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3 years ago

In math the "Base" is defined as

1 answer:

6 0

In math Base is Defined as the number of digits or combination of digits that a system of counting numbers used to represent numbers a base can be any whole number greater than 0

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Prove that sin3a-cos3a/sina+cosa=2sin2a-1

Sloan [31]

Answer:

$\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1$

Step-by-step explanation:

we are given

$\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1$

we can simplify left side and make it equal to right side

we can use trig identity

$sin(3a)=3sin(a)-4sin^3(a)$

$cos(3a)=4cos^3(a)-3cos(a)$

now, we can plug values

$\frac{(3sin(a)-4sin^3(a))-(4cos^3(a)-3cos(a))}{sin(a)+cos(a)}$

now, we can simplify

$\frac{3sin(a)-4sin^3(a)-4cos^3(a)+3cos(a)}{sin(a)+cos(a)}$

$\frac{3sin(a)+3cos(a)-4sin^3(a)-4cos^3(a)}{sin(a)+cos(a)}$

$\frac{3(sin(a)+cos(a))-4(sin^3(a)+cos^3(a))}{sin(a)+cos(a)}$

now, we can factor it

$\frac{3(sin(a)+cos(a))-4(sin(a)+cos(a))(sin^2(a)+cos^2(a)-sin(a)cos(a)}{sin(a)+cos(a)}$

$\frac{(sin(a)+cos(a))[3-4(sin^2(a)+cos^2(a)-sin(a)cos(a)]}{sin(a)+cos(a)}$

we can use trig identity

$sin^2(a)+cos^2(a)=1$

$\frac{(sin(a)+cos(a))[3-4(1-sin(a)cos(a)]}{sin(a)+cos(a)}$

we can cancel terms

$=3-4(1-sin(a)cos(a))$

now, we can simplify it further

$=3-4+4sin(a)cos(a))$

$=-1+4sin(a)cos(a))$

$=4sin(a)cos(a)-1$

$=2\times 2sin(a)cos(a)-1$

now, we can use trig identity

$2sin(a)cos(a)=sin(2a)$

we can replace it

$=2sin(2a)-1$

so,

$\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1$

7 0

3 years ago

Read 2 more answers

Choose the function that the graph represents

gayaneshka [121]

Answer:

Where are the functions and the graph?

Step-by-step explanation:

6 0

3 years ago

12x - 5 = 8x - x + 50<br> Help please show work and check the solution

Inga [223]

Answer:

x = 11

Step-by-step explanation:

$12x - 5 = 8x - x + 50 \\ 12x - 5 = 7x + 50 \\ 12x - 5 - 7x = 7x + 50 - 7x \\ 12x - 7x - 5 = 50 \\ 5x - 5 = 50 \\ 5x - 5 + 5 = 50 + 5 \\ 5x = 55 \\ x = 11$

and check:

$12(11) - 5 = 8(11) - (11) + 50 \\ 132 - 5 = 77 + 50 \\ 127 = 127$

3 0

3 years ago

Dimensions of a Box A large plywood box has a volume of . Its length is ft greater than its height, and its width is ft less tha

cupoosta [38]

Answer:

Few things are missing, they are volume of the box is 180 feet cube. Length is 9 feet greater than its height, and weight is 4 feet less than its height.

Step-by-step explanation:

Given, the volume of the box, V = 180 feet cube

Let the height of the box, h = x feet

Therefore, length is, l = ( 9+x ) feet

And width is, b = ( x-4) feet

so volume of the box is

V = l x b x h

$180= (x+9) \times (x-4) \times (x)$

$x^3 +5x^2-36x -180 =0$

Factorizing we get

(x+5)(x-6)(x+6)=0

Therefore,

x = -5, -6, 6

Now since the height of the box cannot be negative, so taking the positive value of x, we get

Height of the box, h = x = 6 feet

Length , l = ( 9+x ) = 9+6 = 15 feet

Width , b = ( x-4) = 6-4 = 2 feet

8 0

3 years ago

What is the answer to 3+x=y

NARA [144]

Answer: x=y-3 or y=3+x

Step-by-step explanation:

7 0

3 years ago