Answer:
-7i
Step-by-step explanation:
Sqrt-49 = Sqrt49 *(- 1)
= Sqrt49 * sqrt-1
= ±7 * i
= ±7i
n order to examine the relationship between the selling price of a used car and its age, an analyst uses data from 20 recent transactions and estimates price
The equation which he used to perform the analysis is
Price = + Age + ε .
An analyst utilizes data from 20 recent transactions to estimate fee = 0 + 1 Age + in order to study the relationship between a used car's promoting charge and age.
In the table that follows, a fraction of the regression effects are displayed.
Coefficients Standard
Error test stat p-value
Detect 21,228.95, 738.41, 28,750, and 1.70E-16
Age −1,206.23 129.97 2.78E-08
Describe the opposing theories so that you can decide if the selling price of a used car and its age are linearly related or not.
H0: β1 ≥ 0; HA: β1 < 0
H0: β1 = 0; HA: β1 ≠ 0
H0: β1 ≤ 0; HA: β1 > 0
selling cost
Every day, we benefit from special circumstances when we want to compute or assess things. scenarios, particularly those involving the sale or purchase of goods.
The selling price is used to market the item at a specific price and can be computed by using the formula for the promotion fee. The selling charge is the sum the customer spends to purchase the item.
The price a customer pays to purchase a good or service is the actual promoting rate.
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The graph shows the relationship between the number of hours Teresa spends
knitting and the number of squares she completes for a blanket. Based on the
equivalent ratios shown in the graph, how many hours does it take Teresa to
knit 265 squares? Show your work.
3:15, 6:30, 9:45, 12:60
When 15 squares are knit in three hours, 265 squares are knit in 53 hours.
What is proportion?A part, share, or quantity is a percentage when it is compared to the total. It can be any number between 0 and 1, 0, or 1. A number or percentage can be used to represent it. The percentage of Canadians who reside in a certain province is one illustration from official statistics. A unique kind of ratio called a percentage has the numerator and denominator combined. An illustration is the ratio of deaths to men, which is calculated by dividing deaths to men by deaths to men and women (i.e. the total population).
Here,
Let x be hours does it take Teresa to knit 265 squares,
3/15=x/265
3*265/15=x
x=53 hours
It takes 53 hours to knit 265 squares when it takes 3 hours to knit 15 squares.
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Complete the solution of the equation. Find the value of y whey x equals -5. -7x + 6y = -13
Answer:
4
Step-by-step explanation:
Because
Solve for n.
4.8 = 3n
If necessary explain in the simplest way possible.
The value of n is 1.6 if 4.8=3n by using simplest method.
What is meant by simplest equation?A mathematical equation links the two phrases on either side of the sign. It typically simply has an equal sign and one variable. similar to 2x - 4 = 2. Simple equations are used to demonstrate the relationship between two terms when they are positioned on each side of an equal sign. Simple equations are all used to follow the four mathematical operations of addition, subtraction, multiplication, and division.
By employing the shorthand symbol for "equal to" (=), it ensures that both expressions of the equation are equal. Equations utilize arithmetic operations like addition, subtraction, division, and multiplication to balance the expressions on both sides.
4.8=3n
Dividing on both sides with 3, we get
3n/3=4.8/3
n=1.6
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A machine cuts 25 circuit boards every 5 minutes.what is the unit rate of production for the machine?
Solve the equation mx" + Bx' = mg for r(t), given that you step off the bridge-no jumping, no diving! Stepping off means (0) = -100, x' (0) = 0, You may use mg = 160, B = 1, and g = 32. Use the solution from Problem 1 to compute the length of time t, that you freefall (the time it takes to go the natural length of the cord: 100 feet).
