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Andrej [43]
3 years ago
8

Please do it on a piece of paper if possible <3

Mathematics
1 answer:
sesenic [268]3 years ago
7 0
To find the area, we need the height of the triangle first. We already have the base.

Let's find the height (BA)
tan = opposite / adjacent

tan 35 = BA / 12
BA = 12 * tan35
BA = 12 * 0.7002079283708176
BA = 8.402


Area of the triangle = 12*BA/2 = 6*BA = 50.412 square units
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In fig if x+y=w+z then prove that AOB is a line.​
frez [133]

Answer:

As Given, x+y=w+z

To Prove: AOB is a line or x+y=180

∘

(linear pair.)

According to the question,

x+y+w+z=360

∘

∣ Angles around a point.

(x+y)+(w+z)=360

∘

(x+y)+(x+y)=360

∘

∣ Given x+y=w+z

2(x+y)=360

∘

(x+y)=180

∘

Hence, x+y makes a linear pair.

Therefore, AOB is a straight line

4 0
3 years ago
How many words can be formed by using the W,X,Y,Z if repetitions is not allowed?
Setler [38]

Answer:

24

Step-by-step explanation:

What you have here is a permutation, seeing as each element can only be used once.

We have 4 letters initially, so we can choose any 1 as our first letter. We have 4 choices for our first letter

However, once we choose our first letter, we can't use it anymore, so, for our second letter, we can only choose from the remaining 3 letters.

Furthermore, once we choose our second letter, we can only choose our 3rd letter from the remaining two letters we didn't choose yet.

Finally, our last letter will always be the one we didn't choose the last 3 times. So there is only one choice here.

Going off of this, we have four choices for the 1st letter, three choices for the 2nd letter, two choices for the 3rd letter, and one choice for the 4th letter

The way to calculate how many permutations we have without repetition is using factorials

N!

Where N is the number of elements you have.

In this case, it would be 4!

4! is 4 * 3 * 2 * 1

Which equals 24

If you notice, each number in 4! is the number of options we have for each choice. 4, then 3, and so on

5 0
2 years ago
A right triangle has a leg that measures 15 ft and the hypotenuse measures 24 ft. What would the
Serhud [2]

Answer:

x=19

Step-by-step explanation:

First, you place the numbers in place of the variables in their relative positions using the pythagorean theorem:

15^{2} +x^{2}=24^{2}

Then you square the numbers that you currently have:

225+x^{2}=576

Then subtract 225 from both sides to isolate the x:

x^{2} =576-225

This gives you the equation:

x^{2} =351

Then take the square root of both sides which gives you:

x=18.7349939952

Then round to the nearest whole number which gives you x=19

3 0
2 years ago
Among all right circular cones with a slant height of 24​, what are the dimensions​ (radius and​ height) that maximize the volum
aleksklad [387]

Answer:

5571.99

Step-by-step explanation:

We need to use the Pythagorean theorem to solve the problem.

The theorem indicates that,

r^2+h^2=24^2 \\r^2+h^2=576\\r^2=576-h^2

Once this is defined, we proceed to define the volume of a cone,

v=\frac{1}{3}\pi r^2 h

Substituting,

v=\frac{1}{3} \pi (576-h^2)h\\v=\frac{1}{3} \pi (576h-h^3)

We need to find the maximum height, so we proceed to calculate h, by means of its derivative and equalizing 0,

\frac{dv}{dh} = \frac{1}{3} \pi (576-3h^2)

\frac{dv}{dh} = 0 then \rightarrow \frac{1}{3}\pi(576-3h^2)=0

h_1=-8\sqrt{3}\\h_2=8\sqrt{3}

<em>We select the positiv value.</em>

We have then,

r^2 = 576-(8\sqrt3)^2 = 384\\r=\sqrt{384}

We can now calculate the maximum volume,

V_{max}= \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (\sqrt{384})^2 (8\sqrt{3}) = 5571.99

4 0
3 years ago
Admission to the circus costs $4 plus $0.50 per ride. Ella spent $17.50 at the circus.
klemol [59]

Answer:

Ella went on 27 rides.

Step-by-step explanation:

$17.50 - $4 = $13.50

6 0
2 years ago
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