If f(x) = x sinx/1+cos x find f'(π/2).​

In response to the above question, we may state that in the rectangle [tex]4,241,455[/tex] gallons [tex]= 4,570,000[/tex] Cubic feet[tex]x 7.48052[/tex] Gallons/cubic foot.

In the geometry of the Euclidean plane, a rectangle is a quadrilateral having four right angles. You may also refer to it as an equiangular quadrilateral, meaning that all of its angles are equal. A straight angle could also be present in the parallelogram.

Rectangles with four evenly sized sides are called squares. Four 90-degree vertices and equal parallel sides make up a quadrilateral with the shape of a rectangle.

As a result, it's also known as an equirectangular rectangle. A rectangle is also referred to as a parallelogram, since its opposite sides are parallel and equal.

Volume of rectangular solid is L × W × H

[tex]50 × 30 × 20 = 30000[/tex] cubic yards

[tex]50 × 30 × 6 = 9000[/tex]cubic yards

[tex]30000–9000 = 21000[/tex]cubic yards

This needs to be converted to gallons of water. We are given the conversion factor between a gallon of water and cubic feet, therefore even though we have cubic yards rather than cubic feet, we must first convert the [tex]21,000[/tex] Cubic yards to cubic feet.

A cubic yard has a volume of 27 cubic feet.27 cubic feet per cubic yard times [tex]21,000[/tex]cubic yards equals 567,000 cubic feet.

7.48052 gallons make up 1 cubic foot.

Therefore, 4,241,455 gallons are equal to 567000 cubic feet times 7.48052 gallons/cubic foot.

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The value of the composite functions of h(g(x)) is h(g(x)) = -20x + 6.

In mathematics, a function is composed when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.

Given that, h(x) = 4x + 6 and g(x) = -5x.

The value of h(g(x)) is calculated by substituting x = -5x in the equation of h(x).

h(g(x)) = 4(-5x) + 6

h(g(x)) = -20x + 6

Hence, the value of the composite functions of h(g(x)) is h(g(x)) = -20x + 6.

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The reason why AC must be congruent to BD is the hypotenuse - leg theorem and CPCTC

According to the hypotenuse-leg (HL) theorem, a right triangle is congruent if each of its hypotenuse and one leg are congruent with their corresponding hypotenuse and one leg in another right triangle.

The problem have the hypotenuse and a leg of the two triangles stated to be equal. This completes the requirement for the theorem and hence the two triangles are said to be equal

Then applying the CPCTC theorem which says that if two triangles are congruent, every corresponding part of one triangle is congruent to the other side hence, the sides AC = BD

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Answer:

To approximate the area between the x-axis and the graph of f(x) = x^2 + 4 over the interval [0, 2], we can use the right rectangle method, where the heights of the rectangles are given by the value of the function at the right endpoint of each subinterval. If we divide the interval [0, 2] into 4 equal subintervals of width 0.5, the right endpoint of each subinterval would be 0.5, 1, 1.5, 2.

The height of the first rectangle would be f(0.5) = 0.5^2 + 4 = 4.25, the height of the second rectangle would be f(1) = 1^2 + 4 = 5, the height of the third rectangle would be f(1.5) = 1.5^2 + 4 = 6.25, and the height of the fourth rectangle would be f(2) = 2^2 + 4 = 8.

The sum of the areas of the rectangles is equal to (0.5) × (4.25 + 5 + 6.25 + 8) = (0.5) × 24 = 12.

So, the approximate area between the x-axis and the graph of f(x) = x^2 + 4 over the interval [0, 2] is 12.

Answer:

41°

Step-by-step explanation:

We know that,

y°+49°= 90°

y° = 90°-49°

y=41°

So, the value of y is 41°

The average rate of change over the interval (-1, 2) is; 3

The formula for the average rate of change over an interval (a, b) is expressed as;

f'(x) = [f(b) - f(a)]/[b - a]

We want to find the average rate of change over the interval (-1, 2). Thus;

a = -1 and b = 2

Thus;

f(-1) = -4

f(2) = 5

Thus;

f'(x) = (5 - (-4))/(2 - (-1))

f'(x) = 9/3

f'(x) = 3

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The 55th term of the arithmetic sequence is 131.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.

