how is algebraic expression solve
Answer:
Step-by-step explanation:
you must work in a certain order, usually starting with parentheses, then exponents, then multiplication or division, and finally addition or subtraction.
An inductor of l = 250 is subjected to a voltage v(t) = 8 e-4t V:
A. Knowing that, integrate both sides to determine the current i(t). You may assume that the initial current is zero.
B. Given that the absorbed power is, determine the total stored energy.
Total stored energy = (1/625) ∞
What understand by voltage?Voltage, also known as electric potential difference, is the measure of the electric potential energy per unit of charge in an electric circuit. It is the force that drives the electric charge in a circuit, similar to how pressure drives water through a pipe. Voltage is measured in volts (V) and is usually represented by the symbol "V". Voltage can be either positive or negative, depending on the direction of current flow and the orientation of the voltage source.
A. The voltage across an inductor is proportional to the time derivative of the current through it, according to Faraday's law of electromagnetic induction. This can be expressed mathematically as:
v(t) = L di/dt
where v(t) is the voltage across the inductor, L is the inductance in henries, and di/dt is the time derivative of the current through the inductor.
In this case, we have [tex]v(t) = 8e^{(-4t)[/tex] V and L = 250 H. Integrating both sides of the above equation with respect to time gives:
∫v(t) dt = L ∫di/dt dt
∫[tex]8e^{(-4t)} dt = 250[/tex] ∫di/dt dt
[tex]-2e^{(-4t)[/tex]= 250i(t) + C
where C is the constant of integration. We can assume that the initial current is zero, so at t = 0, i(0) = 0. This means that C = -2. Substituting this into the equation above, we get:
[tex]-2e^{(-4t)[/tex]= 250i(t) - 2
Solving for i(t), we get:
i(t) = (2/250) [tex]- (2/250)e^{(4t)[/tex]
B. The power absorbed by an inductor is given by:
P = i² R
where P is the power, i is the current, and R is the resistance of the circuit. In an ideal inductor, the resistance is zero, so the power absorbed is also zero.
However, the energy stored in an inductor can be calculated using the following formula:
E = 1/2 L i²
where E is the energy stored, L is the inductance, and i is the current.
In this case, we have L = 250 H and i(t) = (2/250) [tex]- (2/250)e^{(4t)[/tex]Substituting these values into the above equation, we get:
E = 1/2 (250) [(2/250) [tex]- (2/250)e^{(4t)]^2[/tex]
Simplifying this expression, we get:
E = (1/625) [tex]- (2/625)e^{(4t)[/tex]+ (2/625)e^(8t)
To determine the total stored energy, we need to integrate this expression over the interval 0 to infinity, since the voltage and current are given for all values of t. This gives:
Total stored energy = ∫E dt from 0 to infinity
Total stored energy = (1/625) ∫1 dt from 0 to infinity[tex]- (2/625) ∫e^{(4t)[/tex]dt from 0 to infinity + (2/625) ∫e^(8t) dt from 0 to infinity
Total stored energy = (1/625) ∞ [tex]- (2/625) [1/4 e^{(4t)][/tex]from 0 to infinity + (2/625) [1/8 e^(8t)] from 0 to infinity
Since the integrals involving exponential functions go to infinity as t goes to infinity, these terms become zero. Therefore, we are left with:
Total stored energy = (1/625) ∞
which is an infinite value. This is because the energy stored in an inductor is not finite, but rather is dependent on the magnetic field generated by the inductor, which can extend infinitely far.
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What is the ratio of yellow to Red
6 yellow = 5 green
4 green = 3 purple
5 purple = 2 red
A.3 to 1
B.4 to 1
C.5 to 1
D.6 to 1
Yellow to red hence has a 4 to 1 ratio. Solution: B. 4 to 1 as 2 red times 5 purple (Instead of purple).
what is proportion ?A percent is a claim that two factors are equal in mathematics. When two quantities are compared by dividing them, the result is expressed as a ratio as a fraction. For instance, the number of girls to boys in a class can be expressed as "girls: boys" or "girls/boys." One way to express a percentage is as follows: a/b = c/d in which a, b, c, and d were four values that prevent b and d from being equal to zero. As a result, the ratio of a to b is the same as the ratio of c to d. The first term (a) is therefore equal to the reelection campaign (b), and the τ (c) is equal to the fourth term.
given
The given equalities can be used to calculate the proportion of yellow to red:
5 green times 6 yellow (Subtract both sides by 5)
(6/5) Yellow is equivalent to green.
