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4 years ago

Solve the equation 3 1/2 - 1 1/3 * x = 1 How do you find the value of x????

1 answer:

3 0

$3\dfrac{1}{2}-1\dfrac{1}{3}x=1\\\\\dfrac{3\cdot2+1}{2}-\dfrac{1\cdot3+1}{3}x=1\ \ \ |\cdot6\\\\3\cdot7-2\cdot4x=6\\\\21-8x=6\ \ \ |-21\\\\-8x=-15\ \ \ |:(-8)\\\\x=\dfrac{15}{8}\\\\x=1\dfrac{7}{8}$

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Simplify the trigonometric expression sin(4x)+2 sin(2x) using Double-Angle

drek231 [11]

Answer:

${ \bf{ = \sin(4x) + 2 \sin(2x) }} \\ = { \bf{2 \sin(2x) \cos(2x) + 4 \sin(x) \cos(x) }} \\ { \bf{ = 4 \sin(x) \cos(x) . ({ \cos }^{2} x - { \sin}^{2} }x) + 4 \sin(x) \cos(x) } \\ = { \bf{4 \sin(x) \cos(x) ( { \cos }^{2}x - { \sin }^{2}x + 1) }} \\ = { \bf{4 \sin(x) \cos(x) }(2 { \cos }^{2} x)} \\ = { \bf{8 \sin(x) { \cos}^{3}x }}$

8 0

3 years ago

A triangle has sides of 18cm and 32cm. The measurement of the longest side is missing. Ted says that one possibility for the unk

gulaghasi [49]

Since the measurement of the longest side is missing we can use the pythagorean theorem to find the hypotenuse or longest side.

18^2 + 32^2 = c (hypotenuse) ^2
324 + 1,024 = c^2
1,348 = c^2
sqrt 1,348 = c
36.72 = c
i do not agree with ted because when you use the pythagorean theorem you do not get 47cm

this can be proved by
18^2 + 32 ^2 = 47^2
we already know the left side is 1,348
1,348 = 47^2
1,348 does not equal 2,209 which is 47 squared

4 0

3 years ago

Kevin buys a car. His car payment is $248 per month.After 55 payments how much was Kevin paying?

NNADVOKAT [17]

Answer:

hes paid 13,640

Step-by-step explanation:

5 0

3 years ago

Q15) 1.0 marks<br>Choose the missing term in the below series.<br>26, 37, 50, 65, 82, ?<br>

Illusion [34]

Answer:

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

What is Permutations and Combinations?

marissa [1.9K]

Answer:

See below

Step-by-step explanation:

Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.

Permutation can be expressed in math as:

$\displaystyle{_n P _r = \dfrac{n!}{(n-r)!} \ \ \ (n \geq r) }$

where n is a number of total object and r is a number of selected object to arrange. Hence. n cannot be less than r.

Now let's see an example of permutation, suppose we have letter A, B and C. I'd like to know how many ways these words can be arranged:

Since there are 3 letters total and 3 selected letters to arrange then:

$\displaystyle{_3 P _3 = \dfrac{3!}{(3-3)!}}\\\\\displaystyle{_3 P _3 = \dfrac{3 \times 2 \times 1}{0!}}\\\\\displaystyle{_3 P _3 = \dfrac{6}{1}}\\\\\displaystyle{_3 P _3 = 6}$

Therefore, there are 6 ways to arrange the letters - we can also demonstrate visually:

ABC - 1

ACB - 2

BAC - 3

BCA - 4

CAB - 5

CBA - 6

Notice that if you do visually, you'll get the same answer as the calculation of permutation!

----

Combination can be expressed mathematically as:

$\displaystyle{_n C _r = \dfrac{n!}{(n-r)!r!} = \dfrac{_n P _r}{r!} \ \ \ (n \geq r) }$

The difference between permutation and combination is that you only find how many ways you can select object in combination. Therefore, no arrange and doesn't care about order, just ways to select.

Suppose we have same 3 letters: A, B and C. I want to find how many ways I can select these 3 letters:

Since there are 3 letters total and 3 selected letters:

$\displaystyle{_3 C _3 = \dfrac{3!}{(3-3)!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{0!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{3!}}\\\\\displaystyle{_3 C _3 = 1}$

Hence, there is only one way to select 3 letters. This makes sense because if you have 3 letters then you can only select 3 letters only one way.

5 0

2 years ago