The general solution for mx" + Bx' = mg for r(t) is x(t) = 25e^(-x/5) + 5x -125
According to the question,
The given equation = mx" + Bx' = mg
Also , mg = 160, B = 1, and g = 32
=> m = 160/g
=> m = 160/32 = 5
Substituting the values in equation ,
5x" + x' = 160 , x(0) = -100, x' (0) = 0
The characteristic equation of the homogeneous differential equation is
5x" + x' = 0
=> 5r² + r = 0
=> r = 0 , -1/5
The complementary solution is x = c₁e⁰ + c₂e⁻⁰°²
Solution for complementary is yc = ax + b
Substitute yc = ax + b in 5x" + x' = 160 to get
5(0) + a = 160
=> a = 160
So the general solution is
x(t) = 25e^(-x/5) + 5x -125
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i need help with this please ,thankful for all help:)
The value of f(-2) is -8 and the value of [tex]f(v+1)=\frac{3v+1}{|v+2|}[/tex] for the given function [tex]f(v)=\frac{3v-2}{|v+1|}[/tex].
How to evaluate a function?A function is represented by f(x) = y. Where x is the input variable and y is the output variable. To evaluate the function for a value of x, substitute the value of x in the function f(x), and by simplifying, we get the required answer.Calculation:Given function is
[tex]f(v)=\frac{3v-2}{|v+1|}[/tex]
To evaluate f(-2), we need to substitute v = -2 in the given function.
So, on substituting v = -2, we get
f(-2) = (3(-2) - 2)/|-2+1|
= (-6 - 2)/|-1|
= -8/1
Since we know that |-a| = a; we can write |-1| = 1.
Thus, f(-2) = -8
To evaluate f(v+1), we need to substitute v = v+1 in the given function.
So, on substituting v = v+1, we get
f(v+1) = (3(v+1) - 2)/|v+1+1|
= (3v+3-2)/|v+2|
= (3v+1)/|v+2|
Thus, f(v+1) = (3v+1)/|v+2|.
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Suppose you can afford to pay $ 325 a month for 9 years towards a new car with no down payment. If the current interest rates are 4.25%, how expensive a car can you afford?
The expensive a car that you can afford is $42666.42.
What is interest rates?
The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR (APR).
Given that you can deposit $325 each month. The interest rates is 4.25%.
Future Value of an Ordinary Annuity
[tex]S = R[\frac{(1+i)^n-1}{i}][/tex]
where
S is the future value;
R is the periodic payment;
i is the interest rate per period;
n is the number of periods.
The value of R is $325, i = 0.0425/12 = 0.00354
n = (12 × 9) =108
The future value is
[tex]S = 325[\frac{(1+0.00354)^{108}-1}{0.00354}][/tex]
S = 42666.42
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in computing the standard error of the mean, the finite population correction factor is not used when
The finite population correction factor is not used when you sample without replacement from less than 5% of a finite population.
When you sample without replacement from more than 5% of a finite population, the Finite Population Correction Factor (FPC) is applied.
The Central Limit Theorem does not apply in this situation, and the estimated standard error (such as the mean or proportion) will be excessive. Basic differences between sampling with replacement and sample without replacement are captured by the FPC.
It is employed to modify a variance estimate for an estimated mean or total in order to limit the scope of the variance to that fraction of the population that is not included in the sample.
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. Communicate and Justify Benjamin walks
from his house to Timothy's house and then
to school. Describe Benjamin's walk as a
composition of translations. If Benjami
walks from his house directly to school, what
translation describes his walk?
Benjamin's walk described as a composition of two translations is (8, 0) and (2, 3) respectively.
The translation walks from his house directly to school is (10, 3)
How to describe Benjamin's walk as a composition of translations?A translation is a type of transformation that moves every point in a figure by a fixed distance in a certain direction. This can be thought of as sliding the figure along a straight line.
Looking at the image:
The coordinate of Benjamin's house is (5,4) and he walks to Timothy's house (13, 4) and then to school (15, 7)
The displacement vector from Benjamin's house to Timothy's house is (13, 4) - (5, 4) = (8, 0), which represents an 8 unit move to the right.
