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The unit vector pointing in the same direction as vector 7 is u = (47/56, 33/56). False is the appropriate choice for the unit normal for the top half of the sphere S bounded by the curve C.

The surface S₁ is indeed the top half of a sphere with a radius of 3, and its boundary C is a circle of the same radius. S₂ is the flat face bounded by C. The vector field F has a divergence of -1 everywhere between S₁ and S₂. The value of the integral fF.ds is A, where A is an integer.

To find the unit vector u in the same direction as vector 7 = (47, 33), we divide each component by the magnitude of 7. The magnitude of 7 is sqrt(47² + 33²) = sqrt(2209 + 1089) = sqrt(3298) = 56. Therefore, u = (47/56, 33/56).

For the surface S bounded by the curve C: x² + y² = 16, the appropriate unit normal to choose points outward, away from the origin. Thus, the correct answer is False.

The statement regarding S₁ being the top half of a sphere of radius 3 and its boundary C being a circle of the same radius is true. S₂ is the flat face bounded by C.

Given that the divergence of vector field F is -1 everywhere between S₁ and S₂, the value of the integral fF.ds represents the flux of F across the surface S₁. The integral evaluates to A, where A is an integer. Unfortunately, the specific value of A is not provided in the question, so it cannot be determined without further information.

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Answer:

Robyn is 41years

Step-by-step explanation:

so Robyn=x

child=x-28

Robyn=x+1

child=x-28+1 =x-27

"Robyn will be three times as old as her child"

here multiply 3 by the child's age

child=3(x-27)

=3x-81

hence,x-1=3x-81. (group like terms)

x-3x=(-81-1)

-2x=-82 (divide both side by -2)

x=-82/-2

x=41

Therefore Robyn's age is 41

Answer:

  Robyn is 41

Step-by-step explanation:

You want to know Robyn's current age if she will be 3 times as old as her 28-year younger daughter in one year from now.

The difference in ages remains constant. When Robyn is 3 times as old as her daughter, the ratio of their ages is ...

  Robyn : daughter = 3 : 1

The difference in their ages is 3 -1 = 2 ratio units. Each ratio unit stands for 28/2 = 14 years, so Robyn's age of 3 ratio units represents 42 years.

That will be 1 year from now, so Robyn is 41.

1. 4

2. -4

3. -5

4. 8

When water is pumped out from well A in a square formed by wells A, B, C, and D, the drawdown at the center is 15 ft. If water is pumped out from A, B, and C while pumped into D, the drawdown at the center is uncertain.

In the given scenario, pumping water out only from well A causes a drawdown of 15 ft at the center of the square formed by wells A, B, C, and D. However, when water is simultaneously pumped out from wells A, B, and C, while being replenished at well D, determining the drawdown at the center becomes more complex. The drawdown at the center of the square will depend on various factors such as the rate of pumping, the permeability of the aquifer, the distance between the wells, and the properties of the surrounding geology. Without specific information regarding these factors, it is not possible to determine the exact drawdown at the center.

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1 solution of a triangle exists because all of the angles are less than 180 degrees and the sides and angles have non-negative values.

Therefore, there exists only one triangle.

The given values are:

a = √2, b = √7, and p = 105

The sine law is applied to determine the angle opposite to a. We know that sin(A)/a = sin(B)/b = sin(C)/c

where A, B, and C are the angles of a triangle, and a, b, and c are the opposite sides to A, B, and C, respectively.

Therefore, sin(A)/√2 = sin(B)/√7

We can now get sin(A) and sin(B) by cross-multiplication:

√7 * sin(A) = √2 * sin(B)sin(A) / sin(B) = √(2/7)

Using the sine law, we can now calculate the angle C:

sin(C)/p = sin(B)/b

Therefore, sin(C) = (105 sin(B))/√7

Using the equation sin²(B) + cos²(B) = 1, we can determine

cos(B) and cos(A)cos(B)

= √(1 - sin²(B)) = √(1 - 2/7)

= √(5/7)cos(A) = (b cos(C))/a

= (√7 cos(C))/√2Since sin(A)/√2

= sin(B)/√7sin(A)

= (√2/√7)sin(B)sin(A)

= (√2/√7) [√(1 - cos²(B))]

We can solve the equations above using substitution to find sin(B) and sin(A).

1 solution of a triangle exists because all of the angles are less than 180 degrees and the sides and angles have non-negative values.

Therefore, there exists only one triangle.

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The value of b is 3.

The value of c is 1/8.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 5 = 9 is an equation.

We have,

Two equations given are:

b = 24c ____(1)

(1/4)b + 4c = 5/4 _____(2)

Putting (1) in (2) we get,

(1/4)24c + 4c = 5/4

6c + 4c = 5/4

10c = 5/4

c = 5/40

c = 1/8

Putting c = 1/8 in (1) we get,

b = 24/8

b = 3

Thus,

b = 3.

c = 1/8.

