what must be true for any direction if the instantaneous rate of change from (1,3,2) is equal to 0? what shape is formed by the collection of these vectors? (be as specific as you can.)

The Reimann sum with n rectangle will be given as [tex]\sum^{n-1}_{i = 0} f{(x_i)} \Delta x[/tex]

Let us suppose that f is a non-negative function, defined over a closed interval represented by [a, b].

The integral of f with respect to x signifies the area between the graph of f and X-axis. This area would be called definite integral of a function f from a to b. Then Riemannian method of determining this area is:

“if the area is divided into n rectangles of very small breadth, then it would be simpler to calculate the area of such rectangles and then we can add them up

(i ) The width of each rectangle will be denoted as Δx

Δx = b-a/n,

where , a is lower bound

b is upper bound of the integral

(ii) The right-hand endpoints of each rectangle are refer as [tex]x_i[/tex] and we can find the right endpoints by [tex]x_i[/tex] = a + Δx.i

(iii) The height of each rectangle is the value of the function at the upper point of the interval.

a + (b-a)/n for the first rectangle , a + 2(b-a)/n for the second rectangle and so on

(iv) The area of the each rectangle will be

Area = Width × height

=> A = (b-a)/2 × a + i(b-a)/2

(v) The Riemann sum with n rectangles is

Area of rectangle = [tex]\sum^{n-1}_{i = 0} f{(x_i)} \Delta x[/tex]

Which is also known as Reimann sum

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Answer:56

Step-by-step explanation:

C

Step-by-step explanation:

add x on both sides

-5y=10+x

divide both sides by -5

y=-1/5x-2

Given any set of seven numbers that should be at least 2 that must have the same remainder when divided by 6

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product since the product is divisible by them.

Step 1: factor the provided number into primes, or describe it as the product of primes.

Step 2: Write the prime factorization in exponent form in step three.

Step 3: Increase each exponent by one.

Step 4: Multiply each of the results.

There can only be a maximum of six different remainders when dividing by six: 0, 1, 2, 3, 4, and 5.

In any set of seven integers, two must have the same remainder when divided by seven according to the pigeon hole principle.

b) Consider set of integers 0, 1 ,2, 3, 4, 5 and 66. All these have different remainders upon division by 8 and hence the answer is no.

The interpretation is yes

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Answer:

Area = 121pi sq cm

Step-by-step explanation:

Circumference is the distance around the circle. The formula for circumference is:

C = pi•d

The question has the info in it that the circumference is 22pi.

C = 22pi

remember,

C = pi•d this means that the circle has a diameter (the d in the formula is diameter) 22cm.

The radius is half the diameter. The diameter is 22cm, so the radius is 11cm.

The formula for the area is:

Area = pi•r^2

= pi•11^2

= pi•121

= 121pi

The area is 121pi sq cm.

The gravitational potential energy gained by the group of skydivers before jumping is 4,410 kJ.

Gravitational Potential Energy (GPE) is estimated as;

GPE = m×g×h              

In which

m = mass of parachuting outfit (kg)

g = acceleration due to gravity (m/s²)

h = height (meters)

Put the values in the formula.

GPE = 90× 9.8× 5000

GPE = 4,410,000‬ joules

GPE = 4,410 kJ

Thus, the gravitational potential energy gained by the group of skydivers before jumping is 4,410 kJ.

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Answer:

6

Step-by-step explanation:

DF = [tex]\sqrt{10^2 - 8^2}[/tex]

[tex]\sqrt{10^2-8^2} = \sqrt{100-64}[/tex]

[tex]\sqrt{100-64} = \sqrt{36}[/tex]

[tex]\sqrt{36} =6[/tex]

Answer:

The rates are equivalent.

Step-by-step explanation:

Liam practiced piano 24 times in 4 weeks. 1 week = 7 days. 4 weeks = 28 days.

Answer: 135

Step-by-step explanation:

Answer: 145

Step-by-step explanation:

100% of 90 is, welll 90, and 50% of 90 is 45, so 150% of 90 is 145

36% of the variability equation to predict income (y) in thousands of dollars from age (x1) and educational status (x2) found a significant interaction between age and educational status (x3).