Given that, the nth term of the sequence is aₙ= -1+3(n−1)

Here, the 55th term in the sequence is

a₅₅= -1+3(55-1)

= -1+132

= 131

Therefore, the 55th term is 131.

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we get two possible solutions: L = 6 and W = 4. Therefore, the length of the land could be 6 meters.

If the rectangular plot has length L and width W, then we know that 2L + 2W = 20 since 20 meters of wire mesh were used. We also know that L × W = 24 since the area of the plot is 24 square meters. Solving these two equations simultaneously, We have the equations:

2L + 2W = 20

L × W = 24

From the first equation, we can solve for L in terms of W:

2L = 20 - 2W

L = 10 - W

Substituting this into the second equation, we get:

(10 - W) × W = 24

Expanding the brackets, we get: 10W - W² = 24

Rearranging and setting equal to zero, we get: W² - 10W + 24 = 0

We can solve this quadratic equation by factoring: (W - 6) × (W - 4) = 0

So the possible solutions for W are: W = 6 or W = 4

If W = 6, then L = 10 - W = 4, so the rectangular plot has dimensions 4 meters by 6 meters. If W = 4, then L = 10 - W = 6, so the rectangular plot has dimensions 6 meters by 4 meters. Therefore, the length of the land is 6 meters. because the length is assumed as the longer side of a shape or an object.

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Complete Question

To enclose a rectangular plot of 24 m², 20 m of wire mesh were used, what is the length of the land?

The number of adult and children in the group is given as follows:

The amounts are obtained by a system of equations, for which the variables are given as follows:

There were a total of 28 people, hence:

x + y = 28

y = 28 - x.

They spent a total of $308, hence:

15x + 8y = 308.

Replacing the second equation into the first, the value of x is given as follows:

15x + 8(28 - x) = 308

7x = 84

x = 84/7

x = 12.

Then the value of y is given as follows:

y = 28 - x = 28 - 12 = 16.

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Hakeem made 10 shots. The solution has been obtained by using proportions.

What is proportion?

Two numbers are compared. It is known as a proportion in mathematics. The law of proportion states that if two sets of given numbers rise or decrease in the same ratio, they are considered to be directly proportionate to one another.

We are given that Hakeem made 5% of his free throws over the season.

He shot 200 free throws and was able to make 5% from them.

So,

Number of throws he made = Number of free throws x Percentage made

Using this, we get

⇒Number of throws he made = 200 x 5%

⇒Number of throws he made = 10

Hence, Hakeem made 10 shots.

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Answer:

1. The monthly premium for workers' compensation insurance for the Winston Tree Farm and Nursery can be calculated as follows:

Monthly payroll: $3,560 Base rate: $5.93 per $100 Rate per $1,000: $5.93 * 10 = $59.30 Premium: $3,560 / 1,000 * $59.30 = $209.51

So, the monthly premium for workers' compensation insurance is $209.51.

2. The amount that Takis Machine Shop will pay each year for workers' compensation insurance can be calculated as follows:

Old base rate: $9.40 per $100 New base rate: $10.40 per $100 Monthly payroll: $53,896.84 Old rate per $1,000: $9.40 * 10 = $94.00 New rate per $1,000: $10.40 * 10 = $104.00 Old premium: $53,896.84 / 1,000 * $94.00 = $5,045.65 New premium: $53,896.84 / 1,000 * $104.00 = $5,610.71 Increase in premium: $5,610.71 - $5,045.65 = $565.06

So, Takis Machine Shop will pay an additional $565.06 each year for workers' compensation insurance.

3.The real estate tax for the home in Madison County can be calculated as follows:

Market value: $590,000 Rate of assessment: 40% of market value = $590,000 * 0.4 = $236,000 Tax rate: 42.73 mills = 0.04273 Tax: $236,000 * 0.04273 = $10,130.68

So, the real estate tax for the home in Madison County is $10,130.68.

