What is the slope of a line that contains the points (4, -2) and (-1, 4)

Answer:

sq. root(330)

Step-by-step explanation:

[tex] \sqrt{-55 \sqrt[3]{-216} } = \sqrt{-55(-6)} = \sqrt{330} [/tex]

[Cube root of -216 = -6]

Answer:

The triangle inequality states that the sum of the lengths of the two shortest sides of a triangle must be greater than the length of the largest side. Because 4 + 12 > 17 is not a true statement, the answer is "This triangle does not exist because the sum of 4 and 12 is less than 17."

Answer:

This triangle does not exist due to the fact that the sum of 4 and 12 is less than 17

Step-by-step explanation:

The triangle formaction rule states that the 2 smaller sides must be able to combine and be greater than the greatest side.

Triangle

Sides - 3, 4, 5

3+4=7

Meaning the two smaller sides add up to because greater than 5.

Non-Triangle

Sides - 5, 6, 13

5+6=11

This means that this is not a triangle because the smaller sides ‘5 and 6’ do not add up to become greater than 13.

Gemma’s Triangle

Sides - 4, 12, 17

4+12=16

Hence, Gemma‘s figure is not a triangle because the 2 smaller sides ‘4 and 12’ don‘t add up to be greater than 17.

Answer:

First option is the correct option.

Step-by-step explanation:

[tex] \frac{2x + 5}{ {x}^{2} - 3x } - \frac{3x + 5}{ {x}^{3} - 9x } - \frac{x + 1}{ {x}^{2} - 9 } [/tex]

Factor out X from the expression

[tex] \frac{2x + 5}{x(x - 3)} - \frac{3x + 5}{x( {x}^{2} - 9)} - \frac{x + 1}{ {x}^{2} - 9} [/tex]

Using [tex] {a}^{2} - {b}^{2} = (a - b)(a + b)[/tex] , factor the expression

[tex] \frac{2x + 5}{x(x - 3)} - \frac{3x + 5}{x(x - 3)(x + 3) } - \frac{x + 1}{(x - 3)(x + 3)} [/tex]

Write all numerators above the Least Common Denominators x ( x - 3 ) ( x + 3 )

[tex] \frac{(x + 3) \times (2x - 5) - (3x + 5) - x \times (x + 1)}{x(x - 3)(x + 3)} [/tex]

Multiply the parentheses

[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - (3x + 5) - x(x + 1)}{x(x - 3)(x + 3)} [/tex]

When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression

[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - 3x - 5 - x \times (x + 1)}{x(x - 3)(x + 3)} [/tex]

Distribute -x through the parentheses

[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - 3x - 5 - {x}^{2} - x }{x(x - 3)(x + 3)} [/tex]

Using [tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex] , simplify the product

[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - 3x - 5 - {x}^{2} - x}{x( {x}^{2} - 9)} [/tex]

Collect like terms

[tex] \frac{ {x}^{2} + 7x + 15 - 5}{x( {x}^{2} - 9)} [/tex]

Subtract the numbers

[tex] \frac{ {x}^{2} + 7x + 10}{ x({x}^{2} - 9)} [/tex]

Distribute x through the parentheses

[tex] \frac{ {x}^{2} + 7x + 10}{ {x}^{3} - 9x} [/tex]

Write 7x as a sum

[tex] \frac{ {x}^{2} + 5x +2x + 10 }{ {x}^{3} - 9x } [/tex]

Factor out X from the expression

[tex] \frac{x(x + 5) + 2x + 10}{ {x}^{3} - 9x} [/tex]

Factor out 2 from the expression

[tex] \frac{x( x + 5) + 2(x + 5)}{ {x}^{3} - 9x } [/tex]

Factor out x + 5 from the expression

[tex] \frac{(x + 5)(x + 2)}{ {x}^{3} - 9x } [/tex]

Hope this helps...

Best regards!!

