Suppose the line tangent to the graph of f at x is yx and suppose yx is the line tangent to the graph of g at x. Find the line tangent to the following curves. I need help with the f(x)=g(x) part of the question.

The  work required to pump the water out of the spout is 70.9 * 10⁶ joules which is 71 M Joules approx.

Let the spherical tank be divided into a series of horizontal disks.

Let x be the height of each disk, g = gravity and p = density

Volume of each disk = πr2dx

Where r is the radius of each disk and dx is the thickness

By Pythagoras r² = 6² - x²= 36 -x²

Therefore Volume = π*(36-x²)*dx cubic metres

The distance each disk has to be lifted to escape the top of the spout = 2 + 6-x meters = (8-x)

Work needed to lift each disk to outlet = distance * mass where

mass = volume * density * gravity

        = pi(36-x²)*p*g = 9800pi(36-x²)dx

dW =  (8-x)* 9800pi(36-x²)dx

Since we have already accounted for the height of the spout, the work required is obtained by integrating the above expression from the bottom of the tank to the top. In other words, - 6 to + 6.

W = ⌠(8-x)*9800pi(36-x2)dx = 9800pi⌠[288 - 36x - 8x² +x³]dx

The odd terms evaluate to zero and we can rewrite the above as 2* I from 0 to 6.

W = 9800pi*2 [288x - 8x³/3] at x = 6 = 1152*19600π Joules = 22579200π joules = 70963200j

Total work required = 70.9 * 10⁶ joules

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Answer:

B. False

Step-by-step explanation:

The domain is the set of values of x.

There is no restriction on the value of x.

x can be any real number.

Answer: B. False

The formula for the circumference of a circle is given by 2 * pi * r, where r is the radius. If the circumference is 9.42 inches, then we can write the equation:

9.42 = 2 * pi * r

Solving for r, we get:

r = 9.42 / (2 * pi)

The diameter of the circle is equal to 2 * r, so:

d = 2 * r = 2 * (9.42 / (2 * pi)) = 9.42 / pi

So, the radius of the circular donut is approximately 3 inches, and the diameter is approximately 9.42 inches.

The number of the 3 / 5 in a tape diagram is 3.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator. Any number of equal parts is represented by a fraction, which also represents a portion of a whole.

A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated.

Given that the fraction is 3 / 5. When we add the fraction three times we will get the value that is closest to 2.

E = 3 / 5 + 3 / 5 + 3 / 5

E = ( 3 + 3 + 3 ) / 5

E = 9 / 5

E = 1.8 ≅ 2

Hence, in a tape diagram, the 3/5 is represented by the number 3.

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Answer:

Radius = 5 units

Diameter = 10 units

Circumference = 10π units

Area = 25π square units.

Step-by-step explanation:

i choose diameter.

Let's say the diameter of the circle is 10 units.

The radius of the circle can be found by dividing the diameter by 2:

Radius = Diameter / 2 = 10 / 2 = 5 units

The circumference of the circle can be found using the formula:

Circumference = 2πr = 2π * 5 = 10π units

The area of the circle can be found using the formula:

Area = πr^2 = π * 5^2 = 25π square units.

So, for a circle with a diameter of 10 units:

Radius = 5 units

Diameter = 10 units

Circumference = 10π units

Area = 25π square units.

A system of equations in standard form to model this scenario include the following:

2x + 10y = 74.

x + y = 17.

In order to write a system of linear equations that could be used to model the situation and determine the number of small boxes shipped and the number of large boxes shipped, we would assign variables to the number of small boxes that were shipped, the number of large boxes that were shipped respectively as follows:

Next, we would translate the word problem into system of linear equations as follows:

Since x small boxes weigh 2 pounds each and y large boxes weigh 10 pounds each and  all the boxes she ships is 74 pounds;

2x + 10y = 74.

Additionally, she is shipping 17 boxes altogether;

x + y = 17.

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The number in question is 28.

To make solving this problem easier, we need to consider the number.

Let the number is ab.

So that,

4 × a = b

4a = b

We spread the numbers on the options.

28

(4 × 2 = 8) → True

32

(4 × 3 = 2) → False

15

(4 × 1 = 5) → False

25

(4 × 2 = 5) → False

We prove what number of 28 is when the digits is reversed to be greater than 54.

