Base of building 180 meters

The net outward flux across the boundary of the tetrahedron is: -4

What is the gradient of a function in a vector field?

The gradient of a function is related to a vector field and it is derived by using the vector operator ∇ to the scalar function f(x, y, z).

Given vector field:

F = ( -2x, y, - 2 z )

[tex]\mathbf{\nabla \cdot F = ( i \dfrac{\partial }{\partial x }+ j \dfrac{\partial}{\partial y} + k \dfrac{\partial}{\partial z}) \langle -2x, y, -2z \rangle}[/tex]

[tex]\mathbf{ \nabla \cdot F = ( \dfrac{\partial }{\partial x }(-2x)+ \dfrac{\partial}{\partial y}(y) + \dfrac{\partial}{\partial z}(-2z))}[/tex]

= -2 + 1 -2

= -3

According to divergence theorem;

Flux [tex]\mathbf{=\iiint _v \nabla \cdot (F) \ dv}[/tex]

x+y+z = 2; [tex]1^{st}[/tex]  Octant

[tex]= \int\limits^2_0 \int\limits^{2-x}_0 \int\limits^{2-x-y}_0 -3dzdydx[/tex]

[tex]=-3 \int\limits^2_0 \int\limits^{2-x}_0 (2-x-y)dy dx[/tex]

[tex]= -3 \int\limits^2_0[(2-x)y - \dfrac{y^2}{2}]^{2-x}__0 \ \ dx[/tex]

[tex]= -3 \int\limits^2_0(2-x)^2 - \dfrac{(2-x)^2}{2} dx[/tex]

[tex]= -3 \int\limits^2_0\dfrac{(2-x)^2}{2} dx = - \dfrac{3}{2} \int\limits^2_0(4-4x+x^2) dx[/tex]

[tex]=- \dfrac{3}{2}(4x-x^2 + \dfrac{x^3}{3})^2_0[/tex]

[tex]=- \dfrac{3}{2}(8-8+\dfrac{8}{3})[/tex]

[tex]=- \dfrac{3}{2}(\dfrac{8}{3})[/tex]

= -4

Therefore, we can conclude that the net outward flux across the boundary of the tetrahedron is: -4

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Answer:

a

Step-by-step explanation:

The difference between a rational number and an irrational number is always an irrational number. The correct option is B.

A Rational Number is a number of the form p/q, p & q are integers, and q ≠ 0.  An irrational number is all real numbers except rational numbers i.e. it is a non-repeating and non-terminating decimal number or it can not be expressed in a ratio of two integers.

Further, natural numbers can be rational numbers. Also, all repeating and terminating decimals are rational.

The difference between a rational number and an irrational number is always an irrational number. For example:

2 - √3 is always an irrational number where 2 is rational and √3 is an irrational number.

Hence addition and subtraction of rational and irrational numbers is always an irrational number.

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Answer:

The rate of change of the Coyote population in 2002 is 32

Step-by-step explanation:

Given the formula for the population of a Coyotes in the Northwestern portion of Alabama, we are to calculate rate of change of the Coyote population in the year 2002 where t = 2

The formula is given as;

P(t) = (t^2 + 100) ln (t + 2)

The rate of change refers to the first integral of the formula;

Thus we need to calculate this by the use of product formula;

The first differential of t^2 + 100 is 2t

while that of ln(t + 2) is 1/(t + 2)

P’(t) = 2t(ln (t+2)) + (t^2 + 100) (1/t+2)

Now, we substitute 2 for the value of t here.

P’(2) = 2(2)( ln (2 + 2) + (2^2 + 100)(1/(2+2))

P’(2) = 4 ln 4 + 104(1/4)

P’(2) = 4ln 4 + 26

P’(2) = 5.55 + 26 = 31.55 which is approximately 32

Answer:

B. [[0,4]

   [-6,1]

  [3,-4]]

Step-by-step explanation:

If you multiply the matrices, you get the answer.

Yes, B. Rising action is correct

Answer:

The horizontal distance from the center is 49.3883 feet

Step-by-step explanation:

The equation of an ellipse is equal to:

[tex]\frac{x^2}{a^{2} } +\frac{y^2}{b^{2} } =1[/tex]

Where a is the half of the wide, b is the high of the ellipse, x is the horizontal distance from the center and y is the height of the ellipse at that distance.

