Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.x2+y2=100a) Find dy/dt when x=6, y=8 given that dx/dt=4.b) Find dx/dt when x=8, y=6 given that dy/dt=-2.

Answer:11

Step-by-step explanation:

The equation representing total fraction strip is  ³/₃ + ¹/₃ = ⁴/₃.

option B.

A fraction is a mathematical representation of a part of a whole or a ratio between two numbers. It consists of a numerator, which represents the number of parts being considered, and a denominator, which represents the total number of parts in the whole.

For this case, 1 is divided into, and 1 divide into 3.

To obtain the total fractions, we will add the individual fractions as shown below;

For this first fraction = ¹/₃ + ¹/₃ + ¹/₃

For the second fraction = ¹/₃

Total fraction = 3(¹/₃ + ¹/₃ + ¹/₃) + ¹/₃

Total fraction = ³/₃ + ¹/₃ = ⁴/₃

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Answer:

NO.2- SSA is not the method to show the congruency of two triangles.

The largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9 has dimensions x = 1.5, y = 1, and z = 2.25, with a maximum volume of 3.375 cubic units.

To find the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9, we can use the method of Lagrange multipliers.

Let the sides of the rectangular box be represented by the variables x, y, and z. We want to maximize the volume V = xyz subject to the constraint x + 3y + 4z = 9.

The Lagrangian function is then given by L = xyz + λ(x + 3y + 4z - 9).

Taking the partial derivatives of L with respect to x, y, z, and λ, and setting them equal to zero, we get:

yz + λ = 0

xz + 3λ = 0

x*y + 4λ = 0

x + 3y + 4z - 9 = 0

Solving these equations simultaneously, we get:

x = 1.5, y = 1, z = 2.25, and λ = -0.5625

Therefore, the maximum volume of the rectangular box is V = 1.512.25 = 3.375 cubic units.

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Answer:

Step-by-step explanation:

To find the perimeter of an equilateral triangle is equalled to 3s.

35 x 3

105

'cell '. The element in the second row and first column of the cell array C is accessed using the phrase c(2,1). The first element in the second row of C is the string "cell," which is that element.

The element in the second row and first column of the cell array C is accessible by the equation c(2,1). The first element in the second row of C is the string "cell," which makes up that element. The string "cell" is the result of c(2,1).

The curly braces in MATLAB are used to retrieve the contents of a cell array. "Access the contents of the cell in the second row and first column of C" is what the phrase C2,1 implies. The string in question is the outcome of the expression since it is present in the relevant cell.

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Leo might therefore have 36 or 48 toy soldiers, which is a choice between the two numbers.

The attempt to demonstrate that your integer is larger than anyone else's integer has persisted through the ages, despite their being more numbers than there are atoms in the universe. The largest number that is frequently used is a googolplex (10googol), which equals 101¹⁰⁰.

We'll name Leo's collection of toy soldiers "x" the amount. We are aware of:

We can infer x to be one of the following figures from the first condition: 28, 32, 36, 40, 44, 48, or 52.

To find out which of these integers meets the other two requirements, we can try each one individually:

x + 6 = 34 and x + 3 = 31, neither of which is a multiple of five, if x = 28.

X + 6 = 38 and X + 3 = 35, none of which is a multiple of 5, follow if x = 32.

When x = 36, x + 6 = 42, a multiple of 7, and x + 3 = 39, a multiple of 5, follow. This might be the answer.

x + 6 = 46 and x + 3 = 43, neither of which is a multiple of five, if x = 40.

x + 6 = 50 and x + 3 = 47, neither of which is a multiple of five, if x = 44.

When x = 48, x + 6 = 54, a multiple of 7, and x + 3 = 51, a multiple of 5, follow.

x + 6 = 58 and x + 3 = 55, neither of which is a multiple of five, if x = 52.

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The set [1 0 −3 , −3 1 6 , 1 −1 0] is not a basis for set of real numbers R cubed(ℝ3).

The reason why it is not a basis is because it is not linearly independent. However, the set does span set of real numbers R cubed(ℝ3).To determine if the given set is a basis for set of real numbers R cubed(ℝ3), we need to test for linear independence and for span.Linear independence

The given set is said to be linearly independent if and only if the only solution to the equation a[1 0 −3] + b[−3 1 6] + c[1 −1 0] = [0 0 0] is the trivial solution where a, b and c are constants.If the given set is linearly independent then it is a basis for R3; if it is not linearly independent, it is not a basis for R3.