3 purple + 4 green (substitute for green)
4 (6/5) Purple x 3 yellow
(24/5) Purple x 3 yellow (divide both sides by 4)
(8/5) Purple x yellow
2 red times 5 purple (Instead of purple)
(5/8) yellow Equals 2 red.
2 red x 8 yellow (divide both sides by 5)
Red + 4 yellows
Yellow to red hence has a 4 to 1 ratio. Solution: B. 4 to 1 as 2 red times 5 purple (Instead of purple).
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Question 4(Multiple Choice Worth 1 points)
(04.03 MC)
On a number line, point A is located at 4, point C is located at 11, and point B lies between points A and C. What is the location of B such that the ratio of AB BC is 2:3
8.2
6.8
5.9
5.6
can someone please help me
Find the Center and Radius (x-9)^2+(y+4)^2=36
Answer:
The center is (9, -4), and the radius is
√36 = 6.
Mrs. Smith made 6 ¼ dozen cookies for the birthday party. At the end of the party, there were 3 ½ dozen cookies left. How many cookies did the guests eat?
The guests in the birthday party ate 33 cookies.
How many cookies did the guests eat?We know that Mrs. Smith made 6 1/4 dozen cookies and there were 3 1/2 dozen cookies left.
Let's first convert these fractions to a common denominator of 4, so we can easily subtract them.
6 1/4 dozen = 25/4 dozen
3 1/2 dozen = 14/4 dozen
Now we can subtract the number of cookies that were left from the number of cookies that were made:
25/4 - 14/4 = 11/4 dozen
To find out how many cookies this represents, we need to multiply by the number of cookies in one dozen.
There are 12 cookies in one dozen, so:
11/4 x 12 = 33
Therefore, the guests ate 33 cookies.
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F(x)=x-1/x+1 show that f(2x)=3f(x)+1/f(x)+3?
The proof that f(2x)=3f(x)+1/f(x)+3 is shown below.
Mathematical functionTo show that f(2x) = 3f(x) + 1/f(x) + 3, we substitute 2x for x in the expression for f(x):
f(x) = x - 1 / x + 1
f(2x) = 2x - 1 / 2x + 1
Next, we substitute x into the expression for f(x) and add the result to itself twice:
f(x) = x - 1 / x + 1
f(x) + f(x) + f(x) = (x - 1 / x + 1) + (x - 1 / x + 1) + (x - 1 / x + 1)
= 3x - 3 / 3x + 3
We can simplify the expression by dividing both the numerator and denominator by 3:
f(x) + f(x) + f(x) = x - 1 / x + 1
= (1/3) (3x - 3) / (1/3) (3x + 3)
= (x - 1) / (x + 1)
= f(x)
Now, we substitute f(x) and f(2x) back into the original equation:
f(2x) = 2x - 1 / 2x + 1
3f(x) + 1/f(x) + 3 = 3(x - 1 / x + 1) + 1/(x - 1 / x + 1) + 3
= (3x - 3 / x + 1) + (1 / (x - 1 / x + 1)) + 3
= (3x - 3 + (x + 1) / (x - 1)) / (x + 1)
= (2x + 2) / (x + 1)
= 2(x + 1) / (x + 1)
= 2
Thus, we have shown that f(2x) = 3f(x) + 1/f(x) + 3.
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Altina Restaurant Flexible Budget for November 2010
A. What was Watson’s actual check average? Was this higher or lower than the original budget and flexible budget check average?
b. Were Watson’s actual food sales higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?
c. Was Watson’s actual food cost higher or lower than the original budget? Why do you think this is so?
d. Was Watson’s actual food cost higher or lower than the flexible budget? By how much? Was this favorable or unfavorable? How can Watson use this information in his report to his general manager?
e. Were Watson’s variable salaries, wages, and benefits higher or lower than the original budget?
f. Were Watson’s variable salaries, wages, and benefits higher or lower than the flexible budget? By looking at both the original budget and the flexible budget, what conclusion can you draw about Watson’s ability to control his labor costs?
g. Was Watson’s actual net income higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?
h. Overall, how do you think Watson is doing at meeting the budget goals set by the general manager? How should he respond to his general manager’s claim that his department is operating at a “sub-par” performance level?
Walton's actual check average is $9.52
The actual food cost is lower than the flexible budget by $5020
What is Net Income?Net income considered a vital financial metric of an organization, delineates the earned sum after deducting expenses and taxes from total revenue.
