The Sutton family's condo's worth in 8 years will be $216000.
What is exponential function?An exponential function is a mathematical function in the form f(x) = aˣ, where {x} is a variable and {a} is a constant which is called the base.
Given is that Condos in Georgetown go up in value by 10% each year. Sutton family's condo's current worth is $120,000.
We can write the function to calculate the worth after {T} years as follows.
A{T, R} = A{i} {1 + RT}
A{T, R} = {120000} {1 + (10/100) x 8}
A{T, R} = {120000} {1 + 0.1 x 8}
A{T, R} = {120000} {1 + 0.8}
A{T, R} = {120000 x 1.8}
A{T, R} = 216000
Therefore, the Sutton family's condo's worth in 8 years will be $216000.
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Explain why the initial value of any function of the form
f(x) = a(b*) is equal to a.
The formula becomes a times 1, which is merely a, when you swap out 0 for the exponent x. This is so because 1 equals any number raised to the power of 0. The value of a will always be the initial value for any function with this form since the initial value is the function's value with an input of 0.
How do you determine F's starting value?By looking for an equation's constant, one can also locate initial values. Graph functions benefit from understanding the y-intercept.
Any number that is multiplied by 0 equals 1.
A number is equal to a number multiplied by 1.
The value of a multiplied by one will equal its starting value.
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A piece of paper is folded into thirds multiple times. The area, A, of the piece of
paper in square inches, after n folds, is A=90(1/3)^n.
How many folds are needed before the area is less than 1 square inch?
The paper is folded into 5 folds before the area is less than 1 square inches.
What is area?
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.
Here the area of the folded paper after n folds is,
A = 90[tex](\frac{1}{3})^n[/tex]
Now put n=0 into given formula,
A = 90[tex](\frac{1}{3})^0[/tex]=90×1 = 90 square inches.
Here Area of the paper before being fold is 90 square inches.
Now area is less than 1 square inches then
=> 90[tex](\frac{1}{3}) ^n[/tex] < 1
=> [tex](\frac{1}{3}) ^n < \frac{1}{90}[/tex]
Here if n= 4 then [tex](\frac{1}{3}) ^4 > \frac{1}{90} = \frac{1}{81} > \frac{1}{90}[/tex] then n=5.
Hence the paper is folded into 5 folds before the area is less than 1 square inches.
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Which of the following is the quotient of the rational expressions shown
below?
X/3x-1 divide x-2/2x
Answer: To divide two rational expressions, you need to first find the least common denominator (LCD) of the two expressions. The LCD is the least common multiple of the two denominators.
In this case, the rational expressions are x/(3x-1) and (x-2)/(2x). The LCD of these two expressions is (3x-1)(2x), which can be factored as 6x(x-1).
To divide the two rational expressions, you need to express each expression as a fraction with the LCD as the denominator.
The first expression, x/(3x-1), can be rewritten as (x * (2x))/(3x-1 * (2x)) = (2x^2)/(6x^2-2x).
The second expression, (x-2)/(2x), can be rewritten as ((x-2) * (3x-1))/(2x * (3x-1)) = (3x^2-3x+2)/(6x^2-2x).
To divide these two expressions, you can divide the numerators and the denominators separately:
(2x^2)/(6x^2-2x) ÷ (3x^2-3x+2)/(6x^2-2x)
= (2x^2) ÷ (3x^2-3x+2)
= (2/3)x^2 ÷ (x^2-x+2/3)
Therefore, the quotient of the rational expressions x/(3x-1) and (x-2)/(2x) is (2/3)
Step-by-step explanation:
Mr Espinoza randomly chooses one of five toll booths when entering a toll road when driving to work. What is the probability he will select the middle toll booth on Monday and Tuesday
The probability that Mr. Espinoza will select the middle toll booth on Monday and Tuesday is 8%.
What is the probability?Probability refers to the odds of Mr. Espinoza selecting the middle toll booth on Monday and Tuesday when he could have selected toll booths 1, 2, 4, or 5.
