(6) (Bonus) A rectangular tank with a bottom and sides but no top is to have volume 500 cubic feet. Determine the dimensions (length, width, height) with the smallest possible surface area.

Answers

Answer 1

The dimensions length is 10 feet, width is 10 feet and height is 5 feet and the smallest possible surface area is 300 square feet.

Volume=lbh

lbh=500 cubic feet

h=500/lb

Surface area S=lb+2bh+2lh...(1) {rectangular tank has no top}

S=lb+2b(500/lb)+2l(500/lb) {substituting the value of h in 1}

S=lb+1000/l+1000/b { partially differentiating S with respect to l and b}

for S to be minimum dS/dl=0 and dS/db=0

dS/dl= b-1000/l^2

dS/dl=0

b=1000/l^2...(2)

dS/db= l-1000/b^2

dS/db=0

l=1000/b^2

l=1000/(1000/l^2)^2 {substituting the value of b from 2}

l=(1000 x l^4)/(1000000)

1000000/1000=l^4/l

1000=l^3

l=10  feet

b=1000/l^2

b=1000/100=10  feet

lbh=500

h=500/(10x10(

h=5  feet

S=10x10+2x5x10+2x10x5

S=300 square  feet

Length is 10 feet, width is 10 feet and height is 5 feet and the smallest possible surface area is 300 square feet of the  rectangular tank.

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Related Questions

Work out the area of this shape. Give your answer
in cm².


3 cm
4 cm
10 cm

Answers

The area of the given shape is 46 cm²

Formulas used:

Area of the triangle = (1/2) × Base × Height

Area of rectangle = Base × Width

Here we have  

The composite figure with a right-angled triangle and a rectangle

In a right-angled triangle,

The base of the triangle = 3 cm

Height of the triangle = 4 cm

Area of the triangle

= (1/2) × base × height

= (1/2) × 3 × 4

=  (1) × 3 cm × 2 cm

=  6 cm²  

In rectangle,

Length of the rectangle = 10 cm

Width of the rectangle = 4 cm

Area of the rectangle

= Length × Width

= 10 cm × 4 cm

= 40 cm²

By the above calculations,

Area of the given figure = Area of triangle + Area of rectangle

= 6 cm² + 40 cm² = 46 cm²

Therefore,

The area of the given shape is 46 cm²

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The sample points of a sample space are a equally likely events. b equally unlikely events. c simple events. d complex events.

Answers

The correct option is option A , the sample points of a sample space are equally likely events.

In probability when two the occurrence of two events are having a 50 - 50 possibility then those two events are said to be equally likely events. Example , on tossing a coin the probability of getting a H or a tail is 1/2 . Therefore, these events are said to be equally likely events.

Probability is a field of mathematics which tells us about the possibility of occurrence of an event. P = number of favorable outcomes / total number of outcomes , is the formula to calculate probability.

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[tex] \frac{1}{5} + \frac{3}{4} [/tex]

Answers

Answer:

19/20

Step-by-step explanation:

the answer is 19/20 <3

Step-by-step explanation:

<3

<3

<3

<3

hope you have a good day ^^<3

Write a formula for arc length S in terms of r for the following figure.
1.2
S
The angle in the figure is a central angle in radians.
SE

Answers

Answer:

1.2r

Step-by-step explanation:

The arc length in terms of r will be equal to 1.2r.

What is the arc length of the circle?

The distance between two places along a segment of a curve is known as the arc length. Curve rectification is the process of measuring the length of an irregular arc section by simulating it with connected line segments.

It is given that the angle in radians is 1.2 and the radius is r then the arc length will be calculated as below:-

The arc length = Angle x radius

The arc length  = 1.2 x r

The arc length  = 1.2r

Therefore, the arc length in terms of r will be equal to 1.2r.

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20 points help asap!!!

Find B n C Given
B

Answers

Answer:

Step-by-step explanation:

Sets B and C have nothing in common and therefore B ∩ C = empty set

Which data set has a relatively low mean and variability when compared with a data set that has a mean of 20 and a MAD of 3.1? A. Mean: 5 and MAD: 4.6 B. Mean: 25 and MAD: 6.5 C. Mean: 41 and MAD: 0.9 D. Mean: 8 and MAD: 1.2

Answers

Answer:

Mean: 8 and MAD: 1.2

Step-by-step explanation:

Given a data with :

Mean = 20 ; mean absolute deviation (MAD) = 3.1

DATA with a low mean and variability Than The above from the options given :

The most appropriate option is : Mean: 8 and MAD: 1.2 ; because both values of the mean and mean absolute deviation are lesser than the value given.

