Homework: Section 15.1 Homework Question 3, 15.1.22 > Find the domain of the following function. f(x,y)=cos -'(5y - x2) Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. {(x,y) <0} O B. {(x,y); -13 - s1} O C. {(x,y): > >0} and y}(Use a comma to separate answers as needed.) OD. {(x,y): x* O E. R2
Answers
The given function is: f(x,y)=cos -'(5y - x2)
We need to find the domain of the given function.Let us first understand the concept of domain.
Definition: The domain is the set of all possible values of the independent variable (x-values) for which a function is defined.
Let y = 5y - x2 ………………… (1)From equation (1), x2 = 5y - y
Now, x2 = y(5 - y)
We know that the range of the cosine inverse function is between 0 and π.
Therefore, we have to find the domain of y such that x2 should not be negative.
Hence, 5 - y ≥ 0 ⇒ y ≤ 5In the interval [0,5],
the function x2 = y(5 - y) is non-negative.
Hence the domain is (x,y) ∈ R2 such that 0 ≤ y ≤ 5.
Answer: The correct choice is {(x,y): y ≤ 5}
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Related Questions
Porter is visiting India and would like to purchase some local spices. He finds some spices that cost 401.39 rupees. If the current exchange rate is 1 dollar:73.6500 rupees, how much do the spices cost in U.S. dollars?
$29,562.37
$18.35
$5.45
$0.05
Answers
The cost of spices in US dollars is $5.45
The cost of spices in Indian rupees = 401.39 rupees
The exchange rate is
1 dollar:73.6500 rupees
So we have to exchange the Indian rupees to the US dollars
The cost of spices in Indian rupees = 401.39 rupees
The cost of spices in US dollars = The cost of spices in Indian rupees / 73.6500
Substitute the values in the equation and fins the cost of spices in US dollars
The cost of spices in US dollars = 401.39 / 73.6500
Divide the numbers
= $5.45
Hence, the cost of spices in US dollars is $5.45
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Carlisle Transport had $4,520 cash at the beginning of the period. During the period, the firm collected $1,654 in receivables, paid $1,961 to supplier, had credit sales of $6,916, and incurred cash expenses of $500. What was the cash balance at the end of the period?
Answers
To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.
Starting cash balance: $4,520
Cash inflows: $1,654 (receivables collected)
Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)
Total cash inflows: $1,654
Total cash outflows: $1,961 + $500 = $2,461
To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:
Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows
Cash balance at the end of the period = $4,520 + $1,654 - $2,461
Cash balance at the end of the period = $4,520 - $807
Cash balance at the end of the period = $3,713
Therefore, the cash balance at the end of the period is $3,713.
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In 1912, the RMS Titanic, a British passenger ship, sank in the North Atlantic Ocean after colliding with an iceberg. Historians do not know the exact passenger list, so the death toll is estimated. Here is data from the 2201 passengers on board, by cabin class.
First Class Second Class Third Class Crew Row totals
Died 122 167 528 673 1490
Survived 203 118 178 212 711
Column Totals 325 285 706 885 2201
Wikipedia, RMS Titanic. (2015). Retrieved from: http://en.wikipedia.org/wiki/RMS_Titanic#Survivors_and_victims
Which proportions are most useful in analyzing the relationship between passenger class and surviving the Titanic?
· 122 / 325 and 203 / 325
· 203 / 325 and 528 / 706
· 203 / 325 and 178 /706
· 203 / 711 and 178 / 711
In 1912, the RMS Titanic, a British passenger ship, sank in the North Atlantic Ocean after colliding with an iceberg. Historians do not know the exact passenger list, so the death toll is estimated. Here is data from the 2201 passengers on board, by cabin class. First Class Second Class Third Class Crew Row totals Died 122 167 528 673 1490 Survived 203 118 178 212 711 Column Totals 325 285 706 885 2201 Wikipedia, RMS Titanic. (2015). Which proportions are most useful in analyzing the relationship between passenger class and surviving the Titanic? • 122 / 325 and 203 / 325 • 203 / 325 and 528 / 706 • 203 / 325 and 178 /706 • 203 / 711 and 178 / 711
Answers
The resulting equation would be AD = BC. Therefore, to calculate the proportion, you need to multiply the numerator of one ratio by the denominator of the other ratio and equate the products.
What are proportions? Proportions are two ratios that are equivalent or equal to each other. The ratios can be represented as a fraction or a decimal. Proportions are useful in math when dealing with solving problems that involve ratios or comparisons between two values or quantities. How to calculate proportions? To calculate a proportion, you need to compare two ratios. For instance, if you have two ratios A:B and C:D, the proportion will be A:B = C:D. It implies that A is to B as C is to D. Then you can cross-multiply the proportion, which means multiplying the numerator on the left by the denominator on the right, and then multiplying the numerator on the right by the denominator on the left. The proportions that are most useful in analysing the relationship between passenger class and surviving the Titanic are 203/325 and 178/706. The resulting equation would be AD = BC. Therefore, to calculate the proportion, you need to multiply the numerator of one ratio by the denominator of the other ratio and equate the products.