SpanThe given set is said to span R3 if every vector in R3 can be written as a linear combination of vectors in the given set.

If the given set spans R3, then it can be considered a basis for R3.For us to test if the given set is linearly independent, we can form a matrix by placing the three given vectors into the columns of a 3 x 3 matrix as follows:[1 0 1] [−3 1 −1] [−3 6 0]

By expanding the determinant of the matrix above, we get: det(A) = 0 - 0 - (-3) = 3

Since the determinant is non-zero, we can say that the given set is linearly independent. Since the given set is linearly independent, we can then use it to span R3. Hence the given set does not form a basis for R3 but it is linearly independent and spans R3.

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By answering the presented question, we may conclude that Therefore, the solution to the system of equations is: x = 36/31 and y = 57/31.

In mathematics, an equation is a statement stating the equivalence of two expressions. An equation generally made up of two sides delimited by a system of equations (=). For example, the argument "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The objective of equation solving is to identify the amount or amounts of the variables ( independent variables) that will allow this equation to really be true. Mathematics can be simple or complex, regular or quadratic, and contain one or more parts. In the equation "x2 + 2x - 3 = 0," for illustration, the variable x is elevated to the second power. Lines are employed in numerous different fields of mathematics, including arithmetic, calculus, and geometry.

From the given system of equations, we have:

[tex]8x + 7y = 17 ...(1)\\x - 3y = -5 ...(2)\\x = 3y - 5 ...(3)\\8(3y - 5) + 7y = 17\\24y - 40 + 7y = 17\\31y = 57\\y = 57/31\\x = 3(57/31) - 5\\x = 36/31[/tex]

Therefore, the solution to the system of equations is:

x = 36/31 and y = 57/31.

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The solution to the system of equations is: x = 36/31 and y = 57/31.

In mathematics, an equation is a statement stating the equivalence of two expressions. An equation generally made up of two sides delimited by a system of equations (=). For example, the argument "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The objective of equation solving is to identify the amount or amounts of the variables ( independent variables) that will allow this equation to really be true. Mathematics can be simple or complex, regular or quadratic, and contain one or more parts. In the equation [tex]"x^2 + 2x - 3 = 0,[/tex]" for illustration, the variable x is elevated to the second power. Lines are employed in numerous different fields of mathematics, including arithmetic, calculus, and geometry.

From the given system of equations, we have:

[tex]$\begin{aligned} & 8 x+7 y=17 \ldots(1) \\ & x-3 y=-5 \ldots(2) \\ & x=3 y-5 \ldots(3) \\ & 8(3 y-5)+7 y=17 \\ & 24 y-40+7 y=17 \\ & 31 y=57 \\ & y=57 / 31 \\ & x=3(57 / 31)-5 \\ & x=36 / 31\end{aligned}$[/tex]

Therefore, the solution to the system of equations is:

x = 36/31 and y = 57/31.

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The contrapositive of the zero product property is that if neither of the two real numbers is 0, then the product of the two numbers will not be 0. In plain language, this means that if neither of the two numbers are 0, then the product of the two numbers cannot be 0.

In an informal version, this can be stated as "if neither number is 0, then their product cannot be 0". This can be understood as "if neither number is 0, the result of multiplying them together cannot be 0". In other words, the product of two real numbers will not be 0 if neither of them is 0.

Step-by-step explanation:

4x + y^2 + 2y =  - 5

4x = - y^2 -2y - 5          

4x = - (y^2 + 2y)   - 5      'complete the square' for y

4x = - ( y +1)^2   + 1    - 5

 x = - 1/4 ( y+1)^2  - 1             vertex is at -1, -1

-14x+2y^2-8y -20 = 0

14x = 2y^2 -8y-20

14x = 2 ( y^2 - 4y) - 20     complete the square for y

14x = 2(y-2)^2  -8 - 20

x = 1/7 ( y-2)^2 - 2                Vertex is at   -2 , 2

If the volume of a right triangular prism is 72 cubic feet, the area of the base is 2 square feet and the length of DF is approximately 2.83 feet.

To solve the problem, we can use the formula for the volume of a right triangular prism, which is:

Volume = (1/2) x base x height x length

where base is the area of the triangular base, height is the height of the prism, and length is the length of the prism.

We are given that the volume is 72 cubic feet and the height is 9 feet. Therefore, we can write:

72 = (1/2) x base x 9 x length

Simplifying this equation, we get:

base x length = 16

We are also given that the base is an isosceles right triangle. This means that the two legs of the triangle are equal, and the hypotenuse is equal to the length of one leg times the square root of 2.

