What is the quotient of the given values to the correct level of precision? 16.017 in. ÷ 0.370 in. 43 43.289 43.29 43.3

The volume of the cone is  84.9 km³

Volume of a cone = 1 / 3 πr²h

where

Therefore,

radius = 3 km

height = √9.5² - 3²

height = √81.25

height = 9.01387818866

height = 9.014 km

Volume of a cone = 1 / 3 × 3.14 × 3² × 9.014

volume of the cone = 254.732197612 / 3

volume of the cone = 84.9107325372

volume of the cone = 84.9 km³

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What is an algebraic expression?

An expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, etc.

What is the substitution method?

The substitution method is generally used to solve the system of equations. In this method, first, solve the equation for one variable, and substitute the value of the variable in the other equation

5th question :

⇒ x(2y-x)²+2x²(x-2y)

let (x-2y) = A

⇒we can also write (2y-x)² as (x-2y)² as both have the same value

x(x-2y)²+2x²(x-2y)

x(A)²+2x²(A)

By taking xA common

⇒ xA(A+2x)

On putting the value of A=(x-2y)

⇒ x(x-2y) (x-2y+2x)

⇒x(x-2y) (3x-2y)

6th question :

2(x-y)-(y-x)²

let (x-y) = B

⇒we can also write (y-x)² as (x-y)² as both have the same value

2(x-y)-(x-y)²

2B-(B)²

By taking B common

⇒ B(2-B)

On putting the value of B=(x-y)

⇒(x-y) (2-{x-y})

⇒(x-y) (2-x+y)

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Answer:

4

Step-by-step explanation:

h(x) = -1/3x+2 where we need to find -4h(9)

h(9): x = 9

h(x) = -1/3(9) + 2

h(x) = -3 + 2

h(x) = -1

-4h(9) is -4h(x):

-4(-1) = 4

Answer:

Assunming that the equation is y = -16x² +85x, I suggest Dario find a new profession.  He kicks the ball 133 feet high, but it only travels 2.7 feet downfield at that point.  It will have travelled 2*2.7 feet or 5.4 feet horizontal when it returns to ground.

Step-by-step explanation:

We can answer the question of how hiogh and far the ball travels (in feet) by either of two methods.  The first is to differentiate the equation and set it equal to 0, and the second is the graph it and look for the vertex and x intercept.

Differentiate

y = -16x² +85x

The first derivative produces an equation that gives us the slope of the line at any point x.  At the ball's top height, it stops and reverses direction, a point at which the slope is zero.

y = -16x² +85x

d(y)/d(x) = -32x + 85

0 = -32x + 85

32x = 85

x = 2.66 feet horizontal distance when the ball reaches its peak.

At x = 2.66, y is 112.9 feet high

When the ball returns, it adds amnother 2.66 feet to the horizontal distance, for a total of 5.4 feet.

Graph:

See attached plot of the function.

Horizontal distance is 2.66 feet and height is 133 feet. The x-intercept is at 5.4 feet.

After all that, the ball only travelled downfield (we hope downfield) a total of 5.4 feet.

Answer:

x=1

Step-by-step explanation:

2/3(9x-6) = 1/4(12-4x)

We want to solve for x

Distribute

6x-4=3-x

Add x to each side

6x-4+x = 3-x+x

7x-4 = 3

Add 4 to each side

7x-4+4 = 3+4

7x=7

Divide by 7

7x/7 = 7/7

x=1

Answer:

x = 1

Step-by-step explanation:

[tex]\frac{2}{3}[/tex] (9x - 6) = [tex]\frac{1}{4}[/tex] (12 - 4x) ← distribute parenthesis on both sides

6x - 4 = 3 - x ( add x to both sides )

7x - 4 = 3 ( add 4 to both sides )

7x = 7 ( divide both sides by 7 )

x = 1

A sky wheel is a mechanical device that has a shape of a circle divided into a given number of equal sectors. Thus, the measure of each central angle required in the question is [tex]8.6^{o}[/tex].