The chances of selecting one out of five toll booths = 1/5 or 0.2
The likelihood of Monday and Tuesday out of the five working days = 2/5 or 0.4
The probability of selecting the middle toll booth on Monday and Tuesday = 1/5 x 2/5
= 0.2 x 0.4
= 0.08
= 8%
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Can someone please help me with this? and also help me understand how to do it I have a test this Friday.
[tex]T=2\pi \sqrt{\cfrac{L}{g}}\implies \cfrac{T}{2\pi }=\sqrt{\cfrac{L}{g}}\implies \cfrac{T}{2\pi }=\cfrac{\sqrt{L}}{\sqrt{g}}\implies T\sqrt{g}=2\pi \sqrt{L} \\\\\\ \sqrt{g}=\cfrac{2\pi \sqrt{L}}{T}\implies (\sqrt{g})^2=\left( \cfrac{2\pi \sqrt{L}}{T} \right)^2\implies g=\left( \cfrac{2\pi \sqrt{L}}{T} \right)^2 \\\\\\ g=\cfrac{(2\pi \sqrt{L})^2}{(T)^2}\implies g=\cfrac{4\pi ^2L}{T^2}[/tex]
Elliot purchased 3 trick cameras and 4 fake
snakes and spent a total of $40. Kaci bought 7
trick cameras and 8 fake snakes, and her total
was $85. Let x be the price of the trick
cameras and let y be the price of the snakes. What are equation can be used to solve this system of equations?
If Elliot purchased 3 trick cameras and 4 fake snakes for $40 and Kaci bought 7 trick cameras and 8 fake snakes for $85 , then the system of equations that can be used to find the cost of trick camera and fake snakes are [tex]3x+4y=40[/tex] and [tex]7x+8y=85[/tex] .
Elliot purchased 3 trick cameras and 4 fake snakes for $40 ;
Kaci purchased 7 trick cameras and 8 fake snakes for $85 ;
let the number of trick cameras purchased be = x ;
let the number of fake snakes purchased be = y ;
So , the equation for Elliot's purchase is ⇒ [tex]3x+4y=40[/tex] ;
and the equation for Kaci's purchase is ⇒ [tex]7x+8y=85[/tex] ;
Therefore , the equations to solve for the number of trick cameras and number of fake cameras are [tex]3x+4y=40[/tex] and [tex]7x+8y=85[/tex] .
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The amount of money in a savings account is given by � = 580(1.03)" where t is the
time in years. After how many years will the account have reached $1000? Clearly
demonstrate your strategy for figuring it out.
An initial investment of $580, earning 3% annually-compounded interest, will take 18.429 years (investment period) to reach $1,000.
How the period is determined?The period for the investment to accumulate to $1,000 at 3% compounded interest is computed using an online finance calculator.
The parameters required include identifying the interest rate, compounding period, present investment, and future value., from the given formula:
A = 580(1.03)^t
$1,000 = 580(1.03)^18.429
Investment Period:I/Y (Interest per year) = 3%
PV (Present Value) = $580
PMT (Periodic Payment) = $0
FV (Future Value) = $-1000
Results:
N = 18.429
= 18 years and 5 months
Total Interest = $420
Thus, for the account to reach $1,000, it will take 18 years and 5 months.
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Question Completion:A = 580(1.03)^t
b. The original amount on the gift card was $200. Does Arleen have
enough left on the card to buy a
wheelbarrow for $50? Explain.
Answer:
Yes
Step-by-step explanation:
If there was 200 hundred dollars just subtract 50 dollars if there is still money then yes.
Answer: yes
Step-by-step explanation:
200-50=159
The city of vine View is building a new rectangular park for the townspeople. The park will have an area of 8,925 square yards if the width of the park is to be 84 yards, how much fencing does the city need to surround the park?
The length of the fencing that the city needs to surround the park will be 380.50 yards.