The difference of the expression [tex]\frac{2x + 5}{x^2 -3x} - \frac{3x + 5}{x^3 - 9x} - \frac{x + 1}{x^2 - 9}[/tex] is [tex]\frac{(x+5)(x+ 2) }{x^3- 9x}[/tex]

The expression is given as:

[tex]\frac{2x + 5}{x^2 -3x} - \frac{3x + 5}{x^3 - 9x} - \frac{x + 1}{x^2 - 9}[/tex]

Factorize the denominators

[tex]\frac{2x + 5}{x(x -3)} - \frac{3x + 5}{x(x^2 - 9)} - \frac{x + 1}{x^2 - 9}[/tex]

Apply the difference of two squares to the denominators

[tex]\frac{2x + 5}{x(x -3)} - \frac{3x + 5}{x(x - 3)(x + 3)} - \frac{x + 1}{(x - 3)(x + 3)}[/tex]

Take LCM

[tex]\frac{(2x + 5)(x + 3) - 3x - 5 -x(x + 1) }{x(x - 3)(x + 3)}[/tex]

Expand the numerator

[tex]\frac{2x^2 +6x + 5x + 15 - 3x - 5 -x^2 - x }{x(x - 3)(x + 3)}[/tex]

Collect like terms

[tex]\frac{2x^2 -x^2 - x +6x + 5x - 3x+ 15 - 5 }{x(x - 3)(x + 3)}[/tex]

Simplify

[tex]\frac{x^2+7x+ 10 }{x(x - 3)(x + 3)}[/tex]

Factorize the numerator

[tex]\frac{(x+5)(x+ 2) }{x(x - 3)(x + 3)}[/tex]

Expand the denominator

[tex]\frac{(x+5)(x+ 2) }{x^3- 9x}[/tex]

Hence, the difference of the expression [tex]\frac{2x + 5}{x^2 -3x} - \frac{3x + 5}{x^3 - 9x} - \frac{x + 1}{x^2 - 9}[/tex] is [tex]\frac{(x+5)(x+ 2) }{x^3- 9x}[/tex]

Read more about equivalent expressions at:

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Hey Mate !

Your Answer is given in the snip below !!

Please do mark me as brainliest !!!

(ANSWER=  (D)   [tex]\frac{1}{6}[/tex] )

Explanation

Answer:

You have a standard number cube.

What is the probability of rolling a number less than 3, and then rolling a prime number?

D. 1/6

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Find the angle between the given vectors to the nearest tenth of a degree.

u = <8, 7>, v = <9, 7>

we will be using the formula below to calculate the angle between the two vectors;

[tex]u*v = |u||v| cos \theta[/tex]

[tex]\theta[/tex] is the angle between the two vectors.

u = 8i + 7j and v = 9i+7j

u*v = (8i + 7j )*(9i + 7j )

u*v = 8(9) + 7(7)

u*v = 72+49

u*v = 121

|u| = √8²+7²

|u| = √64+49

|u| = √113

|v| = √9²+7²

|v| = √81+49

|v| = √130

Substituting the values into the formula;

121= √113*√130 cos θ

cos θ = 121/121.20

cos θ = 0.998

θ = cos⁻¹0.998

θ = 3.6° (to nearest tenth)

Hence, the angle between the given vectors is 3.6°

Answer:

Step-by-step explanation:

Use the following formulas:

surface area of rectangular prism: A = 2wl + 2lh + 2hw

volume of rectangular prism: lwh

surface area of cylinder: A=2πrh+2πr^2

volume of cylinder: V=πr^2h

using these formulas, the surface area of the box is 424.3

the volume of the box is about 511.3

the surface area of the cylinder is about 275.77

the volume is 342.12

knowing this, the cylinder uses less material but the box holds more soup.

Answer:

2^34 = 17179869184

I hope this helps :)

Answer:

Please find the attached the required inequality graph

Step-by-step explanation:

Given that inequality is 2.5 ≤ x ≤ 4.5, we have;

The region in the given inequality is the region between 2.5 and 4.5 inclusive

Therefore, to represent 2.5 ≤ x ≤ 4.5 on the number line, we have;

A closed circle (representing the less than or equal to inequality symbol, showing inclusiveness) at 2.5, another closed circle at 4.5 (representing the less than or equal to inequality symbol, showing inclusiveness) and the region between 4.5 and 2.5 shaded.

Answer:

D. Decision support systems

Step-by-step explanation:

Operation Support System, sometimes referred to a group of computer programs that is used by the communications service provider for carrying out various operations or functions, such as monitoring, controlling, analyzing and managing a telephone or computer network.

It is often used by professionals such as Network planners, service designers, operations, architects and engineering teams in the service provider.

There are however, types of Operation Support System which are being used for different and specific purpose. They are classified into the following categories:

1. Transaction Processing Systems

2. Process control system

3. Enterprise collaboration system

4. Enterprise Resource

Hence, from the question above, the DECISION SUPPORT SYSTEM is not classified as Operation Support System.

