Find the point on the line -5x + 7y - 4 = 0 which is closest to the point (2,3).

The value that would be obtained using the 5 midpoint rectangles of equal width to estimate the given Integral is; 33/100

First of all, let us partition the interval [0, 1] as;

[0, 1/5] ∪ [1/5, 2/5] ∪ [2/5, 3/5] ∪ [3/5, 4/5] ∪ [4/5, 5]

Thus, the midpoints of the intervals which are the sample points are, respectively;

1/10, 3/10, 1/2, 7/10, 9/10

The integral is approximated by;

(0,1)∫x² dx = (5, n=1)Σf(x_n) Δx

where Δx is the difference between the partition endpoints, i.e.

Δx = (1 - 0)/5 = 1/5

and x_n is the midpoint of the nth partition.

Thus, we have;

(5, n=1)Σf(x_n) Δx = (1/5)[(1/10)² + (3/10)² + (1/2)² + (7/10)² + (9/10)²] = 33/100

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Using the combination formula, it is found that the number of possible outcomes are given by:

1. 3150

2. 700.

3. 3920.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Item 1:

We have combinations of 2 from 6, 5 from 7 and 3 from 5, all independent, hence we multiply them:

[tex]T = C_{6,2}C_{7,5}C_{5,3} = 15 \times 21 \times 10 = 3150[/tex]

3150 different choices are possible.

Item 2:

1 from 5, 1 from 4 and 4 from 7, hence:

[tex]T = C_{5,1}C_{4,1}C_{7,4} = 5 \times 4 \times 35 = 700[/tex]

700 different combinations are possible.

Item 3:

3 men from a set of 8, 4 women from a set of 8, hence:

[tex]T = C_{8,3}C_{8,4} = 56 \times 70 = 3920[/tex]

3920 ways to select the team of 7.

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Thanks for the update. "Irrotational" means curl = zero, so we compute the curl, set it equal to zero, and solve for the constants.

[tex]\vec f(x,y,z) = (axy+z^3) \, \vec\imath + (3x^2-z) \, \vec\jmath + (bz^2-y) \, \vec k[/tex]

[tex]\nabla \times \vec f(x,y,z) = \left(\dfrac{\partial(bz^2-y)}{\partial y} - \dfrac{\partial(3x^2-z)}{\partial z}\right) \, \vec\imath - \left(\dfrac{\partial(bz^2-y)}{\partial x} - \dfrac{\partial(axy+z^3)}{\partial z}\right) \, \vec\jmath \\ ~~~~~~~~~~~~ + \left(\dfrac{\partial(3x^2-z)}{\partial x} - \dfrac{\partial(axy+z^3)}{\partial y}\right) \, \vec k[/tex]

[tex]\nabla \times \vec f(x,y,z) = 3z^2 \, \vec\jmath + (6-a)x \, \vec k[/tex]

At this point, all we can conclude is that a = 6 to make the k-component vanish. Unfortunately there's no zeroing out the j-component, so the field as given is *not* irrotational.

As I mentioned in comments, if the i-component had instead been [tex]axy+bz^3[/tex], we would have ended up with

[tex]\nabla \times \vec f(x,y,z) = 3bz^2 \, \vec\jmath + (6-a)x \, \vec k[/tex]

in which case we would have b = 0.

I'll continue working with this "fixed" field to find Φ, if only to give you an idea of how to proceed. We want a scalar function Φ(x, y, z) such that the given vector field is the gradient of f. This would entail solving the partial differential equations,

[tex]\dfrac{\partial\Phi}{\partial x} = axy+bz^3 = 6xy[/tex]

[tex]\dfrac{\partial\Phi}{\partial y} = 3x^2 - z[/tex]

[tex]\dfrac{\partial\Phi}{\partial z} = bz^2-y = -y[/tex]

Let's start with the last equation. Integrating both sides with respect to z yields

[tex]\Phi(x,y,z) = \displaystyle \int (-y) \, dz = -yz + g(x,y)[/tex]

Now differentiate both sides with respect to y :

