A swimming pool in the shape of a rectangle is surrounded by 3 feet of walkway. the pool is 23 feet wide and 32 feet long. how long would the fence be that just encloses the walkway and the pool?
different lengths of crayons?
One side of a triangle is three times the shortest side. the third side is three feet more then the shortest side. the perimiter is 13 feet.
round 87600.2 to 1 significant figure
Answer:
90000
Step-by-step explanation:
A significant figure is a number different from zero that assigns the value of the quantity.
In this case, you have four significant figures, not counting the zeros. To round this, you need the first upper number with only one significant figure.
For that, we use 9 because is the next number from 8, and then complete the value with zeros.
87600.2 will be 90000.0
What is the vertex of the graph of y= x ^2+4x
what is, x is at most 30 inequality
What is the vertex of y=6x^2-24x+30
The vertex of the quadratic equation y = 6x^2 - 24 + 30 is (2, -6).
Explanation:The given equation is y = 6x^2 - 24x + 30.
To find the vertex of this quadratic equation, we can use the formula x = -b/2a.
In this equation, a = 6 and b = -24. Plugging these values into the formula, we get x = -(-24)/(2*6) = 24/12 = 2.
Now, substitute this value of x into the equation to find the corresponding y-coordinate of the vertex.
Substituting x = 2, we get y = 6(2)^2 - 24(2) + 30 = 12 - 48 + 30 = -6.
Therefore, the vertex of the given quadratic equation is (2, -6).