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3 years ago

Name the triangle congruent to triangle ABC.

Mathematics

1 answer:

raketka [301]3 years ago

3 0

QPR since Q is equal to 1 and P is equal to B and R is equal to C

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15. If x=a Sin2t (I+Cos2t) and y=b Cos 2t (1-Cos2t) then find dy/dx at =22/7*4

Sav [38]

By the chain rule,

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm dt}}{\frac{\mathrm dx}{\mathrm dt}}$

It looks like we're given

$\begin{cases}x=a\sin(2t)(1+\cos(2t))\\y=b\cos(2t)(1-\cos(2t))\end{cases}$

where a and b are presumably constant.

Recall that

$\cos^2t=\dfrac{1+\cos(2t)}2$

$\sin^2t=\dfrac{1-\cos(2t)}2$

so that

$\begin{cases}x=2a\sin(2t)\cos^2t\\y=2b\cos(2t)\sin^2t\end{cases}$

Then we have

$\dfrac{\mathrm dx}{\mathrm dt}=4a\cos(2t)\cos^2t-4a\sin(2t)\cos t\sin t$

$\dfrac{\mathrm dy}{\mathrm dt}=-4b\sin(2t)\sin^2t+4b\cos(2t)\sin t\cos t$

$\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4b\cos(2t)\sin t\cos t-4b\sin(2t)\sin^2}{4a\cos(2t)\cos^2t-4a\sin(2t)\cos t\sin t}$

$\implies\boxed{\dfrac{\mathrm dy}{\mathrm dx}=\dfrac ba\tan t}$

where the last reduction follows from dividing through everything by $\cos(2t)\cos^2t$ and simplifying.

I'm not sure at which point you're supposed to evaluate the derivative (22/7*4, as in 88/7? or something else?), so I'll leave that to you.

8 0

3 years ago

Which is the solution to the inequality |x-4|<3

pishuonlain [190]

Answer:

$\large\boxed{1$

Step-by-step explanation:

$|x-4|$

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3 years ago

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The perimeter of a rectangular field is 350m. If the length of the field is 99m, what is it’s width?

Juliette [100K]

Answer:

The width of the field is 3.535353535m

Step-by-step explanation:

350÷99=3.535353535

Proof: 99×3.535353535=350

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3 years ago

What is the science of collecting,organizing,analyzing,and interpreting data?

Veseljchak [2.6K]

Answer:

statistics

Step-by-step explanation:

Statistics is the science of collecting, organizing, analyzing, and interpreting data in order to make decisions. A population is the complete collection of all elements (scores, people, measurement, and so on) to be studied. The collection is complete in the sense that it includes all subjects to be studied.

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4 years ago

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You go to a restaurant and your bill is $8.00. If you leave a 15% tip, How much did u spend all together at the restaurant?

g100num [7]

Find 15% of $8
Simply do this by multiplying 0.15 and 8
0.15 * 8 = 1.2
This means you left a $1.20 tip on top of your original $8
$8 + $1.20 = $9.20

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4 years ago