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makkiz [27]
3 years ago
14

Ms. Calculation, the math teacher, has an 80 cm long rain stick that makes a sound like running water when she turns it upside d

own. When the students hear its sound, they know that it is a signal for them to be attentive listeners. Her rain stick is made of a big piece of bamboo for the long part of the cylinder and bamboo caps cover each end. It has a circumference of 22cm. What is the surface area of her bamboo rain stick?
Mathematics
1 answer:
Alex17521 [72]3 years ago
8 0

Answer:

The surface area of her bamboo rain stick is 1,837 cm^2

Step-by-step explanation:

The bamboo rain stick can be modeled as a cylinder.

To calculate the surface of a cylinder, we add the lateral surface and 2 times the circular base.

A=A_l+2A_b

The lateral surface is equal to the length of the bamboo rain stick multiplied by the circunference of the base.

Then we have:

A_l=l\cdot C=80\;cm\;\cdot 22\;cm=1,760\;cm^2

The base is calculated as π times the square of the radius. We don't know the radius, but we can calculate it from the circumference as:

C=2\pi r=22\;cm\\\\r=\dfrac{22\;cm}{2\pi}\approx\dfrac{22\;cm}{6.28}=3.5\;cm

Then, we can calculate the base area as:

A_b=\pi r^2\approx3.14(3.5\;cm)^2=3.14*12.27\;cm^2=38.5\;cm^2

The surface area of the bamboo rain stick is:

A=A_l+2A_b=1,760\;cm^2+2*38.5\;cm^2\\\\A=1,760\;cm^2+77\;cm^2\\\\A=1837\;cm^2

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Jlenok [28]

Answer:

x>2

Step-by-step explanation:

When given the following inequality;

(x^2+x-3):(x^2-4)\geq1

Rewrite in a fractional form so that it is easier to work with. Remember, a ratio is another way of expressing a fraction where the first term is the numerator (value over the fraction) and the second is the denominator(value under the fraction);

\frac{x^2+x-3}{x^2-4}\geq1

Now bring all of the terms to one side so that the other side is just a zero, use the idea of inverse operations to achieve this:

\frac{x^2+x-3}{x^2-4}-1\geq0

Convert the (1) to have the like denominator as the other term on the left side. Keep in mind, any term over itself is equal to (1);

\frac{x^2+x-3}{x^2-4}-\frac{x^2-4}{x^2-4}\geq0

Perform the operation on the other side distribute the negative sign and combine like terms;

\frac{(x^2+x-3)-(x^2-4)}{x^2-4}\geq0\\\\\frac{x^2+x-3-x^2+4}{x^2-4}\geq0\\\\\frac{x+1}{x^2-4}\geq0

Factor the equation so that one can find the intervales where the inequality is true;

\frac{x+1}{(x-2)(x+2)}\geq0

Solve to find the intervales when the equation is true. These intervales are the spaces between the zeros. The zeros of the inequality can be found using the zero product property (which states that any number times zero equals zero), these zeros are as follows;

-1, 2, -2

Therefore the intervales are the following, remember, the denominator cannot be zero, therefore some zeros are not included in the domain

x\leq-2\\-2

Substitute a value in these intervales to find out if the inequality is positive or negative, if it is positive then the interval is a solution, if it is negative then it is not a solution. This is because the inequality is greater than or equal to zero;

x\leq-2   -> negative

-2   -> neagtive

-1\leq x   -> neagtive

x>2   -> positive

Therefore, the solution to the inequality is the following;

x>2

6 0
2 years ago
Which statement is true?
gayaneshka [121]

Answer:

Option: C is the correct answer.

C. Buying a needle and buying thread are dependent events.

Step-by-step explanation:

let A denotes the events of buying a thread.

and B denote the event of buying a needle.

Then A∩B denote the event of buying a needle and  a thread.

Also let P denote the probability of an event.

i.e. we are given:

P(A)=0.15

Also P(B|A)=0.25

As we know that:

P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}\\\\i.e.\\\\0.25=\dfrac{P(A\bigcap B)}{0.15}\\\\i.e.\\\\P(A\bigcap B)=0.0375

As we know that when two events A and B are independent then,

P(A∩B)=∅

otherwise they are dependent events.

Hence, option: C is the correct answer.

6 0
3 years ago
Read 2 more answers
A home has a living room that is 14 ft. wide, 22 ft. long, and a height of 9ft. Bob needs to paint
aleksandrvk [35]

Answer:

Step-by-step explanation:

Let's find the volume of the room in ft³ and that will give

14×22×9=2772ft³

There are deductions. Hence we subtract them from this value

3×5=15, but there are two, hence 15×2=30ft²

And 4×7=28ft²

Hence 2772-(30+28)=2714

Dividing this value by 320 gives

8.4(to 2s.f)

3 0
3 years ago
The quotient of a number divided by 6 is 30 .What is the number
Greeley [361]

Answer:

180

Step-by-step explanation:

Let the quotient be X

X/6= 30

cross multiply;

X=30×6=180

8 0
3 years ago
$500 are deposited into an account semiannuallysemiannually  for six years at an interest rate of 7.2​% compounded semiannually.
kobusy [5.1K]
Each year 107.2%increase of budget
first year 500 * 1.072 = 536
second year 536 * 1.072 = 574.592
third year 574.592 * 1.072 = 615.962624
..
..
sixth year 707.854392 *  1.072 = 758.819908

or you can just (1.072)^6 * 500 = 1.517639816659862 * 500 = 758.8199083299308

bingo........

8 0
2 years ago
Read 2 more answers
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