What is the area and perimeter of the rectangle?Assume L is the length and W is the width. Then the area is given as,
A = L × W
And the perimeter is given as,
P = 2(L + W)
The city of vine View is building a new rectangular park for the townspeople. The park will have an area of 8,925 square yards if the width of the park is to be 84 yards. Then the length of the rectangular park is calculated as,
8925 = L × 84
L = 106.25 years
Then the length of the fencing that the city needs to surround the park will be given as,
P = 2(106.25 + 84)
P = 2 × 190.25
P = 380.5 yards
The length of the fencing that the city needs to surround the park will be 380.50 yards.
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Triangle J K L. Side J K is 5 inches and side J L is 10 inches.
Which could be the length of Side K L?
4 in.
9 in.
16 in.
19 in.
Answer:
9 in.
Step-by-step explanation:
the sum of two sides in a triangle is always longer than the 3rd side. so 9 is the only answer that fits this condition.
does the order of the quantities in an inequality matter
Yes, the order of the quantities in an inequality matters, and examples are given to show why.
Why does the order of the symbols matter in an inequality?The four inequality symbols, along with their meaning, are presented as follows:
> x: greater than x.< x: less than x.≥ x: at least x.≤ at most x.It is known that the number 5 is greater than the number 3, hence the inequality that describes these numbers is given as follows:
5 > 3.
However, if we tried to apply the commutative property, that is, changing the order of the numbers, we would have that:
3 > 5.
Which is a false statement, as the number 3 is less than the number 5, and not more.
This shows that the order of the symbols in an inequality in fact does matter.
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How do you select sample size using simple random sampling?
Using the method of simple random sampling, The answer is we select sample before collecting data.
What do you mean by random sampling?Random sampling is a method of selecting a sample from a population in such a way that each member of the population has an equal probability of being selected. This ensures that the sample is representative of the population, and reduces bias in the sampling process. In simple random sampling, a random sample is drawn from a larger population by using random number generators, tables of random numbers, or other methods that ensure that each member of the population has an equal chance of being selected.
What are samples?A sample is a portion or a subset of a population that is selected for the purpose of studying characteristics of the population. The sample is used to make inferences or conclusions about the population from which it was drawn. The sample is usually smaller in size than the population, and it is selected through a process called sampling. The process of sampling is used to select a sample that is representative of the population, meaning that the sample has similar characteristics as the population.
In simple random sampling, the sample size is determined before collecting data. There are several ways to determine the sample size, but one common method is to use a sample size calculation formula, such as: n = (z^2 * p * (1-p)) / e^2
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Given a prime $p$ and an integer $a$, we say that $a$ is a primitive root $\pmod p$ if the set $\{a,a^2,a^3,\ldots,a^{p-1}\}$ contains exactly one element congruent to each of $1,2,3,\ldots,p-1\pmod p$.For example, $2$ is a primitive root $\pmod 5$ because $\{2,2^2,2^3,2^4\}\equiv \{2,4,3,1\}\pmod 5$, and this list contains every residue from $1$ to $4$ exactly once.However, $4$ is not a primitive root $\pmod 5$ because $\{4,4^2,4^3,4^4\}\equiv\{4,1,4,1\}\pmod 5$, and this list does not contain every residue from $1$ to $4$ exactly once.What is the sum of all integers in the set $\{1,2,3,4,5,6\}$ that are primitive roots $\pmod 7$
Only 3 & 5 from the set {1,2,3,4,5,6} are primitive root (mod7), therefore, sum of integers is 3 + 5 = 8.
What is primitive root?A number g is a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n in modular arithmetic. That is, g is a primitive root modulo n if for every integer a coprime to n, some integer k for which gk ≡ a (mod n).
The index or discrete logarithm of a to the base g modulo n is a value k like this. So, if and only if g is a generator of the multiplicative group of integers modulo n, g is a primitive root modulo n.
In Article 57 of his Disquisitiones Arithmeticae (1801), Gauss defined primitive roots and credited Euler with coining the term.
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Identify the graph of y + 11 <3(x+2).