The displacement vector from Timothy's house to school is (15, 7) - (13, 4) = (2, 3), which represents a 2 unit move to the right and a 3 unit move up.
Thus, Benjamin's walk can be described as a composition of two translations can be represented using displacement vectors as (8, 0) and (2, 3) respectively.
If Benjamin walks from his house directly to school:
The displacement vector from Benjamin's house directly to Timothy's house is (15, 7) - (5, 4) = (10, 3), which represents 10 units move to the right and 3 units up.
Thus, the translation describes his walk is (10, 3)
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Using differential calculus, maximize the volume of a box made of cardboard (top is open) as shown in Figure A. 15, subject to the following constraints. 1. Allowable area of the cardboard is equal to 40 in^2. 2. The length of the box L is equal to its width W.
The maximum volume of the box is 40√(10/27) cu in.
Here we see that volume is to be maximized
The surface area of the box is 40 sq in
Since the top lid is open, the surface area will be
lb + 2lh + 2bh = 40
Now, the length is equal to the breadth.
Let them be x in
Hence,
x² + 2xh + 2xh = 40
or, 4xh = 40 - x²
or, h = 10/x - x/4
Let f(x) = volume of the box
= lbh
Hence,
f(x) = x²(10/x - x/4)
= 10x - x³/4
differentiating with respect to x and equating it to 0 gives us
f'(x) = 10 - 3x²/4 = 0
or, 3x²/4 = 10
or, x² = 40/3
Hence x will be equal to 2√(10/3)
Now to check whether this value of x will give us the max volume, we will find
f"(2√(10/3))
f"(x) = -3x/2
hence,
f"(2√(10/3)) = -3√(10/3)
Since the above value is negative, volume is maximum for x = 2√(10/3)
Hence volume
= 10 X 2√(10/3) - [2√(10/3)]³/4
= 2√(10/3) [10 - 10/3]
= 2√(10/3) X 20/3
= 40√(10/27) cu in
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Complete Question
(Image Attached)
Which of the following is an example of a polynomial function? A. F(x)= 4/x³ + 3x -1
B. F(x)= 2x3/2- 3/2x²
C. F(x)= √7x-2x⁶
D. F(x)= x³ + √3x-5
So option B. F(x)= 2x3/2- 3/2x² is the correct option of the given statement.
In math, what is a polynomial?Using just the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables, a polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients.
How can you recognize a polynomial?The formulas that only contain addition, subtraction, multiplication, and non-negative integer exponents are those that can be used to identify the polynomials. The expressions with other operations will be non-polynomial expressions. Justify the expressions' lack of polynomial status.
What guidelines apply to polynomials?A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc., that only uses non-negative integer powers or only positive integer exponents of a variable. A polynomial with an exponent of 1 is, for instance, 2x+5.
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Football and Basketball are the most popular sports in America. Assuming that 70% of Americans do not follow both sports, do we have enough information to find out the percentage of Americans who either do not follow football or do not follow basketball? If yes, what is that value?
Assume Event A: an American follows football; Event B: an American follows basketball.
No, we do not have enough information to find out the percentage of Americans who either do not follow football or do not follow basketball. We would need to know the percentage of Americans who do follow both sports.
In mathematics, what is a percent?When the denominator is 100, percentages are really just fractions. We place the percent symbol (%) beside a number to indicate that it is a percentage. For instance, if you answered 75 out of 100 questions correctly on a test, you would have received a 75%.
What does a decimal percentage mean?The percent sign (%), which denotes a division by 100, is used. Therefore, 25% translates to 25/100, or 1/4. Dividing by 100 will change a percentage to a decimal. Therefore, 25% is equal to 25/100, or 0.25. A decimal can be multiplied by 100 to become a percentage (just move the decimal point 2 places to the right)
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[ - 25.6] +[ - 11.4 ] the number of the value is always positive
The absolute value of the expression |-25.6| + |-11.4| gives a resultant modulus of 37
Absolute Value of ExpressionThe absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign. For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5. The absolute value of a number may be thought of as its distance from zero along real number line.
