Billy is hiking in Colorado. He walks eastward four miles, then turns $60$ degrees northward and walks six miles. How far is he from his starting point

Let [tex]y=\cos(2x)[/tex], with first two derivatives

[tex]Dy = -2\sin(2x)[/tex]

[tex]D^2y = -4\cos(2x)[/tex]

Consider the linear ODE

[tex]aD^2y + bDy + cy = 0[/tex]

Substitute [tex]y[/tex] and its derivatives and solve for the unknown coefficients [tex]a,b,c[/tex].

[tex]-4a\cos(2x) - 2b\sin(2x) + c\cos(2x) = 0[/tex]

[tex]\implies \begin{cases}-4a+c=0 \\ -2b=0 \end{cases}[/tex]

[tex]\implies b=0 \text{ and } c= 4a[/tex]

Then the minimal ODE with this solution is

[tex]aD^2y + 4ay = 0 \implies \boxed{D^2y + 4y = 0}[/tex]

The average IQ test score would be 100.

What is a normal distribution?

A probability distribution that is symmetric about the mean or average is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the average value occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

Average IQ Score

A score of 100 is regarded as the average IQ on various tests. The majority of results (68%) are within one standard deviation of the mean (that is, between 85 and 115). This indicates that the average result is within plus or minus 15 points for almost 70% of test takers.

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Answer:

(or 5/2 or 2 1/2)

Step-by-step explanation:

Remember PEMDAS

10 * (1^2 * 2^-2)

10 * (1 * 0.25)

10 * 0.25 =

2.5

Answer: b. 125

Step-by-step explanation:

Find the square roots of each, and if the square root is a decimal, it is not a perfect square.

Square root of 81: 9

Square root of 49: 7

Square root of 100: 10

That leaves 125.

Answer:

(2, -1).

Step-by-step explanation:

y = 1/4x^2 - x - 1

First convert to vertex form:

y = 1/4(x^2 - 4x) - 1

y = 1/4[(x - 2)^2 - 4] - 1

y =  1/4(x - 2)^2 - 2

The formula for the focus of the parabola y = a(x - h)^2 + k is (h, k+1/4a)

So here it is:

(2, -2+1/ 4*1/4)

=  (2, -1).

Answer:

9/5

Step-by-step explanation:

First we have to find the constant k

m = k/(p-1)^2  (p-1)^ goes on the bottom of the fraction because of the inverse.

5 = k/(4-1)^2

5 = k/3^2

5 = k/9  Multiply both side by 9

45 = k  We know can use this constant to solve our problem

m = 45/(6-1)^2

m = 45/5^

m = 45/24

m = 9/5

Considering the given function, the table is completed as follows:

x|y

-12|15

-6| 11

3|5

15|-3

The function is defined by:

[tex]y = -\frac{2}{3}x + 7[/tex]

Hence, when x = -12:

[tex]y = -\frac{2}{3}(-12) + 7 = 15[/tex]

When x = -6:

[tex]y = -\frac{2}{3}(-6) + 7 = 11[/tex]

When x = 3:

[tex]y = -\frac{2}{3}(3) + 7 = 5[/tex]

When x = 15:

[tex]y = -\frac{2}{3}(15) + 7 = -3[/tex]

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Answer:round to nearest hundredth (4,786.3)

Step-by-step explanation:

hope this helps, if wrong im so sorry :(

The computation shows that the value of blue which is represented by x is 12.

From the information given, it was stated that 30 people were in the kindergarten.

Green = 10

Red = 8

Blue (x) = 30 - (10 + 8)

= 30 - 18

= 12

Since the teacher want to paint the class with the most favorite color, the appropriate color to use will be blue.

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At a rate of 2 m³ per minute, it would take 212.5 minutes to fill this swimming pool.

Based on the information provided, we can logically deduce that the shape of this pool is a prism because it is deep (2.2 m) at one end and shallow (1.2 m) at the other end.

First of all, we would determine the volume of this swimming pool as follows:

Volume = 1/2 × (1.2 + 2.2) × 10 × 25

Volume = 1/2 × (3.4) × 250

Volume = 1.7 × 250

Volume = 425 m³.

For the time, we have:

Time = volume/rate

Time = 425/2

Time = 212.5 minutes.

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Answer:

23 there will be 100 paperclips leftover

The entrance fee is proportional to the number of visitors at A)museum a.

In arithmetic, two sequences of numbers, often experimental statistics, are proportional or at once proportional if their corresponding factors have a regular ratio, that's called the coefficient of proportionality or proportionality consistent.

The definition of proportional is something that has an incredibly correct dating of length or that is appropriate. An example of something proportional is a woman's tiny toes to her quick stature. An instance of something proportional is the quantity of pay a worker receives for the hours that they installed.