A sky wheel is a mechanical device that has a shape of a circle divided into a given number of equal sectors. Thus each sector has an equal central angle. Since the sum of the internal angles of a circle is [tex]360^{o}[/tex].

From the given question, it has been stated that the sky wheel has 42 glass-enclosed gondolas. This implies that the sky wheel has been divided into 42 equal sectors.

Therefore,

the measure of each central angle = [tex]\frac{360^{o} }{n}[/tex]

where n represents the number of gondolas (42).

Thus,

the measure of each central angle between gondolas cars= [tex]\frac{360}{42}[/tex]

                                        = 8.5714

The measure of each central angle between gondolas cars is approximate [tex]8.6^{o}[/tex].

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a. log₈8 = 1

b. log₇6/5

c. log₉3¹

1. log₈ 2 * 4 would produce an integer

= log₈8 = 1

The output is an integer

2. log₇6/5 would give us an irrational number

= log₇1.2

This would give us an irrational number

3. log₉3¹ would give us a rational number

= log₉9^[tex]^\frac{1}{2}[/tex] = 1/2 log⁹9

= 1/2

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Answer:

First answer lol

Step-by-step explanation:

is the domain by any chance x ≥-2?

Order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.

To find the order of matrix:

To prove:

Therefore, order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.

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Answer:B

Step-by-step explanation:

Considering the graph of the velocity of the car, it is found that the interval in which it was stopped at a traffic light was:

Between 3 and 4 minutes.

When a car is stopped at a traffic light, the car is not moving, that is, it's velocity is of zero.

In this problem, the graph gives the velocity as a function of time, and it is at zero between 3 and 4 minutes, hence the interval in which it was stopped at a traffic light was:

Between 3 and 4 minutes.

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6) For the inverse to be a function, f(x) needs to be one to one. To accomplish this, restrict the domain to one side of the axis of symmetry

7) The y-intercept of the inverse is when x=0. This means we want to find when f(x)=0.

[tex]4(1/3)^x = 16 \\ \\ (1/3)^x= 4 \\ \\ x=\log_{1/3}(4) \approx -1.26[/tex]

Answer:

0.075

Step-by-step explanation:

to convert a fraction to a decimal fraction

divide the numerator by the denominator, that is

[tex]\frac{3}{40}[/tex] = 3 ÷ 40 = 0.075

The height of the flagpole is 12.4 meters and the altitude of the balloon is 29.1 meters

See attachment for the diagram, when redrawn

Start by calculating the length AB using the following tangent function

tan(22) = BC/AB

This gives

tan(22) = 9/AB

Make AB the subject

AB = 9/tan(22)

Evaluate the quotient

AB = 22.3

The length DB is then calculated using:

tan(9) = DB/AB

This gives

tan(9) = DB/22.3

Make DB the subject

DB = 22.3 * tan(9)

Evaluate

DB = 3.35

The height of the flagpole is then calculated as:

Height = DB + BC

This gives

Height = 3.35 + 9

Evaluate

Height = 12.35

Approximate

Height = 12.4

Hence, the height of the flagpole is 12.4 meters

The diagram that illustrates the scenario is added as an attachment

Calculate the value of y using the following tangent functions

tan(57) = x/y and tan(72) = (15 + x)/y

Make y the subject in tan(57) = x/y and tan(72) = (15 + x)/y

y = x/tan(57) and y = (15 + x)/tan(72)

Substitute y = x/tan(57) in y = (15 + x)/tan(72)

x/tan(57) = (15 + x)/tan(72)

Evaluate the tangent ratios

x/1.5 = (15 + x)/3.1

Cross multiply

3.1x = 22.5 + 1.5x

Evaluate the like terms

1.6x = 22.5

Divide by 1.6

x = 14.1

The altitude of the balloon is then calculated as:

Altitude = 14.1 + 15

Altitude = 29.1

Hence, the altitude of the balloon is 29.1 meters

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The value of [tex](102)^3[/tex] exists 1061208.