4. The fair market value of Vanesa Vasquez's Roth IRA at age 65 can be calculated as follows:

Contribution: $2,500 Years of contribution: 65 - 35 = 30 Annual interest rate: 7.4% Future value: $2,500 * (1 + 0.074)^30 = $29,706.74

So, the fair market value of her Roth IRA at age 65 is $29,706.74.

The amount of interest earned can be calculated as follows:

Future value: $29,706.74 Present value: $2,500 Interest earned: $29,706.74 - $2,500 = $27,206.74

So, Vanesa Vasquez will have earned $27,206.74 in interest.

5. The interest rate as a percent for the GNMA Mortgage issue bond can be calculated as follows:

Face value: $10,000 Selling price: $10,000 * 103.7% = $10,370.00 Yield: 8.75% Price: $10,370.00 Interest: $10,370.00 - $10,000 = $370.00 Interest rate: ($370 / $10,000) * (12 / 1) = 0.09375 = 9.375%

So, the interest rate for the GNMA Mortgage issue bond is 9.375%, rounded to the nearest hundredth of a percent.

6. Let's call the number of days that Ricardo has to pay back the loan "d".

The interest on the loan can be calculated using the formula:

I = P * r * t

where I is the interest, P is the principal (the amount borrowed, $2,500), r is the annual interest rate as a decimal (7.8% as a decimal is 0.078), and t is the time in years (d divided by 365).

So we have:

I = $2,500 * 0.078 * (d / 365)

We also know that the maturity value of the loan is the sum of the principal and the interest:

$2,548.75 = $2,500 + I

So we can substitute for I:

$2,548.75 = $2,500 + $2,500 * 0.078 * (d / 365)

Expanding the right-hand side:

$2,548.75 = $2,500 + $194.00 * (d / 365)

And solving for d:

d = 365 * ($2,548.75 - $2,500) / $194.00

d = 365 * ($48.75) / $194.00

d = 365 * 0.25191780821917808

d = 91.37 days

So Ricardo would have to pay back the loan in 91.37 days.

Step-by-step explanation:

Since the samples of the study are independent, the condition for inference have been met

The body mass index for adults in the United States = 26.8

BMI stands for Body Mass Index

Body mass index of marathon runners = less than 26.8

The random samples = 35

The body mass index of the random samples = 22.7

Standard deviation = 3.1

Then the researchers will conduct a one sample t test for a population mean.

The one sample t-test is is defined as the hypothesis test that check whether the unknow population mean is different from the specific value

Here the samples are independent

Therefore, the condition for inference have been met

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The amount of profit that the new coffee shop will make after 6 years is; 35.8 thousand dollars

The quadratic equation that represents the annual profit made by the new coffee shop in thousands of dollars is;

p(t) = 0.3t² + 5.5t - 8

where;

t is the number of years for which the profit is measured

Thus, after 6 years, we will substitute 6 for t in the quadratic equation to get;

p(6) = 0.3(6)² + 5.5(6) - 8

p(6) = 10.8 + 33 - 8

p(6) = 35.8 thousand dollars

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Answer:

Step-by-step explanation:

To calculate 8% of 350, we can first calculate 1% of 350 and then multiply it by 8.

1% of 350 is equal to 0.01 times 350 which can be calculated as:

0.01 * 350 = 3.5

Since 1% of 350 is equal to 3.5, 8% of 350 can be calculated as follows:

8 * 3.5 = 28

So, 8% of 350 is equal to 28.

The values of x for which z is greater than y are 7.

In mathematics, an equation is a statement that two mathematical expressions are equal. The expressions can contain variables, constants, mathematical operations, and functions. An equation can be used to represent a relationship between two or more variables, and it is often used to solve problems by finding the values of the variables that satisfy the equation.

Equations can be represented in different forms, such as algebraic equations, differential equations, integral equations, and partial differential equations. Algebraic equations are the most common type of equations, and they involve algebraic operations such as addition, subtraction, multiplication, and division.

Equations can be classified according to their degree, which is the highest power of the variable in the equation. Linear equations are those with a degree of one, and they can be represented by a straight line on a graph. Quadratic equations have a degree of two, and they can be represented by a parabolic curve. Higher degree equations are generally more complex, and they may not have a simple geometric representation.

