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3 years ago

HELPPPP

Mathematics

1 answer:

MissTica3 years ago

8 0

Answer:

$41.0625

Step-by-step explanation:

Divide $054.75 by 4

Multiply the answer to that (13.6875) by 3 or subtract 054.5 by 13.6873

The answer to that step is your answer.

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Find all degree solutions in the interval 0° ≤ θ < 360°. If rounding is necessary, round to the nearest tenth of a degree. Us

xenn [34]

Answer:

$\theta_{1} \approx 30.473^{\textdegree}$

$\theta_{2} \approx 120.473^{\textdegree}$

$\theta_{3} \approx 210.473^{\textdegree}$

$\theta_{4}\approx 300.473^{\textdegree}$

Step-by-step explanation:

The equation needs to be rearranged in terms of one trigonometric function:

$5\cdot \sin 2\theta - 9\cdot \cos 2\theta = 0$

$5\cdot \tan 2\theta - 9 = 0$

$5\cdot \tan 2\theta = 9$

$\tan 2\theta = \frac{9}{5}$

$\theta = \frac{1}{2}\cdot \tan^{-1} \left(\frac{9}{5} \right)$

The tangent function has positive values in the 1st and 3rd Quadrants. Then, the solutions are:

$\theta_{1} \approx 30.473^{\textdegree}$

$\theta_{2} \approx 120.473^{\textdegree}$

$\theta_{3} \approx 210.473^{\textdegree}$

$\theta_{4}\approx 300.473^{\textdegree}$

3 0

3 years ago

Find the largest prime divisor of $15^6 - 7^6$<img src="https://tex.z-dn.net/?f=Find%20the%20largest%20prime%20divisor%20of%20%2

Novosadov [1.4K]

Answer:

Largest prime factor of the given expression is 379.

Step-by-step explanation:

Given the expression:

$15^6 - 7^6$

To find:

The largest prime factor of the given expression.

Solution:

First of all, let us factorize the given expression.

$15^6 - 7^6\\\Rightarrow (15^3)^2 - (7^3)^2\\\\\text{Using } x^{2} -y^2 = (x+y) (x-y)\\\\\Rightarrow (15^3+7^3)(15^3-7^3)$

Let us learn two formula:

$x^3+y^3 = (x+y)(x^2+y^2-xy)$

$x^3-y^3 = (x-y)(x^2+y^2+xy)$

Applying the above formula in the expression written above:

$(15^3+7^3) = (15+7)(15^2+7^2-15\times 7)\\\Rightarrow 22(225+49-105 ) = 2 \times 11 \times 169 \\\Rightarrow 2 \times 11\times 13\times 13\\\Rightarrow 2 \times 11\times 13^2$ ...... (1)

Similarly:

$(15^3-7^3) = (15-7)(15^2+7^2+15\times 7)\\\Rightarrow 8(225+49+105 ) = 2^3 \times 379$ ........ (2)

Multiplying the expressions from (1) and (2) to get the result:

$\therefore 15^6 - 7^6 = 2^4 \times 11 \times \underline{\bold{379}} \times 13 ^2$

So, largest prime factor of the given expression is 379.

7 0

3 years ago

Multiply k+3/4K - 2 (12k2 +2k -4)

Kisachek [45]

Answer:

-204kk+3+32k/4k

Hope this helps!!

6 0

2 years ago

Simplify 4.5+ 3.1(2x + y) + 1.2y.

Mrac [35]

Answer:

see image

Step-by-step explanation:

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3 years ago

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One base of a trapezoid is decreasing at a rate of 888 kilometers per second and the height of the trapezoid is increasing at a

VashaNatasha [74]

Answer:

5 rate decrease

Step-by-step explanation:

One base of the trapezoid is decreasing at a rate of 8 kilometers per second and height of the trapezoid is increasing at rate 5

5 0

2 years ago

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