Step-by-step explanation: A term can be a number, a variable, or a number times one or more variables.

So in this expression, the terms are +2n, +5, -3p, and +4q.

This means that there are 4 terms.

The answer is D - 4 :)

Answer:

Step-by-step explanation:

The length of this triangle is 10 squares

and the width is 4 squares

The diagonals divide the rectangle into four triangles

These traingles are isoceles

Each two triangles facing each others are identical

<B = 90 degree

B = alpha + Beta

Let Beta be the angle next alpha

The segment that is crossing Beta is its bisector since it perpendicular to the diagonals wich means that:

Beta = 2x

Then B = alpha + 2x

90 = alpha +2x

90-alpha = 2x

x = (90-alpha)/2

Answer:

x = 90 - 2α

Step-by-step explanation:

Solution:-

- Consider the right angled triangle " ABD ". The sum of angles of an triangle is always "180°".

                       < BAD > + < ADB > + < ABD > = 180°

                       < ABD > = 180 - 90° - α

                        < ABD > = 90° - α

- Then we look at the figure for the triangle "ABE". Where " E " is the midpoint and intersection point of two diagonals " AC and BD ".

- We name the foot of the perpendicular bisector as " F ":  " BF " would be the perpendicular bisector. The angle < BAE > is equal to < ABD >.

                    < ABD > = < BAE >  = 90° - α   ... ( Isosceles triangle " BEA " )

Where, sides ( BE = AE ).

- Use the law of sum of angles in a triangle and consider the triangle " BFA " as follows:

                     < ABF> + < BFA > + < BAF > = 180°

                     < ABF > = 180 - (90° - α) - 90°

                    < ABF > = α  

Where,       < BAF > = < BAE >

- The angle < ABD > = < ABE > is comprised of two angles namely, < ABF > and < FBE >  = x.

                        < ABD > = < ABE > = < ABF > + x

                         90° - α = α + x

                        x = 90 - 2α   ... Answer

Answer:

piece of wire 8 m long

one piece is bent into square:

the square has four equal sides , so at least 4 m has to be cut from the wire to form a square with side=1 m.

the perimeter of the square =2L+2W=2(1)+2(1)=4 m

that is the max. amount can be cut from the wire, since the other part is bent into a circle.

( note if you cut more, the square will take the whole wire)

Perimeter=2L+2W=2(2)=2(2)=8 m and the area=2*2=4 m²)

Area and perimeter are two crucial characteristics of 2D shapes in mathematics.

The perimeter of the square exists 8 m and the area exists 4 m².

Area and perimeter are two crucial characteristics of 2D shapes in mathematics. The area and perimeter both specify the shape's boundaries and the space they occupy, respectively. Area and perimeter are significant mathematical concepts that are used to daily life. All sizes and shapes, regular or unusual, are covered by this. Each shape's area and perimeter calculations are unique.

Piece of wire is 8 m long and one piece is bent into square:

The square has four equal sides , so at least 4 m has to be cut from the wire to form a square with side = 1 m.

The perimeter of the square = 2L + 2W = 2(1) + 2(1) = 4 m

Which exists the maximum amount that can be cut from the wire, since the other part is bent into a circle.

Perimeter = 2L + 2W =2(2) = 2(2) = 8 m and the area = 2 × 2= 4 m²

To learn more about perimeter and area, refer to:

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$ 1.21 * 10⁷ per minute

Movie Earning = $ 1.1 * 10⁹

Movie lasted for = 9.1 * 10¹ minutes

Money earned in 9.1 * 10¹ minutes = $ 1.1 * 10⁹

Money earned in 1 minutes =  $ 1.1 * 10⁹ / (9.1 * 10¹)

= $ 110 * 10⁷ / (9.1 * 10¹)

= $ 12.09 * 10⁶

= $ 1.209 * 10⁷

= $ 1.21 * 10⁷

Movie earning =   $ 1.21 * 10⁷ per minute

Answer:

$ 1.21 * 10⁷ per minute

Step-by-step explanation:

Answer:

Step-by-step explanation:

REcall that f(x) is a polynomial whose one of its roots is -3+i. The fundamental algebra theorem states that any polynomial of degree n has n complex roots. In the real case, it can be also interpreted as any polynomial can be factored in factors of degree at most 2.

