find ∂ 2 z ∂s∂r (write your answer in terms of r,s, ∂z ∂x , and ∂z ∂y , ∂ 2 z ∂x2 , ∂ 2 z ∂x∂y , and ∂ 2 z ∂y2 )
Answers
To find ∂²z/∂s∂r, we'll use the chain rule and expand the expression step by step. Let's denote the partial derivatives as follows: ∂z/∂x as zₓ, ∂z/∂y as zᵧ, ∂²z/∂x² as zₓₓ, ∂²z/∂x∂y as zₓᵧ, and ∂²z/∂y² as zᵧᵧ.
Using the chain rule, we have:
∂²z/∂s∂r = (∂z/∂s)(∂²z/∂r∂s) + (∂z/∂r)(∂²z/∂s²)
Expanding further:
∂²z/∂s∂r = (∂z/∂s)(∂/∂r)(∂z/∂s) + (∂z/∂r)(∂²z/∂s²)
Next, we express the derivatives in terms of the given variables:
∂²z/∂s∂r = (∂z/∂s)(zₓ∂/∂r(zₓ) + zᵧ∂/∂r(zᵧ)) + (∂z/∂r)(∂²z/∂s²)
Finally, we substitute the given variables into the expression:
∂²z/∂s∂r = (∂z/∂s)(zₓ(∂z/∂r) + zᵧ(∂z/∂r)) + (∂z/∂r)(∂²z/∂s²)
Therefore, ∂²z/∂s∂r is expressed in terms of r, s, ∂z/∂x, ∂z/∂y, ∂²z/∂x², ∂²z/∂x∂y, and ∂²z/∂y² as (∂z/∂s)(zₓ(∂z/∂r) + zᵧ(∂z/∂r)) + (∂z/∂r)(∂²z/∂s²).
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Related Questions
Match each sentence with the inequality that could represent the situation
A. Han got $2 from Clare, but he has less than $20 1. x - 2 < 20
B. Mai spent $2 and has less than $20 2. 2x < 20
C. If Tyler had twice the amount of money he has, he
would have less than $20 3. x + 2 < 20
D. If Priya had half the money she has, he would
have less than $20 4. 1/2x < 20
Answers
Therefore, the area of the trapezoid is 60 cm².
What is trapezoid?A trapezoid is a four-sided polygon with two parallel sides (called bases) of different lengths, and two non-parallel sides (called legs). The legs of a trapezoid are usually not congruent and can be of different lengths. Trapezoids can have different shapes and sizes, but they always have at least one pair of parallel sides. The area of a trapezoid can be calculated using the formula:
\(Area = ((b_1 + b_2) * h) / 2,\)
where b1 and b2 are the lengths of the parallel bases, h is the height or perpendicular distance between the two bases.
To calculate the area of a trapezoid, we use the formula:
\(Area = (b_1 + b_2) * h / 2\)
where b1 and b2 are the lengths of the parallel sides of the trapezoid and h is the height (perpendicular distance) between the parallel sides.
In this case, we are not given which sides are the parallel sides and which one is the height, so we cannot directly apply the formula. However, we can make an educated guess based on the dimensions given.
Assuming that the two 8 cm sides are parallel, we can use the formula as follows:
\(Area = (b_1 + b_2) * h / 2\)
\(Area = (8 cm + 16 cm) * 10 cm / 2\)
\(Area = 120 cm^{2} / 2\)
\(Area = 60 cm^{2}\)
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If l is parallel to m, find the values of x and y in the diagram below
Answers
The values of x and y in the lines are x = 13 and y = 54
How to determine the values of x and yFrom the question, we have the following parameters that can be used in our computation:
The lines m and n are parallel lines
This means that the following angles are congruent by the corresponding angle theorem
7x - 31 + 5x - 8 + 63 = 180
4y + 27 - 180 = 63
Solving the equation 4y + 27 - 180 = 63
We have the following representation
4y + 27 - 180 = 63
Evaluate the like terms
4y = 216
Divide by 4
y = 54
Recall that
7x - 31 + 5x - 8 + 63 = 180
Evaluate the like terms
12x = 156
Divide by 12
x = 13
Hence, the values are x = 13 and y = 54
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the solid enclosed by the paraboloids y = x2 + z2 and y = 72 − x2 − z2.
