Consider the graph of the function f(x)=10^x


which statment describes a key feature of function g if g(x)=f(x+4)

The surface of the solid is bounded by Calculate the cylinder y² + 2² = 4 and the planes is 24π.  Option a is the correct answer.

To calculate the surface integral, we'll use the divergence theorem as mentioned earlier. The divergence of the vector field F is given by:

div(F) = (3y²) + (e²) + (3z²)

Now, we need to evaluate the triple integral of the divergence of F over the volume enclosed by the solid.

The solid is bounded by the cylinder y² + z² = 4 and the planes x = 0 and x = 1. This represents a cylindrical region extending from x = 0 to x = 1, with a radius of 2 in the y-z plane.

Using cylindrical coordinates, we have:

x = ρcos(θ)

y = ρsin(θ)

z = z

The limits of integration are:

ρ: 0 to 2

θ: 0 to 2π

z: -2 to 2

The volume element in cylindrical coordinates is: dV = ρdzdρdθ

Now, we can write the triple integral as follows:

∭ div(F) dV = ∫∫∫ (3y² + e² + 3z²) ρdzdρdθ

Performing the integration, we get:

∫∫∫ (3y² + e² + 3z²) ρdzdρdθ

= ∫₀² ∫₀² ∫₋²² (3(ρsin(θ))² + e² + 3z²) ρdzdρdθ

Simplifying the integrand further:

= ∫₀² ∫₀² ∫₋²² (3ρ²sin²(θ) + e² + 3z²) ρdzdρdθ

Now, let's evaluate the triple integral using these limits and the simplified integrand:

∫₀² ∫₀² ∫₋²² (3ρ²sin²(θ) + e² + 3z²) ρdzdρdθ

= 24π

Therefore, the result of the surface integral is 24π. The correct option is option a.

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Fundamental theorem of arithmetic states that each positive integer n is greater than 1 represented by unique set of prime numbers.

Explanation:

Fundamental theorem of arithmetic states that all the positive integer n is greater than 1 represented by multiples of prime numbers or the number itself is a prime number.

For example :

Let us consider 56 be a integer greater than 1

56 = 2 × 2 × 2 × 7

2 and 7 both are prime numbers

another example :

29 = 29 × 1

29 itself is a prime number.

Factorization of the given numbers itself prove the fundamental theorem of arithmetic.

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The cost of each music video is $1.99.

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

Given total cost of 2 music videos, a TV series and a movie is $42.95

and TV series cost 2 times as much as the movie,

cost of the movie = $12.99

cost of  TV series = 2*12.99

cost of  TV series = $25.98

let the cost of a video be x

so according to condition,

2x + cost of  TV series + cost of the movie = $42.95

2x + 25.98 + 12.99 = 42.95

2x = 42.95 - 25.98 - 12.99

2x = 3.98

x = 3.98/2

x = $1.99

Hence the cost of a music video is $1.99.

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the curl of the vector field f is (0, 0, 8y).

To compute the curl of a vector field, we use the following formula:

curl(f) = (∂f_z/∂y - ∂f_y/∂z) i + (∂f_x/∂z - ∂f_z/∂x) j + (∂f_y/∂x - ∂f_x/∂y) k

where i, j, and k are the unit vectors in the x, y, and z directions, respectively.

In this case, the vector field is given by f = (x^2 - y^2) i + 6xy j.

Let's compute each partial derivative separately:

∂f_z/∂y = 0

∂f_y/∂z = 0

∂f_x/∂z = 0

∂f_z/∂x = 0

∂f_y/∂x = 6y

∂f_x/∂y = -2y

Therefore, the curl of the vector field f is:

curl(f) = (0 - 0) i + (0 - 0) j + (6y - (-2y)) k

= 8y k

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Answer:

7/12 chance

Step-by-step explanation:

(1 2 3 4 5 6)

(1 2 3 4 5 6)

All the possibilities:

(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)

(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)

(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)

(1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)

(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)

(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)

There are 18 odd sums.

(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)

(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)

(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)

(1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)

(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)

(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)

There are 3 possibilities whose sums add up to 10.

Since there are 36 total possibilities and 21 numbers that fit the rule of having an odd sum or a sum of 10. There is a 21/36 chance or simplified, 7/12 chance.

The given side lengths of AC, BC, and EF, of the similar triangles, using the ratio of similarity between segments of similar figures, gives;

The measure of side DF as 15 centimeters

When two figures are similar, the corresponding side pairs have the same ratio of one to the other.