Then, replacing a by 106/2 and b by 33.9, we get:

[tex]\frac{x^2}{53^{2} } +\frac{y^2}{33.9^{2} } =1\\\frac{x^2}{2809} +\frac{y^2}{1149.21} =1[/tex]

Therefore, the horizontal distances from the center of the arch where the height is equal to 12.3 feet is calculated replacing y by 12.3 and solving for x as:

[tex]\frac{x^2}{2809} +\frac{y^2}{1149.21} =1\\\frac{x^2}{2809} +\frac{12.3^2}{1149.21} =1\\\\\frac{x^2}{2809}=1-\frac{12.3^2}{1149.21}\\\\x^{2} =2809(0.8684)\\x=\sqrt{2809(0.8684)}\\x=49.3883[/tex]

So, the horizontal distance from the center is 49.3883 feet

Answer:

6, -6, 6, -6 and 6.

Step-by-step explanation:

Given the recursion formula for a sequence

[tex]a_{n+1}=-a_n\\$where a_1=6\\[/tex]

The first five terms of the sequence are:

[tex]\text{First Term, }a_1=6\\$Second Term, a_2=a_{1+1}=-a_1=-6\\$Third term, a_3=a_{2+1}=-a_2=6\\$Fourth term, a_4=a_{3+1}=-a_3=-6\\$Fifth term, a_5=a_{4+1}=-a_4=6[/tex]

Therefore, the first five terms of the sequence:

[tex]a_1,a_2,a_3,a_4,a_5=6, -6, 6, -6$ and 6.[/tex]

Answer:

The answer is D.

Step-by-step explanation:

First, you have to convert the mixed number into improper fraction :

[tex]6 \frac{2}{3} [/tex]

[tex] = \frac{3 \times 6 + 2}{3} [/tex]

[tex] = \frac{20}{3} [/tex]

Next, you can divide it by cutting out the common factor :

[tex]15 \div \frac{20}{3} [/tex]

[tex] = 15 \times \frac{3}{20} [/tex]

[tex] = 3 \times \frac{3}{4} [/tex]

[tex] = \frac{9}{4} [/tex]

[tex] = 2 \frac{1}{4} [/tex]

The value of the expression after divide is,

⇒ 2 1/4

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The expression is,

⇒ 15 divided by 6 2/3

Now,

We can divide as;

⇒ 15 divided by 6 2/3

⇒ 15 ÷ 6 2/3

⇒ 15 ÷ 20/3

⇒ 15 × 3/20

⇒ 45/20

⇒ 9/4

⇒ 2 1/4

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Answer:

3

Step-by-step explanation:

6/4 (divide numerator and denominator each by 2)

= 3/2

= 3 x (1/2)

hence there are 3  halves in 6/4

Answer:

3

Step-by-step explanation:

To find out, we need to divide.

[tex]\frac{6}{4}[/tex] ÷ [tex]\frac{1}{2}[/tex]

When dividing fractions, you multiply the 1st term by the second term's reciprocal.

so

[tex]\frac{6}{4}[/tex] x 2

If you simplify you get [tex]\frac{6}{2}[/tex] or 3.

Answer: 12 hours

Step-by-step explanation:

Let x = time it takes to fill the pool if the inlet pipe and drain pipe are both open

1/6 = portion of pool filled per hour by the inlet pipe

1/12 = portion of pool emptied per hour by the drain

1/x = portion of pool filled per hour if the inlet pipe and drain are both open

Then, 1/6 - 1/12 = 1/x

Multiply by the LCD, 12x, to obtain

2x - x = 12

x = 12 hours

Answer:

2,322,775

Step-by-step explanation:

Given a1 = 4 and ai =ai-1 +11

when i = 2

a2 = a2-1+11

a2 = a1+11

a2 = 4+11

a2 = 15

when i = 3

a3 = a2+11

a3 = 15+11

a3 = 26

The sequence formed by a1, a2, a3... is am arithmetic sequence as shown;

4, 15, 26...