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For National High Five Day, Ronnie’s class decides that everyone in the class should exchange one high five with each other person in the class. If there are 20 people in Ronnie’s class, how many high fives will be exchanged?
Answers
To determine the number of high fives that will be exchanged, we need to find the total number of unique pairs of students in Ronnie's class Since there are 20 people in the class, each person .
To calculate the number of unique pairs, we can use the formula for combinations, which is nC2, where n is the number of people .So, for Ronnie's class with 20 people, the number of high fives exchanged is:20C2 = (20 * 19) / (2 * 1) = 190.Therefore, a total of 190 high fives will be exchanged in Ronnie's class on National High Five Day. we need to find the total number of unique pairs of students in Ronnie's class Since there are 20 people in the class, each person needs to give a high five to every other person, excluding themselves.
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suppose that two boys named davis, three boys named jones, and four boys named smith are seated at random in a row containing nine seats. what is the probability that the davis boys will occupy the first two seats in the row, the jones boys will occupy the next three seats, and the smith boys will occupy the last four seats?
Answers
The probability that the Davis boys will occupy the first two seats in the row, the Jones boys will occupy the next three seats, and the Smith boys will occupy the last four seats is 7.937×\(10^{-4}\).
There are \(\left[\begin{array}{ccc}9\\2,3,4\\\end{array}\right]\) potential arrangements for the nine boys if we do not make a distinction amongst boys with the same last name. We are curious in the likelihood of a specific one of these configurations.
Probability = \(\frac{1}{\left[\begin{array}{ccc}9\\2,3,4\\\end{array}\right]}\)
= \(\frac{2!3!4!}{9!}\)
= 0.0007937
= 7.937×\(10^{-4}\)
Hence, the probability is 7.937×\(10^{-4}\).
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if the measure of an interior angle of a regular polygon is 120 find the number of the sides in the polygon
Answers
Answer:
6 sides
Step-by-step explanation:
Interior angle and exterior angle are linear pair.
Let exterior angle = x
x + 120 = 180
x = 180 - 120
x = 60
Number of sides (n) = 360 ÷ measurement of exterior angle
n = 360 ÷ 60
n = 6
Answer:
6 sides
Step-by-step explanation:
The exterior angle and interior angle sum to 180° , then
exterior angle + 120° = 180° ( subtract 120° from both sides )
exterior angle = 60°
The sum of the exterior angles of a polygon = 360°
To find number of sides n , divide sum by measure of one exterior angle
n = 360° ÷ 60° = 6
Morgan has a loyalty card good for a discount at her local grocery store. The item she wants to buy is priced at $43, before discount and tax. After the discount, and before tax, the price is $34.40. Find the percent discount.
Answers
Answer:
20%
Step-by-step explanation:
An x-method chart shows the product a c at the top of x and b at the bottom of x. Above the chart is the expression a x squared b x c. Which statement is true of x2 8x – 6? (x – 2) is a factor of the polynomial. (x 2) is a factor of the polynomial. (x – 4) is a factor of the polynomial. The polynomial is prime.
Answers
The polynomial is prime because the provided polynomial can not be factored shown in the X-method chart.
What is X method?X-method is the method to find the factors of the polynomial equation.
An x-method chart shows the product a c at the top of x and b at the bottom of x.
Above the chart is the expression,
\(ax^2+bx+c\)
The given polynomial in the problem is,
\(x^2 +8x - 6\)
Let's check if the factors of polynomial. To find the factor, we need, to find the two number whose sum or different is 8 and the product is 6 (6 × 1).
As there is no number which gives has the sum or different is 8 and the product is 6 (6 × 1). Thus, the above polynomial can not be factored. Thus this polynomial is prime.
Thus, the polynomial is prime because the provided polynomial can not be factored, shown in the X-method chart.
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Answer:
d
Step-by-step explanation:
cuz i know
Write 63 521. 769 correct to the nearest hundred
Answers
Suppose that $5,000 is invested at an interest rate of 7% compounded monthly.
What is the balance after 8 years
Answers
Draw the graph of f(x)=3x^4+4x^3−12x^2+12 and enter all extreme points. Also state whether they are minimum or maximum points.please show a figure and detailed answer
Answers
The draw is:
Now, to find the extreme points we need to calculate the derivative and solve it for equal zero.
