Solve for [tex]z=f(x,y)[/tex] in the plane equation.
[tex]4x + 5y + z = 7 \implies f(x,y) = z = 7 - 4x - 5y[/tex]
Let [tex]E[/tex] be the set of points in the plane [tex]z=0[/tex] bounded by the ellipse [tex]\frac{x^2}{25}+\frac{y^2}{100}=1[/tex], i.e.
[tex]E = \left\{(x,y) ~:~ \dfrac{x^2}{25} + \dfrac{y^2}{100} \le 1\right\}[/tex]
Then the area of the plane bounded by the elliptic cylinder is
[tex]\displaystyle \iint_E dA = \iint_E \sqrt{1 + \left(\dfrac{\partial f}{\partial x}\right)^2 + \left(\frac{\partial f}{\partial y}\right)^2} \, dx \, dy \\\\ ~~~~~~~~ = \iint_E \sqrt{1 + (-4)^2 + (-5)^2} \, dx\, dy \\\\ ~~~~~~~~ = \sqrt{42} \iint_E dx \, dy[/tex]
which is simply √42 times the area of the ellipse in the plane [tex]z=0[/tex]. This ellipse has a minor axis of length 5 and a major axis of length 10, so its area is π•5•10 = 50π, and so the area of the plane in question is 50√42 π.
To confirm this result: In polar coordinates, with
[tex]\begin{cases}x(r,\theta) = 5r\cos(\theta) \\ y(r,\theta) = 10r\sin(\theta) \\ \frac{x^2}{25}+\frac{y^2}{100}=r^2\end{cases}[/tex]
the area element is
[tex]dA = \begin{vmatrix}\frac{\partial x}{\partial r}&\frac{\partial x}{\partial\theta} \\ \frac{\partial y}{\partial r} & \frac{\partial x}{\partial\theta}\end{vmatrix} \, dr \, d\theta \\\\ ~~~~~~~~ = \begin{vmatrix}5\cos(\theta)&-5r\sin(\theta)\\10\sin(\theta)&10r\cos(\theta)\end{vmatrix} \, dr \, d\theta \\\\ ~~~~~~~~ = \left(50r\cos^2(\theta)+50r\sin^2(\theta)\right)\,dr\,d\theta \\\\ ~~~~~~~~ = 50r \, dr \, d\theta[/tex]
The ellipse can be parameterized by
[tex]E = \left\{(r,\theta) ~:~ 0\le\theta\le2\pi \text{ and } 0\le r\le1\right\}[/tex]
so that the integral for the area of the ellipse in the plane [tex]z=0[/tex] is
[tex]\displaystyle \iint_E dA = \int_0^{2\pi} \int_0^1 50r \, dr \, d\theta \\\\ ~~~~~~~~ = 100\pi \int_0^1 r \, dr \\\\ ~~~~~~~~ = 100\pi\left(\frac12-0\right) = 50\pi[/tex]
a certain european automobile has a gas mileage of 19 km/l. what is the gas mileeage in miles per gallon
The gas mileeage in miles per gallon is 44.69 miles per gallon
How to convert 19 Km/L to miles per litresWe'll begin by converting 19 Km/L to miles per litres. This can be obtained as follow:
Gas mileage (in Km/L) = 19 Km/LGas mileage (in mile per litres) =?1 Km/L = 0.621371 mile per litre
Therefore,
19 Km/L = (19 Km/L × 0.621371 mile per litre) / 1 Km/L
19 Km/L = 11.806 miles per lire
How to convert 11.806 miles per litre to miles per gallonWe can convert 11.806 miles per litre to miles per gallon as follow:
1 mile per litre = 3.78541178 miles per gallon
Therefore,
11.806 miles per litre = (11.806 miles per litre × 3.78541178 miles per gallon) / 1 mile per litre
11.806 miles per litre = 44.69 miles per gallon
Thus, the gas mileage is 44.69 miles per gallon
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Which expression represents the product of 3 and 7
Answer:
343.
Step-by-step explanation:
nice :)
The product of 3 and 7 is 21.
What is the product of two number?The product of two numbers is the result you get when you multiply the numbers together.