While something is proportional to something else, it does no longer suggest the values are equal, simply that they trade with admiration for each other. The regular of proportionality serves as a multiplier.

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Answer:

Museum C

Step-by-step explanation:

If you divide them all (like 3/4) you get .75

The minimum value of z is -12.

Given that the system of linear programming

z=-3x+5y

x+y≥-22

x-y≥-4

x-y≤2

Firstly, we will convert the given constraints into equality as

x+y=-22

x-y=-4

x-y=2

Now, we will take the equation x+y=-22 and taking x as 0 as find y and taking y as 0 to find x, we get

If x=0 then y is

0+y=-22

y=-22

If y=0 then x=-22

So, the points lie on the line x+y=-22 is (0,-22) and (-22,0).

Further, we will take the equation x-y=-4 and taking x as 0 as find y and taking y as 0 to find x, we get

If x=0 then y=4

If y=0 then x=-4

So, the points lie on the line x-y=-4 is (0,4) and (-4,0).

Furthermore, we will take the equation x-y=2 and taking x as 0 as find y and taking y as 0 to find x, we get

If x=0 then y=-2

If y=0 then x=2

So, the points lie on the line x-y=2 is (0,-2) and (2,0).

now, we will find the feasible region of the given constraints as shown in figure.

We will find that each constraint will contain origin or not by substituting (0,0), we get

0+0≥-22 containing origin

0-0≥-4 containing origin

0-0≤2 containing origin

From the graph we can see that the minimum value of x is -13 and minimum value of y is -12.

z=-3x+5y

z=-3x+3y+2y

z=-3(x-y)+2y

minmum value of x-y from the given constraints is

-4≤x-y≤2

From here minimum value of x-y is -4

So, z=-3(-4)+2y

z=12+2y

For the minimum value of z the value of y should be minimum.

From the graph we can see the minimum value of y=-12

So, z=12+2(-12)

z=12-24

z=-12

Hence, the minimum value of z for the system of Linear Programming:

z=-3x + 5y, x+y≥-22, x-y≥-4, x - y ≤ 2 is -12.

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Step-by-step explanation:

123456 less then 7

unlimited greater then 7

The numbers from negative infinity to 7, excluding 7."are less than 7 and "all numbers from 7 to positive infinity, excluding 7" are more than 7.

The combination of positive, negative numbers including 0  are called as integers.

The numbers less than 7 are:

This set includes all real numbers that are strictly less than 7.

It can be denoted as (-∞, 7), which means "all numbers from negative infinity to 7, excluding 7."

The numbers greater than 7 are:

This set includes all real numbers that are strictly greater than 7. It can be denoted as (7, +∞), which means "all numbers from 7 to positive infinity, excluding 7."

Thus, there are infinite numbers which are less than 7 and more than 7.

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Check the picture below, so the parabola looks more or less like that one, with a "p" distance of 2 units that is positive, whilst the vertex, which is always half-way between the focus point and the directrix is where you see it there, thus

[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=-1\\ k=2\\ p=2 \end{cases}\implies 4(2)( ~~ x-(-1) ~~ )~~ = ~~(y-2)^2\implies 8(x+1)=(y-2)^2 \\\\\\ x+1=\cfrac{1}{8}(y-2)^2\implies \boxed{x=\cfrac{1}{8}(y-2)^2-1}[/tex]

Answer: UR WELCOME

Step-by-step explanation: ANSWER ON EDMENTUM

The given magic numbers are placed in the appropriate squares, so that the sum in each row, column and diagonal is all equal as shown below.

First of all, we would rewrite all the rational numbers in their lowest forms:

Next, we would write the sum of the numbers in each row as follows:

First row: 16/19 + 9/19 + 2/19 + (-7/-19) = 34/19

Second row: (-6/-19) + (-3/-19) + 12/19 + 2/1 = 34/19

Third row: 11/19 + 14/19 + 5/19 + (-4/-19) = 34/19

Fourth row: 1/19 + (-8/-19) + 15/19 + 10/19 = 34/19

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Answer:

1

Step-by-step explanation:

When dividing fractions i use the method KFC(keep flip change) :

Keep the first fraction :

[tex]\frac{14a^{2} }{10b^{2} }[/tex]

Flip the second fraction :

[tex]\frac{15b^{2} }{21a^{2} }[/tex]

Change the function :

÷ → ×

Now write your new equation :

[tex]\frac{14a^{2} }{10b^{2} }[/tex] ×  [tex]\frac{15b^{2} }{21a^{2} }[/tex]

Now multiply the numerators together and the denominators together :

14a² × 15b²  = 210a²b²

10b² × 21a² = 210a²b²

Now make this into a fraction again :

210a²b² / 210a²b²

Anything divided by itself is always 1 so :

210a²b² / 210a²b² = 1

Hope this helped and have a good day

It's common to hear people say that the Renaissance and Reformation saw numerous significant developments.