The measure is indicative of the profitability status of an entity, portraying cash flow left over subsequent to settling all obligations. To uncover net income, business expenditures spanning across areas such as salaries, interest payments and rents alongside taxations are subtracted from entire receipts.
Ascertaining net income facilitates assessing the fiscal robustness and future prospects of a company for interested investors.
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If you deposit $2000 in an account paying 2% annual interest compounded monthly, how much money will you have in the account after 40 years?
Answer: To calculate the amount of money you will have in the account after 40 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the amount of money in the account after t years, P is the principal (the initial amount of money deposited), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
In this case, P = $2000, r = 0.02 (since the interest rate is 2%), n = 12 (since the interest is compounded monthly), and t = 40. Plugging these values into the formula, we get:
A = 2000(1 + 0.02/12)^(12*40)
A = $5,837.85
So you will have $5,837.85 in the account after 40 years.
Question 1(Multiple Choice Worth 2 points)
(Linear Functions LC)
Which of the following equations represents a linear function?
A x=1
B y=12²
C y-12-1
D4x-2=6
The equation that represents a linear function is D 4x - 2 = 6.
Which equation represents a linear function?A linear function is a function whose graph is a straight line. In general, the equation of a linear function can be written in the form y = mx + b, where m is the slope and b is the y-intercept.
Option A (x = 1) represents a vertical line passing through x = 1. Since the slope of a vertical line is undefined
Option B (y = 12²) represents a horizontal line passing through y = 144. Since the slope of a horizontal line is zero
Option C (y = 12-1) represents a horizontal line passing through y = 11. Since the slope of a horizontal line is zero
Option D (4x - 2 = 6) can be rewritten as 4x = 8 or x = 2. This is the equation of a vertical line passing through x = 2.
Therefore, the only equation that represents a linear function is D 4x - 2 = 6.
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abc x abc x abc in condensed form
The condensed form of the expression abc x abc x abc is (abc)^3
Expressing the expression in a condensed formWhen we have the same base raised to different exponents that are being multiplied together, we can simplify or condense the expression by adding the exponents.
In this case, we have the same base "abc" being raised to the exponent of 1 three times, so we can write it as:
abc x abc x abc
To condense this expression, we add the exponents 1+1+1=3, and write it as:
(abc)^3
So, the condensed form of the expression "abc x abc x abc" is "(abc)^3".
This is an example of the exponent rule for multiplying powers with the same base.
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PLEASE HELP ASAP!!‼️ (proportional Relationships!) Extra points than 5!!
Please tell me which should I click for the 3 BOXES in each one of them!
Using equations, we can find the required equation for each of the cases as follows:
1. t = cd
2. t = qh
3. t = wm
Define equations?Equations are mathematical expressions that have two algebraic expressions on either side of the equals (=) symbol. It proves that the expressions printed on the left and right sides are equally valid. In each mathematical equation, we have LHS = RHS (left hand side = right hand side). Equations can be solved to find the value of an unknown variable that represents an unknown quantity. If there is no "equal to" symbol, a statement is not an equation. We'll consider that to be a term.
As per the question,
The total number of caps per day = c
Total number of caps made = t
Total number of days = d.
Now, the required equation will be:
t = c × d
⇒ t = cd
Coming to the next question,
Quizzes graded per hour = q.
Total number of quizzes = t.
Total number of hours = h.
So, the required equation will be:
t = q × h
⇒ t = qh.
Coming to the final question,
Words typed per minute = w.
Total number of words = t.
Total number of minutes = m
So, the required equation will be:
t = w × m
⇒ t = wm.
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How many ways can 5 different cards be dealt from a standard 52-card deck?
Answer:
There are 2598960 different ways to choose 5 cards from a standard 52-card deck.
Answer:
(52−5)5 = 2598960 different ways to choose 5 cards from the available 52 cards.
Step-by-step explanation:
What is the length of RP
The zero product property's assistance. The RP measures 14 cm in length.
What is the Length?The length of a thing refers to its size or length measured from end to end. Or, to put it a different way, it is the larger of a geometrical shape's upper two or three dimensions.