Answers
the volume of the solid enclosed by the paraboloids \(y = x^2 + z^2\) and \(y = 72 - x^2 - z^2 is 48π√2.\)
To find the solid enclosed by the paraboloids\(y = x^2 + z^2\) and \(y = 72 - x^2 - z^2\), we need to determine the limits of integration for each variable.
First, we note that the paraboloids intersect when:
\(x^2 + z^2 = 36\)
This gives us a circle with radius 6 in the xy-plane.
We can use cylindrical coordinates to integrate over this solid. The limits of integration for the cylindrical radius r are 0 to 6, and the limits for the angle θ are 0 to 2π.
For each value of r and θ, the limits of integration for the cylindrical height z are given by the two paraboloids:
\(x^2 + z^2 ≤ y ≤ 72 - x^2 - z^2\)
Converting these equations to cylindrical coordinates, we have:
\(r^2 ≤ y ≤ 72 - r^2\)
Solving for z in terms of r and y, we get:
\(-z ≤ ±√(y - r^2)\)
Taking the negative square root to get the lower limit of integration, we have:
\(-z ≥ -√(y - r^2) \\z ≤ √(y - r^2)\)
Therefore, the limits of integration for z are \(-√(y - r^2) to √(y - r^2).\)
The volume of the solid is given by the triple integral:
V = ∫∫∫ dz dr dθ
where the limits of integration are:
0 ≤ r ≤ 6
0 ≤ θ ≤ 2π
\(r^2 ≤ y ≤ 72 - r^2\\-√(y - r^2) ≤ z ≤ √(y - r^2)\)
Integrating over z first, we have:
\(∫-√(y-r^2)^(√(y-r^2)) dz = 2√(y-r^2)\)
Substituting this into the triple integral and simplifying, we get:
\(V = ∫∫ 2√(y-r^2) dr dθ\\= 2∫∫√(72-2r^2) r dr dθ (substituting y = 72 - r^2)\\= 2∫0^2π ∫0^6 √(72-2r^2) r dr dθ\)
We can evaluate this integral using a u-substitution, where \(u = 72 - 2r^2\) and du/dr = -4r:
\(V = 2∫0^2π ∫72^0 √u (-du/4) dθ\\= π∫0^72 √u (-du/2)\\= π[-(2/3)u^(3/2)]_0^72\\= π(2/3)(72)^(3/2)\\= 48π√2\)
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what is the surface area of the a cylinder with base radius 3 and height 8.
Answers
Bonjour,
πr² *h
3,14 * 3² *8
= 3,14 *9 *8
=>226, 08 ....²
Answer:
66π square units
Step-by-step explanation:
Mr. Guy pens and pencils. He spends a total of $25. Each pencil cost $1 and each pen cost
$1.50. Use X to represent the number of pencils. Use Y to represent the number of pens. Write an
equation that represents the situation
Answers
Answer:
x + 1.5y = 25
Step-by-step explanation:
Given that Mr. Guy spends a total of $25, we can set the equation equal to 25. Since x is used to represent the number of pencils, we put 1x into the left side of the equation. We also know that it cost $1.50 for each y pens, therefore 1.5y. If we put together what we have, the equation will be x + 1.5y = 25.
Determime the measures of angles X,y and Z
x° = 105°
y° = z°
x = ?
y = ?
z = ?
Answers
Answer:
X = 75°
Y = 105°
Z =75
Step-by-step explanation:
evaluate the line integral, where c is the given curve. c xey dx, c is the arc of the curve x = ey from (1, 0) to (e3, 3)
Answers
line integral, where c is the given curve. c xey dx, c is the arc of the curve x = ey from (1, 0) to (e3, 3), the value of the line integral is 1/2 (e⁶ - 1).
