Calcula el área de las bases y el área lateral, de un cilindro de 10cm de radio y 20cm de altura.

Answer:

Based on the given information, we know the following:

Solid A is formed by joining one hemisphere to the frustum of a cone.

Solid B is formed by joining the other hemisphere to the small cone that was removed from the large cone.

The volume of solid A is 6 times the volume of solid B.

We can use the formulas for the volume of a hemisphere and a frustum of a cone to represent the volumes of solids A and B.

The volume of a hemisphere is (2/3)πr^3, where r is the radius of the hemisphere.

The volume of a frustum of a cone is (1/3)πh(R^2+r^2+Rr), where h is the height of the frustum, R is the radius of the larger base and r is the radius of the smaller base.

The volume of a cone is (1/3)πr^2h

Let's call the height of the frustum h, the radius of the large base R and the radius of the small base r

We can set up the equation: (2/3)πr^3 = 6((1/3)πr^2h + (1/3)πR^2h + (1/3)πRrh)

After simplifying, we get:

2h = 12r + 12Rh + 6Rr

We know k = (R/r)^(1/3)>(7)^1/3, we can substitute it into the equation:

2h = 12r + 12rk + 6rk^2

Solving for h, we get:

h = 6rk + 6rk^2

So h is expressed in terms of k and r.

Answer:

17/20

Step-by-step explanation:

The ratio 8.5 to 10 as a fraction in simplest form is 17/20. 8.5/10 = 85/100 = 17/20

(8.5:10 = 85:100 = 85/100 = 17/20)

Answer:

8 m

Step-by-step explanation:

Volume of a sphere is V = 4/3 π r³.

Volume of a cylinder is V = π r² h.

The two volumes are equal, so:

4/3 π r³ = π r² h

4/3 r = h

The radius is 6 m, so the height of the cylinder is:

h = 4/3 (6 m)

h = 8 m

Answer:

The height of the cylinder is 8m.

Step-by-step explanation:

Given, the Radius and Volume of the cylinder and sphere are equal.

Radius, r = 6m

Formula,

Volume of the sphere =  [tex]\frac{4}{3}\pi r^{3}[/tex]

Volume of the cylinder = [tex]\pi r^{2}h[/tex]

⇒ Volume of the cyliner =  Volume of Sphere

⇒  [tex]\frac{4}{3}\pi r^{3}[/tex] =    [tex]\pi r^{2}h[/tex]

⇒  [tex]h = \frac{4\pi r^{3} }{3\pi r^{2} }[/tex]

⇒  [tex]h = \frac{4r}{3}[/tex]

⇒  [tex]h = \frac{4 * 6}{3}[/tex]

⇒ h = 8m

I) we can substitute x + d = 2x + 1 and x + 2d = 11 into the equation for d:

x - 1 = 2x + 1 - x = 2x - x + 1 = x + 1

x = 0

II) The 30th term of this arithmetic sequence is 29.

To solve this problem, we can use the fact that in an arithmetic sequence, the difference between consecutive terms is constant.

(i) Let's call the common difference d. Then we can set up the equation:

x + d = 2x + 1

d = x - 1

Since we know that x; 2x + 1; 11 are three consecutive terms of an arithmetic sequence, we can substitute x + d = 2x + 1 and x + 2d = 11 into the equation for d:

x - 1 = 2x + 1 - x = 2x - x + 1 = x + 1

x = 0

(ii) To find the 30th term, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where a1 is the first term, d is the common difference, and n is the number of the term we want to find.

Substituting the known values into this formula:

a30 = x + (30 - 1)d

a30 = 0 + (29)(1)

a30 = 29

So the 30th term of this arithmetic sequence is 29.

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Answer:

the black graph is the graph of

y = f(x). Choose the equation for the

red graph.

1

1

a.

b.

c.

d.

y = f(x+3)

y = f(x-3)

y + 3 = f(x)

y-3=f(x)

y = 6(2)^(x-4)-1 is an exponential function with a base of 2 and an exponent of x-4. The coefficient of the base, 6, is called the leading coefficient. The constant term, -1, is the y-intercept, the point where the graph of the function crosses the y-axis. The function is also a shifted version of the basic exponential function y= a*b^x, where a is the leading coefficient and b is the base of the function.