This is on big ideas math
(The top right is wrong)
For given inequality, graph number 3 is correct.
What does a math inequality mean?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality results from a lack of balance.
How is an inequality calculated?Make use of the following steps to solve an inequality: Step 1: Remove fractions by multiplying all terms by the fractions' lowest common denominator. Step 2 Combine like terms on both sides of the inequality to simplify. Step 3 Obtain the unknown on one side and the numbers on the other by adding or subtracting quantities.
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3 An art class is making mosaics with glass squares. Each of the 121 students will get the same number of glass squares to use. The total number of glass squares for the students to use is shown. How many glass squares will each student get? A. Write an expression that can be used to find the number of glass squares each student will receive. B. Complete the given division problem to find the number of squares each student will receive. C. How many whole glass squares will each student receive? 1,240 glass squares D. A remainder is the amount left over when an amount cannot be divided equally. What does the remainder mean in this context? 121)1240 30 R
Answer: A. To find the number of glass squares each student will receive, we need to divide the total number of squares by the number of students.
We can write this as:
x = number of glass squares per student
x = 1240 / 121
B. To find the number of squares each student will receive, we need to solve for x by dividing 1240 by 121.
1240 ÷ 121 = 10.246753246753247
C. Each student will get 10 whole glass squares.
D. The remainder in this context is the number of glass squares that cannot be distributed evenly among the students. In this case, the remainder is 30. It means that there will be 30 glass squares left over after each student has received 10 squares. It's like remainder in division where after dividing 1240 by 121 the quotient is 10 and the remainder is 30.
Step-by-step explanation:
What are the AGI and taxable income? Responses $35,468 and $23,068 $35,468 and $23,068 $47,468 and $35,468 $47,468 and $35,468 $47,868 and $12,400 $47,868 and $12,400 $35,468 and $12,400 $35,468 and $12,400 Gross Income $35,468 Adjustments 0 1 Exemption $12,400 Deduction 0
The amount of GI is $35,468.
The amount of taxable income is $23,068.
Option A is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Gross income = $35,468
Exemption = $12,400
Deduction = 0
Adjustment = 0
Taxable income.
= Gross income - Exemption
= 35,468 - 12,400
= $23068
Thus,
GI and taxable income are $35,468 and $23,068
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In a survey of 2000 people who owned a certain type of car, 1200 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
The percentage of people who are satisfied with the car are 60%.
What is percentage?In mathematics →
a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign "%".Given is that in a survey of 2000 people who owned a certain type of car, 1200 said they would buy that type of car again.
The percentage of people who are satisfied with the car are -
{x}% = (1200/2000) x 100
{x}% = (12/20) x 100
{x}% = 12 x 5
{x}% = 60
Therefore, the percentage of people who are satisfied with the car are 60%.
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A bag of sugar weighs 3.45 kg What is the weight of three such bags (in kilograms)?
Answer:
10.35 kg
Step-by-step explanation:
Given a bag of sugar weighs 3.45 kg, you want the weight of 3 bags.
WeightThe weight of 3 bags will be three times as much as the weight of one bag:
3 × 3.45 kg = 10.35 kg
Three such bags weigh 10.35 kg.
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Gabriel wants to send a parcel to italy.
WeDeliver: The total cost of sending the parcel with WeDeliver is £64.00.
What is total cost?Total cost is the sum of all costs associated with a particular purchase, project, or investment. It includes the cost of materials, labor, and any other expenses incurred such as taxes, fees, and shipping. Total cost is an important factor in determining whether or not a project or purchase is feasible. When evaluating the total cost, one must consider any associated risks, such as the risk of a market downturn or currency fluctuations.
This is calculated by summing the three dimensions of the cuboid (10 cm + 20 cm + 40 cm) and then multiplying this sum by £0.80.
GoParcels: The total cost of sending the parcel with GoParcels is £48.00. This is calculated by multiplying the total area, in cm, of all 6 faces of the cuboid (10 cm x 20 cm x 2 + 10 cm x 40 cm x 2 + 20 cm x 40 cm x 2) by £0.02.