To evaluate the line integral of c xey dx, where c is the arc of the curve x = ey from (1, 0) to (e3, 3), we first need to parameterize the curve c. Since x = ey, we can rewrite c as y from (0,1) to (3, e³).
Next, we can rewrite the integral in terms of y:
∫c xey dx = ∫0³ (ey) (ey) dy
= ∫0³ e^{(2y)} dy
= [1/2 e^{(2y)}] from 0 to 3
= 1/2 (e⁶ - 1)
Therefore, the value of the line integral is 1/2 (e⁶ - 1).
In summary, we parameterized the curve c as y from (0,1) to (3, e³) and rewrote the integral in terms of y. We then evaluated the integral using the fundamental theorem of calculus and obtained the final answer of 1/2 (e⁶ - 1).
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Determine the equation of the parabola graphed.
g(x)=
64
56
48
40
32
24
16
8
0
p
...
-2 -1
(-1, 4)
0
1
2
3 4
]
![Determine the equation of the parabola graphed.g(x)=6456484032241680p...-2 -1(-1, 4)0123 4]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/1dxnV7VwDedX5r2vWySWv4hfkL77nPQI.png)
Answers
The equation of the parabola is y = ( 4/3 ) ( x + 1 )² + 4
What is a Parabola?A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
y = a ( x - h )² + k
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k – p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
Let the equation of parabola be represented as A
Now , the value of A is
Let the vertex of the parabola be V
Now , the coordinates of P is V ( -1 , 4 )
and , equation of the parabola is given by
( x - h )² = 4p ( y - k )
y = a ( x - h )² + k
On simplifying , we get
y = a ( x - ( - 1 ) ) + 4
y = a ( x + 1 )² + 4
Now , the point on the parabola is given by P ( 2 , 16 )
On simplifying , we get
when x = 2 and y = 16
16 = a ( 2 + 1 )² + 4
16 = 9a + 4
12 = 9a
a = 4/3
So , the the value of a is 4/3
And , the equation is g ( x ) = ( 4/3 ) ( x + 1 )² + 4
Therefore , the value of g ( x ) is ( 4/3 ) ( x + 1 )² + 4
Hence , the equation of parabola is g ( x ) = ( 4/3 ) ( x + 1 )² + 4
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What is the positive root of the equation x^2− 5x = 14?
Answers
The positive root of the quadratic equation x² - 5x = 14 is 7.
What is the positive root of the given equation?A quadratic equation in its standard form is expressed as;
ax² + bx + c = 0
Where x is the unknown
To solve for x, we use the quadratic formula
x = (-b±√(b² - 4ac)) / (2a)
Given the equation in the question.
x² - 5x = 14
Rearrange in standard form
x² - 5x - 14 = 0
Plug the values of a, b and c into the quadratic formula and solve for x.
x = (-b±√(b² - 4ac)) / (2a)
x = ( -(-5) ±√( (-5)² - ( 4 × 1 × -14) )) / (2 × 1)
x = ( 5 ±√( 25 - ( -56 ) )) / 2
x = ( 5 ±√( 25 + 56 )) / 2
x = ( 5 ±√( 81 )) / 2
x = ( 5 ± 9 )/2
x = ( 5 - 9 )/2, x = ( 5 + 9 )/2
x = (-4)/2, x = (14)/2
x = -2, x = 7
Therefore, the solutions are x = -2 and x = 7.
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HELP PLs ASAP WIll make brianist
Answers
Answer:
D
Step-by-step explanation:
The slopes of the lines are negative reciprocals, so they are perpendicular.
See the image for complete work.
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if x is a random number between 0 and 1, then we can use x to simulate a variable that is uniformly distributed between 100 and 200. using the formula: a.100 + x b. 200 −x c. 100 + 100x d. 200x
Answers
The correct formula to simulate a variable uniformly distributed between 100 and 200 using x is c. 100 + 100x.
