Consider the function f(x)=10^x . x->[infinity] As , what happens to
the instantaneous rate of change?

We cannot determine the expressions that can be used to find "m" from the given options as none of the options listed are in the format of an expression that could be used to solve for "m".

We would need additional information or context to determine what "m" represents and how it is related to the given options.

y-intercept= 0

asymptote =\(lim_{n}\)→-0 (8/x) = -∞

\(lim_{n}\)→+0 (8/x) = +∞

range = R : { x ∈ R / {0} }

What is Range ?

When the sample maximum and minimum are subtracted, the range of a collection of data is the difference between the greatest and lowest values. It uses the same units as the data to express itself.

I think the formula is:

f(x) = 8/x

(You wrote 8x; since a linear function has no asymptotes and you wrote 8x, I'm assuming the true function was 8/x.)

The amount that makes f(x) equal to 0 is the y-intercept.

Keep in mind that there is no value of x such that 8/x = 0 (because the quotient cannot be zero if the numerator is never zero).

Therefore, there is no y-intercept.

The asymmetry:

These are the four:

If the negative side of x tends to zero, then 8/x tends to negative infinity.

If x from the positive side approaches to zero, then 8/x tends to positive infinity.

These two asymptotes are expressed as follows:

\(lim_{n}\)→-0 (8/x) = -∞

\(lim_{n}\)→+0 (8/x) = +∞

Additionally, there are two cases where x tends to plus infinity (and 8/x goes to zero) and when x tends to minus infinity, where the function tends to zero once more. These two cases are denoted by the formulas:

\(lim_{n}\)→-∞ (8/x) = -∞

\(lim_{n}\)→∞ (8/x) = +∞

Lastly, the scope:

Only on limitations, y never reaches the following value:

y = 0

If so, the set of all real numbers excluding zero is the range, or

R : { x ∈ R / {0} }

Hence, y-intercept= 0

asymptote =\(lim_{n}\)→-0 (8/x) = -∞

\(lim_{n}\)→+0 (8/x) = +∞

range = R : { x ∈ R / {0} }

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Evidence points to the Egyptians using gypsum mortar – also known as plaster of Paris – in constructing pyramids during the Pharaonic period. The first Egyptologist to identify this method was Alfred Lucas in 1926.

Answer:

$1.81

Step-by-step explanation:

Dozen donuts cost 6.60 dollars

You will divide 12 by 6.60

you will get 1.81

Answer:

1.82 dollars per donuts

Step-by-step explanation:

you divide 12 by 6.60

which gets you 1.81 repeating so you round to the nearest cent

which is 1.82 per donut

Answer:

Monica = 48.50

Samuel = 24.25

Kara = 17.25

Step-by-step explanation:

First you write equations as you are reading the text:

m = 2s ("Monica earned twice as much as Samuel")

s = k+7 ("Samual earned 7 more than Kara")

m = 48.50

Next, you convert these equations to solve for s and k respectively.

So, if m=2s, then s=m/2:

s = m/2 = 24.25

Likewise, if s=k+7, then k=s-7

k = s-7 = 17.25

The difference between greatest and least is 48.50 - 17.25 = 31.25

Answer:

31.4

Step-by-step explanation:

2*Pi*5 equals 31.4 ft correct me if I’m wrong

The triple integral of the divergence over the region E is equal to the surface integral of F over the boundary surface of E, we have verified the Divergence Theorem for the given vector field F and the region E.

To verify the Divergence Theorem, we need to compute both sides of the equation for the given vector field F and the region E bounded by the paraboloid Z = 4 - X^2 - y^2 and the xy-plane.

First, we compute the divergence of F:

div F = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z

= 4x + 2

Next, we compute the triple integral of the divergence over the region E:

∫∫∫E div F dV = ∫∫∫E (4x + 2) dV

Since the region E is bounded by the xy-plane and the paraboloid, we can integrate over z from 0 to 4 - x^2 - y^2, over y from -√(4 - x^2) to √(4 - x^2), and over x from -2 to 2:

∫∫∫E div F dV = ∫-2^2 ∫-√(4 - x^2)√(4 - x^2) ∫0^4-x^2-y^2 (4x + 2) dz dy dx

= 128/3

Now, we compute the surface integral of F over the boundary surface of E:

∫∫S F dS = ∫∫P F dP + ∫∫D F dD

where P is the surface of the paraboloid and D is the disk at the bottom of E.