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A small business makes bottles of
temonade. Today, they have 528 ounces
of lemonade to bottle. Each bottle holds
24 ounces of lemonade. They sell each
bottle for $2.
Write two equations with variables that
can be used to find how many dollars
the business will receive by selling all of
the bottles.
The amount of money that the business will receipt is $44.
given:
Small business makes bottles of lemonade today they have 528 oz of lemonade to the bottle each bottle holds 24 oz of lemonade they sell each bottle for $2 how much money will the business receipt
From the above question:
24oz of Lemonade = 1 bottle
528 oz of Lemonade = x
Cross Multiply
24 × x = 528
x = 528/24
x = 22 bottles
We are told that: they sell each bottle for $2
Hence:
1 bottle = $2
22 bottles = y
Cross Multiply
y = 22 × $2
y = $44
Therefore, the amount of money that the business will receipt = $44
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Describe a real-life situation involving markup, markdown, or discount that the equation y=x+0.4x could represent.
the retail price y in dollars for an item with the original cost and a markup of 40%
O the discount price y in dollars for an item with the original cost and a discount of 40%
O the sale price y in dollars of an item with the original cost and a markdown of 40%
O the discount amount y in dollars for an item with the original cost and a discount of 40%
The equation y = x + 0.4x is the retail price y in dollars for an item with the original cost and a markup of 40% .
What is equation ?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.
y = x + 0.4x {markup ↑}y = x - 0.4x {markdown , discount ↓}y = 0.4xSo, we choose the first equation.
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Find an order pair (x,y)that is a solution to the equation
2x+y=3
Answer:
(2, -1)
Step-by-step explanation:
2(2)+ (-1) = 4-1 = 3.
The following federal tax table is for biweekly earnings of a
single person.
A single person earns a gross biweekly salary of $840. By
claiming 2 more withholding allowances, they would have
$30 more in their take home pay. How many withholding
allowances do they currently claim?
Therefore , the solution to the given problem of unitary method comes out to be he will have $870.
What is unitary method, exactly?The unit method is a method of problem-solving that entails calculating the variable of one unit, multiplying that value, and then calculating the required value. To describe it simply, the unit method is employed to obtain a single entity value from a specified multiple. One pen costs 400 rupees, thus 40 needles would cost 400 rupees. There might be a regular procedure for doing this out. merely one nation. anything containing a distinctive component. Logic of matrices or operators, algebra, mathematical analysis, and its adjoint and reciprocal are all equivalent.
Here,
To address the issue,
if the person gets a gross biweekly salary of $840 and claims 2 extra withholding allowances,
their take-home pay would increase by $30.
thus,
They will have 840 + 30 = $870
Therefore , the solution to the given problem of unitary method comes out to be he will have $870.
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In a 45°-45°-90° triangle, the length of the hypotenuse is 11. Find the length of one of the legs.
The length of the leg of the right-angled triangle is (11√2) / 2. The correct option is C.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry. The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that the right angles triangle has 45-45-90 angles. The hypotenuse is 11.
The length of the leg will be,
Cos45 = Base / Hypotenuse
1 / √2 = Base / 11
Base = 11 / √2
Rationalize the numbers,
Base = 11√2 / 2
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Can you help me with this
The equation of the line that passes through the points (-4, -6) and (9, 2) is
y = (8/13)x - 46/13.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The line passes through points (-4, -6) and (9, 2).
Let the equation of the line y = mx + c.
Now,
m = (2 + 6) / (9 + 4) = 8/13
(-4, -6) = (x, y)
-6 = (8/13) x -4 + c
-6 = -32/13 + c
c = -6 + 32/13
c = (-78 + 32)/13
c = -46/13
Thus,
The equation of the line is y = (8/13)x - 46/13.
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help!!!
Let f(x) represent a function.
Which descriptions match the given transformations?