To simulate a variable uniformly distributed between 100 and 200 using a random number x between 0 and 1, you can use the formula:
Variable = 100 + (200 - 100) * x
Let's break down the formula:
a. 100 + x: This will give a variable that ranges from 100 to 101, not between 100 and 200.
b. 200 - x: This will give a variable that ranges from 199 to 200, not between 100 and 200.
c. 100 + 100x: This formula is correct and will give a variable that ranges from 100 to 200, with x ranging from 0 to 1.
d. 200x: This formula will give a variable that ranges from 0 to 200, not between 100 and 200.
Therefore, the correct formula to simulate a variable uniformly distributed between 100 and 200 using x is c. 100 + 100x.
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A circle is centered at $O$ and has an area of $48 \pi.$ Let $Q$ and $R$ be points on the circle, and let $P$ be the circumcenter of triangle $QRO.$ If $P$ is contained in triangle $QRO,$ and triangle $PQR$ is equilateral, then find the area of triangle $PQR.$ Will give brainlyist!
Answers
The area of the Triangle PQR which is in the circle, is given as 784.25. See the computation below.
What is a circle?Mathematically speaking, a circle is a 2-dimensional shape whose boundaries are round and are equidistant from a fixed center.
What is calculation of the answer given above?The area of ΔPQR is given as ((√3)/4) x QR²
= (√3)/4) x (6√2 - 2√6)²
= 0.43301270189 x (8.48528137424 x 4.89897948557)²
= 0.43301270189 x 1728
Area of ΔPQR = 784.25
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2. A football team plays 28 games and wins 4 out of every 7 games played. No match ended in a draw. 20 (a) How many times has this football team lost?
Answers
This ratio has 7 parts to it. 28/7 = 4 so the ratio should be multiplied by 4.
This gives a ratio of 16:12 which has 28 parts.
The first part of the ratio is how many times they won. The second part is how many times they lost so the answer is 12
put these numbers in order least to greatest 1 1/3, -5/6, 0, -2/3, -1
Answers
Answer:
-1, -5/6, -2/3, 0, 1 1/3
Step-by-step explanation:
Answer:
-1, -5/6, -2/3, 0, 1 1/3.
Step-by-step explanation:
1 1/3, -5/6, 0, -2/3, -1
The easiest way is to convert them to decimal fractions first:
= 1.333.... , - 0.8333... , 0, -0.666.... , - 1
So in ascending order they are
-1, -0.833.., -0.666... , 0 , 1.333.....
= -1, -5/6, -2/3, 0, 1 1/3.
If nkf ~ lzf, find nf, please help me with this it’s due tmr!!!!
Answers
Answer:
NF = 25
Step-by-step explanation:
Since ∆NKF ~ ∆LZF, the ratio of their corresponding side lengths would also be the same.
This means that:
KF/ZF = NF/LF
KF = x + 3
ZF = 4
NF = 15 + x + 3 = x + 18
LF = x + 3
Plug in the values into the equation
(x + 3)/4 = (x + 18)/(x + 3)
Cross multiply
(x + 3)(x + 3) = (x + 18)(4)
x² + 3x + 3x + 9 = 4x + 72
x² + 6x + 9 = 4x + 72
x² + 6x + 9 - 4x - 72 = 0
x² + 2x - 63 = 0
Factorize to find x
x² + 9x - 7x - 63 = 0
x(x + 9) -7(x + 9) = 0
(x + 9)(x - 7) = 0
x + 9 = 0 or x - 7 = 0
x = -9 or x = 7
We'd use the positive value of x, which is 7.
Therefore, x = 7.
✅NF = 15 + (x + 3)
Plug in the value of x
NF = 15 + (7 + 3) = 15 + 10
NF = 25
The method of solving a system of equations or inequalities by systematically adding or subtracting a multiple of one equation or inequality to a multiple of another equation to eliminate a variable is called ___ elimination.
Answers
The method of solving a system of equations by systematically adding or subtracting a multiple of one equation to a multiple of another equation to eliminate a variable is called gaussian elimination.
How does the elimination method work?
In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.
What are the rules of Gaussian elimination?
