which of the following is an antiderivative of f(x)=tan(ex π2) on 0≤x≤ln(π2) ?

Answer: They needed to find the hypotenuse of the triangle not the sum of the legs.

Step-by-step explanation:

If angle b is five times the size of angle c, the equation can be used to find the measure of angle is 5x+x=90°.

because complementary angles complete each other to 90 degrees.

These angles b and c add up to 90° because they are complementary.

Let's say angle C is named x.

angle b is five times the size of angle c, this can be written: 5x

Complementary angles add up 90°, so angle B add angle C equal 90°

the equation to find the measure of angle C is 5x+x = 90°.

Types of angles are one of the materials in mathematics that you always encounter at every level of education. Learning about angles is very important, because angles are always present in everyday life and need to be identified.

An angle is a shape formed by two rays having an endpoint at one point. In angles, terms such as the leg of the angle, vertex, and area of the angle are also found.

The legs of the angle are the lines forming the angle. The vertex is the point where the two legs of the angle intersect, and the area of the angle is the area bounded by the two legs of the angle.

Your question is incomplete but most probably your full question was:

Only Interaction Angle B and angle C are complementary: If angle B is five times the size of angle C which equation can be used to find the measure of angle C?

5x+x=180

5x = 180

5x+x=9

5x = 90

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Using inequality views, the compound inequality is given by:

50 ≤ P ≤ 90

            a ≤ x ≤ b

                                          50 ≤ P ≤ 90

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When graphing "AND" inequalites, shading looks like Shading that always connects the 2 dots.

An algebraic statement that connects two values that are not equal is referred to as an inequality in mathematics. Inequality signals state that one of the two variables on either side of the inequality could be greater than, greater than or equal to, less than, or less than or equal to another value.

If a linear inequality has a sign that is either (less than) or, you will shade below the boundary line (less than or equal to). In a linear inequality, if the sign is > (greater than) or, you will shade above the boundary line (more than or equal to).

Follow these steps:

Rearrange the equation so "y" is on the left and everything else on the right.

Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)

Shade above the line for a "greater than" (y> or y≥)

or below the line for a "less than" (y< or y≤).

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Answer:A(-5,4),B(-5,6),C(-7,6),D(-7,4)

Step-by-step explanation:If you draw a big enough graph it is easy to do.

The required length of the arc of the circle is  approximately 13.08 cm.

In mathematics, an arc is defined as a portion of the boundary of a circle or a curve. It can also be referred to as an open curve. The boundary of a circle is the perimeter or the distance around a circle, also known as the circumference.

The length of an arc of a circle is given by the formula:

L = θ * r / 180 * π

Where θ is the central angle in radians, r is the radius, and π is pi.

In your case, the radius of the circle is 6, and the central angle is 126°, so we need to first convert 126° to radians:

θ = 126° * π / 180 = 2.18 radians

Substituting the values in the formula, we get:

L = θ * r / 180 * π = 2.18 * 6 / 180 * π = 2.18 * 6 / π = 13.08 cm

So the length of the arc of the circle with radius 6 and central angle 126° is approximately 13.08 cm.

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The number of ways the elevator buttons can be lighted is (m)(m-1)(m-2)...(m-n+1).

What is Permutations?

The mathematical notion of permutation describes the placement of things in a particular order. It is a method of determining how many unique configurations there are for a given set of objects.

If there are n persons in the elevator, and each one presses a button for a floor between 1 and m, what would happen? (inclusive). The number of permutations of m things taken n at a time, indicated as P, determines the number of ways the elevator buttons can be lit if no two individuals hit the same floor button and each person pushes a different floor button (m, n).

[tex]The formula for permutations is: P(m, n) = m! / (m - n)!.Therefore, the number of ways the elevator buttons can be lighted is:P(m, n) = m! / (m - n)! = m! / (m - n)! = m! / (m - n)! = m! / (m - n)! = (m)(m-1)(m-2)...(m-n+1).[/tex]

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The number of ways the elevator buttons can be lighted is [tex]m(m-1)(m-2)...(m-n+1)[/tex].

What are Permutations?

The placing of things in a specific order is described by the mathematical concept of permutation. It is a technique for figuring out how many different arrangements of a group of things there are.