The given information on the two triangles are;

Triangle ∆ABC is similar to triangle ∆DEF

Triangle ∆ABC and triangle ∆DEF are right triangles

The length of segment AC = 9 centimeter

Length of segment BC = 15 centimeters

In triangle ∆DEF, we have;

Length of segment EF = 25 centimeters

Required;

The length of segment DF

Solution;

By comparison, the corresponding sides of the two triangles are;

AC corresponds to DF

BC corresponds to EF

In similar triangles, the ratio of the corresponding sides are the same, which gives;

\( \displaystyle{ \frac{AC}{DF} = \frac{BC}{EF} }\)

\( \displaystyle{ \frac{9}{DF} = \frac{15}{25} }\)

\( \displaystyle{ DF = \frac{9 \times 25}{15} = 15 }\)

The measure of side DF is 15 centimeters

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Answer:

-9.25

Step-by-step explanation:

-5.75 - 3.5

-9.25

\(\implies {\blue {\boxed {\boxed {\pink {\sf { \:- 9 \frac{1}{4} (or) \:- 9.25 }}}}}}\)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

\( - 5 \frac{3}{4} - 3 \frac{1}{2} \)

➺\( \: \frac{ - 23}{4} - \frac{7}{2} \)

➺\( \: \frac{ - 23}{4} - \frac{7 \times 2}{2 \times 2} \)

➺\( \: \frac{ - 23 - 14}{4} \)

➺\( \frac{ - 37}{4} \)

➺\( \: - 9 \frac{1}{4} \)

➺\( \: -9.25\)

\(\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}\)

Answer:

x=−1/2+1/2√17 or x=−1/2+−1/2√17

Step-by-step explanation:

Answer:

y = 3x + 7

Step-by-step explanation:

As we move from (2, 13) to (5, 22), x (the "run") increases by 3 and y (the "rise") increases by 9.  Thus, the slope, m, must be m = rise / run = 9/3, or 3.

Then we have y = 3x + b and must find b.  Subbing 2 for x and 13 for y, we get

13 = 3(2) + b, so that b must be 7.

The desired equation is y = 3x + 7.

Answer:

Finance charge = $200

Step-by-step explanation:

Cost of the T.V. = $1160

Steve did the down payment = $200

Monthly payment done by Steve = $22.5

Duration for the periodic payments = 2.5 years

Number of periodic payments to be done = 12 × 2.5

                                                                      = 30

Amount paid in periodic payments = Number of periodic payments done × amount paid in each month

= 30 × $55.25

= $1657.5

Total payment done = Down payment + Amount paid in periodic payments

                                  = $200 + $1657.5

                                  = $1857.5

Therefore, finance charges = Total payments done - cost of T.V.

                                              = 1857.5 - 1657.5

                                              = $200

Answer:

PT 1: C

PT 2: B

Step-by-step explanation:

In order to find the volume of a cone use equation

\(V=\pi r^2\frac{h}{3}\)

To find the volume of a cylinder use equation

\(V=\pi r^2h\)

Step-by-step explanation:

There are 3 cubes in the solid's length, 2 in its width, and 3 in its height. Therefore, the number of cubes = length * width * height = 3*2*3 = 18

The volume of a small cube , for a length l, is l³. The length is (1/3)m, so the volume is (1/3)³ = 1/27 m³

volume of solid = number of cubes * area of each cube = 1/27 * 18 = 18/27 m³. This is because we have to figure out the volume of 18 cubes together, and we can just add each cube to the volume 18 times for our answer

A is the correct answer

(i) lim [2 F(x) - 3 G(x)] = 5

(ii) lim [F(x)]³ + lim [G(x)]² = 9

In the given problem, we are asked to find the limits of two expressions involving the functions F(x) and G(x).

In part (i), we have the expression 2 F(x) - 3 G(x). To find its limit, we evaluate the individual limits of F(x) and G(x) and then substitute them into the expression. The limit of F(x) is given as 3, and the limit of G(x) is given as -4. Substituting these values into the expression, we get 2(3) - 3(-4) = 5.

In part (ii), we are asked to find the limit of [F(x)]³ + [G(x)]². Again, we evaluate the individual limits of F(x) and G(x) and substitute them into the expression. The limit of F(x) is given as 3, and the limit of G(x) is given as -4. Substituting these values into the expression, we get (3)³ + (-4)² = 9.

These calculations are based on the Limit Principles, which state that the limit of a sum or difference of functions is equal to the sum or difference of their limits, and the limit of a constant times a function is equal to the constant times the limit of the function.

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Answer:

18

Step-by-step explanation:

125 = 7x - 1 ...... because if the two lines are parallel alternate interior angles are congruent

125 + 1 = 7x

126 = 7x

\( \frac{126}{7} = \frac{7x}{7} \)

x = 18

hope it helps

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Answer:

x=9

Step-by-step explanation:

9 to the power of 6 is 531441

9 to the power of 3 is 729

531441 divided by 729 is 729

a third root of 729 is 9 because 9 times 9 times 9 is 729

so x is 9

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Answer:

Step-by-step explanation:

I think it's X9?