Since the base of the function is 2, the graph of the function will increase or decrease at an increasing rate. The leading coefficient of 6 will affect the steepness of the graph, making it steeper than the basic exponential function y=2^x. The horizontal shift of the graph is 4 units to the left, as the exponent has x-4 instead of x.

In terms of symmetry, the graph of this function has no symmetry.

The function has no rotational symmetry because it is not repeated after any rotation around the origin.

Answer:

[tex]y=-\frac{2}{3}x+4[/tex]

Step-by-step explanation:

[tex]y=\frac{4-0}{0-6}=-\frac{2}{3} \\ \\ b=4 \implies y=-\frac{2}{3}x+4[/tex]

Answer:

111,111,111^2

Step-by-step explanation:

so the denominator is just 1+2+3+4+5......+8 added together multiplied by two since it goes down, then +9 as the middle. So 1+2+3....... to 8 is basically just 1+8, 2+7, 3+6, etc. so we have 4 pairs of 9 which is 36. 36*2 is equal to 72, them plus 9 is 81. 999,999,999*999,999,999 can be written as 999,999,999^2. the bottom is 81 so we can square root both top and bottom to get 999,999,999/9 right, and we just square it back so that equals 111,111,111^2 .

let me know if its correct! also pls give brainliest, thank you! :) so sorry i forgot to add the square but now its updated

Answer: 21:6

Step-by-step explanation: Use the ADAM method to help you with ratio problems like these (Add Divide And Multiply)

Add the numbers in the given ratio: 7+2=9

Divide the amount given by this number: 27/9=3

And (just there for the acronym)

Multiply this number by the numbers in the ratio: 7 x 3 = 21        2 x 3 = 6

final answer= 21:6

Line formed by joining the given points ( 1,3) and ( 2,1) divided in the ratio by the given equation of the line 3x + y = 9 is equal to 3 :2.

As given in the question,

Equation of the given line : 3x + y = 9 __(1)

Standard equation line formed by joining the two points :

( x₁ , y₁ ) = ( 1,3)

(x₂ , y₂) = ( 2,1 )

( y - y₁) / (y₂ -y₁ ) = ( x -x₁)/(x₂ - x₁ )

⇒(y - 3)/(1 - 3) = ( x -1)/(2 -1)

⇒(y -3)/-2 = (x -1)/1

⇒-2x +2 = y - 3

⇒ y + 2x = 5 __(2)

Subtract (2) from (1) we get,

3x + y = 9

2x + y = 5

x = 4

⇒y = -3

Point of intersection is ( 4, -3)

Distance between ( 4, -3) and ( 1,3) is:

= √ ( 4 -1)² + ( -3 -3 )²

= √9 + 36

= √45

= 3√5

Distance between ( 4, -3) and ( 2 ,1) is:

= √ ( 4 -2)² + ( -3 -1 )²

= √4 + 16

= √20

= 2√5

Required ratio to divide a line by given points is :

= 3√5 / 2√5

= 3/2

Therefore, the equation of the line 3x + y =9  divides the line formed by joining the given points in the ratio is 3:2.

The above question is incomplete, the complete question is:

In what ratio is the line joining the points (1,3) and (2,1 ) divided by the line 3x+y=9?

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Since the remaining distance is negative, it implies that Sam has already exceeded his goal distance. Therefore, he doesn't need to walk any further to reach his goal.

To find the remaining distance that Sam needs to walk to reach his goal of (3)1/2 miles, we need to subtract the distance he has already walked from his goal distance.

Sam walks (1)1/8 miles before lunch and 3/4 miles after resting. To calculate the total distance he has walked, we add these two distances:

Total distance walked = (1)1/8 + 3/4

To add these fractions, we need to find a common denominator, which is 8 in this case

Total distance walked = (9/8) + (6/8)

= 15/8

= 1 (7/8)

Now, we subtract the total distance walked from Sam's goal distance:

Remaining distance = (3)1/2 - 1 (7/8)

To subtract fractions, we also need a common denominator. The common denominator is 2 in this case:

Remaining distance = (6/2 + 1/2) - (15/8)

= (12/8 + 1/8) - (15/8)

= 13/8 - 15/8

= -2/8

= -1/4

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The two possible sets of four numbers are (9,-27,81, -243) and (-18,-54,-162,-486).