Sum of nth term of an arithmetic sequence = n/2{2a+(n-1)d}

a is the first term = 4

d is the common difference = 15-4 = 26-15 = 11

n is the number of terms.

Since we are to find the sum of the first 650 terms in the sequence, n = 650

S650 = 650/2{2(4)+(650-1)11}

S650 = 325{8+(649)11}

S650 = 325(8+7,139)

S650 = 325×7147

S650 = 2,322,775

Answer:

10 cm

Step-by-step explanation:

نستخدم فيثاغورس

ٲب²+ب ج²=ج ٲ²

ج ٲ²= 6²+8²

ج ٲ²= 100

ج ٲ= 10 سم

Answer:

The answer is true

Step-by-step explanation:

To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2

Answer:

[tex] E(X) = 7*0.18 +9*0.08 +11*0.09 +15*0.08 +17*0.41 =13.22[/tex]

And we can find the second moment with this formula:

[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i)[/tex]

And replacing we got:

[tex] E(X^2) = 7^2*0.18 +9^2*0.08 +11^2*0.09 +15^2*0.08 +17^2*0.41 =189.72[/tex]

And we can find the variance like this:

[tex] Var(X) = E(X^2) -[E(X)]^2= 189.72- (13.22)^2 =14.9516[/tex]

And the deviation would be:

[tex] Sd(X)= \sqrt{14.9516}= 3.867[/tex]

Step-by-step explanation:

For this case we have the following dataset given:

Payment     $7     $9     $11    $13    $15  $17

Probability 0.18  0.08  0.09  0.16  0.08   0.41

For this case we can calculate the mean with this formula:

[tex] E(X) = \sum_{i=1}^n X_i P(X_i)[/tex]

And replacing we got:

[tex] E(X) = 7*0.18 +9*0.08 +11*0.09 +15*0.08 +17*0.41 =13.22[/tex]

And we can find the second moment with this formula:

[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i)[/tex]

And replacing we got:

[tex] E(X^2) = 7^2*0.18 +9^2*0.08 +11^2*0.09 +15^2*0.08 +17^2*0.41 =189.72[/tex]

And we can find the variance like this:

[tex] Var(X) = E(X^2) -[E(X)]^2= 189.72- (13.22)^2 =14.9516[/tex]

And the deviation would be:

[tex] Sd(X)= \sqrt{14.9516}= 3.867[/tex]

Answer:

Bottom prism: 126*11=1386    

Top Prism: 2*45=90

Total volume: 1386+90= 1746 cubic cm

Answer:

Approximately 23,433 children will have cancer.

Step-by-step explanation:

3/1500 can be simplified to 1/500, which can also be written as 0.002. To find the number of children who have cancer, we do 11,721,722 * 0.002, which gives us 23,433.444 which we can round to 23,433.

Answer:

[tex]\frac{1}{4} x-2=10[/tex]

Step-by-step explanation:

Let x be that number.

[tex]\frac{1}{4} x-2=10[/tex]

If you want to find the number..

[tex]\frac{1}{4} x=10+2[/tex]

[tex]0.25x=12[/tex]

[tex]x=12/0.25[/tex]

[tex]x=48[/tex]

Answer:

462cm^3

Step-by-step explanation:

Volume of a pyramid = 1/3 × base area × height

Now the base is a rectangle with sides 7cm and 18cm; area of base is;

7 × 18 = 126cm^2

Therefore volume =

1/3 × 126 × 11 = 42 × 11= 462cm^3

Answer:

3 1/2

Step-by-step explanation:

7 1/4 - 3 3/4

Borrow 1 from the 7 in the form of 4/4

6 + 4/4 + 1/4 - 3 3/4

6 5/4 - 3 3/4

3 2/4

Simplify the fraction

3 1/2

Answer:

[tex]3 \frac{1}{2} [/tex]

Step-by-step explanation:

[tex]7 \frac{1}{4} - 3 \frac{3}{4} \\ \frac{29}{4} - \frac{15}{4} \\ = \frac{14}{4} \\ = \frac{7}{2} \\ = 3.5 = 3 \frac{1}{2} [/tex]

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Answer:

15

Step-by-step explanation:

The pattern is going by 15 because 10+15=25 and then continue going.