Given are two numbers, 3 and 7.
When we multiply 3 to 7 we get 21,
Mathematically, it can be expressed as,
3x7 = 21
Hence, The product of 3 and 7 is 21.
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3.6w = 2 (0.8w+12) MUST DO WITH AN EXPLANATION IF ITS CORRECT ILL GIVE BRAINLIEST
Answer:
w=12
Step-by-step explanation:
3.6w=2(0.8w+12)
3.6w=2x0.8w+2x12
3.6w=1.6w+24
3.6w-1.6w=24
2w=24
w=12
HOPE THIS WILL HELP;)
QUICK PLS I NEED HELP
Answer:
1/3 is a repeating decimal. 0.33333....
7/12 is a repeating decimal 0.5834....
1/5 is a terminating decimal 0.5
5/8 is a terminating decimal 0.625
2/9 is a repeating decimal 0.2222......
Step-by-step explanation:
Hope it helps! =D
Answer:
1/3 is a repeating decimal
7/12 is a repeating decimal
1/5 is a terminating decimal
5/8 is a terminating decimal
2/9 is a repeating decimal
Solve for x in the diagram below.
Answer: x=6
Step-by-step explanation: (x+54)+5x=90 -> 6x+54=90 -> 6x=36 -> x=6
you know it equals 90 because it's on a 180 and there's a right angle.
simplify the equation to 6x+54=90, subtract 54 from 90, and divide by 6 to isolate x.
terri, aaron, and jamal all walked along straight paths. terri walked 3.95 km north in 48 min. aaron walked 2.65 km west in 31 min. jamal walked 6.50 km south in 81 min.
The option that correctly ranks the three boys in order from lowest to highest average speed is:
Jamal, Terri, AaronHow is the Average speed calculated?The average speed calculated is obtained by dividing the total distance covered by the total time taken. That said, we will obtain the average speeds for each of the boys as follows:
Terri = 3.95 km/48 min
= 0.082 km/min
Aaron = 2.65 km/31 min
= 0.085 km/min
Jamal = 6.50 km/81 min
= 0.080 km/min
When the results are obtained from lovwest to highest we will have:
0.080, 0.082, 0.085 which represent the figures for Jamal, Terri, Aaron.
Complete Question:
Terri, Aaron, and Jamal all walked along straight paths. Terri walked 3.95 km north in 48 min. Aaron walked 2.65 km west in 31 min. Jamal walked 6.50 km south in 81 min. Which of the following correctly ranks the three boys in order from lowest to highest average speed?
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Carla wrote this number:815,247 travis wrote this number: 638.571 the digit 8 in carlas number represents how many times what the digit 8 represents in travis number?
The digit 8 in Carla’s number represents 10 times of what the digit 8 represents in Travis’ number.
The number written by Carla = 814,247
The number written by Travis = 683,571
The place value of digits starting from left is ones, ten's, hundreds, thousands, ten thousand, hundred thousand and so on.
As per this sequence of values, we can see that digit 8 in Carla's number is at hundred thousand place value. Also, digit 8 in Travis' number is at ten thousand place value. So, representing these place value in numeral form and finding the number of times one is greater than other.
Digit 8 in Carla's number: 100,000
Digit 8 in Travis' number: 10,000
Finding the answer -
Value = 100,000 ÷ 10,000
Cancelling common zeroes from numerator and denominator
Value = 10
Hence, digit 8 in Carla’s number represents 10 times of what the digit 8 represents in Travis’ number.
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The correct question is -
Carla wrote this number: 814,247
Travis wrote this number: 683, 571
The digit 8 in Carla’s number represents how many times what the digit 8 represents in Travis’ number?
A. 10
B. 100
C. 1000
D. 1/10
The prediction method _________ is the method used to estimate a point on a line when the point does not lie between the given points.
The prediction method Linear Extrapolation is the method used to estimate a point on a line when the point does not lie between the given points.
What is linear extrapolation?Using the equation of a line to obtain a new data point based on an existing collection of data points is known as linear interpolation in mathematics.
Now,
Since it employs a linear model to forecast the necessary point that does not reside between the given locations, this prediction technique is known as linear extrapolation.
