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ioda
3 years ago
9

How many 4-element subsets containing the letter a can be formed from the set {a,b,c,d,e,f,g}?

Mathematics
1 answer:
Anarel [89]3 years ago
6 0
You would be able to make 20 subsets.
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A 12-meter ladder leans against a building forming a 30° angle with the building.
KatRina [158]

Answer:

will show you two (2) ways to solve this problem.

A diagram is needed to see what is going on....

 

Without loss of generality (WLOG)

The wall is on the right. The ladder leans against the wall

with a POSITIVE slope, from SW to NE (quadrant 3 to quadrant 1).

The measure from the bottom of the ladder to the wall is 6.

 

 

Option 1:

 

The ladder, ground and wall form a right triangle.

 

The hypotenuse (ladder) is 14 feet.

 

 The bottom of the ladder is 6 feet from the wall,

  so the base of this right triangle is 6 feet.

 

The top of the ladder to the ground represents

the missing leg of the right triangle.

 

The pythagorean theorem applies, which says

 6^2 + h^2 = 14^2   where h is the height

                                 of the top of the ladder to the ground

 

36 + h^2 = 196

 

 h^2 = 196 - 36

 

h^2  = 160

 

h = sqrt(160)

 

   = sqrt(16 * 10)

 

    = sqrt(16)* sqrt(10)

 

    = 4*sqrt(10) <--- exact answer

 

    = 4 * 3.16227766016838....

 

     = 12.64911....

 

    12.65 <--- rounded to 2 digits as directed

 

----------------------------------------------

Option #2: using trig

 

With respect to the angle formed by the bottom of the

ladder with the ground

  cos T = 6/14 = 3/7  

 T = inverse-cosine(3/7) = 64.623006647 degrees

 

 sin(64.623006647) = h/14

 

 h = 14*sin(64.62300647) = 12.6491106 <--- same answer                        

hope this helps

Step-by-step explanation:

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3 years ago
Please help me out<br><br><br><br> Find the area .
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Answer:

its27.54 8.1×3.4 =27.54 base×height

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Find the circumference of the circle with the given radius or diameter. (Use 3.14 for it) r=20
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Answer:

C = 2πr = 2 * 3.14 * 20 = 125.6

4 0
3 years ago
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What is the volume of a crate measuring 1 m by 2 m by 1.5 m?
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Answer:

V = l x w x h

V = 2m x 1.5m x  1m

V = 3 cubic meter

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Given f(x) = 5x2 2 and g(x) = 2x3 (f º g)(x) is a function of degree
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Suppose you are given the two functions  <span>f (x) = 2x + 3</span><span> and </span><span>g(x) = –x2 + 5</span><span>. Composition means that you can plug </span><span>g(x)</span><span> into  </span><span>f (x)</span><span>. </span>
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