[tex]\dfrac{\partial\Phi}{\partial y} = -z + \dfrac{\partial g}{\partial y} = 3x^2 - z \implies \dfrac{\partial g}{\partial y} = 3x^2[/tex]

Integrate both sides of the latter PDE with respect to y to solve for g :

[tex]g(x,y) = \displaystyle \int 3x^2 \, dy = 3x^2y + h(x)[/tex]

Now we differentiate Φ with respect to x :

[tex]\Phi(x,y,z) = -yz + 3x^2y + h(x) \\\\ \dfrac{\partial\Phi}{\partial x} = 6xy + \dfrac{dh}{dx} = 6xy \implies \dfrac{dh}{dx} = 0[/tex]

Integrate to solve for h :

[tex]h(x) = \displaystyle \int 0 \, dx = C[/tex]

where C is an arbitrary constant.

So the scalar function whose gradient is our "fixed" field f is

[tex]\Phi(x,y,z) = -yz + 3x^2y + C[/tex]

Answer:

44

Step-by-step explanation:

double both 13 and 9 then add the awnser together to get 44

Answer:

15x^2 6y^2 5z^6

Step-by-step explanation:

area = length x width

area =  5x3y5z^2   *   3x2yz^4

Answer:

There are two rectangular prisms and two right triangular prisms

Step-by-step explanation:

The two right-angle triangular prisms can be found on the right and left. One rectangular prism can be found in the middle between those two triangular prims, and the other can be found at the top. Voila.

Comparing the measurement needed for the batch and the measurement of the scale, Robert does not have enough noodles.

A fraction is a non-integer. It is made up of numerators and denominators. A decimal is a non-integer where the integers are differeniated from a non-integer by a decimal point.

In order to determine the answer, convert the fraction to a decimal by dividing the numerator by the denominator.

4 1/6 = 4. 17

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Answer:

y = -x +0

Step-by-step explanation:

y = mx + b

y= slope * x + y-intercept

To find slope, use any x and y pair from the table, for example (x= 5, y= -5)

slope = y/x = -5/5 = -1

y=  -x + b

To find b the y-intercept, substitute any x and y pair from the table, for example (x= 5, y= -5)

-5 = -5 +b

 b = 0

The linear equation that gives the rule for this table is

y = -x + 0 or just y = -x

Answer:

Thus, 12+14+16=42.

Step-by-step explanation:

Hope this helps.

Answer:

24 [tex]m^{3}[/tex]

Step-by-step explanation:

Volume=l*b*h

as tank is half full so height of water will be 4m

and Voulme will be,

V=3*2*4=24 [tex]m^{3}[/tex]

while capacity of tank is,

V=3*2*8=48  [tex]m^{3}[/tex]

The volume of water in the tank, when it is half full, is 24 cubic meters.

Volume in mathematics and physics refers to how much three-dimensional space is occupied by a substance or an object. It is a measurement of the overall volume of space contained inside a three-dimensional object's limits.

The volume of the rectangular tank is given by the formula:

V = l x b x h

where l is the length, b is the breadth, and h is the height of the tank.

Substituting the given values, we get:

V = 3m x 2m x 8m = 48 cubic meters

If the tank is half full, then the volume of water in the tank is:

Vw = (1/2) * V = (1/2) x 48 = 24 cubic meters

Therefore, the volume of water in the tank when it is half full is 24 cubic meters.

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#SPJ2

Step-by-step explanation:

the side lengths of the base (the ground triangle) are equal. that means every ground side length is 8 in.

and that also makes the 3 triangles of the side areas of the pyramid equal.

so, for the surface area of the pyramid we need to calculate the area of one side area triangle, multiply it by 3 (as we have 3 side areas) and add the area of the ground triangle.

the area of a triangle is

baseline × height / 2

so, for a side area triangle we get

8 × 14 / 2 = 8×7 = 56 in²

all 3 side areas together are then

3×56 = 168 in²

the ground area triangle is then

8 × 6.9 / 2 = 4 × 6.9 = 27.6 in²

so, the total surface area of the pyramid is

168 + 27.6 = 195.6 in²

Check the picture below.

