Use logarithmic differentiation to find the derivative of the function. y = 3x + 5 (2x − 7)^4

The answer is 6.85.

Consider, x-y axis, and side of equilateral triangle is ' a '.

Given,

\($$\begin{aligned}&A P=3 \text { units } \\&B P=2 \text { units } \\&C P=4 \text { units }\end{aligned}$$\)

Let x and y are point in x-y axis.

Using, distance formula here

\($A P^{2}=(x-0)^{2}+(y-0)^{2}$\)

\($3^{2}=x^{2}+y^{2}$\)

\($x^{2}+y^{2}=$\)__________(i)

\($p c^{2}=(x-a)^{2}+(y-0)^{2}$$4^{2}=x^{2}-2 a x+a^{2}+y^{2}$\)

from (i)

\($16=x^{2} 9-2 a x+a^{2}$\)

\($2 a x=a^{2}+9-16$\)

\($\left[x=\frac{\left(a^{2}-7\right)}{2 a}\right]$\)

\($B p^{2}=\left(x-\frac{a}{2}\right)^{2}+\left(y-\frac{\sqrt{3}}{2} a\right)^{2}$\)

\($2^{2}=x^{2}-a x+\frac{a^{2}}{4}+y^{2}-\sqrt{3} a b y+\frac{3}{4} a^{2}$\)

\($4=\left(x^{2}+y^{2}\right)+\frac{a^{2}+3 a^{2}}{4}-a\left(\frac{a^{2}-7}{2 a}\right)-\sqrt{3} a y$\)

from (i)

\($4=9+a^{2}-a^{2}+7-\sqrt{3} a y$\)

\($\sqrt{3} a y=16-4$\)

put x and y in equarion_______(i)

\($\left(\frac{12}{\sqrt{3} a}\right)^{2}+\left(\frac{a^{2}-7}{2 a}\right)^{2}=9$\)

\($\frac{144}{3 a^{2}}+\frac{\left(a^{2}-7\right)^{2}}{4 a^{2}}=9$\)

\($144 \times 4+3\left(a^{2}-7\right)^{2}=12 \times 9 a^{2}$\)

\($576+3\left(a^{2}-7\right)^{2}=108 a^{2}$\)

\(put $a^{2}=t$$$576+3(t-7)^{2}=108 t$$\)

\($\begin{aligned} 576+3\left(t^{2}-14 t+49\right) &=108 t \\ 576+3 t^{2}-42 t+147 &=108 t \end{aligned}$\)

\($3 t^{2}-150 t+429=0$$t^{2}-50 t+143=0$$t=50 \pm \sqrt{50^{2}-4 \times 143}$\)

\(t=\frac{50 \pm \sqrt{1928}}{2}t=\frac{50 \pm 43.91}{2}\)

\(t=\frac{50 \pm 43.91}{2}\\t=46.9545, \quad t=3.0455\)

\($\begin{array}{ll}a^{2}=46.9545, \\ a=\sqrt{46.9545}, & a^{2}=3.0455 \\ a, a=1.745\end{array}$\)

\($a=6.85$\)

for this point P is outside Therefore, it is not consider as solution (because in question inside point ls mention)

\(a=6.85 units\)

What is equilateral triangle?

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Answer:

idk

Step-by-step explanation:

idk just responding

for points

Answer:

120 miles

Step-by-step explanation:

If 1 inch = 20 miles, you can multiply both sides by 6 to figure out how many miles 6 inches represent.

The distance from home plate to second base is 180 feet, which is double the distance from home plate to first base.

A baseball diamond is a square with four bases, with home plate in the middle. 90 feet separate first base from home plate, and 90 more feet separate first base from second base. Therefore, the total distance from home plate to second base is twice that distance, or 180 feet. The same applies to all of the bases; the distance between them is always 90 feet, so the total distance from home plate to any base is twice that of the distance from home plate to first base. This means that the distance from home plate to second base, third base, and home plate is all 180 feet.

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It is reasonable for Stacy to use a normal model for the sampling distribution of the sample proportion. This is because, according to the Central Limit Theorem,

when the sample size is large enough (typically considered to be at least 30), the sampling distribution of the sample proportion will be approximately normal, regardless of the shape of the population distribution.