A geometric progression is a special type of progression where the successive terms bear a constant ratio known as a common ratio. It is also commonly referred to as GP. The GP is generally represented in form a, ar, ar2.... where 'a' is the first term and 'r' is the common ratio of the progression. The common ratio can have both negative as well as positive values. To find the terms of a geometric series, we only need the first term and the constant ratio. Finite geometric progression contains a finite number of terms. It is the progression where the last term is defined. Infinite geometric progression contains an infinite number of terms. It is the progression where the last term is not defined.

Let the first term of the geometric progression be a and the common ratio be r.

The second term is less than the first by 36.

∴ a - ar = 36

⇒ a(1-r) = 36 --- (1)

The third term is greater than the fourth term by 324.

∴ ar² - ar³ = 324

⇒ ar²(1-r) = 324  --- (2)

Divide equation (2) by equation (1):

∴ r² = 9

⇒ r = ±3

Put r in the first equation:

⇒ a - ar = 36

⇒ a(1 - (±3) = 36

⇒ a = 36/4 or 36/-2

∴ a = 9 or -18

Similarly finding the other three terms:

ar = 9× -3 or -18×3  = -27 or -54

ar² = -27×-3 or -54×3 = -81 or -162

ar³ = -81×-3 or -162×3 = 243 or -486

Thus, the two possible sets of four numbers are (9,-27,81, -243) and (-18,-54,-162,-486).

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A type I error, also known as a false positive, is when a test incorrectly rejects the null hypothesis. In this context, a type I error would mean that the test incorrectly concludes that the proportion of water bottles that are recycled is more than 23% after the program, when in reality it is still 23%.

1. Calculate the means of the two samples.

2. Calculate the standard deviation of the two samples.

3. Calculate the degrees of freedom (df) by subtracting 1 from the total

number of samples.

4. Calculate the t-statistic by subtracting the means of the two samples, dividing the result by the standard deviation, and then dividing that result by the square root of the degrees of freedom.

5. Calculate the critical value of t from the t-distribution table for the degrees of freedom and the chosen level of significance.

6. Compare the calculated t-statistic with the critical value of t.

7. Make a decision – accept or reject the null hypothesis.

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Answer:

x = 2√2

Step-by-step explanation:

If is inversely proportional to x², then:

[tex]y \propto \dfrac{1}{x^2} \implies y=\dfrac{k}{x^2} \quad \textsf{(for some constant k)}[/tex]

Given:

Substitute the given values into the found equation and solve for k:

[tex]\implies 2=\dfrac{k}{4^2}[/tex]

[tex]\implies 2=\dfrac{k}{16}[/tex]

[tex]\implies k=32[/tex]

Therefore:

[tex]y=\dfrac{32}{x^2}[/tex]

To find the value of x when y = 4, substitute y = 4 into the found equation and solve for x:

[tex]\implies 4=\dfrac{32}{x^2}[/tex]

[tex]\implies x^2=\dfrac{32}{4}[/tex]

[tex]\implies x^2=8[/tex]

[tex]\implies x=\sqrt{8}[/tex]

[tex]\implies x=\sqrt{4 \cdot 2}[/tex]

[tex]\implies x=\sqrt{4} \sqrt{2}[/tex]

[tex]\implies x=2\sqrt{2}[/tex]

The most effective way to use her 4 hours of study time to get the highest possibility or probability of test scores would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.

From the information given, it is clear that working on multiple-choice problems is the most effective way to improve her test score. Therefore, the highest possibility or probability of test scores would be achieved by spending the most time working on multiple-choice problems.

The available time for studying is 4 hours, so the maximum time that can be spent working on multiple-choice problems is 4 hours. If she spends 4 hours working on multiple-choice problems, she will not have any time left to review lecture notes.

So, the most effective way to use her 4 hours of study time to get the highest possible test score would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.

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Indira should have written the equation negative 6 + a = negative 3, and the equation 1 + b = negative 2 in step 2, as according to coordinate geometry.