On the paraboloid, the normal vector is given by n = (∂f/∂x, ∂f/∂y, -1), where f(x,y) = 4 - x^2 - y^2. Therefore, we have:

∫∫P F dP = ∫-2^2 ∫-√(4 - x^2)√(4 - x^2) (2x^2, 2xy, 4 - x^2 - y^2) ∙ (∂f/∂x, ∂f/∂y, -1) dA

= ∫-2^2 ∫-√(4 - x^2)√(4 - x^2) (2x^2, 2xy, 4 - x^2 - y^2) ∙ (2x, 2y, 1) dA

= 16π/3

On the disk at the bottom, the normal vector is given by n = (0, 0, -1). Therefore, we have:

∫∫D F dD = ∫-2^2 ∫-√(4 - x^2)√(4 - x^2) (2x^2, 2xy, 0) ∙ (0, 0, -1) dA

= 0

Thus, we have:

∫∫S F dS = ∫∫P F dP + ∫∫D F dD = 16π/3 + 0 = 16π/3

Since the triple integral of the divergence over the region E is equal to the surface integral of F over the boundary surface of E, we have verified the Divergence Theorem for the given vector field F and the region E.

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The total surface integral is:

∫∫S F dS = ∫∫S F dS + ∫∫S F dS

= 8π/3 + 0

= 8π/3

To verify the Divergence Theorem, we need to show that the triple integral of the divergence of F over the region E is equal to the surface integral of F over the boundary of E.

First, let's compute the divergence of F:

div F = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z

= 4x + 2y + 3

Next, we'll compute the triple integral of div F over E:

∭E div F dV = ∫∫∫ (4x + 2y + 3) dz dy dx

The region E is bounded by the paraboloid Z = 4 - X^2 - y^2 and the xy-plane. To determine the limits of integration, we need to find the intersection of the paraboloid with the xy-plane:

4 - x^2 - y^2 = 0

x^2 + y^2 = 4

This is the equation of a circle with radius 2 centered at the origin in the xy-plane.

So, the limits of integration are:

x: -2 to 2

y: -√(4 - x^2) to √(4 - x^2)

z: 0 to 4 - x^2 - y^2

∭E div F dV = ∫∫∫ (4x + 2y + 3) dz dy dx

= ∫-2^2 ∫-√(4-x^2)^(√(4-x^2)) ∫0^(4-x^2-y^2) (4x + 2y + 3) dz dy dx

= 32/3

Now, let's compute the surface integral of F over the boundary of E. The boundary of E consists of two parts: the top surface of the paraboloid and the circular disk in the xy-plane.

For the top surface of the paraboloid, we can use the upward-pointing normal vector:

n = (2x, 2y, -1)

For the circular disk in the xy-plane, we can use the upward-pointing normal vector:

n = (0, 0, 1)

The surface integral over the top surface of the paraboloid is:

∫∫S F dS = ∫∫D F(x, y, 4 - x^2 - y^2) ∙ n dA

= ∫∫D (4x + 2y, 2xy, 4 - x^2 - y^2) ∙ (2x, 2y, -1) dA

= ∫∫D (-4x^2 - 4y^2 + 4) dA

= 8π/3

The surface integral over the circular disk in the xy-plane is:

∫∫S F dS = ∫∫D F(x, y, 0) ∙ n dA

= ∫∫D (2x^2, 2xy, 0) ∙ (0, 0, 1) dA

= 0

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Answer:

a. 0, -6, -18, -21, -90

b. 3, 0, -6, -18, -42

c. A starting point of any number ≥ 6 will result in a sequence of positive values

Step-by-step explanation:

Here the sequence is governed by the rule:
\(\sf a_{n} = 2(a_{n-1} - 3)\)
\(\textsf {where $a_n$ is the nth term and $a_{n-1}$ is the previous term}}\)

1) Starting with a₁ = 0 we get
a₂ = 2(a₁ - 3) = 2(0 - 3) = -6
a₃ = 2(a₂ - 3) = 2(-6 -3) = 2(-9) = -18
a₄ = 2(a3 - 3) = 2(-18 - 3) = 2(-21) = -42
a₅ = 2(a₄ - 3) = 2(-42- 3) = 2(-45) = -90

