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3 years ago

What division sentence means the same as the following subtraction sentences?12-4=8,8-4=4,4-4=0

Mathematics

2 answers:

enyata [817]3 years ago

5 0

Its 12/4 = 3
hope this helps

olya-2409 [2.1K]3 years ago

5 0

You started with 12. You are subtracting 4 each time, and you eventually end up with 0. This means your division sentence will be 12 divided by 4 = [the number of times you subtracted 4] 12 ÷ 4 = 3 I got it from Google hope it helps

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If tan theta =3, find the value of tan theta + tan (theta+pi) + tan (theta +2pi)

sweet-ann [11.9K]

Answer:

$tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = 9$

Step-by-step explanation:

Given

$tan\theta = 3$

Required

Find

$tan\theta + tan(\theta + \pi) + tan(\theta+2\pi)$

Calculate $tan(\theta + \pi) \ and\ tan(\theta+2\pi)$

Using tan rule

$tan(\theta + \pi) = \frac{tan\theta + tan\pi}{1 - tan\theta tan\pi}$

So:

$tan(\theta + \pi) = \frac{tan\theta + 0}{1 - tan\theta *0}$

$tan(\theta + \pi) = \frac{tan\theta}{1 }$

$tan(\theta + \pi) = \tan\theta$

$tan(\theta+2\pi)$

$tan(\theta + 2\pi) = \frac{tan\theta + tan2\pi}{1 - tan\theta tan2\pi}$

$tan(\theta + 2\pi) = \frac{tan\theta + 0}{1 - tan\theta *0}$

$tan(\theta + 2\pi) = \tan\theta$ '

'So:

$tan\theta + tan(\theta + \pi) + tan(\theta+2\pi)$ $= tan\theta +tan\theta +tan\theta$

$tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = 3+3+3$

$tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = 9$

4 0

3 years ago

Find the area of the region that lies inside the first curve and outside the second curve. r = 6 − 6 sin θ, r = 6

yan [13]

Each curve completes one loop over the interval $0\le t\le2\pi$ . Find the intersections of the curves within this interval.

$6-6\sin\theta=6\implies 1-\sin\theta=1\implies \sin\theta=0\implies \theta=0,\theta=\pi$

The region of interest has an area given by the double integral

$\displaystyle\int_\pi^{2\pi}\int_6^{6-6\sin\theta}r\,\mathrm dr\,\mathrm d\theta$

equivalent to the single integral

$\displaystyle\frac12\int_\pi^{2\pi}\bigg((6-6\sin\theta)^2-6^2\bigg)\,\mathrm d\theta$

which evaluates to $9\pi+72$ .

8 0

3 years ago

In the diagram, mZXYZ = 115° and mZWXY = 45°.

Allushta [10]

Step-by-step explanation:

mXYZ+mXYW=180°(being straight angle)

mXYW =180-115

mXYW=65

now,

mXWY+mWXY+mXYW=180°(sum of angle of triangle)

mXWY=180-110

mXWY=70°

hope it helps.

4 0

3 years ago

The difference of the square of a number and 24 is equal to 5 times that number. Find the negative solution.

vampirchik [111]

Answer:

the "negative solution" is -3

Step-by-step explanation:

Represent the number by n.

Then n^2 - 24 = 5n

We rewrite this in standard quadratic form:

n^2 - 5n - 24 = 0

This factors as follows; (n + 3)(n - 8) = 0

The roots are n = -3 and n = 8. Thus, the "negative solution" is -3

8 0

3 years ago

PLS HELP ME ASAP WITH QUESTION 30! THANK YOU SO MUCH!!!

nika2105 [10]

30. is just asking where the two equations graphed intersect each other...

x = -3 and x = 1 for intersections.

8 0

3 years ago