The area of the circular base of a cone is 16π cm², and the slant height of the cone is 4 times the radius of the cone.

What is the approximate lateral area of the cone?

Use π≈3.14.

Enter your answer rounded to the nearest whole number in the box.

Note that from the graph given above and their slopes, it is correct to state that mRT = mTV.

First, note that the slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.

Here, Slope RT = Δy/Δx = SR/ST = 2/4 = 1/2

Slope TV =  Δy/Δx = UT/UV = 1/2

Thus, since the Slope of RT = 1/2 and the Slope of TV = 1/2 it i correct to state that mRT = mTV.

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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 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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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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Answer:

4.5

Step-by-step explanation:

Distance that James has to travel = 4.32 km

Distance that Megan has to travel = 0.96 km

How many times as long  
==> 4.32/0.96 = 4.5

Therefore,

The distance James lives from school is 4.5 times, as long as the distance Megan lives from school

4.5 is the answer which goes into the blank

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.

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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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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9) △MST is not similar to △DJZ

10) △ARP is not similar to △TRY.

11) △XYZ is not similar to △RVW

12) △ADE is not similar to △ABC.

What are similar triangles?

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

"If in two triangles, sides of one triangle are proportional to (i.e., in the same ratio of) the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar," states the Side-Side-Side (SSS) criterion.

The length of the sides of △MST are 16, 12, 5.

The length of the sides of △DJZ are 10, 7, 3

The ratio of sides is

16/10 ≠ 12/7 ≠ 5/3.

The length of the sides of △ARP are 15, 12, 5.

The length of the sides of △TRY are 54, 43.2, 18

The ratio of sides is

15/54 ≠ 12/43.2 ≠ 5/18.

The length of the sides of △XYZ are 17, 15, 8

The length of the sides of △RVW are 30.6, 27,4

The ratio of sides is

30.6/17 ≠ 27/15 ≠ 4/8.

The length of the sides of △ABC are 9, 8, 6.

The length of the sides of △ADE are 24, 12+8 = 20, 9+6=15

The ratio of sides is

24/9 ≠ 20/8 ≠ 15/6.

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

Step-by-step explanation:

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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Answer:

dfgss sdffcfsgdbebgndnngsageqfetehashqrvdqhqdhtqi

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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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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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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Step-by-step explanation:

x

x+2

x+4

x+6

x+8

these are the 5 consecutive odd integers.

when starting with an odd number as x, with every added 2 we get again an odd number.

the sum of the last 3 integers is 3 more than the sum of the 2 greatest :

x+4 + x+6 + x+8 = x+6 + x+8 + 3

we can subtract (x+6) abd (x+8) from both sides :

x + 4 = 3

x = -1

so, the 5 numbers are

-1

1

3

5

7

3 + 5 + 7 = 15

5 + 7 + 3 = 15

correct.

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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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 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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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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Using inequality views, the compound inequality is given by:

50 ≤ P ≤ 90

            a ≤ x ≤ b

                                          50 ≤ P ≤ 90

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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 equation that represent the value of the computer in years is: computer cost at (n-1) year - 1/5 (n-1cost) and the computer be worth less than $100 at 10 year

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

According to the data problem,

The cost of computer = $ 800

It lost 1/5 of value every year.

The value of computer after 0 years = cost of computer = $ 800

The value after 1 year = 800 - (1/5*800) = $640

The value after 2 years = 640 - (1/5*640) = $512

The value after 3 years = 512- (1/5*512) = $409.6

Continue with the formula we have:

The value after 9 years = 134.21 - (1/5*134.21) = 107.37

The value after 10 years = 107.37 - (1/5*107.37) = 85.90

The value after n years = computer cost at (n-1) year - 1/5 (n-1cost)

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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.

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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Answer: a (x – x1) + b (y– y1) + c (z –z1) = 0.

Step-by-step explanation:

Recall that the general form of the equation of a straight line in two dimensions is

++=0.

This can also be written in the form 

=+, where  is the gradient and  is the -intercept, which we can determine by knowing two points on the line.

If (,) is a point that lies on the line, we can determine  from the general form as =−(+); thus, the equation of the line can be written as

+−(+)=0.

The equation of the line can also be realized as a dot product of two vectors as (,)⋅(−,−)=0.

Now, if we define the position vectors,⃑=(,),⃑

then the equation of the line can be written in vector form as⃑ ⋅⃑=⃑⋅⃑,where ⃑=(,) is called a normal vector of the line and ⃑−⃑ will lie completely on the line.

A property of the dot product states that two vectors are perpendicular to each other if their dot product is zero. This equation of the line in vector form shows that the normal vector ⃑ and the vector ⃑−⃑ are perpendicular to each other by this property.

The general equation of a plane in three-dimensional space can be represented as Ax + By + Cz = D.

What is the plane?

A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors. The generalization of the plane to higher dimensions is called a hyperplane. The angle between two intersecting planes is known as the dihedral angle.

Where A, B, and C are coefficients and D is a constant.

The coefficients A, B, and C represent the components of the normal vector to the plane, and D represents the distance of the plane from the origin.

The equation defines a set of all points (x, y, z) in space that satisfy the equation and lie on the plane.

Hence, The general equation of a plane in three-dimensional space can be represented as Ax + By + Cz = D.

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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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Answer:

C. (-5,0) ( -2, 0)

Step-by-step explanation:

The X-intercept is when the y = 0

We see the x-intercept on the graph is located at (-5,0) and (-2,0), so the answer is C.