28 ⇄ 82

It is proved that the number 82 is greater than the number 54.

So, the number in question is 28.

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The relationship between the price of balloons and the amount earned is 56f + 120 dollars

The price of the balloons if 400 dollars is earned on friday and saturday is 5 dollars on friday and 8 dollars on saturday

a) If f is the price of a balloon on Friday, then the price of a balloon on Saturday would be f + 3 dollars. The total amount Thomas earns on Friday would be 16 balloons * f dollars/balloon = 16f dollars. The total amount Thomas earns on Saturday would be 40 balloons * (f + 3 dollars/balloon) = 40f + 120 dollars. Hence, the total amount earned on Friday and Saturday would be 16f + 40f + 120 dollars = 56f + 120 dollars.

Therefore, the equation to describe the relationship between the price of a balloon on Friday and the total amount earned is: t = 56f + 120 dollars.

b) We are given that Thomas earns 400 dollars on Friday and Saturday, so we can set t = 400 dollars in the equation derived above:

400 = 56f + 120

Solving for f, we have:

280 = 56f

f = 5 dollars

The price of a balloon on Friday is $5, and the price of a balloon on Saturday would be f + 3 = 5 + 3 = $8.

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There are 353925 committees of 10 persons that can be chosen with exactly 8 men.

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

People = 15 men and 11 women

Committee = 10 persons (8 men)

The number of ways is then calculated as

Ways = Men * Women

So, we have

Ways = C(15, 8) * C(11, 2)

Evaluate the products

Ways = 353925

Hence, the number of committee is 353925

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For a set of data in which the sample mean is 83.3 and the sample standard deviation is 6.3 the z-score given that x = 79.8 would be -0.555

We know that the formula for calculating a z-score is :

z = (x - μ) / σ

where z is the standard z - score

x is the observed value

μ is the mean of the sample

σis the standard deviation of the sample

here, set of data in which the sample mean is 83.3 and the sample standard deviation is 6.3

i.e., μ = 83.3,  σ = 6.3

We calculate the z-score for x = 79.8

Using above formula,

z = (x - μ) / σ

z = (79.8 - 83.3) / (6.3)

z = (-3.5) / (6.3)

z = -0.555

Therefore, the z-score is:  -0.555

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Answer:

see below

Step-by-step explanation:

we need to write the inverse of ,

[tex]\longrightarrow f(x) = 3x -1 \\[/tex]

Substitute [tex] f(x)=y[/tex] ,

[tex]\longrightarrow y = 3x-1 \\[/tex]

Interchange x and y ,

[tex]\longrightarrow x = 3y -1 \\[/tex]

now solve for y ,

[tex]\longrightarrow 3y = x + 1 \\[/tex]

[tex]\longrightarrow y =\dfrac{x+1}{3} \\[/tex]

replace [tex] y[/tex] with [tex] f^{-1}(x)[/tex] as ,

[tex]\longrightarrow \underline{\underline{ f^{-1}(x) =\dfrac{x+1}{3}}}\\[/tex]

And we are done!

Answer:

[tex]f^{-1}(x)=\log_3(x)+1[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=3^{x-1}[/tex]

To find the inverse of the given function, swap y and x:

[tex]\implies x=3^{y-1}[/tex]

Take the log base 3 of each side of the equation:

[tex]\implies \log_3(x)=\log_{3}3^{y-1}[/tex]

[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies \log_3(x)=(y-1)\log_{3}3[/tex]

[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]

[tex]\implies \log_3(x)=(y-1)(1)[/tex]

[tex]\implies \log_3(x)=y-1[/tex]

Add 1 to both sides of the equation:

[tex]\implies \log_3(x)+1=y[/tex]

[tex]\implies y=\log_3(x)+1[/tex]

Replace y for f⁻¹(x):

[tex]\implies f^{-1}(x)=\log_3(x)+1[/tex]

Answer:

we on top

Step-by-step explanation:

Answer:

Step-by-step explanation:

you gotta be kidding me right now b r u h.  Aint no way bro is posting this hahahha get it i guess

The solutions are:

a. x = 7

b. x = 7

The tape diagrams are given in the image below.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Two equations,

a. x + 9 = 16

b. 4x = 28

Solving the first equation,

x + 9 = 16

x = 7

Solving the second equation,

4x = 28

x = 7

The tape diagrams are given in the image below.