The Gaussian elimination rules are the same as the rules for the three elementary row operations, in other words, you can algebraically operate on the rows of a matrix in the next three ways (or combination of): Interchanging two rows. Multiplying a row by a constant (any constant which is not zero)
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у = 3х – 5
2х + 4 = 8
Answers
2. X= 2. That is the answer for these problems
In Mrs. Trainer's math class, Siobhan's first five math quiz scores are 76, 96, 81, 69, and 41. Siobhan takes the sixth math quiz and scores an 85. How will the mean change if the sixth score is added to the list?
Answers
Answer:
the median will go up 2.5 points from 76 to 78.5
Step-by-step explanation:
You want to know the effect on the median of adding 85 to the list of scores: 76, 96, 81, 69, 41.
MedianThe median is the middle value when the list is sorted into order. The ordered list is ...
41, 69, 76, 81, 96
The median is 76.
New MedianWhen 85 is added to the list, the sorted list becomes ...
41, 69, 76, 81, 85, 96
There are two middle scores, so the median is their average:
(76+81)/2 = 78.5
The median increases 2.5 points from 76 to 78.5 when the score is added.
100 points helpppp now
Solve the inequality hurrry show your work
33+6f<33
Answers
\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)
\(\qquad \tt \rightarrow \:f < 0 \)
____________________________________
\( \large \tt Solution \: : \)
\(\qquad \tt \rightarrow \: 33 + 6f < 33\)
[ subtract 33 on both sides ]
\(\qquad \tt \rightarrow \: 33 - 33+ 6f < 33 - 33\)
\(\qquad \tt \rightarrow \: 6f < 0\)
\(\qquad \tt \rightarrow \: f < 0\)
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
variables with values that are determined by chance are called
Answers
Variables with values that are determined by chance are called random variables (option a).
Random variables are variables whose values are determined by chance or randomness. They are often used in probability theory and statistics to model uncertain or unpredictable phenomena. The values of random variables can come from various sources, such as the outcome of a random experiment, the result of a random process, or the measurement of a random quantity.
Random variables can take on different types of values, including numerical values (such as integers or real numbers) or categorical values (such as "heads" or "tails" in a coin toss). The possible values that a random variable can take are known as its sample space.
Random variables are commonly denoted by capital letters, such as X, Y, or Z. Each value in the sample space of a random variable is associated with a probability or likelihood of occurring, which can be described using a probability distribution. The probability distribution provides information about the likelihood of different outcomes or values of the random variable.
Random variables are fundamental in many areas of mathematics, statistics, and science. They play a crucial role in understanding and modeling uncertainty, making predictions, analyzing data, and making informed decisions in various fields, including finance, engineering, biology, and social sciences.
The complete question is:
Variables with values that are determined by chance are called _______.
a) random variables.
b) erratic variables.
c) specialized.
d) inconsistent variables.
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Evaluate f(x) = 4 - 5x for f(-2)
*
Answers
Answer: the answer would be X E R
Step-by-step explanation:
An airplane is flying at an airspeed of 600 km/hr in a cross-wind that is blowing from the northeast at a speed of 50km/hr. In what direction should the plane head to end up going due east?
Answers
The airplane should head approximately 4.76 degrees east of its intended direction to compensate for the crosswind and end up going due east.
To end up going due east, the airplane needs to counteract the effect of the crosswind and maintain a heading that compensates for the wind's direction and speed.
Since the crosswind is coming from the northeast, it forms a right triangle with the airplane's airspeed and ground speed vectors. The angle between the ground speed vector (due east) and the airspeed vector is the heading the plane should take.
Using trigonometry, we can calculate this angle. The opposite side of the triangle is the speed of the crosswind (50 km/hr), and the hypotenuse is the airspeed (600 km/hr).
Let's denote the angle as θ. We can use the sine function:
sin(θ) = opposite/hypotenuse
sin(θ) = 50/600
θ = sin^(-1)(50/600)
Evaluating this expression, we find θ ≈ 4.76 degrees.
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8 = 3a – 4
what is the anser
Answers
Answer:
a=4
Step-by-step explanation:
what minus 4=8? its 12. 12-4=8 so
what times 3 is 12? 4.
