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2 years ago

Martin put 8 pounds of grapes into a bowl. Four friends each took 2

Mathematics

2 answers:

AlekseyPX2 years ago

7 0

8 pounds of grapes into a bowl
4 friends each took two pound
and if there were only 8 pounds to begin with then 8/2=4

Nataly_w [17]2 years ago

5 0

Answer:

Martin pit 8 pounds in a bowl

four friends took each 2

so each will got 2 pounds of grapes

2 pounds got divided I'm 4 friends

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Solve the equation for all real values of x. cosxtanx - 2 cos x=-1

IceJOKER [234]

Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

Step-by-step explanation:

Here we have , $cosxtanx - 2 cos^2 x=-1$ . Let's solve :

⇒ $cosxtanx - 2 cos^2 x=-1$

⇒ $cosx(\frac{sinx}{cosx}) - 2 cos^2 x=-1$

⇒ $sinx = 2 cos^2 x-1$

⇒ $sinx = 2 (1-sin^2x)-1$

⇒ $sinx = 1-2sin^2x$

⇒ $2sin^2x+sinx-1=0$

By quadratic formula :

⇒ $sinx = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

⇒ $sinx = \frac{-1 \pm \sqrt{1^2-4(2)(-1)} }{2(2)}$

⇒ $sinx = \frac{-1 \pm3}{4}$

⇒ $sinx = \frac{1}{2} , sinx =-1$

⇒ $sinx = sin\frac{\pi}{6} , sinx = sin\frac{3\pi}{2}$

⇒ $x=\frac{\pi}{6} , x=\frac{3\pi}{2}$

But at $x=\frac{3\pi}{2}$ we have equation undefined as $cos\frac{3\pi}{2}=0$ . Hence only solution is :

⇒ $x=\frac{\pi}{6}$

Since , $sin(\pi -x)=sinx$

⇒ $x=\pi -\frac{\pi}{6} = \frac{5\pi}{6}$

Now , General Solution is given by :

⇒ $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$

Therefore , Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

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2 years ago

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Evgen [1.6K]

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Step-by-step explanation:

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The point U (-2,0) is translated 1 unit up. What are the coordinates of the resulting point, U’?

MrRissso [65]

Answer:

Point U' (-2, 1)

Step-by-step explanation:

When moving up and down on a graph, this affects the y coordinate only.

Since it is moving up 1 unit, we have to add 1 to the y coordinate. So U' will end up being (-2, 1).

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Read 2 more answers

Select the correct answer from each drop-down menu.

kifflom [539]

Answer:

0.83
0.9
steeper than
slower than

Step-by-step explanation:

Letting t=1 in Ted's equation, we find that he climbs 5/6 stairs in 1 second. As a decimal, 5/6 ≈ 0.83.

Michael climbs 9 stairs in 10 seconds so his rate is ...

... (9 stairs)/(10 seconds) = (9/10) stairs/second = 0.9 stairs/second

Michael's graph will be a line with a slope of 0.9; Ted's graph will be a line with a slope of about 0.83, so the line on Michael's graph is steeper.

Ted climbs fewer stairs per second, so his rate is slower than Michael's.

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Comment on the problem

You're being asked to compare two different rates that are associated with two different people. First the comparison is one way, then it is the other way. This can be confusing. It might be helpful to draw and label a simple chart to help you keep it straight. (The attachment is such a chart scribbled on a bit of scratch paper. It is sufficient for the purpose.)

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Andru [333]

Answer:

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Step-by-step explanation:

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