Hence, all the unknown values are given above.

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The last

M angle 3 = 68 degrees

Step-by-step explanation:

interior angles between parallel lines

sum =180

For the system of equations, y = 10 + 2z and y = 38 - 5z the value of y and z are 18 and 4 respectively.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The first equation is : y = 10 + 2z

The second equation is : y = 38 - 5z

Subtract equation (1) and (2) -

y - y = 10 + 2z - (38 - 5z)

0 = 10 + 2z - 38 + 5z

Collect the like terms -

2z + 5z = -10 + 38

7z = 28

z = 28/7

z = 4

Substitute the value of z in equation (1) -

y = 10 + 2(4)

y = 10 + 8

y = 18

Therefore, the value of y = 18 and z = 4.

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The sum of the squares of the differences between each data value and the mean is given as follows:

828.

The mean of the data-set in this problem is given as follows:

33.

The data-set is given as follows:

28, 34, 27, 42, 52 and 15.

Hence the sum of the squares of the differences between each data value and the mean is obtained as follows:

(28 - 33)² + (34 - 33)² + (27 - 33)² + (42 - 33)² + (52 - 33)² + (15 - 33)² = 828.

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The translation of the sentence 'The sum of 15 and Delia’s age is 65'

is 15 + d = 65.

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

Let, The age of Delia be 'd'.

Therefore, The equation for the statement 'The sum of 15 and Delia’s age is 65'  can be expressed as,'

15 + d = 65.

d = 65 - 15.

d = 50.

So, The age of Delia is 50 years.

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The triangle is congruent by the Angle side Angle property.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.

The Angle side Angle Congruence Theorem (ASA) defines two triangles to be congruent to each other if the included two angles and one side of one are congruent to the included angle and corresponding two sides of the other triangle.

The three parameters that are congruent are:-

BV ≅ BV ( common side)

∠1 ≅ ∠2  ( Bisector)

∠3 ≅ ∠4  ( Bisector)

Hence, the two triangles are congruent with each other.

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Answer: To find the distance fallen after 1.6 seconds, we simply plug this value into the function and solve for h:

h = t^2 * 16

h = 1.6^2 * 16

h = 2.56 * 16

h = 40.96 feet

So, the object has fallen 40.96 feet after 1.6 seconds.

Step-by-step explanation:

The solutions for all the equations are:

1) x = 4

2) x = ±7

3) x = 5²´³

4) x = ±5³´²

The first equation is:

x³ = 64

If we apply the cubic root in both sides we will get:

∛x³ = ∛64

x = ∛64 = 4

2) now we have:

x² = 49

If we apply the square root:

√x² = ± √49

(remember the plus minus sign when you use a even degree root)

x = ±7

In this case we have two solutions.

3) x³ =25

Like in the first case:

x = ∛25 = ∛5² = 5²´³

Now we can't simplify this, so we leave it in this way.

4) x² = 125

Remember that 125 = 5³, then:

x² = 5³

x = ±√5³ = ±5³´²

These are all the solutions.

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a must be the least upper bound of S because it satisfies both conditions: it is an upper bound of S, and any other upper bound b for S must be greater than or equal to a.

What is the difference between the least upper bound and upper bound?

An upper bound of a set S of real numbers is any real number that is greater or equal to all numbers in S. A lower bound is any which is less than or equal to all numbers in S. A least upper bound is an upper bound that is less than or equal to all upper bounds.

To prove that a is the least upper bound (LUB) of the set S, we need to show that a satisfies two conditions:

a is an upper bound of S, meaning that for every element x in S, x <= a.

If there is another upper bound b for S, then a <= b.

First, we already know that a is an upper bound of S because it is given that a is an upper bound of the set S.

Next, suppose there is another upper bound b for S such that b > a. Then, since the sequence xₙ converges to a, there exists a positive integer N such that for all n >= N, xₙ is arbitrarily close to a, meaning that |xₙ - a| < (b - a)/2. This means that xₙ < b for all n >= N, which contradicts the assumption that b is an upper bound of S, since xₙ is an element of S and xₙ < b.

Therefore, a must be the least upper bound of S because it satisfies both conditions: it is an upper bound of S, and any other upper bound b for S must be greater than or equal to a.