Given:

Correlation value: 0.6

The amount of variation in the dependent variable that can be predicted from the independent variable is shown by the coefficient of determination.

The correlation coefficient is equal to;

Since the correlation in this instance is equal to 0.6, our coefficient is 0.36. Therefore, the age of the home can account for 36% of the variation in equation to predict income (y) in thousands of dollars from age (x1) and educational status (x2) found a significant interaction between age and educational status (x3).

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Width of second pan become 11.2 inches

What do you mean by similar figures?

Two figures are said to be similar if they share the same shape. Congruent objects are those that are precisely the same size and shape.

The term "similar figures" refers to two figures that share the same shape but differ in size.

When two figures are comparable, the sign ‘∼’ is used to indicate that they are.

It is given that Amelia has similar cake pans. The first pan is 10 inches long and 8 inches wide. The second pan is 14 inches long.

We know that the ratio of the sides of the similar figures is always equal,

So , [tex]\frac{10}{8}=\frac{14}{x}[/tex]

where x is the width of second pan.

Solve the above equation using cross multiplication we get,

x = [tex]\frac{14 \times 8}{10} = \frac{112}{10}=11.2[/tex]

Hence, width of second pan become 11.2 inches

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The values for the number of tables are 9, 10, 11, 12, and 13 the store must sell in order to meet the requirements.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

Let's assume that the number of tables would be x

According to the given information, we can write the inequality would be as:

x + 23 ≤ 36  ....(i)

23 × 50 + 250x ≥ 3400  ....(ii)

Simultaneus (i) and (ii)

9 ≤ x ≤ 13

Therefore, the value will be lies as 9, 10, 11, 12, and 13.

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The type of sampling used to sample the class split into girls and boys is stratified sampling.

As given in the question,

Sample the class to split into guys and girls

Select at random 3 guys and 3 girls.

Types of sampling :

A simple random : Chances of selection is equally likely. Randomly choose the data.

False

B systematic: Samples are collected from large data so that it can systematically arranged.

False

C convenience : In this sample or data collection is done as per convenience.

False

D cluster : It divides the group into multiple group or clusters.

False

E stratified : This represents the division of heterogeneous group into fairly homogeneous group in form of strata.

True.

Therefore, the stratified sampling represents the splitting of class into guys and girls.

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Step-by-step explanation:

a point on a coordinate grid always creates a right-angled triangle.

the straight distance from the origin (0, 0) is the Hypotenuse (the side opposite of the 90° angle).

the coordinate distances in x and y directions are the 2 legs.

Pythagoras :

c² = a² + b²

c being the Hypotenuse, a and b being the legs.

so,

(distance from origin)² = x² + y²

because the x, y coordinates are the coordinate distances from the origin in x and in y direction.

distance² = 8² + (-6)² = 64 + 36 = 100

distance = sqrt(100) = 10

the point is 10 units apart from the origin.

Answer:

[tex](-4,-5)[/tex]

Step-by-step explanation:

When reflecting over [tex]y=-x[/tex], [tex](x,y) \longrightarrow (-y, -x)[/tex].

After half an hour the two boats will be at a distance of 68 mph

Given,

Both boats are moving in a direction that creates a right angle triangle. The lengths of the triangle's legs are the distances that both boats travelled going straight south and straight east. The hypotenuse of a right angle triangle is the distance between them after t hours.

Let x stand for the length of the triangle's shorter south leg.

Let y stand for the length of the right angle triangle's longer (east) leg.

Assume that z is the hypotenuse.

Using the Pythagorean theorem

Hypotenuse² = opposite side² + adjacent side²

Therefore

z² = x² + y²

We would discriminate with regard to t in order to ascertain the speed of the distances' alterations.