Answer: divide by 10

Step-by-step explanation: you divide the previous number by 10 to get the next number

Answer:

Perpendicular

Step-by-step explanation:

Simplify 3x+9y=9 to 9y=-3x+9 and then to y=-1/3x+1

y=3x-7

and

y=-1/3x+1, 3 and -1/3 are negative reciprocals which makes these equations perpendicular.

164

the unknown angle x.

angle at a point= 360°

x= 360 - ( 164 + 90) (because that's a right angle)

x= 360 - 254

x= 106°

Answer:

Step-by-step explanation:

Probability of drawing 1st red marble

Probability of drawing 2nd red marble

Probability

Answer:

Scale factor of 3

Step-by-step explanation:

[tex]distance = 41km[/tex]

[tex]time = 35min = \frac{35}{60} hr[/tex]

[tex]speed = \frac{distance}{time} [/tex]

[tex]speed = \frac{41}{ \frac{35}{60} } [/tex]

[tex]speed = \frac{41 \times 60}{35} [/tex]

[tex]speed = 70.286 \: or \: 70.3km\hr[/tex]

Answer:

False

Step-by-step explanation:

The measure of an acute angle is less than 90°

Answer:

4

Step-by-step explanation:

if you have 2 apples and you get 2 more apples how many do you have.

[tex]\huge\text{Hey there!}[/tex]

[tex]\\\large\text{ORIGINAL EQUATION: }\\\mathsf{4(3x + 6) - x}\\\large\text{DISTRIBUTE 4 WITHIN the PARENTHESES}\\\mathsf{\rightarrow 4(3x) + 4(6) - x}\\\mathsf{\rightarrow 12x + 24 - x}\\\large\text{COMBINE the LIKE TERMS}\\\mathsf{\rightarrow 12x + 24 - 1x}\\\mathsf{\rightarrow 11x + 24}\\\\\\\huge\text{Therefore, your answer: \boxed{\mathsf{11\bold{x} + 24}}}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

y= -4x

Step-by-step explanation:

it will be more helpful to answer this question if the equations were provided.

Answer:

"Answer: A. m=2;y-int=(0,4);y=2x+4

Step-by-step explanation: I just finished the practice on edge and went back to check the answer. It's 100% correct, swear"

Step-by-step explanation:

Found this on Brainly, hope it helps? :)

When Matthew noticed that the container was one fourth full of sand, the remaining volume quantity needed is 432 inches³.

The container has the following dimensions. 12 in. by 8in. by 6in. Therefore, the volume will be:

= 12 × 8 × 6

= 576 inches.

Since Matthew noticed that the container was one fourth full of sand, the remaining quantity needed will be:

= 576 - (1/4 × 576)

= 576 - 144

= 432 inches³.

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A compound interest formula is a type of exponential equation. That is option C

Exponential equations are those equations that has their variables as exponents. A typical example of this type of equation is the compound interest formula.

The compound interest formula is an exponential equation because the little sum invested as capital, once the interest is added, the balance will earn more capital during the next compounding period.

Therefore, a compound interest formula is a type of exponential equation.

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y=-3x-2

Hope it helps.

Do comment if you have any query.

Answer:

[tex]\Longrightarrow: \boxed{\sf{y=-3x+2}}[/tex]

Step-by-step explanation:

The slope-intercept form is used to write linear equations.

Slope-intercept form:

[tex]\Longrightarrow: \sf{y=mx+b}[/tex]

The m represents the slope.

The b represents the y-intercept.

The slope is -3.

The y-intercept is 2.

y=-3x+2

I hope this helps! Let me know if you have any questions.

Answer:

B. 7

Step-by-step explanation:

7 × n = 42 + 7

7n = 49

n = 49/7

n = 7

______

Hope it helps ⚜

[tex]7 \times n = 42 + 7[/tex]

what the "n" represents

[tex]7 \times n = 42 + 7[/tex]

[tex]7 \times n = 49[/tex]

[tex]n = \frac{49}{7} [/tex]

[tex]n = 7[/tex]

therefore, "n" represents 7.

answer= option B

Answer:

C. 9

Step-by-step explanation:

This is the answer because of how the math works...Its really hard to explain how it works.