11 cm
Diagram NOT
accurately drawn
30 cm
The cylinder has a height of 30 cm and a radius of 11 cm. Work out the total surface area of
the cylinder. Give your answer correct to 2 significant figures.​

Step-by-step explanation:

let's use the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

so,

5.4/sin(K/2) = 12.3/sin(M1)

8.2/sin(K/2) = x/sin(M2)

M1 + M2 = 180 (as complementary angles or linear pair)

M2 = 180 - M1

sin(K/2) = 5.4×sin(M1)/12.3

sin(K/2) = 8.2×sin(M2)/x

therefore

5.4×sin(M1)/12.3 = 8.2×sin(180 - M1)/x

since sin(a) = sin(180 - a)

5.4×sin(M1)/12.3 = 8.2×sin(M1)/x

and then

5.4/12.3 = 8.2/x

x×5.4 = 8.2×12.3

x = 8.2×12.3/5.4 = 18.67777777... ≈ 18.7

Step-by-step explanation:Step-by-step explanation:

let's use the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

so,

5.4/sin(K/2) = 12.3/sin(M1)

8.2/sin(K/2) = x/sin(M2)

M1 + M2 = 180 (as complementary angles or linear pair)

M2 = 180 - M1

An isosceles trapezium is a trapezium in which the non-parallel sides are equal in measure

There are various formulae for isosceles trapezoid area:

Given are the bases a,b, and height h: A = (a + b) * h / 2

Given the bases a,b, and c, determine h using the Pythagorean Theorem (h is the square root of c2 – (a-b)2/4) and A = (a + b) * h / 2

Given are the bases a,b, and angle: h = tan() * (a-b)2 / 4, then A = (a + b) * h / 2.

Given: base a, leg c, and angle If h is defined as c * sin() and b is defined as a – 2 * c * cos(), then A = (a + b) * h / 2

An isosceles trapezoid (also known as an isosceles trapezium by the British; Bronshtein and Semendyayev 1997, p. 174) is a trapezoid with identical base angles on both the left and right sides.

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To prove x > y implies x^2 > y^2 for the domain of positive real numbers, we can do the following:

1. Start with the given inequality x > y.
2. Multiply both sides by x to get x^2 > xy.
3. Multiply both sides by y to get xy^2 > y^2.
4. Subtract y^2 from both sides to get x^2 - y^2 > 0.
5. Factor the left side to get (x-y)(x+y) > 0.
6. Since x > y, we know that (x-y) > 0. And since both x and y are positive real numbers, we also know that (x+y) > 0.
7. Therefore, the product of two positive numbers is also positive, so (x-y)(x+y) > 0 is true.
8. This proves that x^2 > y^2.

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Answer:

It would be $10.

Step-by-step explanation:

Answer:

The Standard form becomes - y = \(-\frac{2}{3}\) x² \(-\frac{4}{3}\) x + \(\frac{70}{3}\)

Step-by-step explanation:

To find - Write the quadratic function in three forms using the three points it goes through (-1,24),(5,0), and (-4,18)

Proof -

There are there forms of quadratic equation :

1) Standard form: y = ax²+ bx + c

where the a,b, and c are constants

2) Factored form: y = (ax + c)(bx + d)

where a,b,c, and d are constants

3) Vertex form: y = a(x + b)² + c

where a, b, and c are constants

Now,

For Standard form -

Given that the quadratic equation passes through three points

(-1, 24), (5, 0), (-4, 18)

24 = a(-1)²+ b(-1) + c

⇒24 = a - b + c                       ............(1)

0 = a(5)²+ b(5) + c

⇒0 = 25a + 5b + c                       ............(2)

18 = a(-4)²+ b(-4) + c

⇒18 = 16a - 4b + c                       ............(3)

By solving equation (1), (2), (3), we get

a = \(-\frac{2}{3}\), b = \(-\frac{4}{3}\), c = \(\frac{70}{3}\)

So,

The Standard form becomes - y = \(-\frac{2}{3}\) x² \(-\frac{4}{3}\) x + \(\frac{70}{3}\)

Answer:

subtract 42 - 7

Step-by-step explanation: u always solve the parenthesis first

Answer:

1000000

Step-by-step explanation:

Answer:A

Step-by-step explanation: because there is an association with the child’s hight and age so the answer is A ( plus I have did this before and got it wrong and the actual Answer was A when I picked B

Answer: A

Step-by-step explanation:

The new perimeter of the rectangle after a dilation with a scale factor of 1/4 will be 28.