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The circle is 360 degrees so,

360 degrees --> 4700 votes

36 degrees ---> x

4700*36 = 360*x

169,200 = 360*x

x= 169,200/360

x= 470

\( \frac{470}{4700} = 0.1 = 10\%\)

Answer:

Step-by-step explanation:

2z = 4a/m +3

 -3        -3

2z - 3 = 4a/m

 ×m        ×m

(2z -3)m = 4a

     ÷4      ÷4

[(2z -3)m]/4 = a

a = (2mz - 3m)/4

Answer:

11

Step-by-step explanation:

11

since it asks the absolute value of -11 it

will be 11 because in absolute value-for negatives it always positive.

Answer:

see attached

Step-by-step explanation:

Answer:

3/7

Step-by-step explanation:

the slope of the line is

-1 -6/ 3-0 = -7/3

the slope of the perpendicular line is:

3/7

Answer:

4.6 is your awnser hope this helps

Answer:

Hope you understand this

Step-by-step explanation:

HAVE A GOOD DAY!

Answer:

Option B is the right option.

solution,

<A=2x-9

<B=4x+2

<ACD=5x+13

The exterior angle of a triangle is sum of two opposite interior angles.

m<A+m<B=m<5x+13

\(or \: 2x - 9 + 4x + 2 = 5x +13 \\ or \: 2x + 4x - 9 + 2 = 5x + 13 \\ or \: 6x - 7 = 5x + 13 \\ or \: 6x - 5x = 13 + 7 \\ x = 20\)

Replacing value,

\(angle \: acd \\ = 5x + 13 \\ = 5 \times 20 + 13 \\ = 100 + 13 \\ = 113\)

Hope this helps....

Good luck on your assignment..

Answer:

300, percentage increased by 12% (percent) of its value = 336

Step-by-step explanation:

The amount of money in Iris's checking account can be modeled by a linear function of the form:

y = mt + b

where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.

In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:

y = 0.04t + 180

For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.

5. The solution to the differential equation (ex + y)dx + (2 + x + yey)dy = 0 with y(0) = 1 is y = 2e^(-x) – x – 1. 6. The solution to the differential equation (x + y)²dx + (2xy + x² – 1)dy = 0 with y(1) = 1 is y = x – 1.

5. To solve the differential equation (ex + y)dx + (2 + x + yey)dy = 0 with the initial condition y(0) = 1, we can use the method of exact differential equations. By identifying the integrating factor as e^(∫dy/(2+yey)), we can rewrite the equation as an exact differential. Solving the resulting equation yields the solution y = 2e^(-x) – x – 1.
To solve the differential equation (x + y)²dx + (2xy + x² – 1)dy = 0 with the initial condition y(1) = 1, we can use the method of separable variables. Rearranging the equation and integrating both sides with respect to x and y, we obtain the solution y = x – 1.
These solutions satisfy their respective initial conditions and represent the family of curves that satisfy the given differential equations.

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7.5 or 7 1/2 or 15/2
explanation:3 3/4 - -3 3/4 = 15/2

have great day… OR DIE BY MY BLADE <3 ^-^

Answer:

B

Step-by-step explanation:

60+40+x=180(angles in a triangle)

x= 180-100

x=80°

80+z=180(angles on a str line)

z= 100°

100+15+y=180(angles in a triangle)

y=180-115

y=65°

Answer:

c: x = 80, y = 65, z = 100

Step-by-step explanation:

The sum of all angles in a triangle is 180

so 40 + 60 + x = 180 and 15 + y + z = 180

40 + 60 + x = 180

100 + x = 80

x = 80

supplementary angles are equal to 180

x and z are supplementary

80 + z = 180

z = 100

15 + 100 + y = 180

115 + y = 180

y = 65

Answer:

the answer is 180miles between them

andi $8,$8,0xFF is the instructions that clears all the bits in register $8 except for the low order byte, which is unchanged.

The byte with the least amount of the value would be the low-order byte. For instance, a 16-bit int with the value 5,243 might be represented in hex as 0x147B. The low-order byte is 0x7B, whereas the high-order byte is 0x14. A word's bits are numbered 0 through 15, with bit 0 being the least important. The word's low byte, which contains bit 0, and high byte, which contains bit 15, are referred to as such. Byte ordering comes in two flavors. Big-endian format places the byte with the most important bit in the first memory location, followed by bytes whose importance decreases.