It develops,

2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1

One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that

dx/dt = 32

dy/dt = 60

Distance = speed × time

Since t = 0.5 hour, then

x = 32 × 0.5 = 16 miles

y = 60 × 0.5 = 30 miles

z² = 16² + 30² = 256 + 900

z = √1156z = 34 miles

Substituting these values into equation 1, it becomes

2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60

68dz/dt = 1024 + 3600

68dz/dt = 4624

dz/dt = 4624/68

dz/dt = 68 mph

Therefore,

The distance between the boats after half an hour is 68 mph

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Completed question is given below with missing parts.

Two boats leave a dock at the same time. One boat travels south at 32 mi divided by hr32 mi/hr and the other travels east at 60 mi divided by hr60 mi/hr. After half an​ hour, how fast is the distance between the boats​ increasing?

5 - 3 (x - 1) = 4 - 7x, initial equation

5 - 3x + 3 = 4 - 7x, distributing 3 (x - 1) to get 3x + 3

8 - 3x = 4 - 7x, adding 3 to 5 to get 8

8 = 4 - 4x, subtracting 3x from both sides of the equation

x= -1, substituting x for the only possible value to make the equation true.

Nulls in a relationship should be avoided as much as possible because of the following reasons:-

• Memory space will be wasted at the storage level

• When aggregate operations such as SUM, AVG etc. are performed on the attribute which has

null value, the result will be incorrect

• When JOIN operation involves an attribute with null values, the result may be unpredictable

• The NULL value has a different meaning. It may be unknown, not applicable or absent

Spurious tuples are generated as the result of bad design or improper decomposition of the base

table.

• Spurious tuples are the tuples generated when a JOIN operation is performed on badly

designed relations. The resultant will have more tuples than the original set of tuples

• The main problem with spurious tuples is that they are considered invalid as they do not

appear in the base tables.

Spurious tuples can be avoided by taking care while designing relation schemas:

• The relations should be designed in such a way that when a JOIN operation is performed, the

attributes involved in the JOIN operation must be a primary key in one table and a foreign key in

another table

• While decomposing a base table into two tables, the tables must have a common attribute. The

the common attribute must be the primary key in one table and the foreign key in another table.

Hence the answer is given.

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Two polygons are similar, and the ratio s1/s2 of their corresponding sides is 8/7 then the ratio of their areas, a1/a2 = 64/49.

In the given question, two polygons are similar, and the ratio s1/s2 of their corresponding sides is 8/7.

We have to find the ratio of their areas, a1/a2.

As we know that, the measurement of the area that a polygon encloses serves as its definition. The area of a polygon is the space that it takes up in a two-dimensional plane since polygons are closed plane structures.

As given that, two polygons are similar.

The ratio of their corresponding sides are

s1/s2 = 8/7

According to properties of similar polygon, the ratio of the areas of the two polygons is the square of the ratio of the sides. Hence,

a1/a2 = (s1/s2)^2

a1/a2 = (8/7)^2

a1/a2 = 64/49

Hence, two polygons are similar, and the ratio s1/s2 of their corresponding sides is 8/7 then the ratio of their areas, a1/a2 = 64/49.

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The work that the force F performs is -36.

F = [ay - cx]

a = 2

b = 3

c = 2

d = 3

Green's theorem is theorem about the relationship between a integral line on a simple closed curve C and a double integral of a plane D bounded by C. So, from Green's Theorem we get,

∫Pdx + Qdy = ∫∫([tex]\frac{\partial Q}{\partial x}[/tex]-[tex]\frac{\partial P}{\partial y}[/tex])dA

Put the a and c value into force F equation. So,

F = [2y - 2x]

From this, we get

P = 2y

Q = -2x

[tex]\frac{\partial P}{\partial y}[/tex] = 2

[tex]\frac{\partial Q}{\partial x}[/tex] = -2

So, the integral formula become

∫∫([tex]\frac{\partial Q}{\partial x}[/tex]-[tex]\frac{\partial P}{\partial y}[/tex])dA = ∫∫(-2-2)dA

= -4 dA

Next, we calculate the work

Work = -4 × b × d

= -4 × 3 × 3

= -36

Thus, the work is -36 for the force F performs.

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Graph option B is the correct answer.

Graphical representation refers to the use of charts and graphs to visually display, analyse, clarify, and interpret numerical data, functions, and other qualitative structures.