Whenever a value is in an absolute value, the result must always be positive no matter what it is. I.e the modulus of any number is always positive.
In the given expression;
|-25.6| + |-11.4| = 37
The modulus of the expression is 37
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Shoppers in two states are asked whether their shopping decisions are made impulsively or after careful consideration. Forty randomly selected shoppers in state A and thirty-six randomly selected shoppers in state B are questioned Shopping Habit State Conscientious ImpulseA 24 16 B 30 6(a) Test at the 5% level whether shoppers in the two states differ with regards to shopping habits. State all assumptions. (b) Find the p-value.
The chi-square test is 5.02 higher than critical value 3.841 so the two states does not differ with regards of shopping habits, and p value is 0.025.
How to calculate test statistic?O = observed value
E = expected value
n = size of sample = 2
df = degree of freedom = n - 1 = 2 - 1
α = significance level = 5% = 0.05
Chi-square is a one of many test statistic, chi-square is a test to see the different from observed value and expected value.
Chi-square formula is,
[tex]\chi^2[/tex] = [tex]\sum\frac{(O_i - E_i)^2}{E_i}[/tex]
Since, in question only give us the observed value, we need to calculate the expected value first.
Expected value conscientious state A can be calculate by this formula
E(ca) = total of state A value × total of conscientious value ÷ grand total
Repeat this process to all observed value.
We use excel to simplified and for precise calculation. Then, we put the obtained value from excel formula to Chi-square formula,
[tex]\chi^2[/tex] = 0.69 + 1.69 + 0.76 + 1.88
= 5.02
a) Critical value for df = 1 and α = 0.05 from chi-square table is 3.841
Since, the result is 5.02 higher than 3.841, it can be concluded that the two states does not differ with regards of shopping habits.
Assumptions for we use is the study group is independent and the each expected value is higher than 5.
b) We use chi-square p-value calculator with P([tex]\chi^2[/tex] > 5.02) and df = 1, α = 0.05. So, we get 0.025.
Thus, two states doesn't differ with regards of shopping habits since chi-square result is higher than critical value, and p value is 0.025.
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When Daniel rounded a number to the nearest hundred thousand, and the answer was 700,000. Which of the following could have been the original number?
The original number that could have been rounded to the nearest hundredth thousand to 700,000 is given as follows:
Any number between 650,000 and 749,999.
How to round a number to the nearest hundredth thousand?The hundredth thousand numbers are given as follows:
One hundredth thousand: 100,000.Two hundredth thousand: 200,000.Three hundredth thousand: 300,000.Four hundredth thousand: 400,000.Five hundredth thousand: 500,000.Six hundredth thousand: 600,000.Seven hundredth thousand: 700,000.Eight hundredth thousand: 800,000.Nine hundredth thousand: 900,000.Then the numbers are rounded as follows:
If the second digit of the number is of 4 and less, the number is rounded down, for example, 749,999 = 700,000. If the second digit of the number is of 5 and greater, the number is rounded up, for example, 650,000 = 700,000.Then the interval is given as follows:
Numbers between 650,000 and 749,999.
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what is an equation that passes through (4,-2) and is perpendicualar to the tine y=1/5x+3?
The equation of the perpendicular line is y = -5x + 18
How to determine the perpendicular line equation?From the question, we have the following parameters that can be used in our computation:
y = 1/5x + 3
Also, from the question;
We have the following points
Point = (4, -2) i.e. (x, y) = (4, -2)
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = 1/5
This means that the slope is 1/5
The slopes of perpendicular lines are opposite reciprocals
This means that the slope of the other line is -5
The equation of the line is then calculated as
y = m(x - x₁) +y₁
Where
m = -5
(x₁, y₁) = (4, -2)
So, we have
y = -5(x - 4) - 2
Evaluate
y = -5x + 18
Hence, the line has an equation of y = -5x + 18
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in the transformation abc a'b'c', the preimage of b' is ____. type the answer in the space provided.; point v(-2, 4) is translated using the rule (x, y) โ (x, y โ 4). where is the image, vโ, located?; point w 5 6 is reflected across the line y x which of the following is the location of its image w; pre- image x 2 1 y 4,-3 z 3,2 image x 2 1 y 4,-3 z 3,2; isometry; transformations in math
In the transformation of triangle abc, the pre-image of b' is b.