Answer: $105

Step-by-step explanation:

origional price multiplied by discount = x/ 100

150 x 30 = 4500/ 100= 45$ off

150- 45= 105

The amount of yellow paint Curt and Melanie should use is 0.45 quarts so that they can make 1.5 quarts bucket of seafoam green paint.We can use per cent equation.

Given that to make 1.5 quarts bucket of seafoam green paint Curt and Melanie have to mix 70 parts blue paint and 30 parts yellow paint.If 100 percent represent total paint then for 1.5 quarts we have to find the proportion of yellow paint.Let it be x.

30%  / 100% =30 / 100 = x / 1.5 quarts.

We can reduce the equation further,

0.3  = x / 1.5.

0.3 * 1.5 = x

x = 0.45

We can also find blue paint proportion similar by substituting 30 per cent to 70 per cent.

As a result of our calculation, we found the amount of yellow paint to be 0.45 quarts.

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Answer:

Step-by-step explanation:

Answer:

A. Add 1/6 to both sides.

Step-by-step explanation:

Hope it helps

Step-by-step explanation:

-Multiply inside the brackets

-Add like terms ( Or in this case move it to the others side to find p)

-Add

- Then do some substitution to check for the answers

If gasoline costs $1.95 per gallon $0.52 is its cost per liter?

One gallon of gasoline costs $1.95. To find the cost per liter, we need to convert gallons to liters. The conversion factor between gallons and liters is 1 gallon = 3.78541 liters.

So, to convert gallons to liters, we multiply the number of gallons by 3.78541.

In this case, the cost of one gallon of gasoline is $1.95. To find the cost per liter, we need to convert $1.95 from dollars per gallon to dollars per liter.

To do this, we divide $1.95 by the conversion factor between gallons and liters:

$1.95 / 3.78541

= $0.52/liter.

Therefore, the cost of one liter of gasoline is $0.52.

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Answer:

Original: $733 million

Sequel: $860 million

Step-by-step explanation:

Let's say the original movie grossed x dollars. Since the sequel grossed 127 million more than that, we can write the expression x + 127 to represent the sequel.

Their total is 1593 million, so let's add them up:

x + (x + 127) = 1593

2x + 127 = 1593

2x = 1466

x = 1466/2 = 733

To find the sequel gross amount, add 127 to 733:

127 + 733 = 860

So, the original movie grossed $733 million, while the sequel grossed $860 million.

Since 4 is a divisor of 28 and 20, we will have to:

\( \bold{28 = 4 * 7}\)

\( \bold{20 = 4 * 5}\)

Subtracting member by member the previous equalities we will have:

\( \bold{28 - 20 = 4*7 - 4*5}\)

Taking out a common factor in the previous expression will result:

\( \bold{28 - 20 = 4(7 - 5) = 4 * 2}\)

That is to say, that 4 is a divisor of 28 - 20 since it is contained exactly 2 times in said difference.

Answer:

1. Room size (length * width) for carpet

2. From window top to floor for curtains

Step-by-step explanation:

(a) In the theory of learning, the rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized. This is also a first-order linear differential equation of the form dy/dx + p(x)y = q(x), which can be solved using an integrating factor.

Suppose M denotes the total amount of a subject to be memorized and A(t) is the amount memorized in time t.

To determine a differential equation for the amount A(t), we first note that the rate of memorization is proportional to the amount left to be memorized. This means that the rate of memorization is given by dA/dt = k(M − A), where k is a constant of proportionality. This equation can be rearranged as:

dA/dt + kA = kM

This is a first-order linear differential equation of the form dy/dx + p(x)y = q(x), which can be solved using an integrating factor.

(b) Now assume that the rate at which material is forgotten is proportional to the amount memorized in time t. To determine a differential equation for the amount A(t) when forgetfulness is taken into account, we use a similar approach. Let b be a constant of proportionality that represents the rate of forgetting. Then, the rate of change of A is given by:

dA/dt = k(M − A) − bA

which simplifies to:

dA/dt + (k + b)A = kM

This is also a first-order linear differential equation of the form dy/dx + p(x)y = q(x), which can be solved using an integrating factor.

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Answer:

The correct answer would be A. I have attached a picture of how to solve it below. Please have a look at it and give the crown.

Answer:

The average wage in the us increase by about five percent

Step-by-step explanation:

The 1.05 represents the rate of increasing average wages in the US, and it depicts that average wages are increasing by 5 %.

As it is clear from the term per cent means measuring anything per hundred. For example, you get marks per 100 marks, so you get the percentage.

Given the expression,

\(1350(1.05)^t\)

As it is clear that this is the formula for the amount,

\(A = P \times (1+r/100)^t\)

Here, the value of the middle expression is 1.05, which can be written as 1 + 5 / 100.

Therefore, it is the rate of increasing wages in the US, and it depicts that the wages are increasing by 5 %.

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