Answer:

15 is the answer

Step-by-step explanation:

Answer:

As you know, a year has around 365 + 1/4 days.

This means that in two years, we have:

365 + 356 + 1/4 + 1/4 = 730 + 1/2

and so on.

adding this up, when we have 4 years we have a full day extra, this is:

1460 + 1

When we divide 1461 by 4, we have 365 with a surpass of 1.

The rule used to keep the calendar in sync with this extra day is adding an extra day to each fourth year.

So each fourth year, we have an extra day in Februray (the Februray 29th), this is called a bisiest year.

The "math rule" used to know if a year is leap or not is:

if a year is not divisible by 4, then it is a common year

else if the year is not divisible by 100 then it is a leap year,

else if the year is not divisible by 400, then it is a common year

if not, the year is a leap year.

Where "year" represents the number of the year.

Answer:

a) Particle has a constant speed of 4, b) Velocity and acceleration vector are orthogonal to each other, c) Clockwise, d) False, the particle begin at the point (0,1).

Step-by-step explanation:

a) Let is find first the velocity vector by differentiation:

[tex]\vec v = \frac{dr_{x}}{dt} i + \frac {dr_{y}}{dt} j[/tex]

[tex]\vec v = 4\cdot \cos 4t\, i - 4 \cdot \sin 4t \,j[/tex]

[tex]\vec v = 4 \cdot (\cos 4t \, i - \sin 4t\,j)[/tex]

Where the resultant vector is the product of a unit vector and magnitude of the velocity vector (speed). Velocity vector has a constant speed only if magnitude of unit vector is constant in time. That is:

[tex]\|\vec u \| = 1[/tex]

Then,

[tex]\| \vec u \| = \sqrt{\cos^{2} 4t + \sin^{2}4t }[/tex]

[tex]\| \vec u \| = \sqrt{1}[/tex]

[tex]\|\vec u \| = 1[/tex]

Hence, the particle has a constant speed of 4.

b) The acceleration vector is obtained by deriving the velocity vector.

[tex]\vec a = \frac{dv_{x}}{dt} i + \frac {dv_{y}}{dt} j[/tex]

[tex]\vec a = 16\cdot (-\sin 4t \,i -\cos 4t \,j)[/tex]

Velocity and acceleration are orthogonal to each other only if [tex]\vec v \bullet \vec a = 0[/tex]. Then,

[tex]\vec v \bullet \vec a = 64 \cdot (\cos 4t)\cdot (-\sin 4t) + 64 \cdot (-\sin 4t) \cdot (-\cos 4t)[/tex]

[tex]\vec v \bullet \vec a = -64\cdot \sin 4t\cdot \cos 4t + 64 \cdot \sin 4t \cdot \cos 4t[/tex]

[tex]\vec v \bullet \vec a = 0[/tex]

Which demonstrates the orthogonality between velocity and acceleration vectors.

c) The particle is rotating clockwise as right-hand rule is applied to model vectors in 2 and 3 dimensions, which are associated with positive angles for position vector. That is: [tex]t \geq 0[/tex]

And cosine decrease and sine increase inasmuch as t becomes bigger.

d) Let evaluate the vector in [tex]t = 0[/tex].

[tex]r(0) = \sin (4\cdot 0) \,i + \cos (4\cdot 0)\,j[/tex]

[tex]r(0) = 0\,i + 1 \,j[/tex]

False, the particle begin at the point (0,1).

Answer:I think it -5 wait lemme check answer again

The solution to the inequality will be greater than or equal to –5. Then the correct option is B.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

3(x – 4) ≥ 5x – 2

Simplify the equation, then the solution to inequality will be

3(x – 4) ≥ 5x –2

3x – 12 ≥ 5x –2

5x – 3x ≤ – 12 + 2

2x ≤ – 10

x ≤ –5

The solution to the inequality will be greater than or equal to –5.

Then the correct option is B.

The correct equation is 3(x – 4) ≥ 5x – 2.

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Answer:

 A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, negative 1.5, 1.5, 3, 4.5.

