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Natali [406]
3 years ago
10

Find ST if S is between R and T, SR = 2x + 7, ST = x - 6, and RT = 100

Mathematics
1 answer:
pav-90 [236]3 years ago
7 0
Since SR+ST adds up to RT, we have 2x+7+x-6=100=3x+1. 
Subtracting 1 from both sides, we get 3x=99

Dividing both sides by 3, we have x=33
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Factorize <br>2x²-x²-x <br>Please help me fast to solve this problem.​
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Step-by-step explanation:

2x^{2} - x^{2} -x

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x (x - 1)

6 0
2 years ago
A cone-shaped paper drinking cup is to be made to hold 27 cm of water. Find the height h and radius r of the cup that will use t
andreyandreev [35.5K]

Answer:

  • r = 2.632 cm
  • h = 3.722 cm

Step-by-step explanation:

The formula for the volume of a cone of radius r and height h is ...

  V = (1/3)πr²h

Then r² can be found in terms of h and V as ...

  r² = 3V/(πh)

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  A = (1/2)(2πr)√(r² +h²) = πr√(r² +h²)

The square of the area is ...

  T = A² = π²r²(r² +h²)

Substituting for r² using the expression above, we have ...

  T = π²(3V/(πh))((3V/(πh) +h²) = 9V²/h² +3πVh

We want to find the minimum, which we can do by setting the derivative to zero.

  dT/dh = -18V²/h³ +3πV

This will be zero when ...

  3πV = 18V²/h³

  h³ = 6V/π . . . . . multiply by h³/(3πV)

For V = 27 cm³, the value of h that minimizes paper area is ...

  h = 3∛(6/π) ≈ 3.7221029

The corresponding value of r is ...

  r = √(3V/(πh)) = 9/√(π·h) ≈ 2.6319242

The optimal radius is 2.632 cm; the optimal height is 3.722 cm.

_____

The second derivative test applied to T finds that T is always concave upward, so the value we found is a minimum.

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Interestingly, the ratio of h to r is √2.

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3 years ago
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Helga [31]
I think it would be too confusing to type but it would look like this

3 0
3 years ago
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Alex787 [66]

It looks like your instructor wants you to write in point-slope form.

the equation for point slope form is quite simple

y-y1=m(x-x1)

your variables:

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your final answer would be

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I hope this helped :)

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3 0
2 years ago
The isosceles triangle has two sides with the same length. The base is one-half the length of a side. The expression which repre
gavmur [86]

Answer:

20 units

Step-by-step explanation:

s = 8

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                = 8 + 8 + \frac{1}{2}*8

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8 0
3 years ago
Read 2 more answers
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