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Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

Answer:

the answer is x=−10

Step-by-step explanation:

hoped I helped:)

Answer:

4

Step-by-step explanation:

We plug x in as -5 so we have: |-5+1|

|-5+1| = |-4| = 4

l= 4.2 m = 4.2 * 100 = 420 cm

b = 1.4 m = 1.4*100 = 140 cm

h =1.2 m =1.2 *100 =120 cm

Volume of cuboid = l*b*h =  420 * 140 * 120  = 705600 cubic cm

Volume of cube = a*a*a = 20*20*20 = 8000 cubic cm

No.of cubes = Volume of cuboid / volume of cube

      = 705600 / 8000 = 882 cubes

or  420*140*120 / 20*20*20 = 42*14*12/2*2*2 = 21*7*6 = 882 cubes

a) the annual inflation rate is approximately 4.9%.

b) the monthly inflation rate is approximately 0.63%.

a. To find the annual inflation rate when given a monthly rate of 0.4%, you can use the formula: Annual Inflation Rate = (1 + Monthly Inflation Rate)^12 - 1.

Plugging in the values, we get:

Annual Inflation Rate = (1 + 0.004)^12 - 1 = 0.0491 or 4.9%

So, the annual inflation rate is approximately 4.9%.

b. To find the monthly inflation rate when given an annual rate of 8%, you can use the formula:

Monthly Inflation Rate = (1 + Annual Inflation Rate)^(1/12) - 1.

Plugging in the values, we get:

Monthly Inflation Rate = (1 + 0.08)^(1/12) - 1 = 0.0063 or 0.63%

So, the monthly inflation rate is approximately 0.63%.

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Yes, it is possible to solve the system of equations \(xy^2 + xzu + yv^2 = 3u^3yz + 2xv - u^2v^2 = 2\) for u(x, y, z) and v(x, y, z) near (x, y, z) = (1, 1, 1) and (u, v) = (1, 1).

To solve this system of equations, we need to eliminate one variable at a time. Let's start with eliminating v.

From the second equation, we can isolate v:
\(u^2v^2 = 2 - 3u^3yz - 2xv\)
\(v^2 = (2 - 3u^3yz - 2xv) / u^2\)

Now, substitute this expression for v^2 into the first equation:
\(xy^2 + xzu + y((2 - 3u^3yz - 2xv) / u^2) = 3u^3yz + 2x((2 - 3u^3yz - 2xv) / u^2)\)
Simplify this equation by multiplying through by u^2:
\(u^2xy^2 + u^2xzu + y(2 - 3u^3yz - 2xv) = 3u^5yz + 2x(2 - 3u^3yz - 2xv)\)
Expand and collect like terms:
\(u^2xy^2 + u^2xzu + 2y - 3uyzv - 2xyv = 3u^5yz + 4x - 6u^3xyz - 4x^2v\)

Rearrange the terms:
\(3u^5yz + 6u^3xyz - u^2xy^2 - 3uyzv + 2xyv - 2y + 4x - 4x^2v + u^2xzu = 0\)

Now, let's focus on finding ∂v/∂y at (x, y, z) = (1, 1, 1). To do this, we need to find the partial derivative of v with respect to y while keeping other variables constant.

Differentiating the equation with respect to y, we get:
\(6u^3xz - 3uzv + 2x\)= ∂v/∂y

Substituting (x, y, z) = (1, 1, 1), we have:
\(6u^3z - 3uz + 2\)= ∂v/∂y

Therefore, at (x, y, z) = (1, 1, 1), ∂v/∂y = \(6u^3z - 3uz + 2\).

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The given expression \(m^6p^{-3}v^{10} .\ m^2p^5v^2\) for all values of m, p, and v is equivalent to \(m^{8}p^{2}v^{12}\). Therefore, option D is the right choice for this question.

Monomials are algebraic expressions with single terms. They can be said to be specialized cases of polynomials.

We are given the algebraic expression - \(m^6p^{-3}v^{10}\) . \(m^2p^5v^2\)

To simplify it we will use the rules of the indices as follows -

\(a^{m}.\ a^{n} = a^{m+n}\)

Now,

\(m^6p^{-3}v^{10}\) . \(m^2p^5v^2\)

Segregating the like variables, we get,

= \((m^6.\ m^2) .\ (p^{-3}.\ p^{5}) .\ (v^{10}.\ v^{2})\)

by using the rules of indices, we will get,

= \((m^{6+2}) .\ (p^{-3+5}) .\ (v^{10+2})\)

= \((m^{8}) .\ (p^{2}) .\ (v^{12})\)

= \(m^{8}p^{2}v^{12}\)

Hence, the given expression \(m^6p^{-3}v^{10} .\ m^2p^5v^2\) is equivalent to \(m^{8}p^{2}v^{12}\).

Therefore, option D is the right choice for this question.

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Answer:

Step-by-step explanation:

\(9^{-4}\)

=\(\frac{1}{9^{4} }\)                   ∴     \(x^{-n} = \frac{1}{x^{n} }\)

=\(\frac{1}{9*9*9*9}\)

=\(\frac{1}{6561}\)