It would be inclusive if there were n people in the elevator and each one pressed a button for a floor between 1 and m. If no two people press the same floor button and everyone presses a separate floor button, the number of P permutations of m items taken n at a time defines how many ways the elevator buttons can be lit (m, n).

The formula for permutations is:

[tex]P(m,n)=m(m-1)(m-2)...(m-n+1)[/tex]

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the speed from kilometers per year to kilometers per hour 4.3x107 km/hr, the distance of 4.4 light years to kilometers.

1. First, convert the distance of 4.4 light years to kilometers.

1 light year = 9.46x1012 km

4.4 light years = 4.1x1013 km

2. Next, divide the distance by the time to calculate the speed:

Speed = Distance/Time

Speed = 4.1x1013 km/110 years

Speed = 3.7x1011 km/year

3. Finally, convert the speed from kilometers per year to kilometers per hour:

1 year = 8760 hours

Speed = 3.7x1011 km/8760 hours

Speed = 4.3x107 km/hr

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Maria spent $100 in total. She spent $60 at the supermarket and $40 at the hair salon.

This problem involves calculations with fractions. Maria had $160. She spent 3/8 of it at the supermarket and 1/4 of it at the hair salon. To find out much money she spent, add the fractions and then multiply the result by the total amount of money she had.

To find how much Maria spent at the supermarket, multiply $160 by 3/8: 160 * 3/8 = $60.

To find how much Maria spent at the hair salon, multiply $160 by 1/4: 160 * 1/4 = $40.

Now, add the amounts spent at the supermarket and the hair salon: $60 + $40 = $100. So Maria spent $100 in total.

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The set {7, 7, 7, 7} have only one element because we can write that set as {7}.

The empty set and the original set itself are included in the power set, which is a set that contains all other subsets as well. P is typically used to indicate it. The number of subsets that can be generated from a given set determines the cardinality of a power set.

In set theory, the set of all subsets of a Set A, including the Set itself and the null or empty set, is referred to as the power set (or power set). The Power Set of the given set will consist of 2n elements if the given set has n elements. It also symbolizes the power set's cardinality.

The set is {7, 7, 7, 7}.

We can write this set as {7}. So the element of set {7, 7, 7, 7} has one element only.

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There are an infinite number of planes that are orthogonal to a given plane in space, and this is due to the fact that a plane can be thought of as a flat surface that extends indefinitely in all directions.

Orthogonal Planes in Space: In three-dimensional space, a plane is said to be orthogonal to another plane if the two planes are perpendicular to each other, i.e., their normal vectors are perpendicular. Since the normal vectors of two orthogonal planes are perpendicular to each other, this means that the angle between them is equal to 90 degrees.

Given a plane in space, there are an infinite number of planes that are orthogonal to it. This is because a plane can be thought of as a flat surface that extends indefinitely in all directions.

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The amount of payment for the first month that Erica pays will be $1,000. Then the correct option is A.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Rent = $850 per month

Security fee = $150

Then the amount of payment for the first month that Erica pays will be given as,

⇒ $850 + $150

⇒ $1,000

The amount of payment for the first month that Erica pays will be $1,000. Then the correct option is A.

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The number of cans are 9 and number of frozen food is 4.

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, Jayden bought cans of soup and frozen dinners. Each can of soup has 200 mg of sodium and each frozen dinner has 650 mg of sodium. Jayden purchased a total of 13 cans of soup and frozen dinners which collectively contain 4400 mg of sodium.

Let she bought x cans and y frozen food.

Therefore, establishing the equations,

x + y = 13

y = 13-x...(i)

200x + 650y = 4400...(ii)

Put eq(i) in eq(ii)

200x + 650(13-x) = 4400

200x + 8450 - 650x = 4400

450x = 4050

x = 9

Put x = 9 in eq(I)

y = 13-9

y = 4

Hence, the number of cans are 9 and number of frozen food is 4.

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Answer: B. x=6 only

Explanation: A fast way to check these kind of multiple choice questions is to just plug in one of the values into the equation and see if it works. For example you can put (6^2)-(12×6)+36 and it would equal 0 making the equation true. All other options wouldn't have equaled 0 so it would make x=6 the only right option.