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

We know the perimeter of a rectangle is 2(l + b).

Given, 2(l + b) = 112.

(l + b) = 112/2.

(l + b) = 56.

Now It has been dilated by a scale factor of 1/4, so the length and breadth will be (1/4)th of the original rectangle.

Therefore, (l/4 + b/4) = 56/4.

Now, 2(l/4 + b/4) = (56×2)/4.

2(l/4 + b/4) = 56/2.

2(l/4 + b/4) = 28.

So, The new perimeter of the rectangle will be 28.

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Answer:

24

Step-by-step explanation:

-3(1(-8))

1x(-8) = -8

-3 x -8 =24

The correct answer is option B. No value of k will make AB = BA

To check whether AB = BA, we need to multiply the matrices AB and BA and see if they are equal.

AB = [ 2 3-1 1] [ 2 9-3 k ]

[ 1 0 2 ] [ 0 0 1 ]

= [ 4 + 3(0) - 2k 18 - 9(0) - 3k ]

[ 0 + 0 + 2 0 + 0 + 1 ]

= [ 4 - 2k 18 - 3k ]

[ 2 1 ]

BA = [ 2 9-3 k ] [ 2 3-1 1]

[ 0 0 1 ] [ 1 0 2 ]

= [ 4 + 27 - 6k 6 - 3k - 3 ]

[ 1 0 ]

= [ 31 - 6k 3 - 3k ]

[ 1 0 ]

For AB = BA, we need to have

4 - 2k = 31 - 6k and 18 - 3k = 3 - 3k

Solving the first equation gives k = 9, and substituting k = 9 into the second equation gives 15 = 0, which is not true. Therefore, there is no value of k that makes AB = BA.

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Patrick received a total of approximately $6,785.97 over the course of 52 weeks.

To calculate the total amount of money Patrick received over the 52 weeks, we can use the concept of a geometric sequence. The first term of the sequence is $10, and each subsequent term is 10% more than the previous term.

To find the sum of a geometric sequence, we can use the formula:

Sn = a * (r^n - 1) / (r - 1),

where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = $10, r = 1 + 10% = 1.1 (common ratio), and n = 52 (number of weeks).

Plugging these values into the formula, we can calculate the sum of the sequence:

S52 = 10 * (1.1^52 - 1) / (1.1 - 1)

After evaluating this expression, we find that Patrick received approximately $6,785.97 over the 52 weeks.

As a result, Patrick collected about $6,785.97 in total over the course of 52 weeks.

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The time taken by the rocket to reach its maximum height is 3.25 seconds. The maximum height reached by the rocket is 174 feet.

A toy rocket is shot vertically into the air from a launching pad 5 feet above the ground with an initial velocity of 104 feet per second. The height h, in feet, of the rocket above the ground at "t" seconds after launch is given by the function h(t) = -16t² + 104t + 5. We need to calculate the time taken by the rocket to reach its maximum height and the maximum height.

Let the time taken and the maximum height be denoted by the variables "T" and "H". We will differentiate the given function to get the velocity of the rocket as a function of time.

v(t) = (d/dt)h(t)

v(t) = (d/dt)(-16t² + 104t + 5)

v(t) = -32t + 104

The velocity of the rocket must be equal to zero when it reaches its maximum height.

v(t) = 0

-32t + 104 = 0

32t = 104

t = 3.25

Hence, the time taken to reach the maximum height is 3.25 seconds.

The maximum height is calculated below.

H = h(3.25)

H = -16*(3.25)² + 104*(3.25) + 5

H = -16*10.5625 + 338 + 5

H = -169 + 343

H = 174

Hence, the maximum height reached by the rocket is 174 feet.

