use implicit differentiation to find an equation of the tangent line to the graph of the equation at the given point.1 ln 7xy = e7x − y, (1/7, 1)

Answer:C

Step-by-step explanation:

The values of the composite functions are

From the question, we have the following functions that can be used in our computation:

f(x) = 2x³ - 10x + 3, h(x) = x - 5 and g(x)=2x

Using the above as a guide, we have the following:

a) (f + h)(x) = 2x³ - 10x + 3 + x - 5 = 2x³ - 9x - 2

b) (f - h)(x) = 2x³ - 10x + 3 - x + 5 = 2x³ - 11x + 8

c) (fg)(x) = f(g(x)) = f(2x) = 2(2x)³ - 10(2x) + 3 = 16x³ - 20x + 3

d) (fh)(x) = f(h(x)) = f(x - 5) = 2(x - 5)³ - 10(x - 5) + 3

e) (f/g)(x) = f(x)/g(x) = (2x³ - 10x + 3)/(2x)

The above are the values of the composite functions

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Answer:

4.7 miles per day

Step-by-step explanation:

35.8 - 17 = 18.8 miles

So, she needs to ride 18.8 miles in 4days

18.8 divided by 4 = 4.7 miles per day

So, she needs to ride 4.7 miles each day to meet her goal.

34 questions was answered correctly by the student, while 6 questions were incorrect

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

A math test has 40 questions. A student answers 85% of the questions correctly.

Number of questions answered correctly = 85% of total questions = 0.85 * 40 questions = 34 questions

Number of questions not answered correctly = 40 - 34 = 6 questions

34 questions was answered correctly by the student.

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In the exponential function y = 3 × q⁵ the starting value is 3.

The formula for an exponential function is f(x) = aˣ, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

Given is an exponential function is -

y = 3 × q⁵

The exponential function is written in the form abˣ.

Here, a is considered to be the initial value, b is considered to be the base and x represents the growth factor.

So, the initial or starting value in function y = 3 × q⁵ is -

a = 3

Hence, the starting value is 3.

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The values mean, variance and standard deviation for Pomona and Anaheim are compared to identify the deviation in the air quality level.

The air quality index values for various area of southern California. Here the random variable (X) represents the air quality index values for Pomona.

From the given information the data values are 28, 42, 58, 48, 45, 55, 60, 49 and 50

Range = max. value - min.value

           = 60 - 28 = 32

mean for air quality index for Pomona = x'

                                            = sum of the values/total no.of samples

                                            = (∑Xi )/ (n)

                                            = 435/9 = 48.33

sample variance , ∑(Xi - x')/ n-1 = 92.75

standard deviation is the sq.root of variance , i.e √92.75

                                            = 11.66

Use mean 48.3, variance 136 and standard deviation 11.66 to compare with the air quality in Pomona and Anaheim.

The air quality index reading for Pomona mean is equal to Anaheim. That is, The Pomona mean (48.3) is equal to the Anaheim mean (48.3).

The variance and sample standard deviation for Anaheim are 136 and 11.66, respectively.

The variance and sample standard deviation for Pomona are 92.75 and 9.63, respectively.

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The equation of the circle,

x² + (y – 3)² = 36.

The correct option is A.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.

And the general formula of the circle,

(x – h)²+ (y - k)² = r²,

where (h, k) is the center and r is the radius of the circle.

Given:

A circle that has a diameter of 12 units and a center that lies on the y-axis.

That means, radius = 6.

And h = 0.

From the given choices:

Now, the equation of the circle,

x² + (y – 3)² = 36.

Therefore, x² + (y – 3)² = 36 is the equation.

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The increasing and decreasing behavior of the function f(x) on the given intervals is as follows:

On the interval (-∞, -3), f(x) is increasing.

On the interval (-3, 0), f(x) is decreasing.

On the interval (0, 3), f(x) is increasing.

On the interval (3, ∞), f(x) is decreasing.

We have,

To determine the increasing and decreasing behavior of the function f(x) = x / (x² - 9) on the given intervals, we can evaluate the sign of the derivative of the function.

