Billy jogs 4/5 kilometer every minute.How many kilometers does he jog after 6 1/8 minutes

The mass density in kg/m3 will be -  15 x [tex]10^{-2}[/tex] Kg/m3.

We have a 100.0 m long polymer cable of uniform circular cross section and of diameter 0.4cm has a mass of 1885.0 gm.

We have to determine its mass density in kg/m3.

The amount of mass per unit volume present in the body is called its mass density.

According to question, we have -

Length of polymer cable = 100.0 m

diameter of polymer cable = 0.4 cm = 0.004 m

Therefore, its radius = 0.002 m

The mass density of the wire will be -

[tex]\rho =\frac{m}{\pi r^{2} l}[/tex]

[tex]\rho[/tex] = [tex]\frac{1885}{3.14 \times0.002 \times 0.002 \times 100 }[/tex]

[tex]\rho = \frac{1885}{0.001256}[/tex] = 1500796.1 g/m3

1 Kg = 1000g

1g = 1/1000kg

1500796.1g = 1500.7 Kg = 15 x [tex]10^{-2}[/tex] Kg

Therefore, mass density = 15 x [tex]10^{-2}[/tex] Kg/m3

Hence, the mass density in kg/m3 will be -  15 x [tex]10^{-2}[/tex] Kg/m3.

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Answer:

Spherical-Like Shape

Step-by-step explanation:

An s-orbital is spherical with the nucleus at its center.

Answer:

K(t)=37

Step-by-step explanation:

k(t) = 13t - 2

k(3) = 13(3) - 2

k(3) = 39 - 2

k(3) = 37 <===

Answer:

I think cubic polynomial cause degree is 3

Answer:

[tex]41.89\ cm^2[/tex]

Step-by-step explanation:

[tex]We\ are\ given:\\In\ two\ concentric\ circles,\\OD=3\ cm\\BC=4\ cm\\\angle DOB=\angle AOC=120\\Now,\\We\ know\ that:\\Area\ of\ a\ sector\ with\ a\ central\ angle\ \theta\ and\ a\ radius\ r\ is:\\A=\frac{\theta}{360}* \pi r^2\\Here,\\Area\ between\ the\ sectors=Area\ of\ Larger\ Sector - Area\ of\ smaller\ sector=\frac{\theta}{360}*\pi(R^2-r^2),\ where\ R\ and\ r\ are\ radii\ of\ the\ respective\ circles\ and\\ \theta\ is\ the\ common\ central\ angle.\\Here,\\R=4+3=7\ cm\\r=3\ cm\\ \theta=120\\ Hence,[/tex]

[tex]Area\ of\ the\ shaded\ region=\frac{120}{360}*\pi(7^2-3^2)=\frac{1}{3}*\pi(49-9)=\frac{1}{3}*\pi(40) \approx 41.89\ cm^2[/tex]

Answer:

2 is the factor of every even number hope this help you

Answer:

100 different shoes

Step-by-step explanation:

4 styles * 5 sizes * 5 colors

4*5*5 = 100

9514 1404 393

Explanation:

You can check your answer by making sure that each of the primes you found is actually a prime. (Compare to a list of known primes, for example.) After you have determined your factors are primes, multiply them together to see if the result is 73. If so, you have found the correct prime factorization.

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Additional comment

73 is prime, so its prime factor is 73.

  73 = 73

Answer:

Step-by-step explanation: Hello! Do

Answer:

x = -11/5 or -2.2

y = 13/5 or 2.6

Step-by-step explanation:

well, start by doing the multiplication. then we will see better.

2x + 2yi + xi + yii = -7 + 3i

2x + 2yi + xi - y = -7 + 3i

this is because, remember, i = sqrt(-1), and ii = -1.

now we group the i-factors and the terms without i and compare it to the corresponding parts on the right side.