Let's call the length of one leg of the triangle DF. Then, we can write:

base = (1/2) x DF x DF

Substituting this expression for base into the equation we derived earlier, we get:

(1/2) x DF x DF x length = 16

Simplifying this equation, we get:

DF x DF x length = 32

We know that the hypotenuse of the triangle is DF times the square root of 2. Since the hypotenuse is also one of the edges of the base of the prism, we can set it equal to the length of the prism:

DF x √(2) = length

Substituting this expression for length into the equation we derived earlier, we get:

DF x DF x DF x sqrt(2) = 32

Simplifying this equation, we get:

DF^3 = 16

Taking the cube root of both sides, we get:

DF = 2

Therefore, the area of the base is:

base = (1/2) x DF x DF = 2 square feet

And the length of DF is:

DF x √(2) = 2 x √(2) feet = approximately 2.83 feet.

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Option (A) x+1 is a positive odd integer.

Given that, x < y < z and all three are consecutive non-zero integers.Let the first number be x, then the other two consecutive non-zero integers will be (x+1) and (x+2).To find out the positive odd integer among these, let us take each of them and verify if they are positive odd integers.∴ x+1 is odd, x+2 is even∴ x+1 is the only positive odd integer out of the three.

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The definition of vector space that fails is part A and B  because it does not satisfy the any property of vector space.

The following statement can be determined if at-least one part of vector space definition that fails as:

(a) A is not a vector space because it does not contain the zero vector.

The zero vector is the unique vector that satisfies the property that when it is added to any other vector in the space, the result is the original vector.

However, in this case, the [a1, b1] + [a2, b2] = [a1 - a2, b1 - b2] is 0x² + 1, which is not an element of A. Therefore, A fails to satisfy the requirement of having a zero vector, and it is not a vector space.

(b) B is not a vector space because it does not satisfy the distributive property of scalar multiplication over vector addition.

In general, scalar multiplication must distribute over vector addition, meaning that for any scalar a and any vectors u and v in the space, a(u+v) = au + av.

However, in B, the scalar multiplication is defined as usual for R², but the vector addition is defined differently. In particular,[a1, b1] + [a2, b2] = [a1 - a2, b1 - b2].

The vector space definition fails because the vector addition is not associative, and it is also not commutative, which are the first two conditions for vector spaces. Therefore, the first and second conditions of the definition are not met.

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The rounded value of 25.71 to 2 decimal places is 25.71 itself.

To round 25.71 to 2 decimal places, we need to look at the third decimal place, which is 1.

If the third decimal place is 5 or greater, we round up the second decimal place. If the third decimal place is less than 5, we simply drop it and keep the second decimal place as is.

In this case, the third decimal place is 1, which is less than 5, so we simply drop it and keep the second decimal place as is. Therefore, 25.71 rounded to 2 decimal places is:

25.71 ≈ 25.71 (no rounding necessary)

So, the rounded value of 25.71 to 2 decimal places is 25.71 itself.

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Answer:

A survey found that 34% of the students spend time with your family eating dinner. Oh the 500 student surveyed, about how many spend time with their family eating dinner?

Step-by-step explanation:

If 34% of the students surveyed spend time with their family eating dinner, we can find the approximate number of students who do so by multiplying the percentage by the total number of students surveyed:

34% of 500 students = 0.34 x 500 = 170 students

Therefore, about 170 of the 500 students surveyed spend time with their family eating dinner.

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The waterproof jackets that last five years offer the biggest savings, as they have a lower cost per jacket per year.

The cost curve, which in economics expresses production costs as a function of output. The loss function is a function that has to be minimised in mathematical optimization. A cost function evaluates how inaccurate the model is in estimating the connection between X and y.

Given that, cost of waterproof jackets that last for 5 years = $150 for 50 jackets.

Thus, cost of one jacket = 150/50 = $3.

The jacket lasts 5 years thus for 1 year the equivalent cost is:

3/5 = $0.60.

Now, for the other jacket:

Cost per year is = (80/50) / 2 = $0.80 per jacket per year.

Hence, the waterproof jackets that last five years offer the biggest savings, as they have a lower cost per jacket per year.

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There are 720 different choices if order matters and there are 120 different choices if order does not matter.

a) If order matters,

The player can choose the first number in 10 ways (any of the digits 0-9), the second number in 9 ways (since one digit has already been chosen), and the third number in 8 ways (since two digits have already been chosen).

