Find d/dx (5x tan x⁻¹ x)
Explain your answer.

Answer:

y - 1 = x + 3

Step-by-step explanation:

Point-slope form: y - y1 = x - x1

since y1 is 1 and x1 is -3

then y - 1 = x - -3

=> y - 1 = x + 3

Answer:

A rational equation is an equation containing rational expressions. More About Rational Equation Rational.

In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials (a polynomial is an expression consisting of variables and coefficients which only employs the operations of addition, subtraction, multiplication, and non-negative integer exponents.)

Answer:

D on edge

Step-by-step explanation:

A. If a worm can move 20cm in one second, its speed is 20cm/s (20cm per second).

B. If an elevator can travel 500m in one minute, its speed is 500m/m (500 meters per minute).

C. If a cheetah can run 120km in one hour, its speed is 120km/h (120 kilometers per hour).

D. If Ben runs at a speed of 4m/s. He runs 4 m in one second.

E. If a snail moves at a speed of 32cm/min, it moves 32 cm in one minute.

F. If an airplane travels at speed of 965km/h. It travels 965 Km in one hour.

The speed refers to the quotient of the total distance and the time.

The speed describes the unit rate at which an object or person moves or operates or is moved or operated.

Thus, the speed can be described as the rate of change of distance with respect to time.

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Answer:

(-x+2)(2x+1) — first option

Step-by-step explanation:

The rectangles represent an x, red means negative and yellow is positive.

The squares represent a unit (the number 1).

The diagram attached below demonstrates how this works.

Basically the top row of this tile equation is (-x + 2)And the column is (2x+1).

Expanding this makes -2x²+3x+2

To determine the value of \( n \) such that the average rate of change of the function \( f(x) = x^2 - 3x + 7 \) on the interval \( -5 \leq x \leq n \) is \( -1 \), we need to find the average rate of change of the function and set it equal to \( -1 \). By using the formula for the average rate of change, \(\frac{{f(b) - f(a)}}{{b - a}}\), where \( a \) is the starting point of the interval and \( b \) is the ending point, we can set up the equation and solve for \( n \).

The average rate of change of a function on an interval is defined as the difference in the function values divided by the difference in the corresponding input values. In this case, we have the function \( f(x) = x^2 - 3x + 7 \) and the interval \( -5 \leq x \leq n \).

To find the average rate of change, we use the formula: \(\frac{{f(b) - f(a)}}{{b - a}}\), where \( a \) is the starting point of the interval and \( b \) is the ending point. In this case, \( a = -5 \) and \( b = n \).

We want the average rate of change to be \( -1 \), so we set up the equation: \(\frac{{f(n) - f(-5)}}{{n - (-5)}} = -1\). Substituting the function \( f(x) = x^2 - 3x + 7 \) and solving for \( n \), we can determine the value of \( n \) that satisfies the given condition.

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Answer:

y = -1/2x - 8

Step-by-step explanation:

y = -1/2x - 8

Nearly half of the newborns among nonsmokers (56 out of 115, 48.7%) have birth weights between 3,000 and 4,000 grammes. 40 of 74, or 54%, of the infants born to smokers have birth weights between 2,000 and 3,000 grammes, with fewer infants in the larger weight groups.

What is birth weight?

The body weight of a newborn is referred to as birth weight. Infants of European descent typically weigh between 2.5 and 4.5 kilogrammes at birth, with an average of 3.5 kilograms. South Asian and Chinese babies weigh about 3.26 kilogrammes on average.

Babies born to nonsmokers typically weighed between 1,000 and 5,000 grammes. Babies born to smokers often ranged in weight from 500 to 4500 grammes.

However, we also notice some significant variations between the two groups' normal ranges of birth weights. With fewer infants in the lower weight ranges, nearly half of the newborns among nonsmokers (56 out of 115, 48.7%) have birth weights between 3,000 and 4,000 grammes. 40 of 74, or 54%, of the infants born to smokers have birth weights between 2,000 and 3,000 grammes, with fewer infants in the larger weight groups.

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The amount it would cost to buy 3.9 pounds of steak is $2.59

From the question, we are to determine how much it would cost to buy 3.9 pounds of steak

Let the cost be $x

From the given information, we have that

55 pounds of steak cost $36.50

If 55 pounds of steak cost $36.50

Then,

3.9 pounds of steak will cost $x

Thus,

55 × x = 3.9 × 36.50

55x = 142.35

x = 142.35/55

x = 2.588

x ≈ 2.59

Hence, the cost is $2.59

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Answer:

m∠D = 109

Step-by-step explanation:

This is a parallelogram.

In parallelograms, the opposite interior angles are congruent, so we can write the following equation to find, first value x the measure of m∠D:

9x - 44 = 6x + 7

9x - 6x = 7 + 44

3x = 51

x = 17

Now we can calculate measure of m∠D:

m∠D = 9x - 44

9×17 + 44 = 109

Answer:

standard form: 66937

scientific notation: 6.6937 * 10^4

Step-by-step explanation:

first, convert both answers to standard form: 6.7 * 10^4 = 67000 and 6.3 * 10 = 63

67000 - 63 = 66937

if you want the answer in scientific notation, it is 6.6937 * 10^4

hope this helps! <3

The area enclosed by the curves is approximately 21.333, which corresponds to option d.

