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frozen [14]
3 years ago
10

It takes ten identical pieces to form a circular track for a pair of toy racing cars. If the inside arc of each piece is 3.4 inc

hes shorter than the outside arc, what is the width of the track? ...?
Mathematics
1 answer:
dsp733 years ago
6 0
 <span>Length of outer track = sum of length of 10 pieces = circumference of the outer circle 


if R is the Radius of outer circle then... 

Circumference of the outer track = 2pi*R 


Similarly the circumference of the inner track (with radius r) = 2pi*r 


length of each outer piece is 3.4 inch more than length of inner piece 

So total outer length is 10*3.4 =34 inches more than the inner length. 


=> Outer Circumference - Inner Circumference = 34 inches 

=> 2pi*R - 2pi*r = 34 

=> 2pi(R -r) = 34 

=> R-r = 34/2pi = 5.41 inches 

=> R-r = Width of the track = 5.41 inches</span>
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On a certain game show, contestants pick 5 number balls from a bag containing 20 numbered balls (0-19). After each draw, the bal
Gnoma [55]

Answer:

5/20 or 25% probability of winning $1,000,000

Step-by-step explanation:

How many numbered balls do they need to win?

5

How many balls are there?

20

Therefor your answer is (balls need to win/number of balls).

4 0
2 years ago
Factor 2x2+25x+50. Rewrite the trinomial with the x-term expanded, using the two factors.
zlopas [31]

9514 1404 393

Answer:

  • rewrite: 2x^2 +5x +20x +50
  • factored: (x +10)(2x +5)

Step-by-step explanation:

I find this approach the most straightforward of the various ways that trinomial factoring is explained or diagramed.

You want two factors of "ac" that have a total of "b". Here, that means you want factors of 2·50 = 100 that have a total of 25. It is helpful to know your times tables.

  100 = 1·100 = 2·50 = 4·25 = 5·20 = 10·10

The sums of these factor pairs are 101, 52, 29, 25, and 20. We want the pair with a sum of 25, so that's 5 and 20.

The trinomial can be rewritten using these factors as ...

  2x^2 +5x +20x +50

Then it can be factored by grouping consecutive pairs:

  (2x^2 +5x) +(20x +50) = x(2x +5) +10(2x +5) = (x +10)(2x +5)

_____

<em>Additional comment</em>

It doesn't matter which of the factors of the pair you write first. If our rewrite were ...

  2x^2 +20x +5x +50

Then the grouping and factoring would be (2x^2 +20x) +(5x +50)

  = 2x(x +10) +5(x +10) = (2x +5)(x +10) . . . . . same factoring

6 0
2 years ago
What is the solution to the equation 6x + 2 = 9x-1
liubo4ka [24]

Answer:

1

Step-by-step explanation:

Step 1:

6x + 2 = 9x - 1

Step 2:

2 = 3x - 1

Step 3:

3 = 3x

Answer:

1 = x

Hope This Helps :)

3 0
3 years ago
Read 2 more answers
What’s the numerator for the following rational expression s/t+7/t=?/t
avanturin [10]

Answer:

s+7 is numerator of the given expression.

Step-by-step explanation:

We have bee given a rational expression:

\frac{p}{q} is the general representation of the Rational expression where, p is numerator and q is denominator.

So, our given expression is:\frac{s}{t}+\frac{7}{t}

We will take the LCM so, given expression can be rewritten as:

\frac{s+7}{t}     (1)

Comparing (1) with general rational expression written above

p=s+7 which is numerator of the given expression.


4 0
3 years ago
Use calculus to find the absolute maximum and minimum values of the function. (round all answers to three decimal places.) f(x)
Allisa [31]
Part A:

Given the function f(x)=x+2\cos(x), the absolute maximum or minimum occurs when f'(x)=0.

f'(x)=0 \\  \\ \Rightarrow1-2\sin{x}=0 \\  \\ \Rightarrow2\sin{x}=1 \\  \\ \Rightarrow\sin{x}= \frac{1}{2}  \\  \\ \Rightarrow x=\sin^{-1}{\frac{1}{2}}= \frac{\pi}{6}

Using the second derivative test,

f''(x)=-2cosx \\  \\ \Rightarrow f''\left( \frac{\pi}{6} \right)=-2\cos{\left( \frac{\pi}{6} \right)}=-1.732

Since the second derivative gives a negative number, the given function has a maximum point at x=\frac{\pi}{6}.

And the maximum point is given by:

f\left( \frac{\pi}{6} \right)=\frac{\pi}{6}+2\cos\left( \frac{\pi}{6} \right) \\  \\ =0.5236+2(0.8660)=0.5236+1.732 \\  \\ =\bold{2.256}

i.e. \left(\frac{\pi}{6},\ 2.256\right)



Part B:

Given the function f(x)=e^{-x}-e^{-2x}, the absolute maximum or minimum occurs when f'(x)=0.

f'(x)=0 \\ \\ \Rightarrow-e^{-x}+2e^{-2x}=0 \\ \\ \Rightarrow2e^{-2x}=e^{-x} \\ \\ \Rightarrow2e^{-x}=1 \\ \\ \Rightarrow e^{-x}=\frac{1}{2} \\  \\ \Rightarrow-x=\ln \frac{1}{2}=-0.6931 \\  \\ \Rightarrow x=0.6931

Using the second derivative test,

f''(x)=e^{-x}-4e^{-2x} \\ \\ \Rightarrow f''(0.6931)=e^{-0.6931}-4e^{-2(0.6931)} \\  \\ =0.5-4e^{-1.386}=0.5-4(0.25)=0.5-1 \\  \\ =-0.5

Since the second derivative gives a negative number, the given function has a maximum point at x=0.6931.

And the maximum point is given by:

f(0.6931)=e^{-0.6931}-e^{-2(0.6931)} \\  \\ =0.5-e^{-1.386}=0.5-0.25=\bold{0.25}

i.e. (0.693, 0.25)
3 0
3 years ago
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