So the first 5 numbers in the sequence starting with 0 are:
0, -6, -18, -21, -90

2) I will approach this slightly differently

We have the relationship:
\(\sf a_{n} = 2(a_{n-1} - 3)\)

Expanding the brackets we get
\(\sf a_{n} = 2a_{n-1} - 6\)

We have a₁ = 3
a₂ = 2(a₁) - 6 = 2(3) - 6 = 6 - 6 = 0
a₃ = 2(a₂) - 6 = 2(0) - 6 = -6
a₄ = 2(a₃) - 6 = 2(-6) - 6 = -18
a₅ = 2(a₄ ) - 6 = 2(-18) - 6 = -42

The sequence starting with 3 is:
3, 0, -6, -18, -42

Both methods work exactly the same, some students find expanding the brackets easier to deal with

c. We can see that as a₁ increases, the number of negative numbers decreases by 2. So, in order for all numbers to be positive (> 0) we should start with a sufficiently large number so that all numbers are positive

The smallest such number is 6.
When a₁ = 6, the sequence is all 6s because
a₂ = 2(6) - 6 = 12 - 6 = 6

So the next number is a₃ = 12(6) - 6 = 6 and so on

So any starting point ≥ 6 will yield positive values. At 5 the sequence would be: 5, 4, 2, -2, -10 so starting point of 5 will not work

The number of regions created when constructing a Venn diagram with three overlapping sets is 8.

In a Venn diagram, each set is represented by a circle, and the overlapping regions represent the elements that belong to multiple sets.

When three sets overlap, there are different combinations of elements that can be present in each region.

For three sets, the number of regions can be calculated using the formula:

Number of Regions = 2^(Number of Sets)

In this case, since we have three sets, the formula becomes:

Number of Regions = 2^3 = 8

So, when constructing a Venn diagram with three overlapping sets, there will be a total of 8 regions formed.

Each region represents a unique combination of elements belonging to different sets.

These regions help visualize the relationships and intersections between the sets, providing a graphical representation of set theory concepts and aiding in analyzing data that falls into multiple categories.

Therefore, the correct answer is 8.

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Answer:

x=22

Step-by-step explanation:

(5x+4)+44+x = 180. reason [being co-interior angle)

48+6x = 180

6x = 132

x=22

Answer:

i think 6 is ans

hope u like it

Answer:

$17.50

Step-by-step explanation:

(70/2)/2

Answer:

a. i. x + y = 180  (1) and  x - 4y = 5   (2)

ii. The two acute angles are 35° each and the two obtuse angles are 145° each.

Step-by-step explanation:

a. The measures of the obtuse angles in the isosceles trapezoid are five more than four times the measures of the acute angles. Write and solve a system of equations to find the measures of all the angles.

i. Write a system of equations to find the measures of all the angles.

Let x be the obtuse angles and y be the acute angles.

Since we have two obtuse angles at the top of the isosceles trapezoid and two acute angles at the bottom of the isosceles trapezoid, and also, since the sum of angles in a quadrilateral is 360, we have

2x + 2y = 360

x + y = 180  (1)

Its is also given that the measures of the obtuse angles in the isosceles trapezoid are five more than four times the measures of the acute angles.

So, x = 4y + 5   (2)

x - 4y = 5   (2)

So, our system of equations are

x + y = 180  (1) and  x - 4y = 5   (2)

ii. Solve a system of equations to find the measures of all the angles.

Since

x + y = 180  (1) and  x - 4y = 5   (2)

Subtracting (2) from (1), we have

x + y = 180  (1)

-

x - 4y = 5   (2)

5y = 175

dividing both sides by 5, we have

y = 175/5

y = 35°

From (1), x = 180° - y = 180° - 35° = 145°

So, the two acute angles are 35° each and the two obtuse angles are 145° each.

After 5 years, Mr. Taylor will earn approximately $36,770.76, rounded to the nearest cent.

Mr. Taylor's salary starts at $32,500 per year, and he receives a 2.5% increase in his salary each year.

To calculate his earnings after 5 years, we need to calculate the cumulative increase in his salary over the 5-year period.