2x - y = -7

2yi + xi = 3i

=> 2y + x = 3

x = 3 - 2y

and that we use ihr the first equation again

2×(3-2y) - y = -7

6 - 4y - y = -7

-5y = -13

y = 13/5

x = 3 - 2×13/5 = 3 - 26/5 = 15/5 - 26/5 = -11/5

Answer:

[tex] \rm \displaystyle y' = 2 {e}^{2x} + \frac{1}{x} {e}^{2x} + 2 \ln(x) {e}^{2x} [/tex]

Step-by-step explanation:

we would like to figure out the differential coefficient of [tex]e^{2x}(1+\ln(x))[/tex]

remember that,

the differential coefficient of a function y is what is now called its derivative y', therefore let,

[tex] \displaystyle y = {e}^{2x} \cdot (1 + \ln(x) )[/tex]

to do so distribute:

[tex] \displaystyle y = {e}^{2x} + \ln(x) \cdot {e}^{2x} [/tex]

take derivative in both sides which yields:

[tex] \displaystyle y' = \frac{d}{dx} ( {e}^{2x} + \ln(x) \cdot {e}^{2x} )[/tex]

by sum derivation rule we acquire:

[tex] \rm \displaystyle y' = \frac{d}{dx} {e}^{2x} + \frac{d}{dx} \ln(x) \cdot {e}^{2x} [/tex]

Part-A: differentiating $e^{2x}$

[tex] \displaystyle \frac{d}{dx} {e}^{2x} [/tex]

the rule of composite function derivation is given by:

[tex] \rm\displaystyle \frac{d}{dx} f(g(x)) = \frac{d}{dg} f(g(x)) \times \frac{d}{dx} g(x)[/tex]

so let g(x) [2x] be u and transform it:

[tex] \displaystyle \frac{d}{du} {e}^{u} \cdot \frac{d}{dx} 2x[/tex]

differentiate:

[tex] \displaystyle {e}^{u} \cdot 2[/tex]

substitute back:

[tex] \displaystyle \boxed{2{e}^{2x} }[/tex]

Part-B: differentiating ln(x)•e^2x

Product rule of differentiating is given by:

[tex] \displaystyle \frac{d}{dx} f(x) \cdot g(x) = f'(x)g(x) + f(x)g'(x)[/tex]

let

substitute

[tex] \rm\displaystyle \frac{d}{dx} \ln(x) \cdot {e}^{2x} = \frac{d}{dx}( \ln(x) ) {e}^{2x} + \ln(x) \frac{d}{dx} {e}^{2x} [/tex]

differentiate:

[tex] \rm\displaystyle \frac{d}{dx} \ln(x) \cdot {e}^{2x} = \boxed{\frac{1}{x} {e}^{2x} + 2\ln(x) {e}^{2x} }[/tex]

Final part:

substitute what we got:

[tex] \rm \displaystyle y' = \boxed{2 {e}^{2x} + \frac{1}{x} {e}^{2x} + 2 \ln(x) {e}^{2x} }[/tex]

and we're done!

Answer:

Product Rule for Differentiation

[tex]\textsf{If }y=uv[/tex]

[tex]\dfrac{dy}{dx}=u\dfrac{dv}{dx}+v\dfrac{du}{dx}[/tex]

Given equation:

[tex]y=e^{2x}(1+\ln x)[/tex]

Define the variables:

[tex]\textsf{Let }u=e^{2x} \implies \dfrac{du}{dx}=2e^{2x}[/tex]

[tex]\textsf{Let }v=1+\ln x \implies \dfrac{dv}{dx}=\dfrac{1}{x}[/tex]

Therefore:

[tex]\begin{aligned}\dfrac{dy}{dx} & =u\dfrac{dv}{dx}+v\dfrac{du}{dx}\\\\\implies \dfrac{dy}{dx} & =e^{2x} \cdot \dfrac{1}{x}+(1+\ln x) \cdot 2e^{2x}\\\\& = \dfrac{e^{2x}}{x}+2e^{2x}(1+\ln x)\\\\ & = \dfrac{e^{2x}}{x}+2e^{2x}+2e^{2x} \ln x\\\\& = e^{2x}\left(\dfrac{1}{x}+2+2 \ln x \right)\end{aligned}[/tex]

Answer:

(5*sqrt(2), 5pi/4)

Step-by-step explanation:

In Polar coordinates, tan(theta)=y/x and r=sqrt(x^2+y^2)

tan(theta)=-5/5=-1. Theta=5pi/4

r=sqrt(5^2+5^2)=5*sqrt(2)

Hence the Polar coordinate is (5*sqrt(2), 5pi/4)

The polar coordinate is [tex](5\sqrt{2},\frac{-\pi }{4} )[/tex].

The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

To convert rectangular coordinate (x, y) to polar coordinate(r, θ) by using some formula

tanθ = y/x and [tex]r =\sqrt{x^{2} +y^{2} }[/tex]

According to the given question

We have

A rectangular coordinate (5, -5).