Hence, The prediction method Linear Extrapolation is the method used to estimate a point on a line when the point does not lie between the given points.
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Clyde and mason each leave a rest area on the flordia turnpike. Clyde travels north and mason travels south. After 4 hr, Clyde has gone 248 mi and mason, who ran into heavy traffic, traveled only 184 mi. How far apart are they
Clyde and Mason are 432 mi apart from each other in distance.
We are given that:
Clyde and mason can each leave a rest area on the Florida turnpike.
Clyde travels north whereas Mason travels south.
After 4 hr., we get that Clyde has gone 248 mi and Mason, due to the heavy traffic he got , traveled only 184 mi.
We need to tell how far are they from each other.
We will do this by addition.
Distance = 248 mi + 184 mi
Distance = 432 mi.
Therefore, we get that, Clyde and Mason are 432 mi apart from each other in distance.
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Cherries cost 4 dollars per pound.my mother r lb of cherries and my father bought 2 lb of cherries.how much more money did my mother spent on cherries than my father
Mother spent (4r - 8) dollars more on cherries than did the father.
An expression using numbers and related operations is called a numerical expression.
According to the question, a pound of cherries costs $4.
Mom purchased r pounds.
The price of the cherry is calculated as follows: 4r = weight x $/lb.
Father purchased 2 pounds, thus the price of the cherries is 4 (2), or $8.
We remove the smaller value from the higher value, which is 4r - 8, where r must be more than two. Given that the mother spent more money on cherries than the father, the mother's cost of cherries is a greater value.
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How do you get 2.718?
Answer:
Step-by-step explanation:
[tex]\lim\limits_{x \to 0} (1+x)^\frac{1}{x} =e\ (the\ second\ remarkable\ limit.)\\\\ \lim\limits_{x \to 0} (1+x)^\frac{1}{x} \approx2.718[/tex]
Evaluate 2X^2 + 3X -10 for the domain of {-2, 3}
The values of the expression at the domain {-2, 3} are {-8, 4}
How to evaluate the expression for the domain?The expression is given as
2x^2 + 3x - 10
The domain of the function is given as
{-2, 3}
Rewrite the domain as
x = {-2, 3}
Next, we substitute these values of x in the expression 2x^2 + 3x - 10
So, we have
x = -2:⇒ 2(-2)^2 + 3(-2) - 10 = -8
x = 2:⇒ 2(2)^2 + 3(2) - 10 = 4
Hence, the values of the expression at the domain {-2, 3} are {-8, 4}
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For a real number a, a + 0 = a is that true?
For a real number a, a + 0 = a: TRUE
What are real numbers?In mathematics, a real number is a quantity that can be expressed as an infinite decimal expansion. In contrast to the natural numbers 1, 2, 3,..., which are derived from counting, real numbers are used in measurements of continuously varying quantities such as size and time.For a real number a, a + 0 = a:
This is due to the identity property for addition, which states that zero added to any number equals the number itself. So, in this case, the number is, and it is true that: a + 0 = aTherefore, the statement "for a real number a, a + 0 = a" is TRUE.
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if q is the point (x, 3/(2 − x)), use your calculator to find the slope mpq of the secant line pq (correct to six decimal places) for the following values of x.
According to the given data the slope mpq of the secant line pq for the following values of x are :
m for x3.333333 for 2.93.030303 for 2.993.003003 for 2.9993.00030003 for 2.99992.727272 for 3.12.90297 for 3.012.997002 for 3.0012.999700 for 3.0001What is the definition of the slope inside a graph?The slope is defined as the proportion of both the vertical difference of two points, known as the rise, towards the horizontal change between those same two points, known as the run.
How do you calculate slope?Calculate the values of two line points. Determine the difference in y-coordinates between these two locations (rise). Calculate the x-coordinate distinction between these two locations (run). Divide the x-coordinate variation (rise/run or slope) by the y-coordinate difference.
According to the given data:Slope(m) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
so,
m for x
3.333333 for 2.9
3.030303 for 2.99
3.003003 for 2.999
3.00030003 for 2.9999
2.727272 for 3.1
2.90297 for 3.01
2.997002 for 3.001
2.999700 for 3.0001
this shows that the slope m for the required x.
