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2 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]2 years ago

4 0

Answer:

Step-by-step explanation:

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WILL MARK BRAINLIEST FOR BEST ANSWER! SERIOUS ANSWERS ONLY!

Veronika [31]

Answer:

$ 1850

Step-by-step explanation:

As it is simple interest, the interest will be same each year.

Interest = 2312.50 - 2081.25 = $ 231.25

The amount borrowed = 2081.25 - 231.25 = $ 1850

3 0

2 years ago

A rectangular box which is open at the top can be made from an12-by-18-inch piece of metal by cutting a square from each corner

algol [13]

Answer:

h=2.35in, l=13.3in and w=7.3in

Step-by-step explanation:

In order to solve this problem, we must start by drawing a diagram that will represent the prolem. (Look at attached picture)

From the diagram we can see that the length ad the width of the box are found by using the following expressions:

L=18-2x

W= 12-2x

H=x

next, we can make use of the volume formula of a rectangular prism, which is the following:

V=WLH

so we can substitute the expressions we got before on the formula:

V=x(12-2x)(18-2x)

and for ease of calculation, we can multiply the terms, so we get:

$V=x(216-24x-36x+4x^{2})$

$V=x(4x^{2}-60x+216)$

$V=4x^{3}-60x^{2}+216x$

So now we can find the derivative of the volume:

$V'=12x^{2}-120x+216$

and set it equal to zero, so we get:

$12x^{2}-120x+216=0$

and now we can solve. We can start by factoring the left side of the equation, so we get:

$12(x^{2}-10x+18)=0$

which yields:

x^{2}-10x+18=0

This one can only be solved by using the quadratic formula:

$x=\frac{-b\pm \sqrt{-b^{2}-4ac}}{2a}$

so we substitute the corresponding values:

$x=\frac{-(-10)\pm \sqrt{-(-10)^{2}-4(1)(18)}}{2(1)}$

which yields:

x=7.65in or x=2.35in

we keep the 2.35in only, because the 7.65in returns an impossible box, since that would make the width a negative width.

So the 2.35in height would give us the greatest box. Now we can use it to find the height, the width and the length of the box.

Height=x=2.35

W=12-2x=12-2*2.35=7.3in

L=18-2x=18-2(2.35)=13.3in

5 0

3 years ago

Please help me out with this so I can keep my kitten.

notka56 [123]

Answer:

$y = \frac{32}{3}$

Step-by-step explanation:

Firstly, move over the negative 3/4 fraction (don't forget to swap the operation i.e subtract to add):

$\frac{y}{8} = \frac{7}{12} + \frac{3}{4}$

Now, to add the two fractions, simply multiply the numerator and denominator by 3:

$\frac{3*3}{4*3} = \frac{9}{12}$

Now add this to the other fraction:

$\frac{9}{12} + \frac{7}{12} = \frac{16}{12}$

This can be simplified down by dividing both the numerator and denominator by 4:

$\frac{4}{3}$

Which now simplifies the original equation to:

$\frac{y}{8} = \frac{4}{3}$

Remove the y out of the fraction:

$\frac{1}{8}y = \frac{4}{3}$

Now multiply both sides by 8:

$(\frac{1}{8}y) * 8 = (\frac{4}{3}) * 8$

$y = \frac{4*8}{3}$

$y = \frac{32}{3}$

Hope this helps!

5 0

3 years ago

Read 2 more answers

The image of the polygon ABCDE reflected across the x-axis. A(-1,-1),B(0,1),C(4,2),D(6,0),E(3,-3) The vertices of the image are.

4vir4ik [10]

A reflection across the x-axis has the rule:

(x,y)→(x,-y).

Then:

A(-1,-1)→A'(-1,1),
B(0,1)→B'(0,-1),
C(4,2)→C'(4,-2),
D(6,0)→D'(6,0),
E(3,-3)→E'(3,3).

Answer: the vertices of the image are A'(-1,1), B'(0,-1), C'(4,-2), D'(6,0) and E'(3,3).

6 0

3 years ago

Which pair of rectangles is similar? a b c d

cricket20 [7]

B) the one that has the sides 4 & 8 and 3 & 6.

The length on both of these rectangles are twice as long as the width

one rectangle goes from a width of 4 and its length is doubled to a length of 8
it is similar to the 3 & 6 because the width of 3 is doubled to get the length of 6

hope this helps

3 0

3 years ago