To find the area enclosed by the curves y = x³ - 8x² + 18x - 5 and y = x + 5, follow these steps:

1. Set the two functions equal to each other to find the points of intersection: x³ - 8x² + 18x - 5 = x + 5.

2. Simplify the equation by subtracting x and 5 from both sides: x³ - 8x² + 18x - 10 = 0.

3. Solve the cubic equation for x to find the points of intersection. You can use a calculator or an online solver. The solutions are approximately x = 1, x = 2, and x = 5.

4. To find the area enclosed by the curves, integrate the difference of the two functions with respect to x between the points of intersection: ∫[x³ - 8x² + 18x - 10 - (x + 5)] dx from x = 1 to x = 5.

5. Simplify the expression inside the integral: ∫[x³ - 8x² + 18x - 15] dx from x = 1 to x = 5.

6. Evaluate the integral: [1/4 × 4x - (8/3) ×  x³ + 9 × x² - 15 × x] from x = 1 to x = 5.

7. Calculate the area by subtracting the values of the integral at the limits: A = F(5) - F(1), where F(x) represents the antiderivative.

8. A = (1/4 × 625 - (8/3) × 125 + 9 × 25 - 15 × 5) - (1/4 × 1 - (8/3) × 1 + 9 × 1 - 15 × 1) ≈ 21.333.

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Answer:

the one you have selected is right

Step-by-step explanation:

The  radius is   r  = 1.5 feet  of  a circle when circumference of a circle is 3pi ft.

What is meant by a circle's circumference?

The circumference of a circle can be found using

circumference=pi × diameter

   3π    = π  ×  d

   3π/π =  d

   3 = d

radius = d/2

  r  =  3/2

  r  = 1.5 feet

Therefore , radius is    r  = 1.5 feet  of  a circle .

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Answer:

The range is all real numbers.

Step-by-step explanation:

The function shown is a line (and not a horizontal line).

The range is all the y's on the graph or all the y's that can be generated by the equation of the function.

f(x) = 3x + 9

You could put ANY, literally any, number in place of the f(x) and be able to calculate an x for it. Looking at the graph of this line, you could go up and down the y-axis to infinity in either direction, and the graph of the line would be there.

The range is All Real Numbers.

The first class, which did not study for the final, is the control group.

The control group serves as a baseline for comparison with the other groups in an experiment. By comparing the outcome of the experimental group(s) with the outcome of the control group, the experimenter can determine if the treatment had an effect.

In this case, the professor can compare the grades of the first class (which did not study) with the grades of the second and third classes (which studied for 5 hours and 10 hours respectively) to see if the amount of time spent studying had an impact on the students' grades.

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Answer:

1.75 = 1 3/4

Step-by-step explanation:

1 3/4 = 1.75

Answer:

=

Step-by-step explanation:

-1.75 is the same as -1 3/4

If the tens digit of a two-digit number is one more than the units digit and the number itself is 6 times the sum of the digits, then the solution is a two-digit number 54.

Let's assume that the units digit of the two-digit number is x. According to the problem statement, the tens digit is one more than the units digit, which means that the tens digit is x + 1. Therefore, the two-digit number can be expressed as 10(x+1) + x, which simplifies to 11x + 10.

The problem also states that the number is 6 times the sum of its digits. The sum of the digits is x + (x + 1) = 2x + 1. Therefore, we can set up an equation:

11x + 10 = 6(2x + 1)

Simplifying the equation, we get:

11x + 10 = 12x + 6

Subtracting 11x from both sides, we get:

10 = x + 6

Subtracting 6 from both sides, we get:

x = 4

Therefore, the units digit is 4, and the tens digit is one more than that, which is 5. The two-digit number is 54. We can check that this is indeed 6 times the sum of its digits:

54 = 6(4 + 5)

54 = 6(9)

54 = 54

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Answer:

3

Step-by-step explanation:

because 2 - 2 = 0 0 + 4 = 4 4 - 3 = 1  1 + 15 = 16 - 9 = 7 + 7 = 14 - 11 = 3

The inequality relating −2\(e^{(-n/n^2)}\) to 121/\(n^2\) for n ≥ 1 is -2\(e^{(-n/n^2)}\) ≤ 121/\(n^2\).

To derive the inequality, we start by comparing the expressions −2\(e^{(-n/n^2)}\)  and 121/\(n^2\).

Since we want to express the numbers in exact form, we keep them as they are.

The inequality states that −2\(e^{(-n/n^2)}\)  is less than or equal to 121/\(n^2\).

This means that the left-hand side is either less than or equal to the right-hand side.

The exponential function e^x is always positive, so −2\(e^{(-n/n^2)}\)  is negative or zero.

On the other hand, 121/\(n^2\) is positive for n ≥ 1.

Therefore, the inequality −2\(e^{(-n/n^2)}\)  ≤ 121/\(n^2\) holds true for n ≥ 1.