Drag and drop the answers into the boxes.
f(x−5/3)
f(x)−5/3
The function f(x - 5/3) is translated 5/3 units right and the function f(x) - 5/3 is translated 5/3 units down.
What are some rules for the transformation of functions?Suppose we have a function f(x).
f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).
f(x ± c) = Horizontal left/right shift by c units (x - + c, y).
(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).
f(-x) = Reflection over the y-axis, (-x, y).
-f(x) = Reflection over x-axis, (x, -y).
Given, A function f(x) is transformed to f(x - 5/3) this results in f(x) is translated 5/3 units to the right along the x-axis.
And, The transformation f(x) - 5/3 is translated 5/3 units down along the y-axis.
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What is the XYZ axis called?
The XYZ axis is called as X-axis, Y-axis, and Z-axis, respectively.
The term axis in math is defined as a line with respect to which a curve or figure is drawn, measured, rotated, etc.
Here we have given that XYZ axis, in math are no standard names for the coordinates in the three axes
Based on these the coordinates are often denoted by the letters X, Y, and Z, or x, y, and z.
And these axes may then be referred to as the X-axis, Y-axis, and Z-axis, respectively.
Here in the graph x-axis and y-axis represent the first two dimensions where as the z-axis, the third dimension. Which is also defines the x and y denote width and height and the z denotes depth.
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i need help asap please
Step-by-step explanation:
the range is (-32, 28)
note that when the bubble is not filled in it should be an open bracket
Show that the vector field defined by the vector function v=xyz(yzi^xzj^xyk^) i conervative
The process to show the vector field V(x,y,z) as conservative is show below and the scalar potential f is [tex]f(x,y,z) =xyz^{2} + e^{\pi }[/tex] .
A Vector field can be called as conservative if we are able to find the potential function "f" , whose gradient is field .
The Gradient is vector that is made from partial derivatives of potential function .
The Vector function is given as , V(x,y,z) = [tex](yz^{2} )i + (xz^{2} )j + (2xyz)k[/tex] ,
So , we can write the partial derivatives function of potential function as :
[tex]\frac{\partial f}{\partial x} = yz^{2}[/tex] ; [tex]\frac{\partial f}{\partial y} = xz^{2}[/tex] ; [tex]\frac{\partial f}{\partial z} = 2xyz[/tex],
On Antidifferentiating any of the above three partial derivatives ,
we get ; [tex]f=xyz^{2} + C[/tex] , here the constant C can take any value ,
so , we take C as [tex]e^{\pi }[/tex] .
Therefore , the potential Function is [tex]f(x,y,z) =xyz^{2} + e^{\pi }[/tex] .
The given question is incomplete , the complete question is
Show that the vector field defined by the vector function V(x,y,z) = (yz²)i + (xz²)j + (2xyz)k is conservative by finding a scalar potential f .
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Question content area top
Part 1
A computer store buys a computer system at a cost of $. The selling price was first at , but then the store advertised a markdown on the system. Answer parts a and b.
Question content area bottom
Part 1
a. Find the current sale price.
The sale price is $
enter your response here.
(Round to the nearest cent as needed.)
Part 2
b. Members of the store's loyalty club get an additional % off their computer purchases. How much do club members pay for the computer with their discount?
The price for club members is $
enter your response here.
(Round to the nearest cent as needed.)
a. The current sale price for the computer system is given as follows: $618.4.
b. The amount paid by the club members, with the discount, is given as follows: $587.48.
How to obtain the prices?The prices are found applying the proportions, which are the decimal equivalent of the percentages relative to each discount.
The selling price is of:
$773.
The markdown is of 20%, hence the current sale price is 100 - 20 = 80% of the selling price, hence:
0.8 x 773 = $618.4.
Club members get an additional discount, of 5%, meaning that they pay 95% of $618.4, and the amount is obtained as follows:
0.95 x 618.4 = $587.48.
Missing InformationThe problem is given by the image presented at the end of the answer.
More can be learned about proportions at https://brainly.com/question/24372153
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