It's a triangle denoted as abc. abc is changed so that the resulting image is a'b'c''. It should be noted that there are many other forms of transformations, including dilation, vertical shift, horizontal shift, rotation about a point, reflection on a line, etc.
Corresponding vertices will be matched in all transformations. In other words, a will change to a'', b to b', and c to c''. Preimage of b' would just be b itself due to the transformation's ability to maintain image similarity and convert vertices appropriately.
Note that the correct question is:
In the transformation ABC A'B'C', the preimage of B' is ____.
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determine whether the series is convergent or divergent. 1 4 3 16 1 64 3 256 1 1024 3 4096 convergent divergent if it is convergent, find its sum. (if the quantity diverges, enter diverges.)
It is a convergent series as both component series are geometric with ratios less than 1, so they both converge. The sum is 7/15.
What is convergent series?If the sequence is converging (or converges), the series is convergent. The total of its partial sums tends to a limit; that is, while adding one after the other in the sequence specified by the indices, partial sums move closer and closer to a particular number. A divergent series is an infinite series that is not convergent, which means that the infinite sequence of the series' partial sums has no finite limit. If a series converges, the series' individual terms must approach zero.
Here,
sum(3/4ⁿ)₁₋ₓ - sum(1/2⁴ⁿ⁺¹)₁₋ₓ
sum(3/4ⁿ)₁₋ₓ=1
sum(1/2⁴ⁿ⁺¹)₁₋ₓ=8/15
=1-8/15
=7/15
It is a convergent series since both component series are geometric and have ratios smaller than one. The total is 7/15.
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3. consider all triangles formed by lines passing through the point ( 8 9 , 3) and both the x- and y-axes. find the dimensions of the triangle with the shortest hypotenuse.
The dimension of the triangle with the shortest hypotenuse is 2.98.
Here we have to find the dimensions of the triangle.
Given data:
the point given as (8/9, 3) and both passes through x and y-axis.
Let the slope of the line be m.
The line passing through (8/9,
Slope(m) = (y-3)/{x-(8/9)
y-3=m{x-(8/9)
y-mx=3–8m/9.
As this along with the coordinate axes make the right angled ∆, for the shortest hypotenuse
The x and y the intercepts for the line. So,
y/(3–8m/9)+x/{(3-8m/9)/(-m)}=1.
Where y intercept=(3–8m/9),
x intercept={(8m/9–3)/m.
So the length of hypotenuse;
Hypotenuse(h) = √[{(8m/9–3)/m}²+(3–8m/9)²]|
=|(8m/9–3)√(1+m²)/m
So the length of the hypotenuse is to be minimum for m, the hypotenuse is (19/9)×√2=2.98.
Therefore we get the hypotenuse as 2.98.
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What are the rules of multiplying decimals?
Answer:
To multiply decimals, first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.
Step-by-step explanation:
What are 3 characteristics of exponential functions?
A GENERAL NOTE: CHARACTERISTICS OF THE GRAPH OF THE PARENT FUNCTION [tex]f(x) = b^{x}[/tex]
-It’s a one-to-one function
-The graph passes through y-intercept of the point (0,1)
-x-intercept: none
-The domain is all real numbers: (−∞,∞)
-The range is y > 0 or (0,∞)
-The graph is increasing
-The graph is asymptotic to the x-axis as x approaches negative infinity
-Horizontal asymptote: y=0
-The graph increases without bound as x approaches positive infinity
-Increasing if b > 1
-Decreasing if b < 1
-The graph is continuous
-The graph is smooth
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An online pharmaceutical company obtained the following frequency distribution of shipping times (number of hours between the time an order is placed and the time the order is shipped) for a random sample of 40 orders. (Be sure to complete all appropriate columns and show your work).