3*4=12
12-4=8
a=4
Grant just joined a new gym and signed up for a one-year membership. Membership fees can be paid in 12 monthly payments of $55, due at the beginning of each month or in one payment today. If the appropriate interest rate is 10%, how much should he pay today for the annual membership?
Answers
Grant should pay approximately $211.96 today for the annual membership, considering an interest rate of 10% and the option to pay in 12 monthly installments of $55 each.
To determine how much Grant should pay today for the annual membership, we need to calculate the present value of the 12 monthly payments of $55 each, considering an interest rate of 10%.
The present value (PV) can be calculated using the formula:
PV = C * (1 - (1 + r)^(-n)) / r
Where:
C = the monthly payment amount ($55)
r = the monthly interest rate (10% / 12 = 0.00833)
n = the number of payments (12)
Plugging in the values into the formula, we can calculate the present value:
PV = 55 * (1 - (1 + 0.00833)^(-12)) / 0.00833
PV ≈ 55 * (1 - 0.6806) / 0.00833
PV ≈ 55 * 0.3194 / 0.00833
PV ≈ 211.96
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make the statement for those situations: (i) conclusion (i.e., reject h0 or fail to reject h0); (ii) what this means about the parameter being tested (i.e., "there is no evidence that…" or "there is evidence that…") (iii) what you see in the test statistic and critical value that leads to this conclusion; a) h0: μ
Answers
(i) Conclusion: Reject H0 or fail to reject H0.
(ii) Meaning about the parameter being tested: "There is no evidence that..." or "There is evidence that..."
(iii) Test statistic and critical value: What you see in the test statistic and critical value that leads to this conclusion.
For the situation where H0: μ (null hypothesis is that the population mean is equal to a specific value):
(i) Conclusion: If the test statistic falls in the critical region, we reject H0. If the test statistic does not fall in the critical region, we fail to reject H0.
(ii) Meaning about the parameter being tested: If we reject H0, it means that there is evidence to suggest that the population mean is not equal to the specific value. If we fail to reject H0, it means that there is no evidence to suggest that the population mean is different from the specific value.
(iii) Test statistic and critical value: In this case, we compare the test statistic (calculated from the sample data) to the critical value (based on the chosen significance level and the distribution of the test statistic). If the test statistic falls in the critical region (i.e., it is more extreme than the critical value), we reject H0. If the test statistic falls outside the critical region, we fail to reject H0.
To summarize, for the situation where H0: μ, we determine the conclusion based on whether the test statistic falls in the critical region or not. This conclusion provides evidence or lack of evidence regarding whether the population mean is equal to the specific value stated in the null hypothesis.
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8 – 2x =
Helpppo pleaseee
Answers
This proplem is wrong there is a variable and no answer
Determine and sketch y[n] = x[n] * h[n] if • x[n] = (−0.25)" u[n + 4] and h[n] = 2u[n — 5]. x[n] = {1,2,−2} and h[n] = {0, 1,2,3}
Answers
y[n] = {0, 1, 4, 2, -4, 0, 0}.
To determine y[n] = x[n] * h[n], we need to perform the convolution operation between the sequences x[n] and h[n].
Given x[n] = {1, 2, -2} and h[n] = {0, 1, 2, 3}, we can compute y[n] as follows:
For n = 0: y[0] = x[0] * h[0] = 1 * 0 = 0
For n = 1: y[1] = x[1] * h[0] + x[0] * h[1] = 2 * 0 + 1 * 1 = 1
For n = 2:y[2] = x[2] * h[0] + x[1] * h[1] + x[0] * h[2] = -2 * 0 + 2 * 1 + 1 * 2 = 4
For n = 3: y[3] = x[3] * h[0] + x[2] * h[1] + x[1] * h[2] = 0 * 0 + (-2) * 1 + 2 * 2 = 2
For n = 4: y[4] = x[4] * h[0] + x[3] * h[1] + x[2] * h[2] = 0 * 0 + 0 * 1 + (-2) * 2 = -4
For n = 5: y[5] = x[5] * h[0] + x[4] * h[1] + x[3] * h[2] = 0 * 0 + 0 * 1 + 0 * 2 = 0
For n = 6: y[6] = x[6] * h[0] + x[5] * h[1] + x[4] * h[2] = 0 * 0 + 0 * 1 + 0 * 2 = 0
Therefore, y[n] = {0, 1, 4, 2, -4, 0, 0}.