5 flight attendants are required.

The number of flight attendants required on an aircraft is determined by regulatory agencies such as the Federal Aviation Administration (FAA) in the United States and the European Aviation Safety Agency (EASA) in Europe.

The number of flight attendants depends on several factors, including the type of aircraft, the number of passenger seats, the length of the flight, and the number of passenger exits.

The number of flight attendants required can be determined by the following formula:

The minimum number of flight attendants = (N / 50) + 1 where N is the number of passenger seats.

So, for an aircraft with 275 seats and 249 passengers:

(249 / 50) + 1

= 5 flight attendants are required.

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Answer: 90 degrees.

Step-by-step explanation:

Step 1: The smallest angle must be 90/2 = 45 degrees.

Step 2: The largest angle is twice the size of the smallest angle, so it is 90 degrees.

Answer:

dfgss sdffcfsgdbebgndnngsageqfetehashqrvdqhqdhtqi

If gasoline costs $1.95 per gallon $0.52 is its cost per liter?

One gallon of gasoline costs $1.95. To find the cost per liter, we need to convert gallons to liters. The conversion factor between gallons and liters is 1 gallon = 3.78541 liters.

So, to convert gallons to liters, we multiply the number of gallons by 3.78541.

In this case, the cost of one gallon of gasoline is $1.95. To find the cost per liter, we need to convert $1.95 from dollars per gallon to dollars per liter.

To do this, we divide $1.95 by the conversion factor between gallons and liters:

$1.95 / 3.78541

= $0.52/liter.

Therefore, the cost of one liter of gasoline is $0.52.

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The two digit number is 38.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Le x be the number at the ten's place and y be the number at the unit's place.

So, the number is 10x+y

The sum of digits of a two-digit number is 11.

That is, x+y=11 -------(i)

If the digit at tens place is increase by 5 and the digit at unit place is decreased by 5, the digits of the number are found to be reversed.

10(x+5(y-5)=10y+x

9x-9y=-45

x-y=-5 -------(ii)

Add equation (i) and (ii), we get

2x=6

x=3

Substitute x=3 in equation (i), we get

y=8

So, the number is 38

Therefore, the two digit number is 38.

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The range of the values of x is

|x| [tex]\leq[/tex] 0.5304 [tex]\leq[/tex] 1

Now, According to the question:

Let us consider the polynomial function as f(x) . Hence we need to find

[tex]T_5(x)[/tex] he formula for the Taylor series is:

[tex]T_n(x) =[/tex] Σ[tex]\left \{ {{n} \atop {j=0}} \right.}[/tex] [tex]\frac{f^(^f^)(a)}{f!}[/tex]

Suppose n =5, a=0 then

[tex]T_5 (x)= \frac{f(0)}{0!}(x -0)^0 + \frac{f'(0)}{1!}(x -0)^1+ \frac{f"(0)}{2!}(x -0)^2+...+ \frac{f^(^5^)(0)}{5!}(x -0)^5[/tex]

[tex]T_5(x)=\frac{f(0)}{0!}+ \frac{f'(0)}{1!}x+\frac{f"(0)}{2!}x^{2} + \frac{f"'(0)}{3!}x^3+\frac{f""(0)}{4!}x^4+\frac{f^(^5^)(0)}{5!}x^5[/tex]

From the data:

f(x) = cos x => f(0) = cos(0) = 1

f'(x) = -sin x => f'(0) = -sin(0) = 0

f"(x) = -cos x => f"(0) = -cos(0) = -1

f"'(x) = sin x => f'"(0) = sin(0) = 0

f""(x) = cos x => f""(0) = cos0 = 1

f""'(x) = -sin x => f""'(0) = -sin(0) = 0

Substitute this data in the Taylor series:

[tex]T_5(x)=\frac{f(0)}{0!}+ \frac{f'(0)}{1!}x+\frac{f"(0)}{2!}x^{2} + \frac{f"'(0)}{3!}x^3+\frac{f""(0)}{4!}x^4+\frac{f^(^5^)(0)}{5!}x^5[/tex]

[tex]T_5(x) =\frac{1}{0!}+\frac{0}{1!}x+\frac{(-1)}{2!}x^{2} + \frac{0}{3!}x^3+\frac{1}{4!}x^4+\frac{(0)}{5!}x^5[/tex]

[tex]T_5(x) = 1 - \frac{1}{2!}x^{2} +\frac{1}{4!}x^4[/tex]

Now, the remainder of the Taylor series is Taylor series satisfies the following inequality.