What impact did the Renaissance have on the Reformation?

Why was the Renaissance important?

The Renaissance period cultivated a new change in art, knowledge, and culture.

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If a grocery store sells a bag of 4 oranges for $1.04 then it will cost $2.86 for 11 oranges.

Given that a grocery store sells a bag of 4 oranges for $1.04 means revenue is $1.04 with no profits.

We have to find the cost of 11 oranges. We have assumed that there are no profits as we are require to find cost.  But there is huge difference between cost and profits.

We know that average cost is total cost divided by number of items.

Cost of 4 oranges=$1.04

cost of 1 orange=1.04/4

=$0.26 per orange

Cost of 11 oranges=0.26*11

=$2,86.

Hence if a grocery store sells a bag of 4 oranges for $1.04 then it will cost $2.86 for 11 oranges.

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Answer:

slope = 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, 6) ← 2 points on the line

m = [tex]\frac{6-0}{0-(-3)}[/tex] = [tex]\frac{6}{0+3}[/tex] = [tex]\frac{6}{3}[/tex] = 2

Answer: reflection across x axis and y axis?

Step-by-step explanation: repost question with the possible answers!

The perimeter of the polygon that circumscribes the circle is 78 cm

An equation is an expression that shows the relationship between two or more variables and numbers.

The circle tangent theorem states that tangents which meet at the same point are equal in length. Hence:

The missing lengths are 8, 6, 9 and 16.

Perimeter of the polygon = 2(8) + 2(6) + 2(9) + 2(16) = 78 cm

The perimeter of the polygon that circumscribes the circle is 78 cm

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Answer:

{-14,-26}

Step-by-step explanation:

lx+20l=6

So x+20 is either 6 or -6

x=6-20=-14

x=-6-20=-26

Answer:

3/8

Step-by-step explanation:

Let's use a sample number of 100 miles

If 3/8 was traveled the first day, then 37.5m were traveled on the first day.

Now on Sunday, there are 62.5m remaining in the trip. They travel 3/5 of that, meaning they went 62.5 * 3/5m. This turns out to be 37.5 miles that were traveled on Sunday.

37.5/100 = 3.8

The volume of wedge is 4/15 by use of Triple integral.

According to the statement

we  have to find the volume of wedge which is bounded by the parabolic cylinder.

So, because of the given shape of z=√y

the plane y=0 is a boundary, in addition to the given x = 0, z = 0.

so we are in the first octant for all of this. and the further constraint is the plane x + y = 1

Triple integrals are 3 successive integrations, used to calculate a volume, or to integrate in a 4th dimension, over 3 other independent dimensions.

but as a triple integral you would write:

∫x=0 ∫y=0∫z=0 dz dy dx

And after put the values in it and solving it we get the

[−4/15(1−x)^5/2] at x=0

Then after that the answer will become 4/15.

So, The volume of wedge is 4/15 by use of Triple integral.

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Answer:22-0.22y

Step-by-step explanation: we have to decrease 22 by y%

we need to calculate what is y% of 22. y% of 22 simply means y% into 22 that is y% x 22

= 0.01(y) x 22

= 0.22y

= 22 - 0.22y

The number of chickens she had was 352

From the question, we are to determine the number of chicken she has

Let c represent chicken

and d represent ducks

From the given information,

Mrs. Anderson had twice as many chickens as ducks

c = 2d ---------- (1)

She sold 272 chickens and 16 ducks and then had half as many chickens as ducks

(c-272) = 1/2(d -16) ---------- (2)

Put equation (1) into (2)

2d - 272 = 1/2(d - 16)

2(2d - 272) = d- 16

4d - 544 = d - 16

4d - d = 544 - 16

3d = 528

d = 528/3

d = 176

Substitute the value of d into equation (1)

c = 2d

c = 2(176)

c = 352

Hence, the number of chickens she had was 352

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The polynomial equation [tex]2x^{3} - 5 x^{2} + x + 2 = 0[/tex] given that 2 is zero of

f(x) = [tex]2x^{3} - 5 x^{2} + x +2[/tex]

According to the question,

f(x)  [tex]=2x^{3} - 5 x^{2} + x + 2[/tex]

[tex]f(2)= 2(2)^{3} - 5 (2)^{2} + 2 + 2 \\= 2(8) - 5(4) +4\\= 16 - 20 + 4\\= -4 + 4\\= 0.[/tex]

Hence, the polynomial equation [tex]2x^{3} - 5 x^{2} + x + 2 = 0[/tex] given that 2 is zero of f(x)  [tex]=2x^{3} - 5 x^{2} + x + 2[/tex].

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Answer: about 260 Lb

Step-by-step explanation: