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ikadub [295]
3 years ago
9

A ceramic tile is in the shape of a triangle. The angle measurements of this triangle are 30 degrees, 60 degrees, and 90 degrees

. The leg across from the 30 degree angle is 6.25 cm long. How long is the hypotenuse of this triangle?
Mathematics
2 answers:
adell [148]3 years ago
7 0
Ratio of 30-60-90 triangles in terms of side lengths is 1-\sqrt{3} 
-2

So, the side across the 30-degree angle is 6.25.
Thus, the side across the 90-degree angle (hypotenuse) is 12.5.
adell [148]3 years ago
5 0
A 30 60 90 triangle is a special triangle that has simple proportions for it's side lengths. The short leg to long leg ratio is 1:sqrt(3); the short leg to hypotenuse ratio is 1:2. If the length of the short leg (across from the 30 degree angel) is 6.25 cm long, then the length of the hypotenuse is twice that: 12.5 cm.
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The volume of a cone varies jointly with the area of the base and the height. When the area of the base is 27 cm2 and the height
Tomtit [17]
Cone=cup:
V=124<span>cm^3.
h=12cm
V=Bh
P=r</span>^2π+rsπ:
B=r^2π
B=V/h=124/12=10,3cm^2
r^2=B/π
r=√(B/π)=1,81 cm
S=√(r^2+h^2)=√(12^2+1.81^2)=√(144+3,28)=12,13 cm
P=r^2π+rSπ=3,28*3,14+1,81*12,13*3,14=10,29+68,93=79,22 cm^2
3 0
3 years ago
Use a known maclaurin series to obtain the maclaurin series for the given function. f(x = 8x2 tan?1(7x3
11Alexandr11 [23.1K]
Going out on a limb here and guessing that the function is

f(x)=8x^2\tan^{-1}(7x^3)

Please correct me if this isn't the case.

Recall that

\tan^{-1}x=\displaystyle\sum_{n\ge0}\frac{(-1)^nx^{2n+1}}{2n+1}

which converges for |x|.

It follows that

8x^2\tan^{-1}(7x^3)=8x^2\displaystyle\sum_{n\ge0}\frac{(-1)^n(7x^3)^{2n+1}}{2n+1}
=\displaystyle\sum_{n\ge0}\frac{56(-49)^nx^{6n+3}}{2n+1}
6 0
3 years ago
There are 7 acts in a talent show.
lara31 [8.8K]

Answer:

<u><em></em></u>

  • <u><em>Event A: 1/35</em></u>
  • <u><em>Event B: 1/840</em></u>

<u><em></em></u>

Explanation:

<u>Event A</u>

For the event A, the order of the first 4 acts does not matter.

The number of different four acts taken from a set of seven acts, when the order does not matter, is calculated using the concept of combinations.

Thus, the number of ways that the first <em>four acts</em> can be scheduled is:

          C(m,n)=\dfrac{m!}{n!(m-n)!}

         C(7,4)=\dfrac{7!}{4!(7-4)!}=\dfrac{7!}{4!(3)!}=35

And<em> the number of ways that four acts is the singer, the juggler, the guitarist, and the violinist, in any order</em>, is 1: C(4,4).

Therefore the<em> probability of Event A</em> is:

           P(A)=1/35

Event B

Now the order matters. The difference between combinations and permutations is ordering. When the order matters you need to use permutations.

The number of ways in which <em>four acts </em>can be scheculed when the order matters is:

           P(m,n)=\dfrac{m!}{(m-n)!}

         P(m,n)=\dfrac{7!}{(7-4)!}=P(m,n)=\dfrac{7!}{4!}=840

The number of ways <em>the comedian is first, the guitarist is second, the dancer is third, and the juggler is fourth</em> is 1: P(4,4)

Therefore, <em>the probability of Event B</em> is:

            P(B)=1/840

7 0
3 years ago
emily just hired a new employee to work in your bakeshop . in one hour the empolyee burned 750 choclat chip cookies . if this re
Ivan
You planned on making 5000 cookies
4 0
3 years ago
Using Newton's Method, what is the formula for determining the nth term in a sequence of approximations to a solution of a polyn
lorasvet [3.4K]

Step-by-step explanation:

in newton rapson method

x_{n+1}=x_{n}-\frac{f\left(x_{n}\right)}{f^{\prime}\left(x_{n}\right)}

Let n=n-1

x_{(n-1)+1}=x_{n-1}-\frac{f\left(x_{n-1}\right)}{f^{\prime}\left(x_{n-1}\right)}

x_{n}=x_{n-1}-\frac{f\left(x_{n-1}\right)}{f^{\prime}\left(x_{n-1}\right)}

7 0
2 years ago
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