⇒ x = 5 and y = -5

Therefore,

[tex]r=\sqrt{(5)^{2} +(-5)^{2} } =\sqrt{25+25} =\sqrt{50} =5\sqrt{2}[/tex]

and

tanθ = [tex]\frac{-5}{5} =-1[/tex]

⇒ θ = [tex]tan^{-1} (-1)[/tex] = [tex]-\frac{\pi }{4}[/tex]

Therefore, the polar coordinate is [tex](5\sqrt{2},\frac{-\pi }{4} )[/tex].

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You're looking for a solution of the form

[tex]\displaystyle y = \sum_{n=0}^\infty a_n x^n[/tex]

Differentiating twice yields

[tex]\displaystyle y' = \sum_{n=0}^\infty n a_n x^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n[/tex]

[tex]\displaystyle y'' = \sum_{n=0}^\infty n(n-1) a_n x^{n-2} = \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n[/tex]

Substitute these series into the DE:

[tex]\displaystyle (x-1) \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n - x \sum_{n=0}^\infty (n+1) a_{n+1} x^n + \sum_{n=0}^\infty a_n x^n = 0[/tex]

[tex]\displaystyle \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^{n+1} - \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n \\\\ \ldots \ldots \ldots - \sum_{n=0}^\infty (n+1) a_{n+1} x^{n+1} + \sum_{n=0}^\infty a_n x^n = 0[/tex]

[tex]\displaystyle \sum_{n=1}^\infty n(n+1) a_{n+1} x^n - \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n \\\\ \ldots \ldots \ldots - \sum_{n=1}^\infty n a_n x^n + \sum_{n=0}^\infty a_n x^n = 0[/tex]

Two of these series start with a linear term, while the other two start with a constant. Remove the constant terms of the latter two series, then condense the remaining series into one:

[tex]\displaystyle a_0-2a_2 + \sum_{n=1}^\infty \bigg(n(n+1)a_{n+1}-(n+1)(n+2)a_{n+2}-na_n+a_n\bigg) x^n = 0[/tex]

which indicates that the coefficients in the series solution are governed by the recurrence,

[tex]\begin{cases}y(0)=a_0 = -7\\y'(0)=a_1 = 3\\(n+1)(n+2)a_{n+2}-n(n+1)a_{n+1}+(n-1)a_n=0&\text{for }n\ge0\end{cases}[/tex]

Use the recurrence to get the first few coefficients:

[tex]\{a_n\}_{n\ge0} = \left\{-7,3,-\dfrac72,-\dfrac76,-\dfrac7{24},-\dfrac7{120},\ldots\right\}[/tex]

You might recognize that each coefficient in the n-th position of the list (starting at n = 0) involving a factor of -7 has a denominator resembling a factorial. Indeed,

-7 = -7/0!

-7/2 = -7/2!

-7/6 = -7/3!

and so on, with only the coefficient in the n = 1 position being the odd one out. So we have

[tex]\displaystyle y = \sum_{n=0}^\infty a_n x^n \\\\ y = -\frac7{0!} + 3x - \frac7{2!}x^2 - \frac7{3!}x^3 - \frac7{4!}x^4 + \cdots[/tex]

which looks a lot like the power series expansion for -7eˣ.

Fortunately, we can rewrite the linear term as

3x = 10x - 7x = 10x - 7/1! x

and in doing so, we can condense this solution to

[tex]\displaystyle y = 10x -\frac7{0!} - \frac7{1!}x - \frac7{2!}x^2 - \frac7{3!}x^3 - \frac7{4!}x^4 + \cdots \\\\ \boxed{y = 10x - 7e^x}[/tex]

Just to confirm this solution is valid: we have

y = 10x - 7eˣ   ==>   y (0) = 0 - 7 = -7

y' = 10 - 7eˣ   ==>   y' (0) = 10 - 7 = 3

y'' = -7eˣ

and substituting into the DE gives

-7eˣ (x - 1) - x (10 - 7eˣ ) + (10x - 7eˣ ) = 0

as required.

Answer:

I would rather use:

(b) 10,000 batches of 10 observations each.

Step-by-step explanation:

It is easier to have 10,000 batches of 10 observations each than to have 50 batches of 2,000 observations.  Human errors are reduced with fewer observations. For example, Hadoop, a framework used for storing and processing big data, relies on batch processing.  Using batch processing that divides the 100,000 stationary waiting times into 10 observations with 10,000 batches each is more efficient than having 2,000 observations with 50 batches each.