Eydin has two strips if stickers,A and B, of the same length.The length of each sticker is 1.2 cm. The stickers in each strip form a repeated patteren as shown below


There are 56 heart stickers all together in both strips of stickers.What is the length of each strip of stickers?​

Answers

Answer:

Each strip is 117.6 cm

Step-by-step explanation:

I created a proportion of hearts to others.  On strip A there is 1 heart to 2 others and B there is 1 heart to 3 others.  I added them and got a proportion of 2 hearts to 5 others for both. With a total of 56 hearts, I set up a proportion to determine the total stickers

2/5=56/x

When I cross multiply, I get 2x=280 and x=140

so for the 56 total hearts, I have 140 others.  I added those to get the total stickers and got 196.  I multiplied that by 1.2cm and got 235.2 cm for both. Since both are the same size, just divide that by 2 and get 117.6 cm each.

Chose the best 3 options

Answers

The beat three options are:  The slope of the line is 1/5, (2) The possible equation if the line is y=1/5x, (3) The slope and the y intercept are the same

What is slope of a line?

Lope is the rate of change of y with respect to x.  slope is also the increase in y over increase in x vice versa

Slope is denoted by rise/run

The Possible solutions from the graph are:

The slope and y-intercept are the sameThe possible equation of the line is y=1/5xThe slope of the line is 1/5

Taking any two points on the graph : (4, 1) and -4, -1,)

We can find the slope as (1--1)/4--4

Therefore, the Slope = 2/3≡1/5

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Jim's marble collection contains 20 marbles, including 4 pink marbles. What is the probability that a randomly selected marble will be a pink marble? Write your answer as a fraction or whole number.

Answers

Answer: 20%

Step-by-step explanation:

The probability that a randomly selected marble will be pink can be found by the formula:

= Number of pink marbles / Number of total marbles

= 4 / 20

= 20%

There is a 20% chance that if you pick a marble, it will be pink.

There are 20 gloves in a drawer: 5 pairs of black gloves, 3 pairs of brown,
and 2 pairs of gray. You select the gloves in the dark and can check them
only after a selection has been made. What is the smallest number of gloves
you need to select to guarantee getting the following?
(a) At least one matching pair
(b) At least one matching pair of each color

Answers

The number of gloves selected for each cases is 11 and 19 gloves respectively.

How is selection done?

In mathematics, most of the times selection is done using permutation and combination.

Putting things or numbers in order is known as a permutation.

Combinations are a means to choose items or numbers from a collection of items or groups of items without regard to their order.

Given,

       Total black gloves = 5 left hand+ 5 right hand

       Total brown gloves = 3 left hand + 3 right hand

        Total gray gloves = 2 left hand + 2 right hand

Now to find the least number of gloves for the given conditions, we start with the worst condition.

a) To get at least one matching pair, we first consider no matching pair, which is (5 +3+2) gloves of only left only or right only hand of each colour.

Now to make one pair, we need to select only one glove of the opposite hand of any colour.

Therefore to get atleast one matching pair, smallest number of gloves to be selected = 5 + 3 + 2 + 1 = 11 gloves

b) In this case also we start with worst case.

   For no matching pair of each colour we have to take 10 black gloves, 6 brown gloves and  2 gray gloves of any one hand.

Therefore to get matching pair of each colour, we have to take one more gray glove.

Therefore to get atleast one matching pair of each colour, smallest number of gloves to be selected = 10 + 6 + 2 + 1 = 19 gloves.

