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3 years ago

14

I need to know what is the sequences?

1 answer:

RSB [31]3 years ago

7 0

Answer:

a particular order in which related things follow each other.

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A cylinder with height 8 units has a volume of 72 cubic units. what is the radius of the cylinder?

nydimaria [60]

Answer:

r= 1.69

Step-by-step explanation:

4 0

3 years ago

Alicia has 7 paintings she wants to hang side by side on her wall.

melisa1 [442]

The question is an illustration of permutation and combinations.

The number of ways she can choose 4 out of the 7 paintings is 35
The number of ways she can arrange 4 out of the 7 paintings is 840

The given parameters are:

$\mathbf{n = 7}$

$\mathbf{r = 4}$

<u>(a) Choose 4 of 7 paintings</u>

Choosing 4 of 7 paintings implies combination.

So, we have:

$\mathbf{^nC_r = \frac{n!}{(n - r)!r!}}$

Substitute values for n and r

$\mathbf{^7C_4 = \frac{7!}{(7 - 4)!4!}}$

$\mathbf{^7C_4 = \frac{7!}{3!4!}}$

Expand

$\mathbf{^7C_4 = \frac{7 \times 6 \times 5 \times 4!}{3 \times 2 \times 1 \times 4 !}}$

$\mathbf{^7C_4 = 35}$

Hence, the number of ways she can choose 4 out of the 7 paintings is 35

<u>(b) Arrange 4 of 7 paintings</u>

Arranging 4 of 7 paintings implies permutation.

So, we have:

$\mathbf{^nP_r = \frac{n!}{(n - r)!}}$

Substitute values for n and r

$\mathbf{^7P_4 = \frac{7!}{(7 - 4)!}}$

$\mathbf{^7P_4 = \frac{7!}{3!}}$

Expand

$\mathbf{^7P_4 = \frac{7 \times 6 \times 5 \times 4 \times 3!}{3!}}$

$\mathbf{^7P_4 = 840}$

Hence, the number of ways she can arrange 4 out of the 7 paintings is 840

Read more about permutation and combinations at:

brainly.com/question/15301090

8 0

3 years ago

How do you calculate the lenght of a triangle with a hypotenuse?

PtichkaEL [24]

Step-by-step explanation:

<em>Triangles and the Pythagorean Theorem</em>

The Pythagorean Theorem, a2+b2=c2, a 2 + b 2 = c 2, can be used to find the length of any side of a right triangle.

The side opposite the right angle is called the hypotenuse (side c in the figure).

<em>(note: Pythagorean means hypotenuse)</em>

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<em>hope this helps </em>

5 0

3 years ago

Trig proofs with Pythagorean Identities.

lorasvet [3.4K]

To prove:

$$\frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}=2 \cot ^{2} x+1$

Solution:

$$LHS = \frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}$

Multiply first term by $\frac{1+cos x}{1+cos x}$ and second term by $\frac{1-cos x}{1-cos x}$ .

$$= \frac{1(1+\cos x)}{(1-\cos x)(1+\cos x)}-\frac{\cos x(1-\cos x)}{(1+\cos x)(1-\cos x)}$

Using the identity: $(a-b)(a+b)=(a^2-b^2)$

$$= \frac{1+\cos x}{(1^2-\cos^2 x)}-\frac{\cos x-\cos^2 x}{(1^2-\cos^2 x)}$

Denominators are same, you can subtract the fractions.

$$= \frac{1+\cos x-\cos x+\cos^2 x}{(1^2-\cos^2 x)}$

Using the identity: $1-\cos ^{2}(x)=\sin ^{2}(x)$

$$= \frac{1+\cos^2 x}{\sin^2x}$

Using the identity: $1=\cos ^{2}(x)+\sin ^{2}(x)$

$$=\frac{\cos ^{2}x+\cos ^{2}x+\sin ^{2}x}{\sin ^{2}x}$

$$=\frac{\sin ^{2}x+2 \cos ^{2}x}{\sin ^{2}x}$ ------------ (1)

$RHS=2 \cot ^{2} x+1$

Using the identity: $\cot (x)=\frac{\cos (x)}{\sin (x)}$

$$=1+2\left(\frac{\cos x}{\sin x}\right)^{2}$

$$=1+2\frac{\cos^{2} x}{\sin^{2} x}$

$$=\frac{\sin^2 x + 2\cos^{2} x}{\sin^2 x}$ ------------ (2)

Equation (1) = Equation (2)

LHS = RHS

$$\frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}=2 \cot ^{2} x+1$

Hence proved.

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4 years ago

PLEASE ANSWER ALL QUESTIONS!!! PLEASE HELP ME!

SCORPION-xisa [38]

Examples of metals: copper, iron, tin,

Examples of nonmetals: hydrogen, helium, nitrogen,

5 0

3 years ago