MATHEMATICS HIGH SCHOOL

Find the area of the triangle
1. C=110 degrees, a=6, b=10
2. B=130 degrees, a=92, c=30

Answers

Answer 1
Answer: 1.\ \ \ |\angle \ ACB|=110^0\n\n.\ \ \ \ \ a=|BC|=6\ [u]\ \ \ and\ \ \ b=|AC|=10\ [u]\n\nArea= (1)/(2) \cdot |AC|\cdot |BC|\cdot sin(|\angle \ ACB|)\n\nArea= (1)/(2) \cdot 6\cdot 10\cdot sin110^0=30\cdot sin (180^0-70^0)=\n\n.\ \ \ \ \ \ =30\cdot sin70^0\approx30\cdot 0.9397=28.191\ [u^2]\n\n

2.\ \ \ |\angle \ ABC|=130^0\n\n.\ \ \ \ \ a=|BC|=92\ [u]\ \ \ and\ \ \ c=|AB|=30\ [u]\n\nArea= (1)/(2) \cdot |AB|\cdot |BC|\cdot sin(|\angle \ ABC|)\n\nArea= (1)/(2) \cdot 30\cdot 92\cdot sin130^0=1380\cdot sin (180^0-50^0)=\n\n.\ \ \ \ \ \ =1380\cdot sin50^0\approx1380\cdot 0.7660=1057.08\ [u^2]\n\n

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A conical tent is to accommodate 77 persons. Each person must have 16m³ of air to breathe. Given the radius of the tent as 7m find the height of the tent and also its curved surface area.

Express the ratio 20:35 in simplest form.

Answers

Answer:4:7

Step-by-step explanation:

20:35

/5 on both sides.

4:7

Insects are best photographed at midday when the insects are more active.

Answers

I think that statement is true. Most of the insects rely on sun light in order to functions. Beside that, the light gave a better vision for the camera, allowing you to capture every movement from the insects, which is very hard to do in night time unless you had a really high end camera

The answer is False

(Just took the test on plato)

A slide is 21 ft long. To get to the top of the slide, you use a vertical 9-foot high rung ladder. What is the distance, b, from the bottom of the slide to the bottom of the stairs? Round your answer to the nearest tenth.A. 22.8
B. 19
C. 30
D. 15 User: Can the set of lengths be the side lengths of a right triangle? 18 m, 24 m, 30 m
A. yes
B. no

Answers

Answer:

First Answer = 19.0

Second Answer = Yes.

Step-by-step explanation:

Length of Side = 21 ft

Vertical length of ladder = 9 ft.

This formal a Right angled triangle situation.

Distance between bottom of slide and bottom of ladder = b

Using Pythagoras theorem,

b² + 9² = 21²

b² + 81 = 441

b² = 441 - 81

b² = 360

b = √360

b =6√10

b = 18.973666...

b = 19.0 (rounded off to nearest tenth)

Given length of sides of the triangle are 18 m , 24 m and 30 m

30² = 900

18² + 24² = 324 + 576 = 900

Since, 30² = 18² + 24²

Therefore, Given set cab be the length of the sides of the right triangle.
FIRST QUESTION:

The slide is 21 ft long. You can imagine that this slide is actually the hypotenuse of a right angled triangle.

To get to the top of the slide you must climb up a vertical 9 foot ladder. You can imagine that this ladder is the opposite side of the right angled triangle.

Now, the distance between the bottom of the ladder and the bottom of the slide can be thought of as the adjacent side of this right angled triangle.

We know, thanks to Pythagoras that:

A²+O²=H²

A = Adjacent length = b

O = Opposite length

H = Hypotenuse

Therefore:

b²+9²=21²

b²=21²-9²

b²=360

b=√360=18.97 (2dp)

So the answer you are looking for is 19 feet to the nearest tenth (answer: B).

SECOND QUESTION:

18²+24²=30²  (Yes)

Therefore the answer to the second question is YES (answer: A).

If the statement if I'm hungry then I am not happy is assumed to be true is its inverse if I'm not hungry then I must be happy also always true ?

Answers

It is not always true. That is because your happiness does not necessarily correspond to your hungriness. An explanation, you might be unhappy while not being hungry, since unhappiness can also come from other sources.

Sean has 1/5 of a cupcake and 1/5 of a large cake. are the wholes the same?

Answers

yes they are because its the same two numbers.
Yes they are the same...

List the first twenty counting numbers in base seven? (only digits 0 thru 6 are used in base 7)

Answers

The correct answer is:


1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14, 15, 16, 20, 21, 22, 23, 24, 25, 26.


Explanation:


The base 7 number system has digits 0 through 6.


When we start counting, we start with 1. In base 7, we would be able to go from 1 to 6, just as in base 10. However, in base 7, after we reach 6, we would hit 2 digits; instead of 7, the next number would be 10.


We would then count from 10 to 16. After we reach 16, instead of 17, we go to 20 and count from 20 to 26.

So the question ask to list the first twenty counting numbers in base seven and the best answer would be 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14, 15, 16 , 20 ,21, 22, 23, 24, 25, 26, 30, 31, 32, 33, 34, 35, 36, 40, 41. I hope you are satisfied with my answer and feel free to ask for more if you have question and further clarification about the said question 
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