For translation from point B(-6,1) to  point B'(-3,-2);

Step 1 : Substitute the original coordinates and the translated coordinates into (x,y) → (x+a,y+b) ; B (negative 6,1) → B prime (negative 6 + a, 1 + b) = B prime (negative 3, negative 2)

Step 2 ( Indira's mistake) : Two equations to be written, as in coordinate geometry; first one being negative 6 + a = negative 3 ; and the second one being 1 + b = negative 2

Step 3 : Solving the equations to get the values of a and b;

a = negative 3 + 6

a = 3, and

b = negative 2 minus 1

b = -3

Step 4 : By substitution method, using values of a and b we find B prime;

original coordinates of point B = (-6,1)

Translated coordinates of point B' = (-6 + a, 1 + b)

                                                          = ((-6) + 3 , 1 + (-3))            

                                                           = (-3,-2)

Thus, that is how, step-by-step using basic linear equation method, we solved for translated coordinates.

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The coefficient of x⁷ in the given expression is 16.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given is the expression [x³ + (4 / x²)]⁴.

[x³ + (4 / x²)]⁴ =  (x³ + 4x⁻²)⁴

                      = (x³ + 4x⁻²)² (x³ + 4x⁻²)²

                      = (x⁶ + 8x + 16x⁻⁴) (x⁶ + 8x + 16x⁻⁴)  

                      = x¹² + 8x⁷ + 16x² + 8x⁷ + 64x² + 128x⁻³ + 16x² + 128x⁻³ +

                         256x⁻⁸

Rearranging with like terms, we get,

                      = x¹² + 16x⁷ + 96x² + 256x⁻³ + 256x⁻⁸

Hence the coefficient of x⁷ is 16.

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Answer:

Gia has 85 beads in the end

Step-by-step explanation:

28+17 beads = 45 beads

94 beads - 45 beads = 49 beads

49 beads + 36 beads = 85 beads

The function f(x) = 3x^4/4 - 32285040.75 and the line 81x + y = 0 is tangent to the graph of f at the point (-3,0)

To find a function f such that f '(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f, we can use the fact that the slope of the tangent line to a function f(x) at a point x = a is given by f'(a).

Since the line 81x + y = 0 has a slope of -81, we know that f'(a) = -81. So, we can set f'(a) = -81 and solve for a:

f'(a) = 3a^3 = -81
a^3 = -27
a = -3

Now we can use the point-slope form of a line to find the equation of the tangent line to the graph of f at x = -3:

y - f(-3) = f'(-3)(x + 3)

y - f(-3) = -81(x + 3)

We also know that the point (-3,0) lies on the graph of f and on the line 81x + y = 0. We can use this information to find the value of f(-3):

0 = -81(-3) + f(-3)
f(-3) = 243

So the equation of the tangent line is:
y - 243 = -81(x + 3)
y = -81x - 222

To find f(x) we can use the fact that f(x) = the antiderivative of f'(x)

∫f'(x)dx = f(x) + C

∫3x^3 dx = f(x) + C

3x^4/4 + C = f(x)

We can find the value of the constant C by using the point (x,y) = (-3,0) on the function f(x)

0 = 3(-3)^4/4 + C
C = -3^4*3/4 - 32285040.75

Therefore the function f(x) = 3x^4/4 - 32285040.75

And the line 81x + y = 0 is tangent to the graph of f at the point (-3,0)

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The difference in values of the two houses when they are each 15 years old is given as follows:

$22,000.

The home values are modeled using linear functions, which in slope-intercept form are given as follows:

y = mx + b.

In which the parameters are given as follows:

For House A, the points are given as follows:

(3,150) and (8, 180).

Then the slope is given as follows:

m = (180 - 150)/(8 - 3)

m = 6.

Hence:

y = 6x + b

When x = 3, y = 150, hence the intercept b is given as follows:

150 = 18 + b

b = 132.

Then the function for the value of the home after x years is given as follows:

y = 5x + 132.

Meaning that the value of the home after 15 years is given as follows:

y = 5(15) + 132

y = $222,000.

For House B, the points are given as follows:

(1,130) and (5, 150).

Then the slope is given as follows:

m = (150 - 130)/(5 - 1)

m = 5.

Hence:

y = 5x + b

When x = 1, y = 130, hence the intercept b is given as follows:

130 = 5 + b

b = 125.

Then the function for the value of the home after x years is given as follows:

y = 5x + 125.

Meaning that the value of the home after 15 years is given as follows:

y = 5(15) + 125

y = $200,000.