So the total number of choices is:

10 x 9 x 8 = 720

Therefore, there are 720 different choices if order matters.

b) If order does not matter,

We need to divide the number of choices by the number of ways the three numbers can be arranged.

Since there are 3 numbers, they can be arranged in 3! = 6 ways.

So the number of choices when order does not matter is:

(10 x 9 x 8) / 6 = 120

Therefore, there are 120 different choices if order does not matter.

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Answer:

We know that, the sum of interior angles of an n-sided polygon is (n−2)×180⁰

For a pentagon, n=5

so,

[tex] \implies \rm \: 6x + 6y = (n - 2)180[/tex]

[tex] \implies \rm \: 6(x + y) = (5 - 2)180[/tex]

[tex] \implies \rm \: 6(x + y )= 3 \times 180[/tex]

[tex] \implies \rm \: (x + y) = \dfrac{3 \times 180}{6} [/tex]

[tex] \implies \rm \: (x + y) = \dfrac{ 3 \times \cancel{180} \: \:30}{ \cancel6} [/tex]

[tex] \rm \implies \: x + y = 90[/tex]

[tex] \underline{\boxed{\implies \rm \: y= 90 - x}}[/tex]

There are many formulas related to a pentagon. A few basic ones are given below.

Answer:

54

Step-by-step explanation:

Add six each time -> 24 + 6 = 30 + 6 = 36 etc

The answer of the given question based on the finding the m∠QTS from a circle with the measure of minor arc the answer is the measure of angle ∠QTS is 60° degrees.

In geometry, arc is  portion of a curve or  circle. It is defined as the part of the curve that is contained between two points, called endpoints, on curve. The length of  arc is  fraction of the circumference of  circle, determined by the measure of  central angle that subtends it.

An arc is typically denoted by  two endpoints, with  small arc or arc symbol above the two letters. For example, an arc with endpoints A and B would be denoted as "⌒AB" or "AB".Arcs can be classified based on their measure or  position of their endpoints.

An arc with measure less than 180 degrees is called  minor arc, while an arc with measure greater than 180 degrees is called  major arc. An arc with measure equal to 180 degrees is called semicircle.

Since arc QS is a minor arc, we know that angle ∠QTS is half the measure of arc QS. Therefore, we have:

m∠QTS = (1/2) m arc QS

m∠QTS = (1/2) (120°) [Substituting the given value of m arc QS]

m∠QTS = 60°

Therefore, the measure of angle ∠QTS is 60° degrees.

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Yes, the data give convincing evidence to support Phoebe's hunch. As the result of the test is a p-value that is 0.1 of less than 0.05.

The p-value is the probability of obtaining a result as extreme or more extreme given that the null hypothesis is true. The p-value is calculated by comparing the test statistic to the probability distribution under the null hypothesis.

The ratio of seniors bringing a bag lunch= 78/104 or 0.75,

while the ratio of sophomores bringing a bag lunch= 52/80 or 0.65.

This indicates that the proportion of seniors bringing a bag lunch is higher than the proportion of sophomores bringing a bag lunch.

Further, the difference between the proportions is

0.75-0.65 = 0.1,

which is a large enough difference to be considered significant.

The result of the test is a p-value of less than 0.05, which is statistically significant and indicates that the difference in the proportions is due to the different ages, and not due to chance.

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The measure of the angle that it is complementary which is represented by 90-x is always true. Option A

An acute angle is simply defined as an angle that measures from 90° and 0°. This means that it is smaller than a right angle.

It is formed in the space between two intersecting lines or planes, or from the intersection of two shapes.

A complementary angle can be defined as a pair of angles whose sum is equal or equivalent to 90 degrees.

From the information given, we have that;

x is the acute angle

The complementary angle is 90 - x

We can see that the angle x must be complementary to be subtracted from 90 degrees.

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The complete question:

If the measure of an acute angle is represented by x, then the measure of its complement is represented by 90 – X.

always true

sometimes true

never true

a) A greedy algorithm is an approach to problem-solving that makes the locally optimal choice at each step with the hope of finding a globally optimal solution.

This means that at each step, the algorithm chooses the best available option without considering the future consequences of that decision.

(b) An example of a greedy algorithm that produces an optimal solution is the activity selection problem.

Given a set of activities with their start and end times, the goal is to select the maximum number of non-overlapping activities. The greedy algorithm sorts the activities by their end times and selects the first non-overlapping activity.

It then repeats this process with the remaining non-overlapping activities until all activities have been selected. This algorithm produces an optimal solution because selecting the activity with the earliest end time leaves the maximum amount of time available for the remaining activities.