Answer:

divide 99 by 5

99/5= 19.8

Answer:

83

Step-by-step explanation:

1∇2= (2+2^1)

=2+2=4

(4)∇3= (2+3^4)

=2+81

=83

Using the fundamental counting principle, it is found that: 50 2-scoop combinations are possible.

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The flavors and the toppings are independent, which means that the fundamental counting principle is used to solve this question, which states that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

----------------------------------

In this question:

So,

[tex]10 \times 5 = 50[/tex]

50 2-scoop combinations are possible.

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9514 1404 393

Answer:

  9 square inches

Step-by-step explanation:

The area is proportional to the square of the linear scale factor. We can use this to write the proportion ...

  A/(144 m²) = ((2 in)/(8 m))²

  A = (144·4/64) in² = 9 in²

The area representing 144 square meters is 9 square inches.

Answer:  Choice C

This is because the input n = 2 leads to the output n-2 = 2-2 = 0

As another example: the input n = 4 leads to the output n-2 = 4-2 = 2

Whatever the input is, subtract 2 from it to get the output.

Answer:

x=12

Step-by-step explanation:

3x=2x+12

3x-2x=12

x=12

Answer:

Step-by-step explanation:

6x=1/2(2x +7)            Multiply both sides by 2

2*6x = 1/2(2x + 7)*2

12x = 2x + 7              Subtract 2x from sides

12x-2x =2x-2x+7

10x = 7                      Divide by 10

x = 7/10

x = 0.7

Let's check it

6(0.7) = 4.2

1/2 (2*0.7 + 7)

1/2 (1.4 + 7)

1/2 ( 8.4)

4.2

Both sides check. The answer must be x = 0.7

Answer:

0.40905 - 0.10204 = .30701 = 30.7 %

Step-by-step explanation:

0.23 0.40905

1.27 0.10204

30.8 m

Step-by-step explanation:

Given: [tex]V = 43\:\text{m}[/tex], [tex]V_y = 30\:\text{m}[/tex]

The x-component of vector [tex]\vec{\text{V}}[/tex] is

[tex]V_x = \sqrt{V^2 - V_y^2} = \sqrt{(43)^2 - (30)^2} = 30.8\:\text{m}[/tex]

The x- component of the vector is 30.8meters.

If [tex]v = < a. b >[/tex] be a position vector then the magnitude of vector v is found by  [tex]|v| =\sqrt{a^{2}+b^{2} } }[/tex] , where a and b are the x and y component respectively.

And the direction is equals to the angle formed x- axis or y axis.

According to the given question

We have

Magnitude of the vector, |v| = 43meters

Y- component of the vector, b = 30meters

Since, we know that

[tex]|v| =\sqrt{a^{2} +b^{2} }[/tex]

Substitute the value of |v| = 43 and b = 30 in the above formula of magnitude.

⇒ [tex]43 = \sqrt{a^{2}+30^{2} }[/tex]

⇒ [tex]43 = \sqrt{a^{2}+900 }[/tex]

⇒ [tex]43^{2} =a^{2} + 900[/tex]

⇒ [tex]1849 = a^{2} + 900[/tex]

⇒ [tex]1849-900=a^{2}[/tex]

⇒ [tex]949=a^{2}[/tex]

⇒ [tex]a =\sqrt{949}[/tex]

⇒ [tex]a = 30.8[/tex]

Hence, the x- component of the vector is 30.8meters.

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Answer:

77/306 or around 25.2%

Step-by-step explanation:

[tex]\frac{7}{18} *\frac{11}{17}[/tex] section 1/total * section 2/(total-1) since there is no replacement

just solve and you get 77/306

Answer:

14m

Step-by-step explanation:

[tex]7m-7+7m-7\\[/tex]

First, we need to eliminate the like term and collect the like term.

[tex]-7+-7=0[/tex]

Now, we have 7m +7m, sum them up and you will get the answer.[tex]7m+7m=14m[/tex]

So, the answer is 14m.

Answer:

14m

Step-by-step explanation:

7m -7 +7m +7​

7m + 7m - 7 + 7

14m

Answer:

B

Step-by-step explanation:

For l1 and l2 to be parallel, these two angles need to be equal. 3x-15=2x+10, x=25

Answer:

A. Sides AC and DF

B. Angles BAC and EDF

Answer:

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Inverse variation is of the form

xy = k where k is a constant

x=4 and y = 32

4*32 = k

128 = k

xy = 128

Let x = 8

8y = 128

Divide each side by 8

8y/8 = 128/8

y =16