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3 years ago

Find the exact value of tan(pi/12) using the sum and difference formulas

2 answers:

7 0

Π/12 is half of π/6, which is 30 degree
tan(α/2)=(1-cosα)/sinα)
plug in the values: tan(π/12)=(1-cosπ/6)/sin(π/6)=(1-√3/2)/(1/2)=2-√3

JulsSmile [24]3 years ago

4 0

Answer:

Step-by-step explanation:

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See attached picture, is there a way to enter equations or algebraic symbols?

coldgirl [10]

SOLUTIONS

Solve a given equations or algebraic symbols?

$\begin{gathered} f(x)=x^2+2x \\ g(x)=1-x^2 \end{gathered}$

(A)

$\begin{gathered} (f+g)(x)=(x^2+2x)+(1-x^2) \\ collect\text{ like terms} \\ x^2-x^2+2x+1 \\ (f+g)(x^)=2x+1 \end{gathered}$

(B)

$\begin{gathered} (f-g)(x)=(x^2+2x)-(1-x^2) \\ =x^2+2x-1+x^2 \\ =x^2+x^2+2x-1 \\ (f-g)(x)=2x^2+2x-1 \end{gathered}$

(C)

$\begin{gathered} fg(x)=(x^2+2x)(1-x^2) \\ =x^2-x^4+2x-2x^3 \\ fg(x)=-x^4-2x^3+x^2+2x \end{gathered}$

(D)

$\begin{gathered} \frac{f}{g}(x)=(x^2+2x)\div(1-x^2) \\ =\frac{x^2+2x}{1-x^2} \end{gathered}$

5 0

1 year ago

Brittany buys 2.55 pounds of turkey for $5.96 per pound and 3.7 pounds of

Galina-37 [17]

Answer:

Brittany needs another $3.7405.

Step-by-step explanation:

Per pound Cost of turkey = $5.96 per pound

The amount Brittany buys the turkey = 2.55 pounds

Brittany's cost for turkey = 2.55 × $5.96 = $15.198

Per pound cost for cheese = $3.35 per pound

The amount Brittany buys the cheese = 3.7 pounds

Brittany's cost for cheese = 2.55 × $3.35 = $8.5425

So,

Brittany's total cost = Turkey cost + Cheese cost

= $15.198 + $8.5425

= $23.7405

As brittany gave the clerk 20 dollars.

So, the amount she further needs will be:

$23.7405 - $20 = $3.7405

Therefore, Brittany needs another $3.7405.

8 0

3 years ago

Work out m and c for the line: 3 y + 6 x = − 3

Usimov [2.4K]

Answer:

m is -2 and c is -1

Step-by-step explanation:

• Let's first phrase out the general equation of a line

${ \rm{y = mx + c}}$

m is the slope
c is the y-intercept

[ remember that a general line equation must be in slope - intercept form as shown above ]

• from our question, we are given the equation;

${ \rm{3y + 6x = - 3}}$

• let's make y the subject in order to make the equation in slope - intercept format.

→ remember to apply "subject making knowledge"

${ \rm{3y = - 3 - 6x}} \\ \\ { \rm{3y = - 6x - 3}} \\ \\ { \rm{ \frac{3y}{3} = \frac{ - 6x}{3} - \frac{3}{3} }} \\ \\ { \boxed{ \rm{y = - 2x - 1}}}$

• The above boxed equation is now a general equation. Let's extract out slope, m and y-intercept, c

${ \rm{m \: \dashrightarrow \: - 2}} \\ \\ { \rm{c \: \dashrightarrow \: - 1}}$

8 0

3 years ago

a rectangle shape whose length is 4 inches less than twice its width. the area is 30 square inches. whats the dimension

Ne4ueva [31]

Using the given information, we can say the following:
Width (W) = x
Length (L) = (2x - 4)
Area of Rectangle = L × W
Using this, we can formulate an equation for rectangle in question:
x(2x - 4) = 30
Expand and move everything to one side:
2x² - 4x - 30 = 0
Simplify by dividing everything on both sides by 2:
x² - 2x - 15 = 0
Factorise:
(x + 5)(x - 3) = 0
Set each factor equal to 0 and solve for x:
x + 5 = 0
x = -5 (a dimension cannot be negative so this is not the solution we want)
x - 3 = 0
x = 3 (this is the solution)
x = W = 3"
L = 2x - 4
L = 2(3) - 4
L = 2"

So, the length the rectangle is 2" and the width is 3"

5 0

3 years ago

The lengths of the legs of a right triangle are consecutive even integers. The hypotenuse is 58 inches. What is the sum of the l

miskamm [114]

Answer:

82 inches

Step-by-step explanation:

The difference between consecutive even integers is 2, thus

let the legs be n and n + 2

Using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

n² + (n + 2)² = 58² ← expand and simplify left side

n² + n² + 4n + 4 = 3364 ( subtract 3364 from both sides )

2n² + 4n - 3360 = 0 ( divide all terms by 2 )

n² + 2n - 1680 = 0 ← in standard form

(n + 42)(n - 40) = 0 ← in factored form

Equate each factor to zero and solve for n

n + 42 = 0 ⇒ n = - 42

n - 40 = 0 ⇒ n = 40

But n > 0 ⇒ n = 40

and n + 2 = 40 + 2 = 42

Thus sum of legs = 40 + 42 = 82 inches

3 0

3 years ago