In Stacy's case, she plans on surveying a random sample of students, which implies that she will have a sufficiently large sample size. Therefore, the conditions for using a normal model are satisfied.

In conclusion, Stacy can use a normal model for the sampling distribution of the sample proportion in her survey for the final project.

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The 14th term of the geometric sequence 10, 20, 40, ... is 81920.

"A geometric sequence is a special type of sequence. It is a sequence in which every term (except the first term) is multiplied by a constant number to get its next term."

The geometric sequence formulas include the formulas for finding its nth term and the sum of its n terms. We will see the geometric sequence formulas related to a geometric sequence with its first term 'a' and common ratio 'r' (i.e., the geometric sequence is of form \(a, ar, ar^{2},ar^{3} ,.............\)). Here are the geometric sequence formulas.

\(a_{n}=ar^{n-1}\)

Given geometric sequence

10, 20, 40, .........

From the given sequence

\(a_{1} = 10\), \(a_{2} = 20\), \(a_{3} = 40\)

Using the formula \(a_{n}=ar^{n-1}\)

⇒ \(a_{4} = 10(2)^{3} =80\)

⇒ \(a_{5} = 10(2)^{4} =160\)

⇒ \(a_{6} = 10(2)^{5} =320\)

⇒ \(a_{7} = 10(2)^{6} =640\)

⇒ \(a_{8} = 10(2)^{7} =1280\)

⇒ \(a_{9} = 10(2)^{8} =2560\)

.

.

.

⇒ \(a_{14} = 10(2)^{13} =81920\)

Hence, the 14th term of the geometric sequence 10, 20, 40, ... is 81920.

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The true statements are (A) 30×400 ml equal the total number of milliliters for 30 bowls of soup

(B) 30 bowls of soup hold 12,000 ml, which is same as 12 Litres

(C) Noah can multiply the number of bowls of soup by 1,000 to find the number of litres

(D) If each family member has 2 bowls of soup , Noah need to make 24 litres of soup

There are 30 people and each person is served soup in a 400 ml bowl, so the total amount of soup needed is 30 × 400 ml = 12,000 ml.

Option A is true

30 bowls of soup hold 30 × 400 ml = 12,000 ml, which is the same as 12 litres (since 1 litre = 1,000 ml).

Option B is true

Since 1 litre = 1,000 ml

Noah can multiply the number of bowls of soup by 1,000 to find the number of litres.

For example, 30 bowls of soup hold 12,000 ml = 12 litres.

Option C is true

If each family member has 2 bowls of soup, then the total amount of soup needed is

30 × 2 × 400 ml

= 24,000 ml, which is 24 litres (since 1 litre = 1,000 ml).

Option D is true.

Noah needs to make 24 litres of soup, and each pot contains 6 litres of soup.

Therefore, he would need to make 24 ÷ 6 = 4 pots of soup to serve each family member 2 bowls of soup.

Option E is false.

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Noah is making soup for a family reunion of 30 people. Each pot he makes contains 6 liters of soup. He uses bowl that 400mL to serve the soup to his family

Select all the true statements

(A) 30×400 ml equal the total number of milliliters for 30 bowls of soup

(B) 30 bowls of soup hold 12,000 ml, which is same as 12 Litres

(C) Noah can multiply the number of bowls of soup by 1,000 to find the number of litres

(D) If each family member has 2 bowls of soup , Noah need to make 24 litres of soup

(E) Noah would need to make 2 pots of soup for each family member to have 2 bowls of soup

Every month, the number of people who receive the email is multiplied by a factor of 8.

We have the following information is:

Venera sent a chain letter to her friends, asking them to forward the letter to more friends.

The relationship between the elapsed time t, in months, since Venera sent the letter, and the number of people, P(t), who receive the email is modeled by the following function:

\(P(t) =2^\\3t+7\)

Every month, the number of people who receive the email is multiplied by a factor will be

For t = 2, we have

P(2) = 2³⁽²⁾ ⁺⁷

P(2) = 2¹³

For t = 3, we have

P(3) = 2³⁽³⁾⁺⁷

P(3) = 2¹⁶

Calculate the \(\frac{P(3)}{P(2)}\)

⇒ \(\frac{P(3)}{P(2)}\)

⇒ 2¹⁶ / 2¹³

⇒ 2³

⇒ 8

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Complete question is:

Venera sent a chain letter to her friends, asking them to forward the letter to more friends.