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The function y=0.18x+0.15 represents the percent y (in decimal form) of battery power remaining x hours after you plug in a laptop computer. Identify and interpret the slope. \

Answers

Step-by-step explanation:

Given

Function is  [tex]y=0.18x+0.15[/tex]

where,

[tex]y=\text{Percent of the battery remaining}\\x=\text{time in hours}[/tex]

Comparing the given function with the standard slope-intercept form of the equation [tex]y=mx+c[/tex]

Here, before plugging into the laptop, the percentage of battery is

[tex]y=0.18\times 0+0.15\\y=0.15\ \text{or}\ 15\%[/tex]

The slope of the given function is [tex]0.18[/tex] i.e. in one hour it charges 18% of battery.

need help asap! will give brainliest!

Answers

Answer:

10.5

Step-by-step explanation:

Sunshine Raisin Company sells snack-sized boxes of raisins. Twenty boxes were randomly selected and the raisins we counted. The results are shown in the list below. What frequency table BEST represents the Sunshine Raisin data? Sunshine Raisins​

Answers

Answer:

a

Step-by-step explanation:

mrk me brainliest

Answer:

the correct answer is A

Step by step explanation


2. If Sarah makes $11 per hour at her part time job and she works 20 hours in a week. How much is her weekly grass
pay?
A. $440
B. $110
C. $220
D. $200

Answers

Sarah makes 220 sorry if that’s wrong

Answer:

C. $220

Step-by-step explanation:

11 x 20 = 220

What is the quotient of -12 divided (1/6)

Answers

3
1
8
=
25
8
2
1
6
=
13
6
Giving us
25
8
/
13
6

A rule for dividing fractions is multiplying by the reciprocal so,
25
8

6
13
=
150
104
150
104
can be simplified to
75
54

Triangle STU is a right triangle.
Write an equation that relates the lengths of sides s, t, and u? (5 points)

Answers

Use the concept of the Pythagorean Theorem, where the sum of the squares of legs 1 and 2 is equal to the square of the hypotenuse. This means you can take the square root of the hypotenuse square and obtain its length since a square’s area is s².

So, here’s the equation:

t²+s²=u²

Where t=leg 1, s=leg 3, and u=hypotenuse

PLEASE ASAP ILL GIVE BRAINLIEST.

Answers

Answer:

12 km/h

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

we don’t know if it would change any other way so i would say D, because 1.5 hours, that’s just divide 18 by 3 (6) to get the half hour. then you figure out that 12 km/h (north?) since the half brings it to 18. sorry if that’s confusing i’m bad with explaining

The average scores on Mrs. Wilson's test and Mr. Lewandowski's test were normally distributed on the last Algebra 2 test they gave. The average in my class Mrs. Wilson's class, was 86 with a standard deviation of 2. The average in my friend's class, Mr. Lewandowski's class was an 82 with a standard deviation of 2. If I made an 88 on the test and my friend made an 85 on their test, who had the better score relative to the rest of their class?

Answers

You had a better score relative to the rest of your class.

To compare the scores of you and your friend relative to the rest of their classes, we need to calculate the standard deviation of your score and your friend's score from the average of their respective classes.

A standard deviation of 2 means that 68% of the scores in the class fall within 1 standard deviation of the mean, or between 84 and 88 in the case of Mrs. Wilson's class. Since 88 is greater than 86 (the mean) and less than 2 standard deviations away (88-86 < 2*2=4) , so your score of 88 is better than the average score in your class.

On the other hand, 85 is less than 82 (the mean) and more than 1 standard deviation away (85-82 > 2) so your friend's score of 85 is less than the average score in their class.

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Identify the two x values?

Answers

When the points are (4, 2) and (6, 5), the slope is 3/2. The slope of a line determines its direction and degree of steepness.

what is slope ?

A line's steepness and direction are determined by the slope of the line. The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. While there has been no net change in the x coordinate, there has been no net change in the y coordinate. hence, the shift in the y coordinate in relation to the shift in the x coordinate. The slope of a line is the rise to run ratio, or the rise divided by the run. It gives information about a line's slope in the coordinate plane. Any two clearly separated points on a line can be used to calculate the slope of any line.

given

slope = [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

points are ( 4, 2 ) and ( 6, 5)

[tex]\frac{5 - 2}{6 - 4} \\= \frac{3}{2}[/tex]

hence the slope is 3 / 2 .

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NOW IT HAS TO EQUAL TO 100 WHERE DO YOU PUT THE PARENTHESES!!!! HELP QUICK PLS


4+2•3^2

IT HAS TO EQUAL 100

Answers

Answer: (4+2)•(3^2?