(c) An example of a greedy algorithm that does not always produce an optimal solution is the knapsack problem.

Given a set of items with their weights and values, the goal is to maximize the value of items that can be carried in a knapsack of a given weight capacity. The greedy algorithm selects items based on their value-to-weight ratio until the knapsack is full.

However, this algorithm can fail to produce an optimal solution if there are items with high value but large weight, which cannot fit in the knapsack after the algorithm selects several low-value items with small weight. In such cases, a more sophisticated algorithm is required to find the optimal solution.

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The sample size cannot be determined from this information alone. A confidence interval for a population mean is calculated based on the mean of a sample, the sample size, and the standard deviation.

Deviation is the difference between the expected value or average of a set of data and the actual value. For example, if the average of a set of numbers is 10 and one of the numbers is 15, the deviation of that number is 5. Deviation is a measure of how much variation exists in a set of data. It is an important tool used to measure the accuracy of a data set and identify outliers within that data set. Deviation is also used to measure the volatility of a stock or other investment, which is a measure of how much its price changes over time.

Therefore, to determine the sample size, the mean, standard deviation, and confidence interval of the sample must all be known.

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The sample size cannot be determined from this information alone. A confidence interval for a population mean is calculated based on the mean of a sample, the sample size, and the standard deviation.

Deviation is the difference between the expected value or average of a set of data and the actual value. For example, if the average of a set of numbers is 10 and one of the numbers is 15, the deviation of that number is 5. Deviation is a measure of how much variation exists in a set of data. It is an important tool used to measure the accuracy of a data set and identify outliers within that data set. Deviation is also used to measure the volatility of a stock or other investment, which is a measure of how much its price changes over time.

Therefore, to determine the sample size, the mean, standard deviation, and confidence interval of the sample must all be known.

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Complete Question:
A 95% confidence interval for a population mean was reported to be 152 to 160. If s 15, what sample size was used in this study?

Answer:3 1 /20

Step-by-step explanation:= 1+3/4+1+3/10

The area's estimated snapping turtIe popuIation, rounded to the cIosest whoIe number, is 56.

That is correct! As 0 is a whoIe number and aII whoIe numbers were integers, 0 is additionaIIy an integer.

The LincoIn-Petersen index method, which is frequentIy empIoyed to determine the size of a popuIation using a capture-mark-recapture approach, can be utiIized to resoIve this issue.

The estimated popuIation (N) is equaI to (M x C) / R using the foIIowing formuIa:

M is the quantity of peopIe incIuded in the initiaI sampIe (marked turtIes)

C is the second sampIe's size (totaI number of turtIes caught in the second sampIe)

R is the quantity of marked peopIe who were Iocated again in the specimen.

When we enter the specified vaIues into the equation, we obtain:

N = (15 x 15) / 4

N = 56.25

The area's snapping turtIe popuIation is thought to be 56, rounded off to the cIosest whoIe number.

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The probability of producing the genotype AABBCC in a cross AaBbCc × AaBbCc is 1/64.

A Punnett square is a grid used to forecast the likelihood of an offspring of a mating between two parents with known genotypes. The grid consists of four boxes or cells with one parent's gamete genotype listed along the top, and the other parent's gamete genotype listed down the side.

To determine what proportion of their offspring will possess a certain genotype or phenotypic characteristic, the gamete genotypes are combined using the grid.

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1) The area of a circle with a diameter of 1 m is approximately 0.7854 square meters.

2) The area of a circle with a diameter of 100 cm is approximately 7853.98 square centimeters.

3) The area of a circle with a radius of 100 cm is approximately 314159.27 square centimeters.

4) The area of a circle with a radius of 500 mm is approximately 785398.16 square millimeters.

The formula for the area of a circle is A = πr², where A is the area and r is the radius of the circle.

1) If the diameter of the circle is 1 m, then the radius is 0.5 m. Therefore, the area of the circle is:

A = πr² = π(0.5)² = π(0.25) ≈ 0.7854 square meters.

2) If the diameter of the circle is 100 cm, then the radius is 50 cm. Therefore, the area of the circle is:

A = πr² = π(50)² = π(2500) ≈ 7853.98 square centimeters.

3) If the radius of the circle is 100 cm, then the area of the circle is:

A = πr² = π(100)² = π(10000) ≈ 314159.27 square centimeters.

4) If the radius of the circle is 500 mm, then the area of the circle is:

A = πr² = π(500)² = π(250000) ≈ 785398.16 square millimeters.

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