[tex]|R_n(x)|\leq \frac{M}{(n +1)^1^!} (x-a)^n^+^1for|x+a|\leq d,here|f^(^n^+^1^)(x)|\leq M\\\\|x|\leq 1,a=0,n=5= > |f^(^6^)(x)|\leq 1[/tex]

Given that the approximation should be within 0.003712

Then,

[tex]\frac{1}{(6)}|x|^6\leq 0.003712\\ \\= > \frac{1}{(6)}|x|^6\leq 0.003712\\ \\= > |x|^6\leq (0.003712)^6\\\\= > |x|^6\leq 0.022272\\\\|x|\leq (0.022272)^\frac{1}{6}\\ \\|x|\leq 0.5304[/tex]

Hence, the range of the values of x is

|x| [tex]\leq[/tex] 0.5304 [tex]\leq[/tex] 1

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The given question is incomplete , complete question is :

Find [tex]T_5(x)[/tex], the degree 5 Taylor polynomial of the function f(x) = cos(x) at

a = 0.

Find all values of x for which this approximation is within 0.003712 of the right answer.  Assume for simplicity that we limit ourselves to |x| [tex]\leq[/tex] 1

The Mean Value Theorem guarantees that the values of c for f(x)=x^3+x^2-4x+2 on the interval [1,3] are [7,9].

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. A function is an equation that depicts the connection between an input x and an output y, with precisely one output for each input. Another name for input is domain, while another one for output is range.

Here,

f(c)=f'(b)-f'(a)/(b-a)

f(x)=x^3+x^2−4x+2

f'(x)=3x²+2x-4

x=-1, 3

f'(-1)=3-2-4

=-3

f'(3)=27+6-4

=29

f(c)=29+3/3+1

=32/4

f(c)=8

=[7,9]

The values of c guaranteed by the Mean Value Theorem for f(x)=x^3+x^2−4x+2 on the interval [−1,3] is [7,9].

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Annual income = 45000 the amount invested at 8% is twice that invested at 12%. 12%        property             $45000 × 0.12 = 5400

10%        property             $8000

8%         property             $7200

The entire amount of money you make during the course of a year is your yearly income, in contrast. Along with your wage, this sum also includes earnings from other sources, such as interest on savings or rent from a home you own. Bonuses and overtime pay are other possible components of your yearly revenue.

let, x in 12%

so, 2x in 8%

and 21,5000 - 3x in 10%

so, annual income = 2x × 0.08 + ( 215000 -3x) × 0.10 + x × 0.12= 20,600

=>  x = 45000

so, 2x = 90000

so, 215000 - 3x = 80000

so,

12%         property             $ 45000

10%         property             $80000

8%         property             $90000

b)

12%        property             $45000 × 0.12 = 5400

10%        property             $8000

8%         property             $7200

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a) The linear function for this problem is defined as follows: y = -0.75x + 20.

b) The time that he worked on Day 0 is given as follows: 20 hours.

c) The daily decrease in the setup time is given as follows: 0.75 hours a day.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Two points from the graph are given as follows:

(8, 14) and (16,8).

When x increases by 8, y decays by 6, hence the slope m is given as follows:

m = -6/8

m = -0.75.

Hence:

y = -0.75x + b.

When x = 8, y = 14, hence the intercept b is given as follows:

14 = -0.75(8) + b

b = 14 + 0.75(8)

b = 20.

Hence the function is defined as follows:

y = -0.75x + 20.

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The circle has a radius of 15 and is centered at (-2,4).

The general equation of a circle is [tex](x - h)^{2} + (y - k)^{2} = r^2[/tex], where (h, k) denotes the position of the circle's center and r is the radius.

The equation for a circle is [tex](x - h)^{2} + (y - k)^{2} = r^2[/tex], where (h, k) stands for the coordinates of the circle's center and r for the radius. A circle touches the x-axis if it is tangent to it at the coordinates (3, 0).

