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Eduardwww [97]
3 years ago
9

Samantha has 54 beads. Amanda has twice as many beads as Samantha. They are making bracelets it takes 8 beads to make a bracelet

. If Samantha and Amanda combine their beads how many bracelets can they make.
Mathematics
1 answer:
wlad13 [49]3 years ago
8 0

Answer:

On combining the beads they can make 20 bracelets.

Step-by-step explanation:

The number of beads Samantha has  =  54 beads

Number of beads Amanda has = 2 x( Number of beads Samantha has)

=  2  x 54  =  108 beads

The total number of beads Amanda and Samantha has  

=   54 beads + 108 beads

= 162 beads

Number of beads required to make 1 bracelet  =  8 beads

Now, \textrm{The number of bracelets made}  = \frac{\textrm{Total number of beads they both have}}{\textrm{Beads required to make 1 bracelet}}

=\frac{162}{8}  = 20.25≈  20

or, the total number of bracelets they can make is 20.

Hence, on combining the beads they can make 20 bracelets .

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The total number of feet travelled by the motorcycle is 396 feet

Step-by-step explanation:

Using the constant speed relationship with the distance:

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Converting in to feet per second.

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Find derivative problem<br> Find B’(6)
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Answer:

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Step-by-step explanation:

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\displaystyle B(t)=24.6\sin(\frac{\pi t}{10})(8-t)

And we want to find B’(6).

So, we will need to find B(t) first. To do so, we will take the derivative of both sides with respect to x. Hence:

\displaystyle B^\prime(t)=\frac{d}{dt}[24.6\sin(\frac{\pi t}{10})(8-t)]

We can move the constant outside:

\displaystyle B^\prime(t)=24.6\frac{d}{dt}[\sin(\frac{\pi t}{10})(8-t)]

Now, we will utilize the product rule. The product rule is:

(uv)^\prime=u^\prime v+u v^\prime

We will let:

\displaystyle u=\sin(\frac{\pi t}{10})\text{ and } \\ \\ v=8-t

Then:

\displaystyle u^\prime=\frac{\pi}{10}\cos(\frac{\pi t}{10})\text{ and } \\ \\ v^\prime= -1

(The derivative of u was determined using the chain rule.)

Then it follows that:

\displaystyle \begin{aligned} B^\prime(t)&=24.6\frac{d}{dt}[\sin(\frac{\pi t}{10})(8-t)] \\ \\ &=24.6[(\frac{\pi}{10}\cos(\frac{\pi t}{10}))(8-t) - \sin(\frac{\pi t}{10})] \end{aligned}

Therefore:

\displaystyle B^\prime(6) =24.6[(\frac{\pi}{10}\cos(\frac{\pi (6)}{10}))(8-(6))- \sin(\frac{\pi (6)}{10})]

By simplification:

\displaystyle B^\prime(6)=24.6 [\frac{\pi}{10}\cos(\frac{3\pi}{5})(2)-\sin(\frac{3\pi}{5})] \approx -28.17

So, the slope of the tangent line to the point (6, B(6)) is -28.17.

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3 years ago
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