Taking the derivative of f(x) with respect to x and simplifying, we have:

[tex]f'(x) = (-x^2 + 9 - x(2x)) / (x^2 - 9)^2\\= (-x^2 + 9 - 2x^2) / (x^2 - 9)^2\\= (-3x^2 + 9) / (x^2 - 9)^2[/tex]

To identify the increasing and decreasing behavior, we need to examine the sign of f'(x) on each interval.

For the interval (-∞, -3):

Plugging in a value less than -3, such as -4, into f'(x) yields a positive result.

Plugging in a value between -3 and 0, such as -2, into f'(x) gives a negative result.

Therefore, f'(x) is positive for x < -3 and negative for -3 < x < 0, indicating that f(x) is increasing on the interval (-∞, -3) and decreasing on the interval (-3, 0).

For the interval (-3, 3):

Plugging in a value between -3 and 0, such as -2, into f'(x) yields a negative result.

Plugging in a value between 0 and 3, such as 1, into f'(x) gives a positive result.

Therefore, f'(x) is negative for -3 < x < 0 and positive for 0 < x < 3, indicating that f(x) is decreasing on the interval (-3, 0) and increasing on the interval (0, 3).

For the interval (3, ∞):

Plugging in a value between 3 and 4, such as 3.5, into f'(x) yields a positive result.

Plugging in a value greater than 4, such as 5, into f'(x) gives a negative result.

Therefore, f'(x) is positive for 3 < x < 4 and negative for x > 4, indicating that f(x) is increasing on the interval (3, 4) and decreasing on the interval (4, ∞).

Thus,

The increasing and decreasing behavior of the function f(x) on the given intervals is as follows:

On the interval (-∞, -3), f(x) is increasing.

On the interval (-3, 0), f(x) is decreasing.

On the interval (0, 3), f(x) is increasing.

On the interval (3, ∞), f(x) is decreasing.

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The bond would pay back its face value of $1000 at the end of the 10 years.

The face value of the bond is the amount the bond will be worth when it matures, and it is also known as the "par value" or the "principal amount."

In this case, the face value of the bond is $1000, so at the end of the 10 years, the bond will pay back $1000 in principal to the bondholder.

The coupon rate, which is 4% in this case, determines the amount of the annual interest payment that the bondholder will receive.

Therefore, regardless of the changes in interest rates, the bond will pay back its face value of $1000 at the end of the 10 years.

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The area under the curve y = |x + 3| above the x-axis and between x = -6 and x = 0 is 9 units^2.

What is the area under the curve?

The area under a curve refers to the area between a curve and the -axis. This area could be entirely above the -axis, entirely below the -axis, or a combination of above and below the -axis. In calculus, the area under a curve is a visual representation of an integral.

The graph of y = |x + 3| is a piecewise linear function that starts at (3,0), increases linearly as x decreases to -3, reaches a maximum value of 3 at x = -3, and then decreases linearly as x decreases further to -6. The area under the curve y = |x + 3| above the x-axis and between x = -6 and x = 0 can be calculated by finding the area of two triangular regions. One triangular region is formed by the line y = x + 3 from x = -6 to x = -3 and the x-axis, and the other triangular region is formed by the line y = -(x + 3) from x = -3 to x = 0 and the x-axis. The area of each triangular region can be calculated using the formula 1/2 * base * height, and the total area is the sum of the areas of the two triangular regions.

So, The area under the curve y = |x + 3| above the x-axis and between x = -6 and x = 0 is 9 units^2.

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The top interval in a frequency table for a set of scores ranging from a high of X = 75 to a low of X = 23 would be 73-75.

This is because the bottom interval is 18-23, and the intervals in a frequency table are generally of equal size. This means that the highest interval must be of a similar size, and would thus be 73-75. The purpose of a frequency table is to show how often values from a numerical data set occur.

The data is usually divided into intervals of equal size, such as the 18-23 interval mentioned in this scenario. The intervals are usually calculated by subtracting the lowest value from the highest value, and then dividing the result by the number of intervals desired. In this case, the highest interval must be of equal size to the 18-23 interval, resulting in a range of 73-75.

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Answer: the meaning of the variable m is Meagan, M is a shortened version to show that 3 is how much money she has.