(x+x+2) * (x+2) = (4+6)*4
Conjoin similar terms
(2x+2)(x+2)=10*4
2(x+1)(x+2) = 40
Divide by 2
(x+1)(x+2) = 20
FOIL
x²+2x+x+2=20
x²+3x+2=0
Subtract 20
x²+3x-18=0
Factor
(x +9) (x-6) = 0
Utilising the zero sum property
x+9=0 x-6 =0
x= -9 x=6
The length cannot be negative, hence
x=6
RP = x+2+x
= 6+2+6
= 14
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Sophia visited a fish farm last week to learn about different fish species. She saw an empty fish tank which has a size of 30 cm x 70 cm x 80 cm. There are 5 cubes of side 20 cm in the tank. A tap that runs at 1 litre per minute was turned on to fill the tank. It was left running for 158 minutes and some water spilt out of the tank after it was full. What was the volume of water that spilt out of the tank?
Step-by-step explanation:
Volume = 20×70×80 = 112000 cm³
Volume of cubes = 20×20×20 ×5 = 8000 ×5 = 40000 cm³
Volume of space in the tank = 112000-40000 = 72000 cm³ = 72000 mL = 72 L
Volume of water from tap = 158 × 1 = 158 L
Volume of water spilt out = 158 - 72 = 86 L
Answer: 30000cm³
Step-by-step explanation:
Capacity of tank-> 30x70x80
=168000
Volume of 1 cube->20x20x20
=8000
Volume of 5 cubes->8000x5
=40000
Volume of space which can be occupied by water->168000-40000
=128000
Volume of water running for 158 min-> 158x1000
=158000
Volume of water spilt out->158000-128000
=30000( Ans)
Find the perimeter of the polygons with vertices at the given points. 11. ( 1, 2 ), ( 4, 6 ), ( 7, 2 )
the perimeter of the polygon is: [tex]5 + 5 + 6 = 16[/tex] So, the perimeter of the polygon with vertices at [tex](1, 2), (4, 6),[/tex] and [tex](7, 2)[/tex] is [tex]16[/tex] units.
What is the perimeter?To find the perimeter of the polygon with vertices at [tex](1, 2), (4, 6),[/tex] and [tex](7, 2),[/tex] we need to find the length of each side of the polygon and add them up.
Using the distance formula, we can find the length of each side:
The length of the side connecting (1, 2) and (4, 6) is:
[tex]\sqrt((4-1)^2 + (6-2)^2) = \sqrt(3^2 + 4^2) = 5[/tex]
The length of the side connecting [tex](4, 6) and (7, 2) is:\sqrt((7-4)^2 + (2-6)^2) = \sqrt(3^2 + (-4)^2) = 5[/tex]
The length of the side connecting [tex](7, 2) and (1, 2) \ is:\ \sqrt((1-7)^2 + (2-2)^2) = \sqrt((-6)^2 + 0^2) = 6[/tex]
Therefore, the perimeter of the polygon is: [tex]5 + 5 + 6 = 16[/tex] So, the perimeter of the polygon with vertices at [tex](1, 2), (4, 6),[/tex] and [tex](7, 2) \ is \ 16[/tex] units.
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A boat leaves a pier and travels 15 miles due east, then turns and travels 15 miles in the direction N 20° E. Which diagram represents the boat’s current distance, x, from the pier?
(diagrams attached below)
Answer: 20.64 miles.
Step-by-step explanation: The assignment of nomenclature to the location of the boat's initiation as point A, the termination of the first course of the excursion as point B, and the termination of the second course of the journey as point C is proposed. The present study reveals that the spatial positioning of point A and point B is separated by a distance of precisely 15 miles in an eastward direction. Similarly, point B and point C are separated by a distance of 15 miles, but oriented along the vector of N 20° E.
The application of trigonometry provides a means to determine the spatial separation between point B and point C. Based on computations, the distance from point B to point C has been estimated to be approximately 7.83 miles along the northward direction and approximately 14.16 miles along the eastward direction.
Henceforth, the computation of the distance between point A and point C (i.e., the prevailing separation of the boat from the pier) can be determined by the ensuing method:
The mathematical expression denoting the distance between points A and C, designated as AC, is given by the square root of the sum of the squares of the distances between points A and B, designated as AB, and between points B and C, designated as BC. In formulaic notation, this can be expressed as AC = √((AB)² + (BC)²).
The magnitude of the distance denoted by AC, between two points A and C, can be calculated using the Euclidean distance formula, which involves the square root of the sum of the squares of the differences between the corresponding coordinates of the two points. In this particular case, the calculation results in the expression √(15² + 14.16²).
The distance between points A and C, denoted as AC, can be expressed mathematically as the square root of the sum of the squares of the horizontal and vertical distances between them. Thus, AC = √(225 + 200.89), where 225 and 200.89 represent the square of the horizontal and vertical distance, respectively. This equation can be simplified to yield the measurement of the physical distance between points A and C in the applicable units of length.