Step-by-step explanation: I hope that helps I don't know how to explain but ya. But that's where u put the parentheses.

Answer:

(4+2×3)^(2)

Step-by-step explanation:

First, because parenthesis are being used, we will start by multiplying 2 by 3, giving us 6

(4+6)^(2)

Then, we add 6 to 4

(10)^2

and we then raise 10 to the 2nd power

100

HELP PLEASE 100 points for EXPLENTATION and ANSWER!!!!
see screenshot

Answers

Answer:

The screenshot is not included!!

A community hall is in the shape of a cuboid.

Answers

Total cost of Painting and tileing is for the cuboidical community hall is  $2172.

What is a Cuboid ?

A three-dimensional form called a cuboid contains six faces, twelve edges, and eight vertices. It differs from a cube in that a cuboid's faces are entirely rectangular in shape whereas a cube's faces are square. A cuboid has three dimensions: length, breadth, and height.

Properties of a Cuboid are :

There are 6 faces, 12 edges, and 8 vertices on a cuboid.

All of the cuboid's faces have rectangular shapes.

The cuboid's opposing edges are parallel to one another.

The dimensions of a cube are length, breadth, and height.

All of the angles created at the cuboid's vertices are 90 degrees.

Surface area of 4 walls and Ceiling is = 40*3*2 + 15*3*2 + 40*15 = 930

Surface area of the floor is 40 *15 = 600

10 lt of tin covers 25

1  can be covered by 10/25 lt

930  can be covered by (10/25) * 930 = 372 lt.

Total cost of Painting is $372.

1  of floor tiles cost $3

600  of floor tiles will cost 3*600 = $ 1800

Total cost of Painting and tileing is for the cuboidical community hall is $ 372 + 1800 = $2172.

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The quotient of 18 and the number is three what is the number

Answers

Answer:

Step-by-step explanation:

Divide: 18 ÷3=?

The answer is 6

This is just for fun...

Explain why every number to the digit 0 is 1 by using an algebraic formula (of sorts).
For example like (a and b or x and y for the substitutes of this and that to the power of 0)

Answers

Answer:

y is for genius factor

a is for angles

b are absoulutely for divides and multiply from the sides of heptagon

X are like EQUAL to 7 tables for example D% 72*(09 1/2 its just like this!!

and Deciamals are apart like 22 . 27 its just like that!!

Step-by-step explanation:

Does this help? let me know!!

Find the geometric mean of 14 and 20. Answer in simplest form

Answers

The Geometric Mean (GM) is the average value or mean that, in mathematics, represents the centre tendency of a group of numbers by calculating the product of their values.

What is geometric mean?

The Geometric Mean (GM) in mathematics is the average value or mean that represents the centre tendency of the group of numbers by calculating the product of their values. Basically, n is the entire amount of data values, and we multiply the numbers collectively before taking their nth root.

The geometric mean can be calculated in two steps: To obtain their product, multiply all values collectively. Calculate the product's nth root (n is the number of values).

The geometric mean of 14 and 20 must be determined. Let's see the numbers:

a = 14 and b = 20

For two numbers, the geometric mean is calculated as follows:

[tex]$M=\sqrt{a b}$[/tex]

Filling in the values as shown in the formula above:

[tex]$M=\sqrt{14 \times 20}$$M=\sqrt{7 \times 2 \times 5 \times 4}$$M=16.73$[/tex]

Therefore, the answer is 16.73.

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The required geometric mean of 14 and 20 is 16.73.

What is geometric mean?

The Geometric Mean (GM) in mathematics is the average value or mean that represents the centre tendency of the group of numbers by calculating the product of their values. Basically, n is the entire amount of data values, and we multiply the numbers collectively before taking their nth root.

The geometric mean can be calculated in two steps: To obtain their product, multiply all values collectively. Calculate the product's nth root (n is the number of values).

The geometric mean of 14 and 20 must be determined. Let's see the numbers:

a = 14 and b = 20

For two numbers, the geometric mean is calculated as follows:

G.M = [tex]\sqrt{ab}[/tex]

Filling in the values as shown in the formula above:

G.M = [tex]\sqrt{14(20)}[/tex]

G.M = [tex]\sqrt{280}[/tex]

Therefore, the answer is 16.73.