For x = -4, y = 4(-4) - 3 = -19 and z = -18, so y is greater.

For x = 2, y = 4(2) - 3 = 5 and z = 6, so z is greater.

For values of x where z is greater than y, we need to compare the values of z and y for each x value in the table.

At x = 3, y = 4(3) - 3 = 9 and z = 9, so they are equal.

At x = 7, y = 4(7) - 3 = 25 and z = 27, so z is greater.

At x = 10, y = 4(10) - 3 = 37 and z = 35, so z is not greater than y.

Therefore, the values of x for which z is greater than y are 7.

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Each bag contains 20 pennies and we have 6 such bags.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

From the given information let the number of pennies in each bag is 'x'

and we have 6 such bags.

Therefore, The equation can be formed as,

6(10 + x) = 180.

60 + 6x = 180.

6x = 180 - 60.

6x = 120.

x = 120/6.

x = 20.

So, The number of pennies in each bag is 20.

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We would expect John to weigh approximately 216.4 pounds at the end of week 8.

To answer this question, we need to fit a regression model to the data to determine the relationship between the number of calories burned and John's weight. We can use linear regression to find the line of best fit that represents this relationship.

We can see that there is a negative relationship between the number of calories burned and John's weight, which is consistent with the statement that "the more someone exercises the less they will weigh." We can use linear regression to find the line of best fit that represents this relationship.

Using a linear regression model, we get the following equation:

Weight = 219.9 - 0.0007 * Exercise

We can use this equation to predict John's weight at the end of week 8 based on the number of calories he burned. Plugging in Exercise = 5000, we get:

Weight = 219.9 - 0.0007 * 5000

Weight = 216.4

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Answer:

x=2

y=0

Step-by-step explanation:

2x=4

x=4/2

x=2

again,

y-1 =2y -1

1-1 =2y -y

0=y

Answer:

5,840,000

Step-by-step explanation:

Let P be the population after x years. The population after 24 years is 2P. So, we have:

P = 365,000 * 2^(x/24)

To find the population after 96 years, we plug in x = 96:

P = 365,000 * 2^(96/24) = 365,000 * 2^4 = 365,000 * 16 = 5,840,000

So, the population of the city will be 5,840,000 after 96 years.

Answer:

Step-by-step explanation:

The solution of the radical expression ∛(4+3) will be 1.91.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

The radical sign, which may be read as either the nth root of x or x radical n, expresses the root of a number. The vinculum, or horizontal line that encircles the number, and the radicand, or number beneath it, are both technical terms.

Given that the expression is ∛(4+3). The solution of the medical expression will be,

E = ∛ ( 4 + 3)

E = ∛(7)

The value of the cube root of the number 7 will be,

E = 1.91

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The number line of the inequality is (d)

from the question, we have the following parameters that can be used in our computation:

3x+2≤4x+5≤9

When this is expanded, we have

3x + 2 ≤ 4x + 5 and 4x + 5 ≤ 9

Evaluate the like terms

So, we have the following representation

-x ≤ 3 and 4x ≤ 4

Divide by the coefficient of x

x ≥ -3 and x ≤ 1

When combined, we have

-3 ≤ x ≤ 1

So x is between -3 and 1, inclusive.

This is represented by the number line (d)

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Answer:

5/2 hours      or      2 hours and 30 minutes

Step-by-step explanation:

The x represents the time it took Mrs. Ritts to mow the front yard. We don't know this time so put it as a variable. We also know that the time to mow her backyard is equal to 2 times the variable and then minus 2.

Equation:   3 = (2x) - 2  

Now we just isolate the x. First, start by adding 2 to both sides.

5 = 2x

Now just divide both sides by 2.

5/2 = x

5/2 as a mixed number would be 2 and 1/2 so that means the time would be 2 and a half hours.

Answer: range is (-4,0,28)

Step-by-step explanation:

Graph the line using the slope and the y-intercept, or the points.

The correct answers are:

The word "domain" is used with other related meanings in some areas of mathematics. In topology, a domain is a connected open set. In real and complex analysis, a domain is an open connected subset of a real or complex vector space.