The negative or zero value of −2\(e^{(-n/n^2)}\)  ensures that it will be less than or equal to the positive value of 121/\(n^2\).

In symbolic notation, the inequality can be written as −2\(e^{(-n/n^2)}\)  ≤ 121/\(n^2\) for n ≥ 1.

This representation captures the relationship between the two expressions and establishes the condition that must be satisfied for the inequality to hold.

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Since there are complementary angles, the value of angle B is 39°.

Angle A = 7x + 23°

Angle B = 5x + 19°

It should be noted that the total angles in a complementary angle are equal to 90°.

Therefore, we need to add angle A and B together and then equate them to 90°. This will be:

7x + 23° + 5x + 19° = 90°

Collect like terms

12x + 42° = 90°

12x = 90° - 42°

12x = 48°

x = 48°/12

x = 4°

Angle A = 7x + 23° = 7(4) + 23° = 28° + 23° = 51°

Angle B = 5x + 19° = 5(4) + 19° = 20° + 19° = 39°

The value of angle B is 39°.

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Answer:

-10

Step-by-step explanation:

x + 75 + x + 125 = 180

2x + 200 = 180

2x = -20

x = -10

The surface area of the rectangular prism is 1,355,531 cm2.

Surface area is a measure of the total area of the surface of an object. It is calculated by taking the total area of its faces, edges, and vertices and combining them into one figure. It is an important factor in determining the volume, mass, and other properties of a three-dimensional object. In the case of a cube, for example, the surface area is the sum of the areas of its six faces. It is also used to measure the total area of a two-dimensional object, such as a circle or a triangle.

The surface area of a rectangular prism is the sum of the areas of all of its faces. To find the surface area, one can use the formula A = 2lw + 2lh + 2hw, where l is the length, w is the width, and h is the height.

In this case, the length of the rectangular prism is 550 1/4 cm, the width is 412 3/4 cm, and the height is 275 1/8 cm. Using the formula, we can calculate the surface area of the prism as follows:

A = 2(550 1/4)(412 3/4) + 2(550 1/4)(275 1/8) + 2(412 3/4)(275 1/8)

A = 936,406 1/2 + 304,437 1/2 + 114,687 1/2

A = 1,355,531 cm2

Therefore, the surface area of the rectangular prism is 1,355,531 cm2.

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The differentiable function the value of f(4) is(d: 7.9541).

To find the value of f(4), integrate the given derivative of f(x). Let's integrate √(x²) + 2cos(x)/3 with respect to x.

∫√(x²) + 2cos(x)/3 dx

The integral of √(x²) simplified as follows:

∫√(x²) dx = ∫|x| dx = (1/2)(x |x|) + C

integrate 2cos(x)/3:

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

∫(√(x²) + 2cos(x)/3) dx = (1/2)(x |x|) + (2/3) sin(x) + C

that f(1) = 2. So, this information to find the constant C.

f(1) = (1/2)(1 |1|) + (2/3) sin(1) + C

2 = (1/2)(1) + (2/3) sin(1) + C

2 = 1/2 + (2/3) sin(1) + C

C = 2 - 1/2 - (2/3) sin(1)

the constant C, f(4):

f(4) = (1/2)(4 |4|) + (2/3) sin(4) + C

f(4) = 2(4) + (2/3) sin(4) + (2 - 1/2 - (2/3) sin(1))

f(4) = 8 + (2/3) sin(4) + (2 - 1/2 - (2/3) sin(1))

To determine the exact value of f(4), the values of sin(4) and sin(1). sin(4) = -0.7568 and sin(1) =0.8415.

Substituting these values,

f(4) = 8 + (2/3)(-0.7568) + (2 - 1/2 - (2/3)(0.8415))

f(4) =8 - 1.511 + 1.666 - 0.5609

f(4) = 8 - 0.0459

f(4) = 7.9541

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Complete question:

let f be a differentiable function such that f(1)=2 and f′(x)=√x2 2cosx 3. what is the value of f(4) ?

a. 10.790

b. 8.790

c. 12.996

d. 7.9541.

e. -6.79

The counter example is ""If the shape is not a polygon, then it does not have four sides."

The converse of a statement is formed by switching the hypothesis and the conclusion.

Given the statement

"If the shape is a polygon, then it has four sides."

The counter example will be the opposite of both the hypothesis and conclusion of the statement to have;

"If the shape is not a polygon, then it does not have four sides."

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Answer:

Wouldnt it be a square.

Step-by-step explanation:

Answer:

$70.84

Step-by-step explanation:

The approximate value of the car in 3 years is $1648.37.

We have,

To calculate the approximate value of the car in 3 years, we can use the formula for exponential decay:

V = Vo e^(-kt)

where V is the value of the car after t years, Vo is the initial value of the car, k is the decay rate (in this case, 0.3), and e is the mathematical constant e (approximately equal to 2.718).

Substituting the given values.

V = 6000 x e^(-0.33)

V = 6000 x e^(-0.9)

V ≈ $1648.37

Therefore,

The approximate value of the car in 3 years is $1648.37.

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