The relationship between the elapsed time t, in months, since Venera sent the letter, and the number of

people, P(t), who receive the email is modeled by the following function:

3t+7

P(t) = 2

Complete the following sentence about the monthly rate of change in the number of people who receive

the email.

Round your answer to two decimal places.

Every month, the number of people who receive the email is multiplied by a factor of

The value of x that satisfies the equation is x = 15/8, which is equivalent to 1.875.

To solve the equation (2/3)x - (1/5)x = x - 1 and find the value of x, we can follow these steps:

Combine like terms on the left side of the equation:

(2/3 - 1/5)x = x - 1

Find a common denominator for the fractions on the left side. The common denominator for 3 and 5 is 15, so we rewrite the equation as:

(10/15 - 3/15)x = x - 1

Simplify the left side of the equation:

(7/15)x = x - 1

To eliminate the fraction, we can multiply both sides of the equation by the denominator of the fraction, which is 15:

15 * (7/15)x = 15 * (x - 1)

This simplifies to:

7x = 15x - 15

Subtract 15x from both sides of the equation to isolate the x term:

7x - 15x = -15

Simplifying further:

-8x = -15

Divide both sides of the equation by -8 to solve for x:

x = (-15) / (-8)

Simplifying the division:

x = 15/8

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The steady-state solution of the heat conduction equation refers to the temperature distribution that remains constant over time. This occurs when the heat flow into a system is balanced by the heat flow out of the system.

To find the steady-state solution of the heat conduction equation, follow these steps:

1. Set up the heat conduction equation: The heat conduction equation describes how heat flows through a medium and is typically given by the formula:

  q = -k * A * dT/dx,

  where q represents the heat flow, k is the thermal conductivity of the material, A is the cross-sectional area through which heat flows, and dT/dx is the temperature gradient in the direction of heat flow.

2. Assume steady-state conditions: In the steady-state, the temperature does not change with time, which means dT/dt = 0.

3. Simplify the heat conduction equation: Since dT/dt = 0, the equation becomes:

  q = -k * A * dT/dx = 0.

4. Apply boundary conditions: Boundary conditions specify the temperature at certain points or surfaces. These conditions are essential to solve the equation. For example, you might be given the temperature at two ends of a rod or the temperature at the surface of an object.

5. Solve for the steady-state temperature distribution: Depending on the specific problem, you may need to solve the heat conduction equation analytically or numerically. Analytical solutions involve techniques like separation of variables or Fourier series expansion. Numerical methods, such as finite difference or finite element methods, can be used to approximate the solution.

It's important to note that the exact method for solving the heat conduction equation depends on the specific problem and the boundary conditions given. However, the general approach is to set up the heat conduction equation, assume steady-state conditions, simplify the equation, apply the boundary conditions, and solve for the steady-state temperature distribution.

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⇒ To find the equation of the straight line we have to first calculate the slope/gradient of the line .

⇒To calculate the slope of the line you use the gradient formula below:

\(m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\\)

⇒Calculating the slope of the line let us  plug in the points of our choice from the graph and simplify.

\(m=\frac{4-1}{8-4} \\m=\frac{3}{4\\} \\m=\frac{3}{4}\)

⇒Note m is just a a letter of alphabet that represents the slope of the line.

⇒The slope of the line is \(\frac{3}{4}\)

⇒ The general equation to calculate the straight line equation is

y=mx+c where y is the y coordinate

x is the x-coordinate

m is the slope

c is the y-intercept.

I will use any point (x,y) ,note you can use any point as you will still get the same value c

I will use the point (4,1) from the graph.

\(1=4(\frac{3}{4} )+c\\1=3+c\\1-3=c\\c=-2\)

∴From the known values of the general equation

\(y=\frac{3}{4} x-2\)  is our equation.

Forming a graph to visually investigate data before performing regression or time series analysis is for the most part optional.