Step-by-step explanation:

When the x-values are evenly spaced, a linear function will have evenly-space y-values.

In the first table, the y-differences are all +8.

In the second table, the y-differences are 0, 1.5, 1.5, so are not all the same.

In the third table, the y-differences are all -3.

The second table represents a non-linear function.

__

In the graph, you can see that the points from the second table (purple) are not on a straight line.

Answer:

B

Step-by-step explanation:

Answer:

[tex] \frac{19}{20} [/tex]

Step-by-step explanation:

[tex] \frac{7}{10} + \frac{1}{4} \\ \frac{14 + 5}{20} \\ = \frac{19}{20} [/tex]

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Answer:

H0: [tex] \sigma^2_1 = \sigma^2_2[/tex]

H1: [tex] \sigma^2_1 \neq \sigma^2_2[/tex]

The statistic would be given by:

[tex]F=\frac{s^2_2}{s^2_1}=\frac{10}{8}=1.25[/tex]

Step-by-step explanation:

Information given

[tex]n_1 = 60 [/tex] represent the sample size 1

[tex]n_2 =40[/tex] represent the sample size 2

[tex]s^2_1 = 8[/tex] represent the sample variance 1

[tex]s^2_2 = 10[/tex] represent the sample variance 2

The statistic to check the hypothesis is given by:

[tex]F=\frac{s^2_2}{s^2_1}[/tex]

Hypothesis to test

We want to test if the two variances are equal, so the system of hypothesis are:

H0: [tex] \sigma^2_1 = \sigma^2_2[/tex]

H1: [tex] \sigma^2_1 \neq \sigma^2_2[/tex]

The statistic would be given by:

[tex]F=\frac{s^2_2}{s^2_1}=\frac{10}{8}=1.25[/tex]

Answer:

The 95% confidence interval for the mean consumption of meat among people over age 29 is between 2.8 pounds and 3 pounds.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96*\frac{1.4}{\sqrt{2092}} = 0.1[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 2.9 - 0.1 = 2.8 pounds

The upper end of the interval is the sample mean added to M. So it is 2.9 + 0.1 = 3 pounds.

The 95% confidence interval for the mean consumption of meat among people over age 29 is between 2.8 pounds and 3 pounds.

Answer:

[tex]2.9-1.96\frac{1.4}{\sqrt{2092}}=2.84[/tex]    

[tex]2.9+1.96\frac{1.4}{\sqrt{2092}}=2.96[/tex]    

The confidence interval is given by [tex]2.84 \leq \mu \leq 2.96[/tex]

Step-by-step explanation:

Information given

[tex]\bar X=2.9[/tex] represent the sample mean

[tex]\mu[/tex] population mean

[tex]\sigma =1.4[/tex] represent the population standard deviation

n=2092 represent the sample size  

Confidence interval

The confidence interval is given by:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

Since the Confidence interval is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value would be [tex]z_{\alpha/2}=1.96[/tex]

Replacing the info we got:

[tex]2.9-1.96\frac{1.4}{\sqrt{2092}}=2.84[/tex]    

[tex]2.9+1.96\frac{1.4}{\sqrt{2092}}=2.96[/tex]    

The confidence interval is given by [tex]2.84 \leq \mu \leq 2.96[/tex]

Answer:

 Slope = 4.000/2.000 = 2.000

 x-intercept = 6/2 = 3

 y-intercept = -6/1 = -6.00000

Step-by-step explanation:

Step by step solution :

Step  1  : Equation of a Straight Line

Graph of a Straight Line

Calculate the Y-Intercept

Calculate the X-Intercept

Calculate the Slope

Answer for y=2x-6  is below

Answer:  

Slope = 4.000/2.000 = 2.000

 x-intercept = 6/2 = 3

 y-intercept = -6/1 = -6.00000

Hope this helps.

Answer:

V(speed)=3.5 mile per hour

Step-by-step explanation:

[tex]V=mile per hour[/tex]

[tex]V=\frac{7}{8}/ \frac{1}{4}[/tex]

[tex]V=\frac{7}{8}*\frac{4}{1}[/tex]

[tex]V=\frac{7}{8}*4[/tex]

[tex]V=3.5[/tex]