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2 years ago

-4= 7x-(-1) / -8 Solve for x (Solving multi step equations)

1 answer:

4 0

Multiply both sides by -8.
Then add the one to both side to cancel it out and get 7x by itself
Then divide the whole thing by 7. So it’ll look like this: 32+1=7x and then add the one then divide by 7

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Find sinϴ and cosϴ if tanϴ=1/4 and sinϴ>0

eduard

If you're using the app, try seeing this answer through your browser: brainly.com/question/2787701

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$\mathsf{tan\,\theta=\dfrac{1}{4}\qquad\qquad(sin\,\theta\ \textgreater \ 0)}\\\\\\
\mathsf{\dfrac{sin\,\theta}{cos\,\theta}=\dfrac{1}{4}}\\\\\\
\mathsf{4\,sin\,\theta=cos\,\theta\qquad\quad(i)}$

Square both sides:

$\mathsf{(4\,sin\,\theta)^2=(cos\,\theta)^2}\\\\
\mathsf{4^2\,sin^2\,\theta=cos^2\,\theta}\\\\
\mathsf{16\,sin^2\,\theta=cos^2\,\theta\qquad\qquad(but,~cos^2\,\theta=1-sin^2\,\theta)}\\\\
\mathsf{16\,sin^2\,\theta=1-sin^2\,\theta}$

$\mathsf{16\,sin^2\,\theta+sin^2\,\theta=1}\\\\
\mathsf{17\,sin^2\,\theta=1}\\\\
\mathsf{sin^2\,\theta=\dfrac{1}{17}}\\\\\\
\mathsf{sin\,\theta=\pm\,\sqrt{\dfrac{1}{17}}}\\\\\\
\mathsf{sin\,\theta=\pm\,\dfrac{1}{\sqrt{17}}}$

Since $\mathsf{sin\,\theta}$ is positive, you can discard the negative sign. So,

$\mathsf{sin\,\theta=\dfrac{1}{\sqrt{17}}\qquad\quad\checkmark}$

Substitute this value back into $\mathsf{(i)}$ to find $\mathsf{cos\,\theta:}$

$\mathsf{4\cdot \dfrac{1}{\sqrt{17}}=cos\,\theta}\\\\\\
\mathsf{cos\,\theta=\dfrac{4}{\sqrt{17}}\qquad\quad\checkmark}$

I hope this helps. =)

Tags: <em>trigonometric identity relation trig sine cosine tangent sin cos tan trigonometry precalculus</em>

7 0

2 years ago

Find the common ratio of the following geometric sequence 5/12, 1/4 , 3/20,9/100,27/500

mixas84 [53]

All you have to is divide two consecutive terms to calculate the common ratio

1/4 divided by 5/12 = 1/4 * 12/5 = 12/20 = 3/5

7 0

3 years ago

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sashaice [31]

87.4 people per square mile

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2 years ago

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A solid cylinder of iron whose diameter is 18 cm and height 12 cm is melted and turned into a solid sphere. Find the diameter of

finlep [7]

Answer:

Diameter of sphere = 18 cm

Step-by-step explanation:

<h2>Volume of Cylinder and Sphere:</h2><h3> Cylinder:</h3>

Diameter = 18 cm

r = 18÷ 2 = 9 cm

h = 12 cm

$\sf \boxed{\bf Volume \ of \ cylinder = \pi r^2h}$

= π * 9 * 9 * 12 cm³

<h3>Sphere:</h3>

$\sf \boxed{\text{\bf Volume of sphere = $\dfrac{4}{3} \pi r^3$}}$

Solid cylinder is melted and turned into a solid sphere.

Volume of sphere = volume of cylinder

$\sf \dfrac{4}{3}\pi r^3 = \pi *9*9*12$

$\sf r^{3}= \dfrac{\pi *9*9*12*3}{4*\pi }\\\\ r^{3}=9 * 9 *3 *3\\\\\\r = \sqrt[3]{9*9*9}\\\\ r = 9 \ cm\\\\diameter = 9*2\\\\\boxed{diameter \ of \ sphere = 18 \ cm}$

6 0

1 year ago

39 less than twice a number is 5 times the sum of a number and two times the number. Find the number

umka2103 [35]

$2n - 39 = 5(n + 2n)\\2n - 39 = 5(3n)\\2n - 39 = 15n\\2n = 15n + 39\\-13n = 39\\\\n = -3$

3 0

2 years ago