While it is not strictly required, it is highly recommended and often considered a best practice. Visualizing data through graphs provides valuable insights and helps in understanding the underlying patterns, trends, and relationships present in the data. It allows us to identify outliers, detect seasonality or cyclic behavior, observe any non-linearities, and assess the overall suitability of the data for the chosen analysis technique.

Graphs also enable us to make informed decisions about data preprocessing, model selection, and the need for any transformations. While modern computing speeds have made it easier to perform complex analyses, the visual exploration of data remains an important step in the data analysis process, aiding in better interpretation and enhancing the overall quality of the analysis.

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The best graphical representation to display the data on the GPA of 318 students at East River High School would be a histogram.

A histogram is a graphical representation of data that groups data into bins or intervals and displays the frequency of occurrences of data within each bin. In this case, the bins would represent GPA ranges, and the frequency would represent the number of students falling within each GPA range.

A histogram is a good choice for displaying this data because it allows the viewer to see the distribution of GPA scores across the student population. It provides a visual representation of how many students fall within certain GPA ranges and can help identify trends in the data.

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Answer:

-1

Step-by-step explanation:

2 * -1 = -2

Then, -2 / 2  = 1

Answer:

Step-by-step explanation:

We are given that T varies as the square root of the ratio of s and t, and we are trying to find the value of T when s=33 and t=18.

The relationship between T, s and t can be represented by the following equation:

T = k * √(s/t)

Where k is a constant.

We are given that when S=36, t=16, T=18. We can use this information to find the value of k.

We know that T = k * √(s/t)

and, T = 18 when s=36, t=16.

So we can substitute these values in the equation

18 = k * √(36/16)

Solving for k, we get:

k = 18/2 = 9

Now that we know the value of k, we can use it to find the value of T when s=33 and t=18.

T = k * √(s/t) = 9 * √(33/18) = 9 * √(11/6) = 9 * √(11/6)

The value of T when s=33, t=18 is 9 * √(11/6),

It is not possible to give the exact value of T because the value of the square root of (11/6) is not a whole number.

By simplifying  45y/30y (7x+49)  this  we get 3 / 2(7x + 49).

45y/30y (7x+49)

45y / 30y(7x +49) : 3 / 2(7x + 49)

45y / 30y(7x + 49)

45y / 30(7x + 49)

Factor the number :45 = 15 . 3

=15.3 / 30(7x + 49)

Factor the Number : 30 = 15 . 2

15.3 / 15.2(7x + 49)

Cancel the common factor : 15

= 3 / 2(7x + 49).

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The factors of the expression (x³ - 6x² + 3x + 10) are (x + 1), (x - 2), and (x - 5).

We are given a mathematical expression. The expression is cubic in nature. We need to find the factors of the algebraic expression. Let the expression be represented by the variable "E". The expression consists of three terms. Hence, the expression is trinomial. The expression is given below.

E = x³ - 6x² + 3x + 10

One of the factors in the expression is already given. The given factor is (x + 1).

Now we will perform the long division method on the expression to break it into the given factor and a quadratic expression.

E = (x + 1)(x² - 7x + 10)

Now we will factorise the quadratic expression.

E = (x + 1)[x² - 2x - 5x + 10]

E = (x + 1)[x(x - 2) - 5(x - 2)]

E = (x + 1)(x - 2)(x - 5)

We cannot simplify and factorise the expression any further.

Hence, the factors of the expression are (x + 1), (x - 2), and (x - 5).

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Answer:

x > 12, so the answer is the last one or D

Step-by-step explanation:

2/3x − 5 > 3

Step 1: Add 5 to both sides.

2/3x − 5 + 5 > 3 + 5

2/3x > 8

Step 2: Multiply both sides by 3/2.

2/3x * (3/2) > 8 * (3/2)

x > 12

> = open circle

< = open circle

≤ = closed circle

≥ = closed circle

Answer:

l = 40 m and b = 30 m

Step-by-step explanation:

Let the length and breadth of a rectangle be 4x and 3x.

We know that,

The perimeter of a rectangle is given by :

P = 2(l+b)

140 = 2(4x+3x)

70 = 7x

x = 10

Length, l = 4x = 4(10) = 40 m

Breadth, b = 3x= 3(10) = 30 m

So, the length and breadth of a rectangle are 40 m and 30 m respectively.