Let us rewrite [tex](102)^3[/tex] as [tex](100+2)^3[/tex]

Now utilizing the identity [tex](a+b)^3=a^3+b^3+3ab(a+b)[/tex], we get

a = 100 and b = 2 then substitute the values of a and b then

[tex](100+2)^3=100^3+2^3+[(3\times100\times2)(100+2)][/tex]

= 1000000 + 8 + (600 × 102)

= 1000000 + 8 + 61200

= 1061208

Hence, [tex](102)^3=1061208[/tex]

Therefore, the value of [tex](102)^3[/tex] exists 1061208.

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100–pound earthling's weight on Saturn using the proportion is (B)

15/4 = 100/x.

To find the 100–pound earthling's weight on Saturn using the proportion:

Therefore, 100–a pound earthling's weight on Saturn using the proportion is (B) 15/4 = 100/x.

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The correct question is given below:
A bowling ball weighs 15 pounds on earth and weighs 4 pounds on the planet Saturn. you could determine a 100–pound earthling's weight on Saturn using the proportion:

a. start fraction 15 over 4 end fraction = start fraction x over 100 end fraction

b. startfraction 15 over 4 endfraction = 100 over x endfraction

c. startfraction 4 over 15 endfraction = startfraction 100 over x endfraction

d. either a or c

Answer:

c = 15

Step-by-step explanation:

expand the left side and compare with like terms on the right side

2x(4x + 5) + 3(4x + 5) ← distribute parenthesis

= 8x² + 10x + 12x + 15 ← collect like terms

= 8x² + 22x + 15

compare to ax² + bx + c

then c = 15

The perimeter of a given shape implies the sum of all its sides. While the area of a given shape is the total value of space it would cover on a 2-dimensional plane.

The perimeter of the shape is 104 cm.

The area of the shape is 640 [tex]cm^{2}[/tex].

The perimeter of a given shape implies the sum of all its length of sides., such that the value of each individual side is summed to a total value.

The area of a given shape is the total value of space it would cover on a 2-dimensional plane. The area of shapes depends on the type of shape.

In the given question, the given shape has 12 sides. Some of these sides can sum up to a given length as shown in the diagram.

So that;

perimeter = 2 + 32 + 10 + 10 + 2 + 32 + 8 + 8

                 = 104 cm

Thus, the perimeter of the shape is 104 cm

ii. The area of the shape = length x width

                                         = 32 x 20

                                         = 640 [tex]cm^{2}[/tex]

Therefore, the area of the given shape is 640 [tex]cm^{2}[/tex].

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Answer:

The bottom graph.

Step-by-step explanation:

The asymptote ( in between the 2 curves) on the bottom graph is  at x = 1, because when x = 1 the denominator = 0.

The new mixture exists 56.5% peanuts.

The first batch of 9 lb of mixed nuts possesses 40% peanuts.

This means the quantity of peanuts exists:

9 [tex]*[/tex] 40/100 = 3.6 lb

The second batch of 9 lb of mixed nuts possesses 73% peanuts.

This means the quantity of peanuts exists:

9 [tex]*[/tex] 73/100 = 6.57 lb

The total quantity of peanuts in the mix exists

3.6 lb + 6.57 lb = 10.17 lb

There exist 9 lb + 9 lb = 18 lb of mix.

Therefore, the percent of peanuts in the mix exists:

10.17 / 18 [tex]*[/tex] 100 = 56.5%

The new mixture exists 56.5% peanuts.

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The number which is express in each of the models as given in the image attached to the task content are as follows;

a). 1.37

b). 1.37

c). 1.37.

It follows from the task content that the models describe that One flat represents 1 whole, One rod represents 1 tenth and one unit represents 1 hundredth.

It therefore follows from the task content that in each of the models, the algebraic sum of flat(s), rods and units as the case may be results in the value; 1.37 as the utmost number represented by the models.

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Answer:

24 dollars.