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I understand that the question you are looking for is:
The point P(3, −3) lies on the curve y = 3/(2 − x).
If Q is the point (x, 3/(2 − x)), use your calculator to find the slope m PQ of the secant line PQ (correct to six decimal places) for the following values of x.
i. 2.9 =
ii 2.99 =
iii. 2.999 =
iv.2.9999 =
v. 731
vi. 3.01
vii. 3.001
viii. 3.0001
a. Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(3,-3)
b. Using the slope from part (b), find an equation of the tangent line to the curve at P(3,- 3).
HELP GUYS! SHOW WORK!!!!!!!!!!!!!!!!! 20 points
The value of x from the given line segment is 5
Addition postulateA line is defined as the shortest distance between two points. From the given line segment, the addition below is true;
NM + ML = NL
Given
NM = 9
ML = 2x-7
NL = x + 7
Substitute to have:
9 + 2x - 7 = x + 7
2x + 2 = x + 7
2x-x = 7 - 2
x = 5
Hence the value of x from the given line segment is 5
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Please help with problem 2
Answer: 4==> D
Step-by-step explanation:
b=1
|2b-5|+1=
|2(1)-5|+1=
|2-5|+1=
|-3|+1= ==> Absolute value equations are always positive: |-x|=x, not -x.
3+1=4==> D
Answer:
Step-by-step explanation:
D 4
Calculate the total surface area of a cube of the following length of side a) 5cm b) 8cm c) 10ft d) 12m
Answer:
the side of a cube is 5 cm.
Total surface area of cube =6× (side)
2
=6×5×5
=150
∴ The total surface area of cube is 150 cm
2
Step-by-step explanation:
Sorry I I don't have much time to answer the rest
A number cube with the numbers 1 through 6 is rolled. The probability of rolling an odd or even number is 1. What is the likelihood of rolling an odd or even number?
1/2 is the likelihood of rolling an odd or even number in probability.
What is probability and how is it calculated?
According to the probability formula, the probability of an event occurring, or P(E), is equal to the proportion of positive outcomes to all outcomes. P(E) is defined mathematically as favorable outcomes divided by total outcomes.A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.The event "rolling an odd number" contains three outcomes. There are 6 equally likely outcomes in the sample space. Divide to find the probability of the event.
P(E) = 3/9 = 1/2
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Neville and his friends are going to a local peach festival. They plan to go on rides all day. The tickets for the rides are $0.50 each. Find the domain and range with words and inequalities.
The domain of x will be a set of whole numbers greater than 2 which is; x > 2
The range of y will be a set of rational numbers greater than or equal to 1.5 which is; y ≥ $1.5
What is the domain and range?
The domain of a function is defined as the set of all possible input values that make the function possible while range is the set of all possible output values that are possible from the input values.
The function is; y = 0.5x
Since the value of x represents the number of people that purchased tickets for the rides including Neville, then we can say that the domain of x will be a set of whole numbers greater than 2 because we are told it is him and his friends which is plural. Thus;
The domain is; x > 2
The range will be;
y ≥ 3(0.5)
y ≥ $1.5
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BRAINLIEST
Choose the word noun, adjective, or verb that correctly answers the question.
What kind of words are crying, mending, and envying?
Answer:
crying -adjective. mending -noun. envying -verb.
Step-by-step explanation:
since an adjective is a word naming an attribute of a noun, the word cry is a noun and so the action being carried out "crying" is an adjective.
a noun is a word used in identifying a person, place or thing. and mending is a... you get the idea?
6−2(8−x)=2x−10
l don't understand the question
Answer: x has infinite number of solutions
Step-by-step explanation:
6−2(8−x)=2x−10
6-16-2(-x)=2x-10
-10+2x=2x-10
2x-10=2x-10 ==> x has infinite number of solutions
What is the relationship between the numerator and the denominator in a fraction?
Answer: GoodMorning: )✨Ok so We should Know that The top number in a fraction is always considered a numerator, and that It shows the number of parts we have. The bottom number in a fraction is considered a denominator. It shows the total number of parts into which anything is divided. For example, in the fraction 8/7, 8 is the numerator and 7 is the denominator.