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As a result, the length is 8.5 cm and the breadth is 3.5 cm, and the total perimeter is 22 cm.

what is perimeter ?

An enclosed line that surrounds, distinguishes, or incorporates a two-dimensional contour or a three-dimensional length is referred to as a boundary. The edge of an ellipse or circle refers to its broadest area. The perimeter calculation has many useful properties. The rim of a form is its edge's radius. Understand how to determine the perimeter by adding the lengths of such sides of various forms. You can always measure the perimeter of a shape by multiplying its side lengths. The perimeter of an object is the space around it. At your house, any enclosed terrace is one illustration. The border of anything is the area encircling it. For a 50 feet x 50 feet yard, a 200 foot fence is required.

given

let the length of the rectangular wallet be x

the width be x - 5

perimeter = sum of all the sides = 22

x + x - 5 = 22

2x - 5 = 22

2x = 17

x = 8.5

length is 8.5 and width is 8.5 - 5 = 3.5

As a result, the length is 8.5 cm and the breadth is 3.5 cm, and the total perimeter is 22 cm.

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Answer:

84

Step-by-step explanation:

Let's call the father's present age "F" and the son's present age "S".

Five years ago, the father's age was F - 5 and the son's age was S - 5.

According to the first statement, F - 5 = 6(S - 5), so F = 6S - 35.

Two years in the future, the father's age will be F + 2 and the son's age will be S + 2.

According to the second statement, F + 2 = 3(S + 2) + 1, so F = 3S + 7.

We can now substitute the first equation into the second:

3S + 7 = 6S - 28,

3S - 6S = -35 - 7 = -42,

-3S = -42,

S = 14.

Finally, the father's present age is F = 6S - 35 = 84.

Answer:

The dad is 35 and the son is 10

Step-by-step explanation:

Let f =  the father's age

let s - the son's age

In the equations f-5 and s-5 represents the father and son's ages 5 years ago.   f + 2 and s +2 represent the father and son's ages two years in the future.

The lines are skew is Lines AD and BF.

Skew lines are two lines that do not intersect, are not parallel, and are not coplanar. This means that the skew lines never cross and are not parallel to each other. For lines to be two-dimensional or coplanar, they can intersect or be parallel. This property does not apply to diagonal lines, which are always non-coplanar and exist in three or more dimensions.

In real life, cities have different types of roads, such as highways and overpasses. These streets are supposed to be on different levels. Lines drawn on such roads never intersect, creating skew lines instead of being parallel to each other.

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Answer:

he item should be put in the oven at 12:25 (in 24-hour format) to be ready for lunch at 13:00.

Step-by-step explanation:

To calculate what time the item should be put in the oven, you need to work backwards from the desired serving time of 13:00 and subtract the cooking time of 35 minutes. Here's how you can do it:

Convert the serving time to 24-hour format: 13:00 is the same as 1:00 PM in 12-hour format. In 24-hour format, it is 13:00.

Subtract the cooking time: Subtract 35 minutes from the serving time of 13:00 to get the time when the item should be put in the oven.

13:00 - 00:35 = 12:25

So, the item should be put in the oven at 12:25 (in 24-hour format) to be ready for lunch at 13:00.

In linear equation, The effect of the time of day a science class is taught on test scores being studied in an experiment will be the length of the class period.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                                 The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

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Answer:

Step-by-step explanation:

We can find the rental cost for each movie and each video game by dividing the total cost by the number of movies and video games rented, respectively.

For the movies:

Rental cost for each movie = Total cost of movies rented / Number of movies rented

= $33 + $24 = $57

= $57 / 6 = $9.50 per movie

For the video games:

Rental cost for each video game = Total cost of video games rented / Number of video games rented

= $18 + $24 = $42

= $42 / 4 = $10.50 per video game.

10 divided by 0 problem would NOT have a solution.

Given:

a. 10 divided by 2

b. 10 divided by 5

c. 10 divided by 0

d. 0 divided by 10

We know that ,

Integer divided by an integer is an integer

Therefore (a) and (b) will have a proper solution

We also know that ,

Zero divided by anything is Zero

Therefore (d) also have a unique answer that is zero

Now , We know that

Any numeric value divided by Zero tends to infinity .

Hence, 10 divided by 0 problem would NOT have a solution.

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