The distance between points A and C is determined to be the square root of 425.89 in units of length.
The measurement of the distance between point A and point C is approximately equivalent to 20.64 miles.
Answer: Graph A.
Step-by-step explanation:
50 Points Please help quickly
Answer:
Step-by-step explanation:
The first one is C!
And the second one is E!
If this helps, go to math-way, and type in each of the equations and it will graph it for you!
Janelle want to know how many square inches of plywood are needed to make the chest and find the number of square inches janelle needs
Therefore, Janelle would need 1872 square inches of plywood to make the chest.
One square inch equals how many inches?A square inch (sometimes known as an in2 or sq. in.) is a unit of area measurement. A square with sides that are one inch long has an area of one square inch: Two lengths are used to measure a square area.
The areas of all the sides must be added up in order to determine the surface area of the chest. For instance, if we use 1/2 inch plywood and the chest is 24 inches by 12 inches by 18 inches, the surface area of the chest would be:
Top and bottom: 2 * (24 inches * 12 inches) = 576 square inches
Front and back: 2 * (18 inches * 12 inches) = 432 square inches
Sides: 2 * (24 inches * 18 inches) = 864 square inches
Total surface area = 576 + 432 + 864 = 1872 square inches
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this. please look at photo fir ref
The coordinates of point H' include the following: H' (0, -1).
What is a translation?In Mathematics, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image while the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.
By translating the pre-image of this trapezoid vertically downward by 2 units and horizontally right by 3 units, the coordinates of the image include the following:
(x, y) → (x + 3, y - 2)
E(-1, 4) → (-1 + 3, 4 - 2) = E' (2, 2).
H (-3, 1) → (-3 + 3, 1 - 2) = H' (0, -1).
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Please address the question
Answer:
The length of AB is
[tex] \sqrt{ {5}^{2} + {5}^{2} + {5}^{2} } = \sqrt{75} = 3 \sqrt{5} [/tex]
3√5 cm is about 6.7 cm.
The null and alternate hypotheses are:
H0: μd = 0
H1: μd ≠ 0
The following paired observations show the number of traffic citations given for speeding by Officer Dhondt and Officer Meredith of the South Carolina Highway Patrol for the last 5 months.
Number of Citations Issued
May/June/July/August/September
Officer Dhondt: 30, 22, 25, 19, 26
Officer Meredith: 26, 19, 20, 15, 19
At the .05 significance level, is there a difference in the mean number of citations given by the two officers?
a. What is the p-value?
The value of p-value is (a) 0.0025. (b). The decision regarding the null hypothesis is to Reject the H0 (c.) Yes there is a difference in the mean given by the two offices.
How to solve the statistics using the data?Recall that The p-value or probability value is a number, calculated from a statistical test, that describes how likely your results would have occurred if the null hypothesis were true.
The first thing is to find the difference between the set of data
30 - 26 = 4
22 - 19 = 3
25 - 20 = 5
19 - 15 = 4
26 - 19 = 7
The find the average of the set of scores
24.4 , 19.8, 1.52
Hypothesis formulation
H0: µ1 = µ2
Ha: µ1 ≤ µ2
Decide the test statistic and the level of significance:
alpha = 0.05
df = 5 - 1 = 4
The upper critical value at the level of significance = 2.7764
And the lower critical value at the level of significance = -2.7764
The decision rule
Reject H0 if |t| > 2.7764
Test statistics calculating
bar x1 - bar x2 =
24.4 - 19.8 = 4.6
standard error = s / √n
= 0.6798
t statistic = 4.6 / 0.6798
= 6.767
The decision would be given that 6.7670 > 2.7764, we would have to reject the null hypothesis and accept the alternate hypothesis.
The p value is given as 0.0025. This is the probability of rejecting the true H0
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A manufacturer records data on the battery life of a new product and discovers the data is normally distributed. The mean life of the battery is 120 hours and has a standard deviation of 10 hours. The manufacturer commits to replacing all batteries that last less than 100 hours. If 32,200 batteries were produced, how many would they expect to replace?
The firm expects replacing around 734 batteries out of the 32,200 produced.
How to determine how many batteries many would they expect to replaceusing the normal distribution formula z = (x - )
When z denotes the z-score,
x denotes the battery life of interest, is the mean battery life, and is the standard deviation.