Step-by-step explanation: Like In this fraction 7/3, 7 is the numerator and 3 is the denominator. In the fraction 9/7, 9 is the numerator and 7 is the denominator.The value placed above the horizontal line in a fraction is called a numerator. It signifies the number of parts taken out of the whole. The numeric value below the vinculum of a fraction is called the denominator. It represents the total number of equal parts as a whole. Hope this helps: )
Have A Nice Day: )
Answer:
A numerator is a value on the upper character set of a rational or fraction value and a denominator is the downer
[tex]{ \rm{fraction = \frac{numerator}{denominator} }} \\ [/tex]
For example;
Three quarters
[tex]{ \rm{ = \frac{3}{4} }} \\ [/tex]
3 is numerator and 4 is denominator
is 22.5 a interger number?
Given 24.8 × 3.5, find the product. 8.68 72.4 75.64 86.8
The product of the given expression 24.8 × 3.5 is 86.8. option D
Product of numbersProduct refers to any operation or a result thereof which generalises multiplication of numbers, like the multiplicative operation in a ring, product of types or a categorical product.
This is also a quantity obtained by multiplication of two or more numbers.
The Multiplication symbol is represented by ( × )
For instance,
product of 2 and 3 is 6.The product of 2, 3, and 4 is 24.24.8 × 3.5
= 86.8
Therefore, the product of the given expression 24.8 × 3.5 is 86.8.
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f(x) = 3x²-x+ 5, 2f(-3) - f(4) =
Answer:
21
Step-by-step explanation:
You want the value of the expression 2f(-3)-f(4), given that f(x) = 3x²-x+ 5.
Function evaluationA function is evaluated by putting the argument where the variable is, and simplifying the result. Polynomials are often easier to evaluate if they are written in Horner form.
f(x) = 3x² -x +5
f(x) = (3x -1)x +5
The values we need are ...
f(-3) = (3(-3) -1)(-3) +5 = (-10)(-3) +5 = 35
f(4) = (3(4) -1)(4) +5 = (11)(4) +5 = 49
Then the expression of interest has the value ...
2f(-3) -f(4) = 2(35) -49 = 70 -49
2f(-3) -f(4) = 21
HELP ILL GIVE YOU 20 POINTS
A carton of apple juice displays the nutritional information shown below.
How many grams of sugar are there in a 200 ml glass of juice?
< Back to task
Bookwork
I
Apple juice
250 ml contains
Carbohydrate
Sugar
Protein
1
29.5 g
25.5 g
| 0.3 g
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Answer >
Answer:
Step-by-step explanation:
200/250 =0.8
25.5x0.8 =20.4
answer=20.4
solve w^4 - 18w + 81 = 0
Answer:
No solution
Step-by-step explanation:
You can solve this in a few ways. One way is to graph the equation, and the solution is the x-value of the point of intersection. Another way would be to factor, which is more difficult to complete with a square bigger than 2.
By graphing, you can see a parabola that never touches that x-axis, which means no solution.
a sports writer studies the batting average, walk to strikeout ratio, and home runs hit for a certain baseball player for five weeks for an article.
Batting common is the the wide variety of runs scored via way of means of the batsman withinside the wide variety of fits performed via way of means of him in that supply weeks Walk to strike out is the wide variety of wickets taken via way of means of the sports activities character withinside the wide variety of fits performed via way of means of him in that week Home runs are the house run hit via way of means of that participant in that 5 weeks throughout which the sports activities creator cited these types of happenings
If participant A's batting common is .312 and he had 596 at-bats , what number of hits did he get?
The number of hits A got is 186 hits.
A player's batting average is calculated by dividing the number of hits by the number of at-bats.
Player A batting average = 0.312
Number of at-bats A did = 596
We have to find the number of hits A got.
0.312 = Number of hits / 596
Number of hits = 0.312 x 596
= 185.952 hits.
Rounding to a whole number we get,
= 186 hits
Thus, the number of hits A got is 186 hits.
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5/8 - (1/4) squared equals