Step-by-step explanation:

1/4 + 1/3 = 3/12 + 4/12 = 7/12

7/12 a + 8 = 22

7/12 a = 14

a = 14 x 12/7

a = 24

Triangles DEF and JKL can be proven to be congruent triangles based on:

C. ASA

E. AAS

F. LA

The ASA congruence theorem states that if two triangles that are have two pairs of corresponding congruent angles and a pair of corresponding included congruent sides, then both triangles are congruent to each other.

The LA congruence theorem states that two right triangles are congruent if they have a pair of congruent legs and a pair of congruent angles that are corresponding to each other.

The AAS congruence theorem states that two triangles with two pairs of congruent angles and a pair of congruent non-included sides are congruent.

From the image given, triangles DEF and JKL can be proven to be congruent triangles using the LA, AAS, and ASA congruence theorems.

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Answer:

Exact form: 78√2 - 17√3 / 54

Decimal form: 1.49747766

Step-by-step explanation:

Rationalize and simplify the expression.

The first five terms of the sequence are 1/5, 2/5, 3/5,4/5, 1

Recursive functions are functions that is used to determine the next term of a given sequence giving the common difference.

Given the recursive function shown below;

f(1) = 1/5

f(n) = f(n-1) + 1/5

For the second term;

f(2) = f(1) + 1/5

f(2) = 1/5 + 1/5

f(2) = 2/5

For the third term;

f(3) = f(2) + 1/5

f(3) = 2/5 + 1/5

f(3) = 3/5

For the fourth term;

f(4) = f(3) + 1/5

f(4) = 3/5 + 1/5

f(4) = 4/5

For the fifth term;

f(5) = f(4) + 1/5

f(5) = 4/5 + 1/5

f(5) = 5/5 = 1

Hence the first five terms of the sequence are 1/5, 2/5, 3/5,4/5, 1

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Multiply 9 with 9, and we get:

9 × 9 = 81

Multiply 10 with 10, and we get:

10 × 10 = 100

We get the final result as:

Hope this helps :)

3435 were children visited the India gate.

What is a linear equation in math?

Given,

             men = 1265

            women = 1150

Total women and men -

        men + women = 2415

         = 5450-2415  ⇒ 3435

Therefore,  3435 were children visited the India gate.

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The value of the solution is 3π/2.

What is a trigonometric equation?

An equation involving one or more trigonometric ratios of unknown angles is called a trigonometric equation.

tan x/2 = -1

tanx/2 = tan(-π/4)

tanx=tanФ

⇒ The general equation of tanx=tanФ is

⇒ x=nπ+Ф

x/2=nπ+(-π/4)

at n=0

x/2=-π/4

x=-π/2

at n=1

x/2=π-π/4

x/2=3π/4

x=3π/2

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Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Questions: Which value is a solution for the equation tan x/2 = -1?

A. 5pi/4

B. 7pi/4

C. 3pi/4

D. 3pi/2

Answer:

Below in bold.

Step-by-step explanation:

9t^2 - u^2     (the difference of 2 squares)

= (3t - u) (3t + u).

2c - 4d - pc + 2pd

= 2(c - 2d) - p(c - 2d)

c -2d is common to both parts so the factors are:

(2 - p)(c - 2d)

Answer:

See below.

Step-by-step explanation:

Converse

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

Given statement:  If n is an even integer, then 2n + 1 is an odd integer.

Converse:  If 2n + 1 is an odd integer, then n is an even integer.

Given statement:  If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.

Converse:  If a transversal intersects two lines such that each pair of corresponding angles is equal, then the two lines are parallel to each other.

Given statement:  If each pair of opposite sides of a quadrilateral is equal, then the quadrilateral is a parallelogram.

Converse:  If a quadrilateral is a parallelogram, then each pair of opposite sides of the quadrilateral is equal.

Given statement:  If the decimal expansion of a real number is terminating, then the number is rational.

Converse:  If a real number is rational, then the decimal expansion of the number is terminating.