Step-by-step explanation:

hope this helps ^^

Answer:

−x^2+x−2

Step-by-step explanation:

Answer:

B. 4w + 10 = 46

Step-by-step explanation:

If we let l be the length of the rectangle and w its width

Fact 1: A rectangle's length is 5 centimeters greater than its width
This translates to l = w + 5 (1)

Fact 2: he perimeter of the rectangle is 46 centimeters
Perimeter is given by 2(l + w)
So fact 2 translates to:
2(l + w) = 45
2l + 2w = 46  (2)

Substitute l = w + 5 from (1) for l in (2):

2(w + 5) + 2w = 46
2w + 10 + 2w = 46

4w + 10 = 46

This is Option B

Answer:

C. 2w + 5 = 46

Reason why is because a rectangle has 4 sides, but you only want to multiply length times the width, to get the perimeter, which is why 2w in the equation is correct.

It also says 5 centimeters greater, the is why it would be + 5 instead of 10.

Step-by-step explanation:

Hope it helps! =D

An engineer is designing a fuel tank in the shape of a cylinder, the approximate radius of the cylinder is 8.2 inches.

Volume:

V = πr²h

Height:

h = 2r

V = πr²h

V= πr²(2r)

V= 2πr³

And we know that the volume must be 3,500 in³, now we can replace that and solve for R, we will get:

V= πr²h

3500 = 3.14 x 2 x (r)³

r = 8.2 inch

The cylinder's approximate radius must be 8.2 inches.

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterised as an infinitely curved surface.

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[tex]\huge\begin{array}{ccc}x=1;&y=\frac{\sqrt3}{2}\end{array}[/tex]

Look at the picture.

We have:

[tex]a=\dfrac{1}{2}\\\\2a=x\\\\a\sqrt3=y[/tex]

Therefore:

[tex]x=2\cdot\dfrac{1}{2}\to\boxed{x=1}\\\\y=\dfrac{1}{2}\cdot\sqrt3\to\boxed{y=\dfrac{\sqrt3}{2}}[/tex]

The result of the original integral is:

∫15sin3(x)cos2(x)dx = (15/2)(cos(3x + 2x) + cos(3x - 2x)) + 2C

What is the integration?

In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data.

The integral of the product of sine and cosine functions can be evaluated using the identity:

sin(a)cos(b) = (1/2)(sin(a + b) + sin(a - b))

Therefore, we can rewrite the integrand as:

15sin3(x)cos2(x) = (15/2)sin(3x + 2x) + (15/2)sin(3x - 2x)

Now, we can integrate each of the two terms separately:

∫(15/2)sin(3x + 2x)dx = (15/2)cos(3x + 2x) + C

∫(15/2)sin(3x - 2x)dx = (15/2)cos(3x - 2x) + C

Therefore, the result of the original integral is:

∫15sin3(x)cos2(x)dx = (15/2)(cos(3x + 2x) + cos(3x - 2x)) + 2C

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Answer:

20 dumplings.

Step-by-step explanation:

Keith can make 16 / (4/5) = 16 * 5/4 = 20 dumplings.

C. The matrix is the augmented matrix of a consistent linear system for every value of h.

What is augmented matrix ?

An augmented matrix is one that is created by joining the columns of two matrices.

The augmented matrix of a consistent linear system can have any value in the last column, as long as it corresponds to a valid solution of the system of linear equations.

The presence of a non-zero value in the last column simply indicates that the system has a unique solution, while a zero value in the last column indicates that the system is either inconsistent or has infinitely many solutions.

In this case, the value of h does not affect the consistency of the system.

Hence,  The matrix is the augmented matrix of a consistent linear system for every value of h.

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Answer:

7.35 million

Step-by-step explanation:

49*0.81^9 =7.35 million

Response variable defined with:

B. The number or quality of the variable for whom the value the experimenter wants to figure out how the explanatory variable affects.

Option B describes the response variable as the variable of interest that the experimenter is trying to study and understand how it is affected by other variables, known as explanatory variables. The response variable is often the dependent variable in a study and the focus of the analysis.

On the other hand, option A describes a situation in which the effect of two factors on the response variable cannot be distinguished, which is not a definition of the response variable itself. Option C describes a placebo, which is a different concept in experimental design.

Option D is similar to option B but does not describe the response variable as being the focus of the experimenter's study.

The response variable, also known as the dependent variable, is a variable in a statistical model or experiment that is being measured or studied. It is the outcome of interest that the experimenter wants to understand and explain by considering the effects of one or more independent variables, also known as explanatory variables.