\(\begin{gathered} f(x)=3x^4+4x^3−12x^2+12 \\ f^{\prime}(x)=12x^3+12x^2−24x \end{gathered}\)Let's solve = 0:
\(\begin{gathered} f^{\prime}(x)=12x^3+12x^2−24x^=0 \\ 12x^3+12x^2−24x=0 \\ 12x(x^2+x-2)=0 \\ x^2+x-2=0 \\ (x+2)(x-1)=0 \\ x=-2 \\ x=1 \\ x=0 \end{gathered}\)We have the extreme points: x= -2, x=1, x=0. To compute what point is minimal or maximal we have to evaluate each point. For x= -2
\(\begin{gathered} f(x)=3x^4+4x^3−12x^2+12 \\ f(-2)=3(-2)^4+4(-2)^3−12(-2)^2+12 \\ f(-2)=48-32-48+12=-20 \end{gathered}\)Now for x=1:
\(f(1)=3(1)^4+4(1)^3-12*1^2+12=3+4-12+12=7\)Now for x=0:
\(f(0)=3*0+4*0-12*0+12=12\)Comparing these 3 points, we have local minimals at -2 and 1, and a local maximal at 0.
A wire, 24 meters in length, is attached from the top of a post to a stake in the ground. The measure of the angle that the wire makes with the ground is 36° Find to the nearest senth of a meter the distance from the stake to the foot of the post
Answers
given the information on the problem, we can draw the following diagram:
then, we can use the cosine function to find the distance from the stake to the foot of the post:
\(\begin{gathered} \cos (36)=\frac{\text{adjacent side}}{hypotenuse}=\frac{x}{24} \\ \Rightarrow x=24\cdot\cos (36)=19.4 \\ x=19.4 \end{gathered}\)therefore, the distance is 19.4 m
What is the common factor of each term in the expression 2b 1 5b?
Answers
Answer:
the common factor is b since it is divisible by both 2b and 5b
Step-by-step explanation:
Find an equation of the tangent plane to the surface at the given point.
f(x, y) = x2 − 2xy + y2 (7, 8, 1)
Answers
To find the equation of the tangent plane to the surface defined by the function f(x, y) = x^2 - 2xy + y^2 at the point (7, 8, 1), we need to consider the gradient of the function.
The gradient of f(x, y) is given by (∂f/∂x, ∂f/∂y), which represents the vector pointing in the direction of steepest ascent at any given point on the surface. In this case, the partial derivatives are:
∂f/∂x = 2x - 2y
∂f/∂y = -2x + 2y
Evaluating these partial derivatives at the point (7, 8), we get:
∂f/∂x = 2(7) - 2(8) = 6
∂f/∂y = -2(7) + 2(8) = 6
So, the gradient at the point (7, 8) is (6, 6). This vector is normal to the tangent plane. Thus, the equation of the tangent plane is given by:
6(x - 7) + 6(y - 8) + (z - 1) = 0
Simplifying, we have:
6x + 6y - 72 + z - 1 = 0
6x + 6y + z - 73 = 0
Therefore, the equation of the tangent plane to the surface at the point (7, 8, 1) is 6x + 6y + z - 73 = 0.
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Triangle ABC is similar to triangle EFD. What scale factor is required to dilate triangle ABC so that it's image, A'B'C' , is congruent to triangle EFD
Answers
Condense the expression to a single logarithm using the properties of logarithms. log (x)-1/2 log (y) +3log (2)
Answers
The expression log(x) - 1/2 log(y) + 3 log(2) can be condensed to a single logarithm using the properties of logarithms.
We can simplify the expression by applying the properties of logarithms, specifically the power rule and the product rule.
The power rule states that log(a^b) = b log(a), and the product rule states that log(ab) = log(a) + log(b).
Using these properties, we can rewrite the expression as:
log(x) - 1/2 log(y) + 3 log(2) = log(x) + log(2^3) - 1/2 log(y)
Applying the power rule to 2^3, we have:
log(x) + log(8) - 1/2 log(y)
Now, using the product rule, we can combine the logarithms:
log(8x) - 1/2 log(y)
Therefore, the condensed expression is log(8x) - 1/2 log(y). This single logarithm represents the original expression in a simplified form.
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Need help I need to turn this in by tomorrow
Answers
Answer:
A: 6 boxes right, 9 boxes down, 9 boxes left, connect back to start.
B: 3 boxes right, 9 boxes up, (diagonal 6 right, 12 down), 9 boxes up, 6 boxes right.
C: 1 box right, 2 boxes down, 1.5 boxes right, 1 box up, .5 box right, 2.5 boxes down, 3 boxes left, 3.5 boxes up to connect.
D: (diagonal 1 up, 1 right), 1 box right, (diagonal 1 down, 1 right), 1 box down, (diagonal 3 down, 3 left), 3 boxes left
Step-by-step explanation:
what is the value of each digit in 312.054
Answers
Answer:
I think this is correct if not lmk please!
