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Alisiya [41]
3 years ago
13

Am i correct? calculus

Mathematics
1 answer:
Advocard [28]3 years ago
8 0
Check the picture below.

now, the "x" is a constant, the rocket is going up, so "y" is changing and so is the angle, but "x" is always just 15 feet from the observer.  That matters because the derivative of a constant is zero.

now, those are the values when the rocket is 30 feet up above.

\bf tan(\theta )=\cfrac{y}{x}\implies tan(\theta )=\cfrac{y}{15}\implies tan(\theta )=\cfrac{1}{15}\cdot y
\\\\\\
\stackrel{chain~rule}{sec^2(\theta )\cfrac{d\theta }{dt}}=\cfrac{1}{15}\cdot \cfrac{dy}{dt}\implies \cfrac{1}{cos^2(\theta )}\cdot\cfrac{d\theta }{dt}=\cfrac{1}{15}\cdot \cfrac{dy}{dt}
\\\\\\
\boxed{\cfrac{d\theta }{dt}=\cfrac{cos^2(\theta )\frac{dy}{dt}}{15}}\\\\
-------------------------------\\\\


\bf cos(\theta )=\cfrac{adjacent}{hypotenuse}\implies cos(\theta )=\cfrac{15}{15\sqrt{5}}\implies cos(\theta )=\cfrac{1}{\sqrt{5}}\\\\
-------------------------------\\\\
\cfrac{d\theta }{dt}=\cfrac{\left( \frac{1}{\sqrt{5}} \right)^2\cdot 11}{15}\implies \cfrac{d\theta }{dt}=\cfrac{\frac{1}{5}\cdot 11}{15}\implies \cfrac{d\theta }{dt}=\cfrac{\frac{11}{5}}{15}\implies \cfrac{d\theta }{dt}=\cfrac{11}{5}\cdot \cfrac{1}{15}
\\\\\\
\cfrac{d\theta }{dt}=\cfrac{11}{75}

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For every 1 litre of water used to make a medicine, 269ml of sucrose and 47ml of saline solution are used. Express the amount of
leonid [27]

Answer:

1000 : 269 : 47

Step-by-step explanation:

A ratio is a way of comparing the value or amount of one quantity to another.

We are to find the ration of water to sucrose to saline solution, hence, it must remain in that order.

Water : Sucrose : Saline solution

The amount of water is 1 litre (1 * 1000 ml = 1000 ml)

The amount of sucrose is 269 ml

The amount of saline solution is 47 ml

Therefore, the ratio of water to sucrose to saline solution is:

W : S : SS = 1000 : 269 : 47

Since 1000, 269 and 47 have no common factors, that is the simplest form of the ratio.

3 0
3 years ago
An inheritance of $40,000 is divided among three investments yielding $3,500 in interest per year. The interest rates for the th
a_sh-v [17]

Answer:

 x = $ 16,000  , y = $13,000  z= $11,000

Step-by-step explanation:

given,

Investment amount $40,000

three investments yielding = $3,500

three investments are 7%, 9%, and 11%

second and third are $3,000 and $5,000 less than the first  

        0.07 x + 0.09 y + 0.11 z = $ 3,500  

        x + (x - 3000 ) + (x - 5000) = $ 40,000

           3x = $48,000

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     y = 16000 - 3000 = $ 13,000

     z = 16000 - 5000 = $ 11,000

the investment by each

 x = $ 16,000  , y = $13,000  z= $11,000

4 0
3 years ago
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Katarina [22]
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2 years ago
MARKING AS BRAINLIEST (geometry)
KonstantinChe [14]

Answer:

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6 0
2 years ago
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Simplify: -12h^2 -4 + 9 -3h^2<br><br> Show all steps/work please!<br><br> ^ = to the power of...
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Answer:

-12h^2-4+9-3h^2  

Final result :

 -5 • (3h^2 - 1)

Hope This Helps!      Have A Nice Day!!

3 0
3 years ago
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