To find Mr. Taylor's earnings after 5 years, we can use the formula for compound interest.

In this case, the starting amount is $32,500, the annual interest rate is 2.5%, and the time period is 5 years.

First, we calculate the increase in salary for each year:

Year 1: $32,500 + 2.5% of $32,500 = $32,500 + $812.50 = $33,312.50

Year 2: $33,312.50 + 2.5% of $33,312.50 = $33,312.50 + $832.81 = $34,145.31

Year 3: $34,145.31 + 2.5% of $34,145.31 = $34,145.31 + $853.63 = $34,998.94

Year 4: $34,998.94 + 2.5% of $34,998.94 = $34,998.94 + $874.97 = $35,873.91

Year 5: $35,873.91 + 2.5% of $35,873.91 = $35,873.91 + $896.85 = $36,770.76

Therefore, after 5 years, Mr. Taylor will earn approximately $36,770.76, rounded to the nearest cent.

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Q.2: A review of the t-test on the significance of individual independent variable suggests that, based on the p-values. None of the independent variables could be retained. This is because if the p-value is high, it means the significance is low.

Q3: Choose the right option below. Based on the full regression model involving all of the independent variables. VIF for Size = 5.3352, VIF for Fireplace = 10.1873, VIF for bedrooms = 2.7885.

Q.4: Based on VIF values, there is concern for collinearity in this dataset. True

Q5: Based on the normal probability plot, the normality assumption seems to be met. True

Q7: Based on conducting residual analysis the model seems. Adequate.

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Answer:

14 would be your answer :)

Answer:

the 24th day they'll be there

Step-by-step explanation:

4 8 12 16 20 24

6 12 18 24

To find the probability of rolling six standard, six-sided dice and getting six distinct numbers, we need to calculate the total number of possible outcomes and the number of outcomes that satisfy the given condition.

Total Number of Outcomes:

The total number of possible outcomes when rolling six dice is 6^6, which is 46,656. Each die has six possible outcomes (1, 2, 3, 4, 5, or 6), and there are six dice being rolled.

Number of Outcomes with Six Distinct Numbers:

To get six distinct numbers when rolling six dice, each number must be different from the others. We can choose any six numbers from 1 to 6, and there are 6! (6 factorial) ways to arrange them on the six dice.

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

Probability of Getting Six Distinct Numbers:

To find the probability of rolling six standard, six-sided dice and getting six distinct numbers, we divide the number of outcomes with six distinct numbers by the total number of possible outcomes:

P(six distinct numbers) = number of outcomes with six distinct numbers / total number of outcomes

P(six distinct numbers) = 720 / 46,656

P(six distinct numbers) = 5 / 324

Therefore, the value of the probability is 5/324 or approximately 0.0154.

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Answer:

I am not certain but I think it is C

Step-by-step explanation:

since your slope will be x and it's not negative so it's 4x+8 since the y is at the right

The value of dy/dt is 0 units per second.

a) Given: y= √x Differentiating with respect to t, we get; \(dy/dt = 1/2√x * dx/dt\)

On substituting the values of x and dx/dt in the above equation, we get; dy/dt = 1/2 * √16 * 3= 1.5 units per second

Therefore, the value of dy/dt is 1.5 units per second.

b) Given: \(y= √x\)

Differentiating with respect to t, we get;

\(dy/dt = 1/2√x * dx/dt\)

Let us assume that y = k, where k is a constant that can be determined by the given value of x.

Substituting the values of x and y in the equation, we get; 25 = √x

Therefore, x = 625dx/dt

= 0

(Given)\(dy/dt = 1/2√x * dx/dt\)

dy/dt = 1/2√625 * 0

= 0

Therefore, the value of dy/dt is 0 units per second.

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The final answer for solving the equation (-2-1)--[] A is A = 0. This means that the matrix A is a zero matrix, where all elements are equal to zero.

To solve for the matrix A in the equation (-2-1)--[] A = [], we need to find the values that satisfy the equation.

The given equation represents a matrix equation, where the left-hand side is a 2x2 matrix (-2-1) and the right-hand side is an unknown matrix A.