Equation for a circle is[tex](x+2)^2 + (y-4)=225[/tex]

(-2,4) = represents the location of the circle's center.

[tex]r^2=(15)^2[/tex]

r = 15 = its radius

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The value of x is -0.03125 or - 1/32.

Solving equations involves finding the value of the unknown variables in the given equation. The condition that the two expressions are equal is satisfied by the value of the variable. Solving a linear equation in one variable results in a unique solution, solving a linear equation involving two variables gives two results.

Solving equations is computing the value of the unknown variable still balancing the equation on both sides. An equation is a condition on a variable such that two expressions in the variable have equal value.

[tex]2^{-5} - x = \frac{1}{16}[/tex]

[tex]x =2^{-5} - \frac{1}{16}[/tex]

[tex]x = \frac{1}{2^{5} } - \frac{1}{16}[/tex]

[tex]x = \frac{1}{32} } - \frac{1}{16}[/tex]

x = (16 - 32) / (16 x 32)

x =  -16 / 512

x = -0.03125

0r

x = [tex]-\frac{1}{32}[/tex]

Therefore, the value of x is -0.03125 or - 1/32.

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The image of the transformation is R' (-12, 3), S' (-12, 12) and T' (-6, 3)

The complete question is added as an attachment

The coordinates of the triangle are given as

R = (-4, 1)

S = (-4, 4)

T = (-2, 1)

The transformation is given as

Dilation by a scale factor of 3

Centered at the origin

The rule of the transformations is

(x, y) = 3(x, y)

So, we have

R' = 3 * (-4, 1) = (-12, 3)

S' = 3 * (-4, 4) = (-12, 12)

T' = 3 * (-2, 1)= (-6, 3)

Hence, the image of the transformation is R' (-12, 3), S' (-12, 12) and T' (-6, 3)

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Answer:v = ωr

v = speed in miles per hour (mph)

is the angle's speed in radians per hour.

r is the radius in miles.

(2400-rpm/60 minutes) =

(two radians per rev) Equals __ radians per hour

r=16 inches/2 = (8 inches)

(1/5280 miles/ft) (1/12 feet/in) = ______ miles

v = r = _ miles per hour

Step-by-step explanation:

v = ωr

v = speed in miles per hour (mph)

is the angle's speed in radians per hour.

r is the radius in miles.

(2400-rpm/60 minutes) =

(two radians per rev) Equals __ radians per hour

r=16 inches/2 = (8 inches)

(1/5280 miles/ft) (1/12 feet/in) = ______ miles

v = r = _ miles per hour

The required 84% of the people attending the basketball game supported the home team.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

To find the percentage of people who supported the home team, we need to calculate the proportion of people supporting the home team and convert it to a percentage.

The total number of people attending the game is,
2940 + 560 = 3500.

The proportion of people supporting the home team is,
= 2940 / 3500
= 0.84.

To convert this proportion to a percentage, we multiply it by 100:

= 0.84 × 100 = 84%

Thus, 84% of the people attending the basketball game supported the home team.

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The solution to the division problem is xyz = −434 with a remainder of 0.

The given equation is [tex]$\frac{4-4-40-1-100-1}{xyz} = -434$[/tex]. To solve this equation, we need to find the value of [tex]$xyz$[/tex]. We can use the distributive property to break up the numerator, yielding [tex]$\frac{(-1)(-100)(-1)}{xyz} = -434$[/tex]. Then, we can multiply both sides by [tex]$xyz$[/tex] to get [tex]$(-1)(-100)(-1)xyz = -434xyz$[/tex] . Since the terms on both sides of the equation are equal, we can simplify to [tex]$(-1)(-1)(-100)xyz = -434xyz$[/tex] . Now, we can factor out the xyz, which yields  [tex]$xyz(-1)(-1)(-100) = -434xyz$[/tex]. Since we want to find the value of xyz, we can divide both sides by the common factor of xyz, yielding [tex]$(-1)(-1)(-100) = -434$[/tex] . Finally, we can solve for xyz by multiplying both sides by the common factor of (-1)(-1)(-100), yielding xyz = -434. Therefore, the value of xyz in the given equation is -434.

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