Number of Hours fi
4 < 10 8
10 < 16 15
16 < 22 10
22 < 28 7
a. What is the approximate mean shipping time?
b. What is the approximate variance and standard deviation?
a) The approximate mean shipping time: X{bar} = 1.64
b) The approximate variance and standard deviation:
S² = 27.03, σ = 5.2
In this question, we have been given the frequency distribution of shipping times (number of hours between the time an order is placed and the time the order is shipped) for a random sample of 40 orders.
We need to find the approximate mean shipping time, variance and standard deviation.
Number of Hours fi midpoint
4 < 10 8 7
10 < 16 15 13
16 < 22 10 19
22 < 28 7 25
SUM: 40
a) the approximate mean shipping time:
X{bar} = (7.8 + 13.15 + 19.10 + 25.7)/40
X{bar} = 65.75/40
X{bar} = 1.64
b) the approximate variance:
S² = [(7.8 - 1.64)² + (13.15 - 1.64)²+(19.10 - 1.64)²+(25.7 - 1.64)²] / 39
S² = 1054.16/39
S² = 27.03
And the standard deviation:
σ = √S²
σ = √27.03
σ = 5.2
Therefore, for given frequency distribution,
a) mean = 1.64
b) variance = 27.03 and standard deviation = 5.2
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Please help I can’t solve it
Answer:
Step-by-step explanation:
to reduce a rational number to its lowest terms, you first compute the greatest common divisor (gcd) of the numerator and the denominator, using euclid's algorithm.
The given statement to reduce a rational number to its lowest terms, you first compute the greatest common divisor (gcd) of the numerator and the denominator, using Euclid's algorithm is correct.
What is Euclid's algorithm?
The Euclidean algorithm, also known as Euclid's algorithm, is an effective way to determine the greatest common divisor of two integers, or the biggest number that divides them both evenly without leaving a remainder. It is named after the Greek mathematician Euclid, who first discussed it in his Elements and gave it that name.
A common fraction can be reduced to its simplest terms using the Euclidean algorithm. For instance, the algorithm will demonstrate that the GCD of 765 and 714 is 51, and that 765/714 = 15/14 as a result. Additionally, it has several applications in more complex mathematics.
Hence, the given statement to reduce a rational number to its lowest terms, you first compute the greatest common divisor (gcd) of the numerator and the denominator, using Euclid's algorithm is correct.
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earns 5.3% annual interest that is compounded continuously. How much will the CD be worth at the end of the 5-year term?
Round to the nearest cent, and do not include the dollar sign in your answer
The worth of the CD at the end of the 5-year term would be = $3605.25
What is annual interest?Annual interest is the amount of money that is being added to an primary capital of an investment or a property which increases with time.
The rate of annual interest = 5.3%
The time for the term = 5 years
The principal amount invested in the CD = $2,850
The simple interest = P×T×R/100
=2850×5×5.3/100
= 75525/100
= $755.25
Therefore, the worth of the CD at the end of the 5-year term would be =$2,850 + $755.25
= $3605.25
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Let f be a scalar field and F a vector field. State whether each expression is meaningful. If not, explain why. If so, state whether it is a scalar field or a vector field.a. curl f b. grad f c. div F d. curl(grad f) e. grad F f. grad(div F) g. div(grad f) h. grad(div f) i. curl(curl F) j. div(div F) k. (grad f) x (div F) l. div(curl(grad f))
Let f be a scalar field and F a vector field.
a) False- can not take the curl of a scalar field.
b)True- it is a vector fields.
c)True- it is a scalar fields.
d)True- it is a vector fields.
e)False- can not take grad of a vector field.
f)True- vector fields.
g)True- - scalar fields.
h)False- can not take div of a scalar field.
i)True- - scalar fields.
j)False- can not take div of a scalar field.
k)False- can not cross product a vector with a scalar.
l)True- vector fields.