For x = 100, use the z-score: z = (100 - 120) / 10 z = -2
Calculate the area under the normal curve to the left of z = -2.
0.0228 is the approximate value.
The number of batteries expected to be replaced by the manufacturer is equal to the proportion of batteries with a battery life of less than 100 hours multiplied by the total number of batteries produced:
Number of batteries to be replaced = 0.0228 x 32,200
734.16 batteries are expected to be replaced.
As a result, the firm anticipates replacing around 734 batteries out of the 32,200 produced.
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Damon recorded the snowfall in his town for each day of January. This line plot shows the distribution.
Snowfall in January
0
1
2
3
4
5
6
7
Inches
Complete the sentences.
The distribution of snowfall amounts is best described as
. So, the
is a more appropriate measure of variation than the
.
The distribution of snowfall amounts is best described as bimodal, with modes at 2 inches and 7 inches. So, the range is a more appropriate measure of variation than the standard deviation.
What is a bimodal distribution?A bimodal distribution can be identified in a histogram when two distinct groups can be seen there. A bimodal distribution actually has two modes or two different data clusters.
In a bimodal distribution, no particular data value has the highest frequency of occurrence, rather two data values have the highest frequency.
The line plot of the distribution by Damon has two modes and is, therefore, bimodal.
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PLEASE HELP
(a) How many total trees are included in the histogram?
(b) What is the least common height range of the trees?
Answer:
a. 31 total trees
b. Least common range is 85-90
Step-by-step explanation:
A. On the side of the chart it is labeled frequency. That is where you will find the number of tree per height range. The tops of the bars indicate the number is directly across.
B. Looking at the lowest bar or the smallest amount of trees indicate the lowest range or the least common range.
ayuda porfavor
necesito resolver esto es simplificarlo no resolverlo ayuda pls
The Simplification of the algebraic expression gives:
a. -2/3x² - (4/15)xy + (11/4)y²
b. -(12/7)x³ + (20/9)y
How to simplify algebraic expressions?Simplification of an algebraic expression is the process of writing an expression in the most efficient and compact form without affecting the value of the original expression
a. (1/3)x² - (2/5)xy + 2y² + (2/15)xy - 3x² + (3/4)y²
To simplify this, add or subtract like terms. That is:
(1/3)x² - (2/5)xy + 2y² + (2/15)xy - 3x² + (3/4)y²
= (1/3)x² - 3x² - (2/5)xy + (2/15)xy + 2y² + (3/4)y²
= -2/3x² - (4/15)xy + (11/4)y²
b. (2/7)x³ - (1/3)y + 2y - 2x³ + (5/9)y
To simplify this, add or subtract like terms. That is:
(2/7)x³ - (1/3)y + 2y - 2x³ + (5/9)y = (2/7)x³- 2x³ - (1/3)y + 2y + (5/9)y
= -(12/7)x³ + (20/9)y
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what is answer to this question please help
Answer:
5 > [tex]\sqrt{18[/tex]
Step-by-step explanation:
The square root of 18 is approximately 4.24.
5 is greater than 4.24, so we can use the inequality sign >.
Determine if the function below is continuous.
A. not continuous
B. both continuous and not continuous
C. cannot be determined
D. continuous
A. not continuous
Step-by-step explanation:Continuous functions have no jumps or vertical asymptotes.
Continuity
For a function to be continuous, each point on the function must be defined. This means that there cannot be points on the graph where there is no value or coordinate point. Additionally, all points must be connected by the graph. Sudden jumps in the graph that are not connected by anything are not continuous.
Determining Continuity
The graph above is not continuous. We know this for 2 reasons. Firstly, the graph is not defined at x = -3. Since there is an open circle at x = -3, the value is not defined. Thus, the function cannot be considered continuous. Additionally, there are multiple jumps. At x = -3, the function suddenly jumps to x = -2 without the points being connected. The same thing happens again at x = 1. This also shows that the graph is not continuous.
a varies inverselv as b^3. If a =
3/2 when b = 2, find a
when b is 3
If a varies inversely as b³, the value of a when b=3 is 4/9.
Given that, a varies inversely as b³.
Here, a∝1/b³
a=k/b³
Substitute a=3/2 and b=2 in a=k/b³, we get
3/2 = k/2³
3/2 = k/8
3 = k/4
k = 12
Substitute k = 12 in a=k/b³, we get
a=12/b³
When b=3
a = 12/3³
a=12/27
a=4/9
Therefore, if a varies inversely as b³, the value of a when b=3 is 4/9.
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