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Shtirlitz [24]
3 years ago
13

Simplify 2x^2-1+4x^2-5

Mathematics
1 answer:
alekssr [168]3 years ago
8 0

Answer:

6x^2-6

Step-by-step explanation: algebra

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Jack is selling wristbands and headbands to earn money for camp. He earns $2 for each wristband and $3 for each headband. He wan
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5 0
2 years ago
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The graphs below have the same shape. What is the equation of the blue graph?
postnew [5]

Answer:

<h2>C. G(x) = (x - 1)² - 3</h2>

Step-by-step explanation:

f(x) + n - shift the graph of f(x) n units up

f(x) - n - shift the graph of f(x) n units down

f(x - n) - shift the graph of f(x) n units to the right

f(x + n) - shift the graph of f(x) n units to the left

===================================

Look at the picture.

The graph of F(x) shifted 1 unit to the right and 3 units down.

Therefore the equation of the function G(x) is

G(x)=(x-1)^2-3

4 0
3 years ago
Find sinϴ and cosϴ if tanϴ=1/4 and sinϴ&gt;0
eduard
If you're using the app, try seeing this answer through your browser:  brainly.com/question/2787701

_______________


\mathsf{tan\,\theta=\dfrac{1}{4}\qquad\qquad(sin\,\theta\ \textgreater \ 0)}\\\\\\&#10;\mathsf{\dfrac{sin\,\theta}{cos\,\theta}=\dfrac{1}{4}}\\\\\\&#10;\mathsf{4\,sin\,\theta=cos\,\theta\qquad\quad(i)}


Square both sides:

\mathsf{(4\,sin\,\theta)^2=(cos\,\theta)^2}\\\\&#10;\mathsf{4^2\,sin^2\,\theta=cos^2\,\theta}\\\\&#10;\mathsf{16\,sin^2\,\theta=cos^2\,\theta\qquad\qquad(but,~cos^2\,\theta=1-sin^2\,\theta)}\\\\&#10;\mathsf{16\,sin^2\,\theta=1-sin^2\,\theta}

\mathsf{16\,sin^2\,\theta+sin^2\,\theta=1}\\\\&#10;\mathsf{17\,sin^2\,\theta=1}\\\\&#10;\mathsf{sin^2\,\theta=\dfrac{1}{17}}\\\\\\&#10;\mathsf{sin\,\theta=\pm\,\sqrt{\dfrac{1}{17}}}\\\\\\&#10;\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}\\\\\\&#10;\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
4x+23=9x-38 21y-1 value of y
PSYCHO15rus [73]

Answer:

4⅗.78 99⁹7./⅜87.5⅞8 /7 ⁰

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2 years ago
the volume v of a right circular cylinder of radius r and heigh h is V = pi r^2 h 1. how is dV/dt related to dr/dt if h is const
laiz [17]
In general, the volume

V=\pi r^2h

has total derivative

\dfrac{\mathrm dV}{\mathrm dt}=\pi\left(2rh\dfrac{\mathrm dr}{\mathrm dt}+r^2\dfrac{\mathrm dh}{\mathrm dt}\right)

If the cylinder's height is kept constant, then \dfrac{\mathrm dh}{\mathrm dt}=0 and we have

\dfrac{\mathrm dV}{\mathrm dt}=2\pi rh\dfrac{\mathrm dt}{\mathrm dt}

which is to say, \dfrac{\mathrm dV}{\mathrm dt} and \dfrac{\mathrm dr}{\mathrm dt} are directly proportional by a factor equivalent to the lateral surface area of the cylinder (2\pi r h).

Meanwhile, if the cylinder's radius is kept fixed, then

\dfrac{\mathrm dV}{\mathrm dt}=\pi r^2\dfrac{\mathrm dh}{\mathrm dt}

since \dfrac{\mathrm dr}{\mathrm dt}=0. In other words, \dfrac{\mathrm dV}{\mathrm dt} and \dfrac{\mathrm dh}{\mathrm dt} are directly proportional by a factor of the surface area of the cylinder's circular face (\pi r^2).

Finally, the general case (r and h not constant), you can see from the total derivative that \dfrac{\mathrm dV}{\mathrm dt} is affected by both \dfrac{\mathrm dh}{\mathrm dt} and \dfrac{\mathrm dr}{\mathrm dt} in combination.
8 0
2 years ago
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