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To find the dimensions of a cylinder with one open end that minimizes its surface area given a volume of 44 cm³, use calculus and the formulas for the cylinder's volume and surface area. The solution results in radius r ≈ 1.34 cm and height h ≈ 9.87 cm.

For a cylinder open at one end, the surface area is given by the formula A = πr² + πrh, where r is the radius and h is the height.
The volume of a cylinder is given by the formula V = πr²h. Given that V=44 cm³, we can write the volume equation as h = V / (πr²).
Substituting this into the surface area equation, we get A = πr² + πr(V / (πr²)) = πr² + V/r.
We want to minimize the surface area, so we take the derivative of A with respect to r, set it equal to zero and solve for r.
Doing this gives us: dA/dr = 2πr - V/r² = 0 => r = cuberoot(V/2π).
Substituting V=44 cm³ into this, we get r = cuberoot(22/π) ≈ 1.34 cm.
Substituting r back into h = V / (πr²), we derive that h = 44 / (π * (1.34)²) ≈ 9.87 cm.
Therefore, the dimensions that will minimize the surface area of the cylinder given that the volume is 44 cm³, are approximately r = 1.34 cm and h = 9.87 cm.
This is a classic problem of optimization in calculus.

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Answer:

Start with x+y=10 and x-y=4

Add the equations to eliminate y:

   x+y=10 

 + x-y=4 

  2x =14 

So now solve for x:

   2x=14    (Divide each side by 2 to get x by itself)

    x=7 

Now you have solved for x, but you still need to solve for y:

  x+y=10

 7+y=10    (Subtract 7 from both sides to get y by itself)

   y=3 

Now you have both x and y but to check it, just plug it into the original equations:

   x+y=10 ---->  7+3=10   (That's correct)

    x-y=4 ---->  7-3=4   (That's correct) 

Step-by-step explanation:

Answer:

9.3+b=14.5

Step-by-step explanation:

The simplified form of the expression 2(x+14)+(2x-14) is 4x + 14.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.

Given:

An expression,

2(x+14)+(2x-14).

Simplifying,

2(x+14)+(2x-14),

= 2x + 28 + 2x - 14

= 4x + 28 - 14

= 4x + 14

Therefore, the solution is 4x + 14.

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Answer:

Commutative additive property.

Step-by-step explanation:

Given  : 3z+4=4+3z

To find : which property is illustrated the following statement.

Solution : We have given  

3z + 4 = 4 + 3z.

Commutative additive property : a + b = b + a .

Example :  2 + 3 = 3 +2 = 5.

Hence  this the commutative additive property 3z + 4 = 4 + 3z.

Therefore, Commutative additive property.

Peter needs 33 whole days to be able to speak 75 words.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Peter begins his kindergarten year able to spell 10 words.

He is going to learn to spell 2 new words every day.

Assuming no. of days it will take him to be able to spell at least 75 words

is d.

∴ The inequality that represents this scenario is 2d + 10 ≥ 75.

2d ≥ 65.

d ≥ 32.5 but it will take him 33 whole days to learn 75 words.'

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The perimeter of the polygon to the nearest tenth of a unit  [tex]\boxed{16.9{\text{ units}}}.[/tex] Option (b) is correct.

Further explanation:

The distance between the two points can be calculated as follows,

[tex]\boxed{{\text{Distance}}=\sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}}}[/tex]

Given:

The coordinates of the vertices of the polygon are [tex]\left({ - 2, - 2}\right),\left( {3, - 3}\right),\left( {4, - 6}\right),\left( {1, - 6}\right)[/tex] and [tex]\left( { - 2, - 4}\right).[/tex]

Explanation:

Consider the points as A [tex]\left( { - 2, - 2} \right), B\left( {3, - 3} \right), C\left( {4, - 6} \right), D\left( {1, - 6} \right)[/tex] and  [tex]E\left({ - 2, - 4} \right).[/tex]

The distance between point A and point B can be calculated as follows,

[tex]\begin{aligned}{\text{Distance}}&=\sqrt {{{\left( {3 + 2} \right)}^2} + {{\left( { - 3 + 2}\right)}^2}}\\ &= \sqrt {25 + 1}\\&= \sqrt {26}\\&= 5.2\\\end{aligned}[/tex]

The distance between point B and point C can be calculated as follows,

[tex]\begin{aligned}{\text{Distance}}&=\sqrt {{{\left( {4 - 3} \right)}^2} + {{\left( { - 6 + 3} \right)}^2}}\\&= \sqrt {{1^2} + 9}\\&= \sqrt {10}\\&= 3.17\\\end{aligned}[/tex]

The distance between point C and point D can be calculated as follows,

[tex]\begin{aligned}{\text{Distance}}&= \sqrt {{{\left({1 - 4} \right)}^2} + {{\left( { - 6 + 6}\right)}^2}}  \\&=\sqrt {{3^2} + 0}\\&= \sqrt9\\&= 3\\\end{aligned}[/tex]