The difference is then given as follows:

$222,000 - $200,000 = $22,000.

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Answer:

We can use the following steps to determine the different amounts of money that can be made from a collection of coins that consists of two pennies, one nickel, and one dime:

Step 1: List out all the different combinations of coins that can be used to make the different amounts of money.

Two pennies

One penny and one nickel

One penny and one dime

Two pennies and one nickel

Two pennies and one dime

One nickel and one dime

Two pennies, one nickel, and one dime

Step 2: Calculate the value of each combination of coins.

Two pennies = $0.02

One penny and one nickel = $0.06

One penny and one dime = $0.11

Two pennies and one nickel = $0.07

Two pennies and one dime = $0.12

One nickel and one dime = $0.15

Two pennies, one nickel, and one dime = $0.17

Step 3: Write down the total amount of money that can be made from each combination.

Final Answer: There are 7 different amounts of money that can be made from a collection of coins that consists of two pennies, one nickel, and one dime, they are $0.02, $0.06, $0.11, $0.07, $0.12, $0.15, and $0.17

2^8, 4^4 and 16^2 are equivalent to 256. We can find this out by using the concept of Factors.

Factors are numbers or algebraic expressions that divide another number of expression without leaving a remainder.

In the question, the number given is 256.

Options are: 2^8, 4^4, 16^2, and 128^2

We will break down all the numbers into the product of their factors and using multiplication, we will verify if they are equivalent to 256 or not.

2^8 = 2*2*2*2*2*2*2*2 = 256

4^4= 4*4*4*4 = 256

16^2= 16*16 = 256

128^2 = 128*128 = 16384

As we can observe, only 128^2 is not equivalent to 256.

Therefore, 2^8, 4^4 and 16^2  are equivalent to 256.

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Answer: 16

Step-by-step explanation:

First, calm down.

The area of the trapezoid cannot be found in a straightforward way.

Instead, what we need to do here is divide the trapezoid into two parts, a right triangle and a trapezoid.

Finding the area of the right triangle is easy. You just need to multiply the sides and divide it by 2.

Area of right triangle = 5*4/2 = 10

Next, you need to find the area of the trapezoid.

Area of trapezoid(small) = (2+1)*4/2 = 6

All you need to do now is add the area of these two together, and you get 16.

Answer:

A = 16 units²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height between the parallel sides b₁ and b₋₂

here h = 4 , b₁ = 6 and b₂ = 2

A = [tex]\frac{1}{2}[/tex] × 4 × (6 + 2) = 2 × 8 = 16 units²

So on solving the provided question we can say that in the equation 15x - y = 25; x = 24/15

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

here,

15x - y = 25

so from provided data we have y = 1

15x - 1 = 25

15x = 24

x = 24/15

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All the values after squares are,

a) 2.3

b) 22.1

c) 65.6

d) 176.9

e) 396

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

The numbers are,

a) 1.5

b) 4.7

c) 8.1

d) 13.3

e) 19.9

Now, Find all the squares as;

a) 1.5

⇒ 1.5² = 1.5 × 1.5

          = 2.25

          = 2.3

b) 4.7

⇒ 4.7² = 4.7 × 4.7

           = 22.09

           = 22.1

c) 8.1

⇒ 8.1²= 8.1 × 8.1

         = 65.61

         = 65.6

d) 13.3

⇒ 13.3² = 13.3 × 13.3

            = 176.89

            = 176.9

e) 19.9

⇒ 19.9² = 19.9 × 19.9

             = 396.01

             = 396

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Answer: 9

Step-by-step explanation: It's 9 because both can be divided by 9, as the largest time without going over. As you can see, 81 divided by 9 is 9, and 72 divided by 9 is 8. 8 and 9 are the closest they can be without going over 81 and 72, so it's 9. I hope this helps!

The GCF of the numbers 81 and 72 is 3², which equals 9.

To find the greatest common factor (GCF) of 81 and 72, we can use several methods.

One common approach is to factorize both numbers and identify the common factors.

The prime factorization of 81 is 3⁴, and the prime factorization of 72 is 2³×3².

To find the GCF, we look for the highest power of common prime factors in both numbers.

The highest power of the common prime factor (3) is 3², since it appears as a factor in both numbers.

Therefore, the GCF of 81 and 72 is 3², which equals 9.

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