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Solve the simultaneous equations
5x−y=8
7x+4y=22

Answers

Answer:

5x-8      m=5

m= -7/4

Step-by-step explanation:

How do you find the zero’s algebraically?

Answers

To find the zeros of a polynomial algebraically, you can use the following steps:

Write the polynomial in standard form, with the terms arranged in descending order of the degree of the term. For example, if the polynomial is 3x^2 - 2x + 5, it is already in standard form.

Set the polynomial equal to zero. For example, if the polynomial is 3x^2 - 2x + 5, you would set the equation equal to zero like this:

3x^2 - 2x + 5 = 0

Use the quadratic formula to find the solutions (i.e., the zeros) of the equation if the polynomial is a quadratic (degree 2). The quadratic formula is:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

where a, b, and c are the coefficients of the polynomial, and sqrt represents the square root.

For example, if the polynomial is 3x^2 - 2x + 5, the solutions would be:

x = (-(-2) +/- sqrt((-2)^2 - 4 * 3 * 5)) / (2 * 3)

x = (2 +/- sqrt(4 - 60)) / 6

x = (2 +/- sqrt(-56)) / 6

Since the square root of a negative number is not a real number, there are no real solutions (zeros) for this polynomial.

Use the Rational Root Theorem to find the solutions of the equation if the polynomial is not a quadratic. The Rational Root Theorem states that if a polynomial of degree n has a rational root p/q (where p and q are integers and q is not equal to zero), then p must be a divisor of the constant term and q must be a divisor of the coefficient of the term of highest degree.

For example, if the polynomial is x^3 - 2x^2 + x - 6, the constant term is -6 and the coefficient of the term of highest degree is 1. The divisors of -6 are -6, -3, -2, -1, 1, 2, 3, and 6. The divisors of 1 are 1 and -1. Therefore, the possible rational roots of this polynomial are -6, -3, -2, -1, 1, 2, 3, and 6.

To find the actual roots, you can try each of these numbers as a root and see if it works. For example, if you try -6 as a root, you would get:

(-6)^3 - 2(-6)^2 + (-6) - 6 = 0

(-216) - (-72) + (-6) - 6 = 0

-144 - 6 - 6 = 0

-156 = 0

This equation is not true, so -6 is not a root of the polynomial. You can repeat this process for each of the other possible rational roots until you find all of the roots of the polynomial.

А
4 yards
B
С
15 yards
Find the area of AABC.
[?] yd ]
Enter

Answers

answer:

30 yd^2

step-by-step explanation:

in order to find the area of a triangle, we can use: A = 1/2 · b · hA = areab = baseh = height

plug in,

A = 1/2(b)(h)

A = 1/2(15)(4)

A = 1/2(60)

A = 30 yd^2

Please help with this question

Answers

Answer: The answer is 25               then if it asks for the equation it is A=1/2bh

Step-by-step explanation:

The b or base is 10

The height or h is 5

A=1/2bh

A=1/2(10)(5)

A=1/2(50)

A=25

I hope this helps :)

Answer:

25m^2

Step-by-step explanation:

the formula for finding the area of a triangle is b*h/2. So 10 times 5 equals 50. When you divide 50 by 2 you get 25. 25m^2 Is the answer.

Solve for x.
-10 <-2x +4≤8
Enter your answer, as one inequality, in the box.

Answers

The solution of the inequality is x < 7 and x >= -2.

What is linear inequality?

An inequality is a mathematical statement comparing two values or expressions, usually involving one of the following relational operators: < (less than), > (greater than), <= (less than or equal to), >= (greater than or equal to), or != (not equal to). The solution to inequality is a set of values that make the inequality true.

To solve the inequality -10 < -2x + 4 ≤ 8, we have to solve the inequality twice because of the less than or equal to symbol and greater than or equal to symbol.

First we have to solve -10 < -2x + 4

-2x + 4 > -10

-2x > -14

x < 7

Second, we have to solve -2x + 4 <= 8

-2x + 4 <= 8

-2x <= 4

x >= -2

Hence, the solution of the inequality is x < 7 and x >= -2. This solution is represented by all the values of x that are less than 7 and greater than or equal to -2.

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