The slope-intercept form is y =mx + b where m is the slope and b is the y-intercept:

→ y = mx + b

Find the values of m and b using the form y = mx + b:

m = 4

b = 12

Therefore, Graph the line using the slope and the y-intercept, or the points.

The correct answers are:

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On solving the provided question we can say that 2 decimal places =29.92 miles per hour

Integer and non-integer numbers are often expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded to include non-integer values. Decimal notation is the name for the method used to represent numbers in the decimal system. A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts. A decimal point separates the complete number and the fractional portion of a decimal number. The dot between the whole number and the fractions is known as the decimal point. A decimal number is, for instance, 25.5. In this instance, 25 is the entire number, while 5 is the

top speed is 26 knots,

1 knot = 1.15078 miles per hour

26 knots = 26 * 1.15078

= 29.92028 miles per hour

2 decimal places

=29.92 miles per hour

boat has a  displacement of 96000 tons

1 ton = 0.907185 metric tonnes

96000 tons = 0.907185 * 96000

= 87,089.76 metric tonnes

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The equation that can be used to find the length of the remaining side is z² = 14² - 9²

Using the Pythagorean theorem that states that the square of the hypotenuse side is equal or equivalent to the sum of square of the other two sides.

This is represented as;

x² = y² + z²

Given that the parameters are enumerated as;

Now, substitute the values

14² = 9² + z²

collect like terms

z² = 14² - 9²

Hence, the equation is z² = 14² - 9²

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The length of the remaining side can be calculated using 14² = x² + 9² is 10.7 units

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given as:

hypotenuse² = adjacent² + opposite²

Let x represent the missing side.

The hypotenuse of a right triangle has a length of 14 units and a side that is 9 units long. Hence:

14² = x² + 9²

x² = 14² - 9²

x² = 115

x = 10.7 units

The length of the remaining side is 10.7 units

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Answer: y > 8

Step-by-step explanation:

6 - 5y < -34

-5y < -40

y > 8

[tex]6-5y < -34[/tex]

Simplify:

[tex]-5y+6 < -34[/tex]

Subtract 6 from both sides:

[tex]-5y+6-6 < -34-6[/tex]

[tex]-5y < -40[/tex]

Since we are dividing by a negative number, the sign will reverse.

Divide both sides by -5:

[tex]\dfrac{-5y}{-5} > \dfrac{-40}{-5}[/tex]

[tex]\boxed{y > 8}[/tex]

The perimeter of the triangle is 23x + 17.

Perimeter is simply the sum of all sides of a polygon.

Given the sides of the triangle;

Side one = 10x + 19

Side two = 12x - 2

Side three = x

To find the perimeter, we add the sides

Perimeter = Side one + Side two + side three

Perimeter = 10x + 19 + 12x - 2 + x

Collect and add like terms

Perimeter = 10x + 12x + x - 2 + 19

Perimeter = 23x - 2 + 19

Perimeter = 23x + 17

Therefore, the perimeter is 23x + 17.

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The absolute humidity is 500g/m³, specific humidity = 16.67% and mixing ratio = 20%.

Absolute humidity is a measure of the amount of water vapor in a given volume of air, regardless of the total mass of the air. It is expressed as the mass of water vapor per unit volume of air, typically in units of grams per cubic meter (g/m³).

First, we need to find the mass of dry air in the package. Since the total volume of air is 1m³ and the volume of dry air is 2.5m³, the volume of water vapor is 1 -2.5 = -1.5 m³. This means that the water vapor must have condensed and become liquid water, which we can ignore for the purposes of this problem. So the mass of dry air is:

mass of dry air = density of air * volume of dry air

mass of dry air = 1000g/m³ × 2.5m³

mass of dry air = 2500 g

Now we can use this value, along with the given mass of water vapor, to calculate the three measures of humidity:

       absolute humidity = 500g/ 1m³

       absolute humidity =  500g/m³

       specific humidity = 500g/(2500g + 500g)

       specific humidity = 0.1667 (or 16.67% as a percentage)

       mixing ratio = 500g/2500g

       mixing ratio = 0.2 (or 20% as a percentage)

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