The distance between point D and point E can be calculated as follows,

[tex]\begin{aligned}{\text{Distance}}&= \sqrt {{{\left( { - 2 - 1}\right)}^2} + {{\left( { - 4 + 6}\right)}^2}}\\&= \sqrt{ - {3^2} + {2^2}}\\&= \sqrt {9 + 4}\\&= \sqrt {13}\\&= 3.61\\\end{aligned}[/tex]

The distance between point E and point A can be calculated as follows,

[tex]\begin{aligned}{\text{Distance}} &= \sqrt {{{\left( { - 2 + 2} \right)}^2} + {{\left( { - 4 + 2} \right)}^2}}\\ &= \sqrt {{0^2} + {2^2}}\\&=\sqrt4\\&= 2\\\end{aligned}[/tex]

The perimeter of the polygon can be calculated as follows,

[tex]\begin{aligned}{\text{Perimeter}}&= 5.12 + 3.17 + 3 + 3.61 + 2\\&= 16.9\\\end{aligned}[/tex]

Option (a) is not correct.

Option (b) is correct.

Option (c) is not correct.

Option (d) is not correct.

The perimeter of the polygon to the nearest tenth of a unit [tex]\boxed{16.9{\text{ units}}}.[/tex] Option (b) is correct.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Coordinate geometry

Keywords: Coordinates, vertices, polygon, x-coordinate, y-coordinate, perimeter, circumference, nearest tenth unit, distance formula.

Answer:

here is the answer

Step-by-step explanation:

Answer:

69 and 11,  took me 1 hour to slove this

Step-by-step explanation:

Answer:

Its 8:11 because theres eleven animals and 8 pigs

Step-by-step explanation:

The probability that John chooses exactly two green marbles is calculated using the binomial probability formula and is found to be 720/3125.

To solve this problem, we can use the binomial probability formula because John is performing independent trials of the same experiment and he is interested in the probability of exactly two successes (picking a green marble) in a specific number of trials (5).

The binomial probability formula is: [tex]P(X = k) = (n choose k) \times p^k \times (1-p)^{n-k[/tex]

For John's case:

n = 5 (since he is picking 5 marbles).

k = 2 (he wants exactly two green marbles).

p = 6/10 or 3/5 (because there are 6 green marbles out of a total of 10 marbles).

Using the formula, the probability that John picks exactly two green marbles is:

[tex]P(X = 2) = (5 choose 2) \times (3/5)^2 \times (2/5)^{5-2[/tex]

Calculating further:

[tex]P(X = 2) = 10 \times (3/5)^2 \times (2/5)^3 = 10 \times 9/25 \times 8/125 \\P(X = 2) = 720/3125[/tex]

Final answer:

Approximately 71 pounds of macadamia nuts and 31 pounds of almonds were sold, after solving the system of equations p + n = 102 and 1.00p + 5.93n = 452.03.

Explanation:

To determine the amount of almonds and macadamia nuts sold, we need to solve the given system of equations:

Let's start by solving the first equation for p:

p = 102 - n

Now, substitute p in the second equation:

1.00(102 - n) + 5.93n = 452.03

Next, distribute and combine like terms:

102 - n + 5.93n = 452.03

4.93n = 350.03

n ≈ 71.041 (macadamia nuts)

Using n to find p:

p = 102 - 71.041 ≈ 30.959 (almonds)

Therefore, approximately 71 pounds of macadamia nuts and 31 pounds of almonds were sold.

Final answer:

A 42.0-gallon barrel of oil is equivalent to 158.97 liters, calculated by multiplying the number of gallons by the conversion factor of 3.785 liters per gallon.

Explanation:

To discover out how numerous liters are in 42.0 gallons of oil, given that 1 gallon is proportionate to 3.785 liters, you'd perform the taking after calculation:

Multiply the number of gallons by the conversion factor from gallons to liters.

42.0 gallons × 3.785 liters/gallon = 158.97 liters.

Therefore, a barrel of oil, which contains 42.0 gallons, is equivalent to 158.97 liters.

After estimating and calculating, we find that 6.51326 is greater than the square root of 39, which is approximately 6.245.

To compare 6.51326 and the square root of 39, we first need to calculate the square root of 39 to see how it measures up against 6.51326. Since the exact square root of 39 is not easily found without a calculator, we can estimate it by finding the nearest perfect squares that surround 39.

36 and 49 are the nearest perfect squares to 39, and their square roots are 6 and 7, respectively. Since 39 is closer to 36 than to 49, we can estimate the square root of 39 to be slightly more than 6. Therefore, without performing the exact calculation, we can intuit that the square root of 39 will be between 6 and 7, but closer to 6.

Doing the exact calculation or using a calculator, we find that the square root of 39 is approximately 6.245, which means that 6.51326 is greater than the square root of 39.

Answer:

5/11

Step-by-step explanation:

5/11 is the equivalent number because its the fraction of the repeating decimal ^^