The goal of the experiment is to determine how changes in the explanatory variables affect the response variable. In a sense, the response variable is the dependent variable because its value depends on the values of the independent variables.

Understanding the relationship between the response and explanatory variables is important in fields such as science, medicine, and engineering, where researchers are often interested in predicting or controlling outcomes based on various inputs.

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An ellipse is described by this equation. It is a conic section because it has two variables, x and y, that are squared and multiplied together. The conic's shape is fixed because the equation also contains a constant.

An ellipse is described by this equation. It is a conic section because it has two variables, x and y, that are squared and multiplied together. A constant in the equation, 4x2 + 3xy + 5y2 - x - y = 0, shows that the conic's shape is fixed.  The equation is neither a parabola nor a hyperbola because it lacks any x or y terms. The equation therefore describes an ellipse. An oval-shaped closed curve known as an ellipse is produced when a plane and a cone intersect. The foci, or the two places at which the ellipse is symmetric, serve as its two defining points. The standard form of an ellipse, which is centred at the origin and contains the equation A(x2) + B(xy) + C(y2) + D(x) + E(y) + F = 0, is described by the equation provided. In this case, the constants are A=4, B=3, C=5, D=1, and E=1, and F=0. The major axis to minor axis ratio in the equation is 4:5, describing a moderately flattened ellipse. The equation can be used to determine the ellipse's area, circumference, and other parameters because it is symmetrical.

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The perimeter is  6x + 8 feet and the area is (2x^2 + 5x + 3) square feet

The perimeter of a rectangle is equal to the sum of the lengths of all four sides.

The length of the shed is 2x + 3 feet, and the width is x + 1 feet, so the perimeter of the shed is:

2 * (2x + 3) + 2 * (x + 1) = 4x + 6 + 2x + 2 = 6x + 8 feet

The area of a rectangle is equal to the product of its length and width.

So, the area of Shirley's shed is:

(2x + 3) * (x + 1) = (2x^2 + 5x + 3) square feet

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There is only one solution to the equation y=3x+4 and -12x+4y=16 since there are neither no solutions nor an unlimited number of them.

curing a problem by a method but rather action; explaining the answer. a range of values for a variable that fulfill an equation, specifically The solution of an equations is any value of both a variable that gets the Left Hand Side (LHS) and thus the Nondominant Hand Side (RHS) of the equations equal. To solve an equation is to identify its answer or solutions. One approach to express the concentration of a solvent is as a percentage of the solute in the solvent. The ratio of the mass of something like the solute here to mass of the solution, or the fraction of the mass of something like the solute here to mass of the solution, is one of two supplementary techniques for computing the percentage.

given

When we multiply equation 1 by 4 we get:

-3x + y = 4

-12x + 4y = 16

Due to the fact that there is no solution for x, -12x + 4y = 16

There is only one solution to the equation y=3x+4 and -12x+4y=16 since there are neither no solutions nor an unlimited number of them.

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Answer:

Step-by-step explanation:

18

A: Range is 4

Range is from the smallest to the greatest so 10 - 6 = 4.

B: There are 5 students in the groups.

Five marks, five students.

C: Mean is 8.

The mean is to add all the marks 6 + 7 + 8 + 9 + 10 = 40. Then, divide by the numbers. There are 5 numbers so, 40 ÷ 5 = 8.

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The sequence diverges.

There is just one possible outcome for a sequence: either it converges or it diverges. This does not imply that we can always detect whether the sequence converges or diverges; in fact, there are occasions when it can be very challenging for us to do so.

The limit of the sequence an = cos(2n) / 5n as n approaches infinity does not exist, so the sequence diverges.

The cosine function oscillates between -1 and 1, so the value of cos(2n) can be arbitrarily large or small as n gets larger. As a result, the ratio of cos(2n) to 5n also becomes arbitrarily large or small, and the limit does not exist.

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The number of degrees counterclockwise that Kevin needs to reach the original position will be 58°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.

Let the angle be 'x'. Then the equation is given as,

x + 13° = 71°

x = 71° - 13°

x = 58°

The number of degrees counterclockwise that Kevin needs to reach the original position will be 58°.

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