Given are function,

y = x+1 ≤0 and y = 3x

The best demonstration of these functions can be seen in graph 2.

Hence, Graph option B is the correct answer.

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Answer:

C

Step-by-step explanation:

1. Change to improper fractions

4 6/8 -> Multiply 4 and 8. Add 6. = 38/8

2 3/5 -> Multiply 2 and 5. Add 3. 13/5

Denominators are different so we have to make the same.

38/8 = 190/40
13/5 = 104/40

190/40-104/40 = 86/40 -> 2 6/40

The distance between the base of the string and the base of the mast of the sailboat is 6.24.

Here we have to find the distance from the base of the mast that should be attached to the end of the light string.

Data given:

length of the string = 20 foot

length of the mast of the sailboat = 19 foot

Distance between the base of the mast and the light string = [tex]\sqrt{20^{2} - 19^{2} }[/tex]

                                                                                             = [tex]\sqrt{400 - 361}[/tex]

                                                                                             = √39

                                                                                             = 6.245

Therefore the distance between the string and the mast is 6.24.

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The required integral for the gasoline tank is [tex]V = \int\limits_{ - 5}^3 {20 \cdot \sqrt {16 - {x^2}} } dx[/tex]

For the given circular cylinder, the desired limit is determined by the depth and radius of the cylinder. And, the integral function is obtained by employing a Pythagoras theorem. The final set-up must be in the form of [tex]{eq}\int\limits_a^b {f\left( x \right)dx}[/tex]

Let x be the vertical distance up from the centre line of the tank.

The radius of the right circular cylinder is 4 ft

The length of the right circular cylinder is 10 ft

The volume of the strip is determined by the front view of the right circular cylinder as follows:

dV=(L+L)dx×14

=2L×10dx

=20Ldx

The front view of the right circular cylinder is

x^2 + L^2 = 4^2

[tex]L = \sqrt{16 - x^2}[/tex]

Substitute the value of L in the equation of dV.

[tex]dV = 20 \cdot \sqrt {16 - {x^2}} dx[/tex]

The integral required to set up the volume at a depth of 6 ft will be given by taking integrals limits from -5 to 3

[tex]V = \int\limits_{ - 5}^3 {20 \cdot \sqrt {16 - {x^2}} } dx[/tex]

This is the required integral

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Answer:

the answer to that is 65.

Step-by-step explanation:

maths

The diameter of the circle pen for the sheep of the farmer is 68 yards.

The total length of the fencing used for the preparation of the fencing for sheep is 213.52 yards.

Thus,

circumference = 213.52 yards

The formula for the calculation of the circumference of circle is,

circumference = 2πr,

In which,

π = 3.14  and radius r.

Thus,

213.52 = 2πr

r = 213.52 / 2π

r = 34

Diameter = 2 x radius

Diameter = 2 x 34

Diameter = 68 yards.

Thus, the diameter of the circle pen for the sheep of the farmer is 68 yards.

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Answer:

The left side represents x, and the right side is y

Step-by-step explanation:

This table is simply going up by 5

The description of the proportional relationship in the context of this problem is given as follows:

For each minute the washing machine runs, it uses five thirds gallons of water.

A proportional relationship is a special case of a linear function, with intercept of zero, meaning that the output variable y is obtained as the multiplication of the input variable x and the constant of proportionality k, as follows:

y = kx.

In this problem, the relationship is given by the equation presented as follows:

g = 3/5m

The variables are given as follows:

The constant is of:

3/5.

Meaning that three fifths gallons of water are used each minute.

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Answer:

A = pi (r)^2, so first you have to find the radius. The radius = 18.5 since its diameter/2. So if you plug it in, its A = pi (18.5)^2 and your answer would be A = 1075.21. Hope I helped :))

Step-by-step explanation:

The number of persons added to the population rises annually if the population's growth rate, r, is positive and stable.

Given statement,

If the growth rate r of a population is positive and remains constant, the number of people added to the population,

In the given case the solution will be the number of people added to the population " increases each year ".

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