To sketch the sequence y[n], we plot the values of y[n] on the y-axis against the corresponding values of n on the x-axis:
n | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
y[n] | 0 | 1 | 4 | 2 | -4 | 0 | 0 |
The plot will consist of discrete points representing the values of y[n] at each value of n. Connect the points with lines to visualize the sequence.
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An on-demand movie company charges $2.95 per movie plus a monthly fee of $39.95. Which expression represents the yearly
cost for x movie rentals?
O 2.95x+ 39.95
O 39.95x+ 2.95
O 2.95x-39.95(12)
O 295x+39.95(12)
Answers
Answer: 2.95x+39.95(12)
Step-by-step explanation:
Hi, to answer this question we have t write an expression with the information given:
The yearly cost for x movie rentals is equal to : the product of the cost of each movie (2.95) and the number of movies (x) ;plus the product of the monthly fee (39.95) and the number of months in a year (12)
Mathematically speaking:
2.95x+39.95(12)
Answer:
D-295x+39.95(12)
Step-by-step explanation:
EDG2021
²\(2x^2-1414x=24\)
Answers
An artist wants to make an elliptical sign out of a rectangular piece of wood. The wood piece has a length of 60 inches and a width of 40 inches. The artist wants to make the largest elliptical piece possible from the wood.
Answers
Answer:
Step-by-step explanation:
The question doesn't seem complete, but the question is likely to ask for 2 things: the equation of the ellipse and it's foci. So I'll respond to that. Also, the ellipse will be at the center since the artist wants the largest.
Firstly, the equation of an ellipse at the center is given by:
(x²/a²) + (y²/b²) = 1 where a > b.
Since the artist wants to make the largest ellipse, then the length of the rectangle will be the length of the ellipse, same applies to the width.
Since the length is 60, then a = 60/2 = 30
Since the width is 40, then b = 40/2 = 20
Therefore, the equation of the ellipse is:
(x²/30²) + (y²/20²) = 1
To find the foci we need to know the center and this can be gotten by
c² = a² – b²
c² = 30² – 20² = (30 + 20)(30 – 20) = (50)(10) = 500
c = √(500) = 10√(5).
The foci, since it's at th center would be:
(–10√(5), 0) and (+10√(5), 0)
The largest ellipse that the artist can make on the considered rectangular wooden piece will have area as: \(\dfrac{x^2}{900} + \dfrac{y^2}{400} = 1\\\)(assuming its major and minor axes lie on x and y axis respectively)
What is the equation of ellipse if its major and minor axis are given?Suppose that the major axis is of the length 2a units, and that minor axis is of 2b units, then if major axis is on x-axis and minor axis is on y-axis, then the equation of that ellipse would be:
\(\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} =1\)
For this case, as we have rectangular piece of board the maximum ellipse will have it's major axis of length 60 inches, and of minor axis as 40 inches.
Thus, we have:
\(a = 60/2 = 30\: \rm inches\\b = 40/2 = 20 \: inches\)
Thus, if the rectangle is placed such that the major axis is on x-axis, and minor axis is on y-axis, then the equation of that ellipse would be:
\(\dfrac{x^2}{30^2} + \dfrac{y^2}{20^2} = 1\\\\\dfrac{x^2}{900} + \dfrac{y^2}{400} = 1\\\)
Thus, the largest ellipse that the artist can make on the considered rectangular wooden piece will have area as: \(\dfrac{x^2}{900} + \dfrac{y^2}{400} = 1\\\)(assuming its major and minor axes lie on x and y axis respectively)
Learn more about ellipse here:
https://brainly.com/question/16868628