Answer:

10

Step-by-step explanation:

2.5 plus 2.5 is 5 and 5 times 2 is 10, so 2.5 times 4 is 10.

The value of the given expression is 10.

We are given that;

The expression= 2.5 x 4

Now,

To multiply 2.5 by 4, we can use the distributive property of multiplication.

This means that we can split 2.5 into 2 and 0.5, and then multiply each part by 4 separately.

2.5 x 4 = (2 + 0.5) x 4

= (2 x 4) + (0.5 x 4)

= 8 + 2

= 10

So, 2.5 x 4 = 10.

Therefore, by algebra the answer will be 10.

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The equation of the line that is perpendicular to line y = 7x/4+7 is y = -4x/7+12/7 and the equation of the line that is parallel to this line is y = 7x/4+11.

According to the question,

We have the following information:

y = 7x/4+7

Now, the slope of this line is 7/4 which will be the slope of the parallel line and the slope of the perpendicular line will be -4/7 (-1/m).

Points through line is passing = (-4,4)

x' = -4 and y' = 4

Now, we know that following formula is used to find the equation of the line:

(y-y') = m(x-x')

Perpendicular line:

y-4 = -4/7(x+4)

y-4 = -4x/7-16/7

y = -4x/7-16/7+4

y = -4x/7+12/7

Parallel line:

y-4 = 7/4(x+4)

y-4 = 7x/4+7

y = 7x/4+7+4

y = 7x/4+11

Hence, the equation of the line that is perpendicular to line y = 7x/4+7 is y = -4x/7+12/7 and the equation of the line that is parallel to this line is y = 7x/4+11.

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Answer:

3/4

Step-by-step explanation:

slope = rise/run

rise = change in y

run = change in x

Use the given points, (02, 0) and (2, 3).

To go from (-2, 0) to (2, 3), go up 3.

rise = 3

Then go right 4.

run = 4

slope = rise/run = 3/4

Answer: 3/4

Answer:

-16 -14 -12

Step-by-step explanation:

This is the answer because if you subtract -18 from 2, you would get -16 and so on and so on.

Answer:

9 laps

Step-by-step explanation:

75% of something is the same as three-fourths, or multiplying by 0.75

12 x 0.75 = 9

or you can divide by 4 and then multiply by three if you know what to separate the original number into

12/4 = 3     3 x 3 = 9

If the parachutist's elevation changes by -143ft in 13 seconds, then the change in the parachutist's elevation each second is -11 ft/s.

To find the change in the parachutist's elevation each second, follow these steps:

Therefore, the change in the parachutist's elevation each second is -11 feet/s.

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Answer:

68

Step-by-step explanation:

In this case, angle P and angle M are equal to each other. So we can set up the equation like this:

4x+36=6x-2

Then we can start to simplify and match up like terms:

2+36=6x-4x

Then add or subtract the like terms:

38=2x

Then, divide both sides by 2:

x=19

So we can insert 19 for x for both expressions:

Angle P: 112

Angle M: 112

So since every quadrilateral adds up to 360, we can subtract 2(112) from 360:

360-2(112)

360-224

=136

Since angle Q and N should be equal, we can divide 136 by 2 to get the measure for angle N and angle Q:

136/2=68

So the measure of angle N is 68

Answer:

x=3

Step-by-step explanation:

7x-3=18

7x=18+3

7x=21

x=3

Answer:

To obtain the g function, move f upward by 5 units and to the left by 3 units.

Step-by-step explanation:

from khanacademy

There should be training and validation sets as both of them have respective contribution in developing the multiple linear regression model.

There are many variables that measure levels of industrialization that have positively correlated. In

There is a positive relationship between the INDUS, NOX and TAX as Boston has high proportion of non-retail businesses and this would lead to high taxes and pollution levels in the region.

The relationship between the dependent and independent variables is shaped in part by the two data sets.

The model is fitted using the training data, and the regression coefficients (β0, β1, …, βp.) are estimated. This will assist us in forecasting the coefficients necessary to establish the relationship between the variables.

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6.1 Predicting Boston Housing Prices

a. Why should the data be partitioned into training and validation sets?

Which predictors are likely to be measuring the same thing among the 14 predictors? Discuss the relationships among INDUS, NOX, and TAX.