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4 years ago

Please explain your answer. THX!!!

Mathematics

1 answer:

patriot [66]4 years ago

4 0

Answer:

tan(5x/8)

Step-by-step explanation:

given expression

$\frac{tan(1/2x)+tan(1/8x)}{1-tan(1/2x)tan(1/8x)}$

Using the trigonometric identity

tan(a+b)= $\frac{tan(a) + tan(b)}{1-tan(a)tan(b)}$

here a= 1/2x and b=1/8x

putting the values we get

=tan(1/2x+1/8x)

=tan(5/8x)!

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Simplify completely. (w^15/w^5)^4

mote1985 [20]

$\text{Use}\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\(a^n)^m=a^{n\cdot m}\\-------------------------\\\\\left(\dfrac{w^{15}}{w^5}\right)^4=\left(w^{15-5}\right)^4=\left(w^{10}\right)^4=w^{10\cdot4}=w^{40}\\\\Answer:\ \boxed{\left(\dfrac{w^{15}}{w^5}\right)^4=w^{40}}$

5 0

3 years ago

The length of a rectangle is one foot more than twice its width if the area of the rectangle is 300 ft^2 find the dimensions of

umka21 [38]

Let's say the length is L, and the width is W
L is one foot more than 2W, so L=1+2W
the area of the rectangle: A=L*W=300
replace L with 1+2W: (1+2W)*W=300 =>2W^2+W-300=0
solve the quadratic equation: (W-12)(2W+25)=0
W=12 or W=-12.5 (impossible)
so the width is 12, and the length is L=1+2*12=25

please refer to this website for how to factor a quadratic equation
http://www.purplemath.com/modules/factquad.htm

7 0

3 years ago

Read 2 more answers

Cos (90-theta) • cosec90-theta) =tano. How?

denis-greek [22]

Answer:

______________________________________________________

TRIGONOMETRY IDENTITIES TO BE USED IN THE QUESTION :-

For any right angled triangle with one angle α ,

$\cos (90 - \alpha ) = \sin \alpha$ or $\sin(90 - \alpha ) = \cos\alpha$

$cosec \: (90 - \alpha ) = \sec\alpha$ or $\sec(90 - \alpha ) = cosec\:\alpha$

SOME GENERAL TRIGNOMETRIC FORMULAS :-

$\sin \alpha = \frac{1}{cosec \: \alpha }$ or $cosec \: \alpha = \frac{1}{\sin \alpha }$

$\cos \alpha = \frac{1}{\sec \alpha }$ or $\sec \alpha = \frac{1}{\cos \alpha }$

______________________________________________________

Now , lets come to the question.

In a right angled triangle , let one angle be α (in place of theta) .

So , lets solve L.H.S.

$\cos (90 - \alpha ) \times cosec(90 - \alpha )$

$=> sin\alpha \times \sec\alpha$

$=> \sin\alpha \times \frac{1}{\cos\alpha }$

$=> \frac{\sin\alpha }{\cos\alpha }$

$=> \tan\alpha$ = R.H.S.

∴ L.H.S. = R.H.S. (Proved)

3 0

3 years ago

Which value, when placed in the box, would result in a system of equations with infinitely many solutions?

cupoosta [38]

Answer:

answer it s 12. just put the value

5 0

3 years ago

Please help for 50 points...

vaieri [72.5K]

Answer:

7. ○ ∆ACB ≅ ∆DFE

6. ○ $\displaystyle 43°$

5. ○ $\displaystyle ∠M ≅ ∠S$

4. ○ $\displaystyle octagon$

3. ○ $\displaystyle squares$

2. ○ $\displaystyle rhombus$

1. ○ $\displaystyle equilateral\:triangle$

Step-by-step explanation:

7. Everything is in correspondence with each other, so just follow the pattern in the order the they were originally.

6. All angles correspond with each other, so just follow the pattern.

5. All segments and angles correspond with each other, so just follow their patterns.

4. An octagon has eight sides, a triangle has three sides, a hexagon has six sides, and a pentagon has five sides. With this being stated, you have your answer.

3. In a previous lesson, we confirmed that all squares are rectangles because it is a quadrilateral with four right angles.

2. This is obviously a rhombus because it is a quadrilateral with four congruent angles and sides.

1. An EQUILATERAL TRIANGLE is a regular polygon because they have three congruent angles and sides.

I am joyous to assist you anytime.

4 0

3 years ago

Read 2 more answers