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Using mathematical induction, it can be proven that 13...(2n-1) <= 24*...*(2n-2) for every n >= 2.

Base Case: For n = 2, we have 13 = 3 and 24 = 8. Since 3 <= 8, the inequality holds true.

Induction Hypothesis: Assume that 13...(2k-1) <= 24*...*(2k-2) holds true for some positive integer k >= 2.

Induction Step: We need to show that the inequality also holds for k+1, i.e., 13...(2k+1) <= 24*...(2k).

To do this, we start with the left-hand side of the inequality:

13*...(2k+1) = (13*...(2k-1))(2k+1) <= (24...(2k-2))(2k+1)

(Using the induction hypothesis and the fact that 2k+1 is greater than or equal to 2).

Next, we simplify the right-hand side:

24...(2k-2))(2k+1) = 2*(24...(2k-2)(k+1))

Finally, we can conclude that:

13...(2k+1) <= 24*...(2k-2))(2k+1) = 2*(24...(2k-2)(k+1)) <= 24...*(2(k+1)-2)

(Since k+1 is greater than or equal to 2, we can use the induction hypothesis again.)

Therefore, by the principle of mathematical induction, we have proven that 13...(2n-1) <= 24*...*(2n-2) for every n >= 2.

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Answer:

k = 10

Step-by-step explanation:

∡ZYX = 180° - 115° = 65° (angles in a line add up to 180°)

*∡ stands for angle.

∑ of  ∡Z , Y and X should be equal to 180° (angles in a triangle add up to 180°)

∴ (4k + 5)° + 65° + (6k + 10)° = 180°

10k + 80 = 180

10k = 100

k = 100 ÷ 10 = 10

Answer: B) Life in the wilderness is a constant struggle against death.

We have evidence of this by the passage (third paragraph)

"On the sled, in the box, lay a third man whose toil was over, --a man whom the Wild had conquered and beaten down until he would never move nor struggle again. It is not the way of the Wild to like movement. Life is an offence to it, for life is movement; and the Wild aims always to destroy movement."

It basically says that the Wild aims to destroy life just due to its destructive, cruel, and cold nature. Unfortunately the man in the box is one example of this where it appears he is dead and his two other friends are possibly carrying his body back to town with the aid of the sled dogs.

The portion "It is not the way of the Wild to like movement" is basically the same as the author saying "It is not the way of the Wild to like life" since the author states that "life is movement". In my opinion, movement isn't just simple locomotion, but it could also apply to more general types of movements that all life possesses (so you could apply this logic to plants as well in some fashion).

Answer:

B?

Step-by-step explanation:

I mean, its about how a dude kicked the can.

All due respect to him though.

The excerpt is about how the sled dogs (wolves) and the men driving the sled is going through a heavy snow, through nature, and through all the obstacles nature threw at them. A guy went boom and died, so they put him in a wooden box (coffin.)

The area of the square is 9 cm², the area is increasing at a rate of 42 cm²/s. To answer your question, we will first relate the given terms "square," "rate," and the requested word count does not apply to my response as I provide concise answers.

A square has all its sides equal in length, and its area is calculated by multiplying the length of one side by itself (A = s^2, where A is the area and s is the length of one side). The problem states that each side of the square is increasing at a rate of 7 cm/s. Let's denote this rate as ds/dt.

We are asked to find the rate at which the area of the square is increasing (dA/dt) when the area is 9 cm². To start, let's determine the length of a side when the area is 9 cm²:

A = s^2
9 = s^2
s = 3 cm

Now we can use the chain rule from calculus to relate dA/dt and ds/dt:

dA/dt = d(A)/ds * ds/dt
dA/dt = d(s^2)/ds * ds/dt

Taking the derivative of s^2 with respect to s gives us:

d(s^2)/ds = 2s

Substituting the values of s (3 cm) and ds/dt (7 cm/s):

dA/dt = 2(3) * 7
dA/dt = 6 * 7
dA/dt = 42 cm²/s

So, when the area of the square is 9 cm², the area is increasing at a rate of 42 cm²/s.