Consider that given a polynomial of degree 2 of the form [tex]ax^2+bx+c[/tex] the solutions are given by

[tex] x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}[/tex]

In this case, the fact that x is real or complex depends on the number [tex]b^2-4ac[/tex] which is called the discriminant. When this number is negative, we have that x is a complex root. Let say that [tex]b^4-4ac<0[/tex] and that [tex]\sqrt[]{b^4-4ac}=di[/tex], so the roots are given by

[tex] x_1 = \frac{-b + di}{2a}, x_2 = x_1 = \frac{-b - di}{2a}[/tex]

this means that, whenever we have a complex root, the other root is the complex conjugate. Recall that the complex conjugate of a complex number of the form a+bi is obtained by changing the sign of the imaginary part, that is a-bi.

So, in our case since -3+i is a root, then -3-i necessarily is another root.

If -3 + i is a root then -3 - i is too.

Therefore, the answer is -3 - i

Answer:

B. 2/3

Step-by-step explanation:

To solve this we have to take into account this axioms:

- The total probability is always equal to 1.

- The probability of a randomly selected point being inside the circle is equal to one minus the probability of being outside the circle.

Then, if the probabilities are proportional to the area, we have 1/3 probability of selecting a point inside a circle and (1-1/3)=2/3 probability of selecting a point that is outside the circle.

Then, the probabilty that a random selected point inside the square (the total probability space) and outside the circle is 2/3.

Answer:

A. Yes

B. Yes

C. No

Step-by-step explanation:

We can substitute each value in to the equation and see if the sides match up. Let's start with a.

[tex]4\cdot(2)-3 = -2\cdot(2)+9\\8-3 = -4+9\\5 = 5[/tex]

So, n = 2 works for equation a. Let's try B.

[tex]9\cdot(\frac{10}{3}) - 19 = 3\cdot(\frac{10}{3}) + 1\\\\\\\frac{90}{3} -19 = \frac{30}{3} + 1 \\ 30 - 19 = 10 + 1\\11 = 11[/tex]

So, m = [tex]\frac{10}{3}[/tex] works for B. Now let's try C.

[tex]3(30+8) = 2\cdot(30)-6\\3(38) = 60-6\\114 \neq 54[/tex]

So y = 30 doesn't work for C.

Hope this helped!

Answer:

total number of students =60

Step-by-step explanation:

total number of students 60

used unfair means 1/3= 20

1/4 caught red handed 1/4 of 20= 5

Answer:

A

Step-by-step explanation:

The line from the vertex to the base is a perpendicular bisector and divides the isosceles triangle into 2 right triangles.

Using Pythagoras' identity in either of the 2 right triangles, then

([tex]\frac{1}{2}[/tex] x )² + 3² = ([tex]\sqrt{45}[/tex] )²

[tex]\frac{1}{4}[/tex] x² + 9 = 45 ( subtract 9 from both sides )

[tex]\frac{1}{4}[/tex] x² = 36 ( multiply both sides by 4 to clear the fraction )

x² = 144 ( take the square root of both sides )

x = [tex]\sqrt{144}[/tex] = 12 → A

======================================================

Work Shown:

A = area of trapezoid RSTU

A = height*(base1+base2)/2

A = ST*(UT+RS)/2

A = 14*(5+10)/2

A = 105 square cm

-----------------------

B = area of rectangle PQWV

B = length*width

B = WV*PV

B = 7*2.5

B = 17.5 square cm

If you're curious how I got PV = 2.5, you basically cut PT = 10 in half twice. So you go from 10 to 5, then from 5 to 2.5; which works because we have a bunch of midpoints.

-----------------------

C = total shaded area

C = A + B

C = 105 + 17.5

C = 122.5

Answer:

See Below

Step-by-step explanation:

Taking Right Hand Side to verify the identity:

tan ( 2π - x)

Resolving Parenthesis

tan 2π + tan (-x)

We know that tan 2π = 0

0 + tan (-x)

=> tan(-x) = Left Hand Side

Hence Proved

Answer:

[tex]\boxed{ \sf {view \: explanation}}[/tex]

Step-by-step explanation:

[tex]\Rightarrow \sf tan ( 2\pi - x)=tan(-x)[/tex]

[tex]\sf Apply \ distributive \ law.[/tex]

[tex]\Rightarrow \sf tan (2\pi) + tan (-x) =tan(-x)[/tex]

[tex]\sf Apply : tan(2\pi) =0[/tex]

[tex]\Rightarrow \sf 0 + tan (-x) =tan(-x)[/tex]

[tex]\Rightarrow \sf tan (-x) =tan(-x)[/tex]

[tex]\sf Hence \ verified.[/tex]

Answer:

18- 14+8=3x

4+8=3x

12=3x

12/3=2x/3

x=4

Answer:

2/3, -8, -1/6, 4.