Step-by-step explanation:
300
10
2
.
0
5
4
two cards are dealt from an ordinary deck of 52 cards. this means that two cards are sampled uniformly at random without replacement. (a) what is the probability that both cards are aces and one of them is the ace of spades? (b) what is the probability that at least one of the cards is an ace? 6.
Answers
The probability that both cards are aces is 0.45%.
Given that,
A standard 52-card deck is used to deal two cards. In other words, two cards are uniformly and randomly sampled without being replaced.
There are four aces in the deck of 52 cards. The likelihood of drawing an ace when you draw a card is 4/52=1/13.
There are only 51 cards left when the second card is drawn, and since an ace has already been drawn, just 3 of those cards are still in the deck. Therefore, there is a 3/51 chance of drawing the second ace. The likelihood that both of these events occur is 1/13 x 3/51 = 0.00452. (approx). Thus, there is a 0.45% chance of drawing two aces.
Combinations and permutations offer a different perspective on this. There are 52C2 different methods to choose two cards from a deck. The entire sample space is shown here.
Therefore, the probability that both cards are aces is 0.45%.
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Based on the data from your previous 10 catches, what is the chance your next catch will be a pink salmon?
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Describe any 3 of the 4 features listed below for the function g(x) = log₂ (x + 4) - 1. Include a description of how you found those answers using complete sentences. HELP
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The features of the given function graph are;
Vertical Asymptote: x = -4
Domain; x > -4
y-intercept: Undefined
x-intercept: x = -3
What are the features of the graph?The equation of the function is given as:
g(x) = log₂(x + 4) - 1
1) The vertical asymptote
Set the argument to 0;
x + 4 = 0
x = -4
That is the vertical asymptote
2) The domain
Since we have the vertical asymptote to be x = -4, then;
Domain is; x > -4
3) From the above, the function is undefined at x = -4
So, the y-intercept is undefined
Set y = 0 to calculate the x-intercept
log₂(x + 4) - 1 = 0
Applying rule of logarithm gives;
x + 4 = 2⁰
x + 4 = 1
x = 1 - 4
x = -3
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Angelo is training for a long-distance bicycle ride. He travels 15 miles each hour. How many hours will it take him to ride 210 miles?
Answers
Answer:
210 divided by 15=14
thats your answer
Step-by-step explanation:
Translation: (x,y)→(x+7,y+5) Coordinates: Y(−5,−4), X(−5,−1), W(−2,0), V(−2,−5)
Answers
Answer:
Y - (2,1)
X - (2,4)
W - 5,5)
V - (5,0)
Step-by-step explanation:
Translation: (x,y) → (x+7,y+5)
Coordinates:
Y(−5,−4) => (-5 + 7, -4 + 5) => (2,1)
X(−5,−1) => (-5 + 7, -1 + 5) = > (2,4)
W(−2,0) => (-2 + 7, 0 + 5) => (5,5)
V(−2,−5) => (-2 + 7, -5 + 5) => (5,0)
2 7/9 × 1 1/5 ÷ 2 1/2
Answers
Answer
5/36 (\(\frac{5}{36}\))
Answer:
22/35
Step-by-step explanation:
27/9 = 3
3 × 11/5 ×2/21
=22/35
Please help me with this homework
Answers
Answer: 12 units
Step-by-step explanation:
What is 1/4 0.75 1/3 0.5 greatest to least
Answers
Answer:
1/4 = 1 ÷ 4 = 0.251/3 = 1 ÷ 3 ≈ 0.330.750.50.75 → 0.5 → 1/3(0.33) → 1/4(0.25)
After buying school supplies ruby had 32 left over. She spent 4 on notebook
Answers
Answer: 32 + 18 + 4 + 30 = 8432+30=6262+18=8080+4=84
Step-by-step explanation: i did this question before so i dont know if you can understand it but i got it correct last week
George records the number of questions he has answered on DFM per day over 14 days, and puts the data in the bar chart below.
Find the total number of questions.
Answers
Answer:
18 is the total number of questions George answered in 14 days.
Step-by-step explanation:
The given chart:
The x-axis is showing the total number of questions George answered The y-axis is showing the frequency of days on which George answered the questions.The given chart is showing that:
George answered the 5 questions on the first 4 days;George answered the next 6 questions on the next 5 days;George answered the next 7 questions on the last 5 days';Hence, the total questions he answered will be:
5 + 6 + 7 = 18
Therefore, 18 is the total number of questions George answered in 14 days.
P = (12, 4) and M = (-8, 8)
Answers
what does 12-(-4)= equal
Answers
Answer:
16
Step-by-step explanation:
12-(-4)
12+4
16
This is the answer you looking for.