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Answer:

Multiply the denominator of the fractional part by the whole number, and add the result to the numerator.

Step-by-step explanation:

You can add or subtract mixed numbers by turning them to improper fractions first. Improper fractions are fractions where the numerator is greater than the denominator.

I am sorry but I cannot see the picture properly, can you add another photo? Sorry for the inconvenience.

Answer:

gggggggggggggggggggggggggggggggggggggggggggggg

Step-by-step explanation:

Answer:

B. -9

Step-by-step explanation:

3(-9)-6/3=-11

7(-9)-3/6=-11

Answer:

Definition of a rational number:

Given number is:

As we see the number can be expressed as a ratio of two integers, hence it is a rational number.

On solving the provided question, we can say that w = 10 in; l = 2 in; volume of prism = WL = 10 X 2 = 20 in sq

The definition of a prism in geometry is a polyhedron with an n-sided polygonal base, a second base that is a shifted copy of the first base, and n additional faces (necessarily all parallelograms), with two Connect the corresponding sides of the base. Translations of the base are all cross sections that are parallel to it. A prism is a two-sided, solid, three-dimensional object. It consists of equal cross-sections, flat sides, and identical bases. A prism has faces that are parallelograms or rectangles without bases. A prism is a homogenous, solid, transparent, refracting object enclosed by two planes that are obliquely angled to one another. Two triangular faces and three parallel rectangular faces make up a typical prism. They are constructed of either glass.

here,

w = 10 in

l = 2 in

volume of prism = WL = 10 X 2 = 20 in sq

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Answer:A

Step-by-step explanation:

Answer:

Option B will be your answer

Step-by-step explanation:

\( \sin(60) = \frac{h}{30} \)

\( \frac{ \sqrt{3} }{2} = \frac{h}{ \frac{3}{15} } \)

\(h = 15 \sqrt{3} ft\)

hope it helps you...

Answer:

r = 2

Step-by-step explanation:

The equation in the point slope form of the line is

y +2 = \(\frac{-1}{4}\)(x -19)  To change to the y intercept form of a line distribute the \(\frac{-1}{4}\)

y + 2 = \(\frac{-1}{4}\) x + \(\frac{19}{4}\)  Subtract 2 from both sides of the equation

y  = \(\frac{-1}{4}\)x + \(\frac{11}{4}\)             ( \(\frac{19}{4}\) - \(\frac{8}{4}\))

Now that we have the equation.  The ask what is r when x is  3  (r is the y in the equation

y = \(\frac{-1}{4}\) (\(\frac{3}{1}\)) + \(\frac{11}{4}\)

y = \(\frac{-3}{4}\) + \(\frac{11}{4}\)

y = \(\frac{8}{4}\) = 2

Answer:

x=-8

Step-by-step explanation:

2x+2=-14

2x=-16

x=-8

Answer: x = -8

Step-by-step explanation:

Student 3's numeric grade percentage is 88.2%.

Based on the given information, we can calculate Student 3's numeric grade percentage by considering the weighting of the tests and project.

To calculate the test score percentage, we need to add up the test scores and divide by the total number of test points (which in this case is 300 since each test is out of 100 points). Then, we multiply the result by the weighted percentage of 80%.

Test score percentage = (Test 1 + Test 2 + Test 3) / (3 * 100) * 80%

For Student 3:

Test score percentage = (89 + 96 + 92) / (3 * 100) * 80% = 0.922 * 80% = 73.76%

Next, we calculate the project score percentage by multiplying the project grade by the weighted percentage of 20%.

Project score percentage = Project / 100 * 20%

For Student 3:

Project score percentage = 72 / 100 * 20% = 0.72 * 20% = 14.4%

Finally, we add the test score percentage and the project score percentage to get the final grade percentage.

Final grade percentage = Test score percentage + Project score percentage

For Student 3:

Final grade percentage = 73.76% + 14.4% = 88.16%

Therefore, Student 3's numeric grade percentage is 88.2%.

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Answer:

$86

Step-by-step explanation:

You multiply 21.50 times 4