Step-by-step explanation:

Step-by-step explanation:

The rational root theorem states that if the leading coefficient is taken to be an and the constant coefficient is taken to be a0 the possible roots of the equation can be expressed as :

Now, from the given options, the possible choices can be :

A, B, C and E

D can be there because after taking any pair the rational root can't be 3

F can't be possible because an does't have 4 in its factors so denominator cannot be 4.

Answer:

A. Pr(8)   = 1/10

B.  Pr(odd)  = 1/2

C.  Pr(even)  = 1/2

D. Pr(less than 6)  = 1/2

E.  Pr(prime) = 2/5

F. Pr(3 or 8)  = 1 / 5

G. Pr(8, 9 or 10) = 3/10

H. Pr(greater than 9)  = P(10) = 1/10

Step-by-step explanation:

We assume a FAIR 10-faced die, meaning there is an equal probability of throwing any one of the ten numbers.

With 10 possible outcomes each with equal probability, the probability of throwing any number is 1/10.

(It is preferable to work with fractions in probability because fractions are exact numbers, while decimals can often be rounded, or truncated).

A. Pr(8)   means probability of throwing an 8,  therefore Pr(8) = 1/10

B. Pr(odd)  there are 5 odd number from 1 to 10, so Pr(odd) = 5/10 = 1/2

C. Pr(even)  there are 5 even number from 1 to 10, so Pr(even) = 5/10 = 1/2

D. Pr(less than 6)  there are 5 numbers less than 6 (between1 to 10),

       so Pr(less than 6) = 5/10 = 1/2

E. Pr(prime) (remember that 1 is not prime)

   A prime number is an integer not divisible by any number except one and itself.

   Between 1 to 10, the four prime numbers are 2,3,5,7

   therefore Pr(prime) = 4/10 = 2/5

F. Pr(3 or 8)  

(3 or 8) make 2 successful outcomes out of 10, so Pr(3 or 8) = 2/10 = 1 / 5

G. Pr(8, 9 or 10)

similarly, (8,9 or 10) make three successful possible outcomes out of 10, so

P(8,9 or 10) = 3/10

H. Pr(greater than 9)

there is only one successful outcome, namely "10" out of 10 possible outcomes.  So

P(greater than 9) = P(10) = 1/10

1. please explain what’s a “die” all I know was “dice” but dice is 6 sided yea?

A die is singular for dice, which can take up any number of faces.  With a 10-faced solid, we can make a 10-faced die numbered 1 to 10.

2. and please explain the answer... I’m international student so I still need some explanation for the questions and answers thank you

See solutions above.

Answer:

Remember that standard probabilities are defined as the ratio between the number of favorable cases, and the total number of possible events.

In this case, we have a 10-sided die, which means its faces are numbered from 1 to 10, which gives us 10 total number of possible events. In other words, the denominator of the ratio is going to be 10.

Now we're able to find each probability.

[tex]P_{8} =\frac{1}{10}=0.10[/tex]

The numerator is 1 because there's only one number 8 in the die, that means the number of favorable cases is 1, and, as we said before, the total number of possible events is 10.

[tex]P_{odd} =\frac{5}{10}=0.5[/tex]

The numerator is 5 because there are 5 odd numbers from 1 to 10. In other words, there are 5 favorable cases to this probability.

[tex]P_{even}=\frac{5}{10}=0.5[/tex]

There are 5 even numbers from 1 to 10, that's why we had the same probability.

We know that there are only 5 numbers less than 6 for this die.

[tex]P_{<6}=\frac{5}{10}=0.5[/tex]

A prime number is such that it can be divided only by itself and the unit. So, there are four prime numbers from 1 to 10, which are 2, 3, 5, 7.

[tex]P_{prime}=\frac{4}{10}=0.4[/tex]

When we are going to find the probability of an event "or" another, we must sum those favorable cases.