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Two friends, Pedro and Oliver, took summer jobs. Pedro earned $521.40 in 22 hours. The graph below represents Oliver's earnings in dollars and cents, yy, for working xx hours.
How much more does Pedro earn per hour than Oliver?
Pedro earns $5.1 per hour more than Oliver
How to determine the extra amount that Pedro earn per hour than Oliver?From the question, we have the following parameters that can be used in our computation:
Pedro earned $521.40 in 22 hours. Oliver's earnings in dollars and cents are represented by the graphThe hourly rate of Pedro is calculated using
Hourly rate = Amount earned/Number of hours
Substitute the known values in the above equation, so, we have the following representation
Hourly rate = 521.40/22
Evaluate
Hourly rate = 23.7
Using the points on Oliver's graph
The hourly rate of Oliver is calculated using
Hourly rate = Amount earned/Number of hours
Substitute the known values in the above equation, so, we have the following representation
Hourly rate = 186/10
Evaluate
Hourly rate = 18.6
The difference between these rates is
Difference = 23.7 - 18.6
Evaluate the difference
Difference = 5.1
Hence, the difference is $5.1
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write the equation of a tangent line to the circle with center 93,6) and the line contains point (-2,3)
The equation of a tangent line to the circle is, [tex]x^{2} +y^{2}[/tex] = 34
Given that,
The equation of a tangent line to the circle with center = (3,6)
The line contains point = (-2,3)
For a circle or curve, the tangent is a line or line segment that touches the circle at one point only. For a circle, the tangent will be perpendicular to a radius drawn to the tangent point.
A tangent to a circle at point P with coordinates is a straight line that touches the circle at P. The tangent is perpendicular to the radius which joins the centre of the circle to the point P. As the tangent is a straight line, the equation of the tangent will be of the form y = m x + c
The equation of circle of radius r and center (h , k) is given by
[tex](x-h)^{2}[/tex] + [tex](y-k)^{2}[/tex] = [tex]r^{2}[/tex] (Equation-1)
And it is given that the center is (3,6) and it passes through (-2,3).
So values of h and k are (3,6) each and values of x and y are 2 and respectively .
Substituting these values in the equation, we will get
(h , k) = (3,6)
We can substitute h , k values in equation-1,
[tex](x-h)^{2}[/tex] + [tex](y-k)^{2}[/tex] = [tex]r^{2}[/tex]
[tex](x-3)^{2}[/tex] + [tex](y-6)^{2}[/tex] = [tex]r^{2}[/tex]
Then we can substitute x , y values,
So,
We can write,
( x , y ) = (-2 , 3)
[tex](-2-3)^{2}[/tex] + [tex](3-6)^{2}[/tex] = [tex]r^{2}[/tex]
[tex](-5)^{2}[/tex] + [tex](-3)^{2}[/tex] = [tex]r^{2}[/tex]
25 + 9 = [tex]r^{2}[/tex]
34 = [tex]r^{2}[/tex]
Substituting the values of h, k and r, we will get
[tex]x^{2} +y^{2}[/tex] = 34
Therefore,
The equation of a tangent line to the circle is, [tex]x^{2} +y^{2}[/tex] = 34
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Find the sum of 4.06 × 1019 and 5.034 × 1017.
4.11034 × 1019
9.094 × 1019
4.11034 × 1036
9.094 × 1036
Answer:
Find the sum of 4.06 x 1019 and 5.034 x 1017, it equals to 9256.718
4.11034 x 1019 = 4188.43646
9.094 × 1019 = 9266.786
4.11034 x 1036 = 4258.31224
9.094 × 1036 = 9421.384
Step-by-step explanation:
4137.14 + 5119.578 = 9256.718