To solve for A, we need to perform matrix algebra. In this case, we can multiply both sides of the equation by the inverse of the given matrix (-2-1) to isolate A. The inverse of a 2x2 matrix can be found by swapping the diagonal elements and changing the sign of the off-diagonal elements, divided by the determinant of the matrix.

After finding the inverse of (-2-1), we can multiply it with both sides of the equation. The resulting equation will be A = (inverse of -2-1) * [], where [] represents the zero matrix.

Performing the matrix multiplication will give us the values of A that satisfy the equation.

Please note that without the specific values provided for the empty matrix [], we cannot provide the exact numerical solution for A. However, by following the steps outlined above, you can solve for A using the given matrix equation.

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Assignment Submission & Scoring Assignment Submission For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer. Assignment Scoring Your last submission is used for your score. 5. [-/10 Points] DETAILS LARLINALG8 2.1.053. MY NOTES Solve for A (-2-1)--[] A = Submit Answer View Previous Question Question 5 of 5

Answer:

\(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\)

Step-by-step explanation:

Integrate v(t) with respect to time

\(\displaystyle \int(3t^3+30t^2+5)\,dt\\\\=\frac{3}{4}t^4+10t^3+5t+C\)

Plug-in initial condition to get C

\(\displaystyle s(0)=\frac{3}{4}(0)^3+10(0)^3+5(0)+C\\\\3=C\)

Thus, the position function is \(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\) given the velocity function and initial condition.

Answer:

m<M is 98°............

The prove of ∠1 equal to ∠2 is shown below.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

⇒ AB = AC, AD = AE and DC = EB

Now,

In ΔDBC and ΔEBC;

⇒ DC = EB   (Given)   ..(i)

Since,  AB = AC

So, the ΔABC is a isosceles triangle.

Hence, ∠DBC = ∠ ECB   ..(ii)

Here,  AB = AC and AD = AE

So, BD = EC   ..(iii)

Hence, By the condition (i), (ii) and (iii);

By SAS condition,

⇒ ΔDBC ≅ ΔEBC

Hence, We get;

⇒ ∠1 = ∠2

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Answer:

a. 0

b. 4^1

c. 14

d. 8

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(a^{m}*a^{n}=a^{m+n}\\\\\frac{a^{m}}{a^{n}}=a^{m-n}\\\\(a^{m})^{n}=a^{m*n}\\\\a) 3^{5}*3^{x} = 3^{3}*9=3^{3}*3^{2}\\\\ 3^{5+x} =3^{3+2}\)

Compare the exponents,

5 +x = 5

     x = 5-5

      x = 0

\(b) \frac{4^{x}*4^{8}}{4^{2}}=(4^{7})^{1}\\\\4^{x+8-2}=4^{7*1}\\4^{x + 6}=4^{7}\)

Compare the exponents,

x +6 = 7

    x = 7-6

    x = 1

\(c)\frac{a^{8}*a^{5}}{a^{2}}=\frac{a^{x}}{a^{2}}\\\\a^{8+5-2}=a^{x-2}\\\\a^{11}=a^{x-2}\)

Compare the exponents,

x - 2 = 11

     x = 11+2

    x = 13

\(d)\frac{(5^{3})^{x}}{5^{6}}=5^{10}*5^{8}\\\\5^{3x-6}=5^{10+8}\\\\5^{3x-6}=5^{18}\)

Compare the exponents,

3x -6= 18

3x = 18 + 6

3x = 24

  x = 24/3

x = 8

Answer:

78.55cm^2

Step-by-step explanation:

Given data

DIameter of pie= 20 cm

Radius of pie= 10cm

Area of pie= πr^2

Area= 3.142*10^2

Area= 3.142*100

Area= 314.2 cm^2

Hence one fourth  of 314.2 cm^2 is

= 314.2/4

= 78.55cm^2

Therefore the area of the sector is 78.55cm^2

Answer:

a^2+a-6

Step-by-step explanation:

i have attached your answer

Let's solve figure by figure

Figure A

This figure has a total of 5 sides, therefore it is a pentagon.

Figure B

This figure has a total of 8 sides, therefore it is an octagon.

Figure C

This figure has a total of 3 sides, therefore it is a triangle.

According to the answer table, it would be

Pentagon: Figure A

Octagon: Figure B

Hexagon: None