[tex]P_{3 \ or \ 8} =\frac{1+1}{10}=\frac{2}{10}=0.2[/tex]

In this case, we need to some all three favorable cases. The die has only one 8, one 9 and one 10. So, the probability is

[tex]P_{8,9,10}=\frac{1+1+1}{10}=\frac{3}{10} =0.3[/tex]

We know that there's only one number greater than 10 on such die.

[tex]P_{>10}=\frac{1}{10}=0.1[/tex]

Lastly, "die" refers to this special 10-sided dice. In other problems, you can find "a die" with more faces even. But, in general, "die" refers to a dice.

Answer:

Hey there!

For the first question we use the triangle area formula: 1/2bh, or 1/2(8)(5). This gives us 20 for the area.

For the second question we get a trapezoid, since the cross section does not pass through the vertex.

Hope this helps :)

The equation of line which is perpendicular to the line FG is

y = -2x -3.

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

[tex](y -y_{1}) = \frac{y_{2}-y_{1} }{x_{2} -x_{1} } (x-x_{1} )[/tex]

If [tex]m_{1}[/tex] be the slope of one line, then the slope of the perpendicular line is [tex]\frac{-1}{m_{1} }[/tex].

The slope intercept form of the line is given by  y = mx + b

Where, m is the slope of a line.

According to the given question

We have a line FG and the coordinates of points F and G are (-5,1) and (9,8) respectively.

Therefore, the slope of the line FG = [tex]\frac{8-1}{9+5}=\frac{7}{14} =\frac{1}{2}[/tex]

⇒ The slope of the line which is parallel to line FG is -2

Now, from the given option of the equation of line , y = -2x -3 has a slope of -2 .

Hence, the equation of line which is perpendicular to the line FG is

y = -2x -3.

Learn more about the equation of a perpendicular line here:

https://brainly.com/question/20712656

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Answer:

$45

Step-by-step explanation:

find the hire purchase price: 12 months x $30 = $360 + $35 deposit = $395

difference: 395 - 350 = $45

Answer:

25x  ²−49y ²

Step-by-step explanation:

We need to find product of (5x+7)(5x−7y)

By using identity (a+b)(a−b)=a −b  ²

We have a=5x,b=7y

Thus (5x+7y)(5x−7y)=(5x)  ²−(7y)  

let me know if it was helpful

25x² - 49y²

Step-by-step explanation:

To Find:

The product of (5x - 7y)(5 x + 7)

How to solve:

Just need to use the formula of a² - b² = (a+b)(a-b)

let's assume a = 5x and b = 7x

Solution:

(5x - 7y)(5 x + 7) = (5x)² - (7y)²

= 25x² - 49y²

Hence required answer is 25x² - 49y².

Answer:

25 is the same lenghth rounded

Step-by-step explanation:

aproximitly it rounded to the 10

The perimeter is the sum of all of the lengths of the sides. To find the perimeter, add together the length of each side.

For this triangle, our side lengths are 7, 7, and  9.

7 + 7 = 14

14 + 9 = 23

The perimeter of a triangle that has two sides measuring 7 centimeters and a third side measuring 9 centimeters is 23 centimeters.

Hope this helps!! :)

Answer:

the dimensions for the can that will minimize production cost is 9.13 cents

Step-by-step explanation:

The volume of a cylinder  V = π r²h

If we make the height h the subject of the formula; we have :

h = V/ π r²

Given that the volume of the cylinder = 400

Then

h = 400/ π r²

The total cost  will be: 0.02 × 2πrh + 0.07 × 2πr²

= 0.04 (πrh) + 0.14 (πr²)

=  0.04 (πr[tex]\frac{400} {\pi r^2}[/tex]) + 0.14 (πr²)

= 16/r +  0.14 (πr²)

total cost(c)= 16/r +  0.14 (πr²)

(c') = -16/r² +  0.28 (πr)

Let differentiate (c') with respect to zero (0); then:

-16/r² =  - 0.28 (πr)

r³ = 16/0.28 π

r³ = 18.19

r = 2.63 cm

Recall that:

h = 400/ π r²

h =  400/ π (2.63)²

h =  400/21.73

h = 18.41 cm

From;  total cost =  0.04 (πrh) + 0.14 (πr²)

replacing the value of r and h ; we have:

= 0.04 (π×2.63×18.41) + 0.14 (π × 2.63²)

= 0.04 (152.11) + 0.14 ( 21.73)

= 6.0844 + 3.0422

= 9.1266

≅ 9.13 cents

Therefore; the dimensions for the can that will minimize production cost is 9.13 cents