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GalinKa [24]
3 years ago
15

Find X using the image.

Mathematics
1 answer:
Temka [501]3 years ago
7 0

9514 1404 393

Answer:

  x = 2

Step-by-step explanation:

The square of the tangent is equal to the product of the secant lengths to the near and far circle intersections.

  (x +4)² = (2x -1)(2x -1 +9)

  0 = (2x -1)(2x +8) -(x +4)² = (4x² +14x -8) -(x² +8x +16)

  0 = 3x² +6x -24 = 3(x² +2x -8) = 3(x +4)(x -2)

This has solutions x = -4 and x = 2. Only the latter works in this geometry.

  x = 2

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box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the box (in cm) that minimize the am
Naya [18.7K]

Answer:

Hence the width, length is 20 cm and height is 10 cm

Step-by-step explanation:

Since the box has a square base, let length = width = x. Also, let the height = y, therefore:

The volume of box = width * length * height

4000 = x * x * y

4000 = x²y

y=4000/x²

The surface area (SA) = area of the base + sum of the area of each side

SA = x² + xy + xy + xy + xy

SA = x² + 4xy

substitute y = 4000/x²

SA = x² + 4x(4000/x²)

SA = x² + 16000/x

Taking the derivative:

SA' = 2x - 16000/x²

making SA' = 0:

0 = 2x - 16000/x²

2x = 16000/x²

2x³ = 16000

x³ = 8000

x = 20 cm

y = 4000 / x² = 4000 / 20² = 10 cm

Hence the width, length is 20 cm and height is 10 cm

6 0
3 years ago
3x-7=4x+10 <br> show the steps pleeease
Fudgin [204]

Answer:

-17

Step-by-step explanation:

3x-7=4x+10

Add 7 to both sides & simplify

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*Negative x equals -1*

Divide both sides by -1 & simplify

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3 0
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Answer:

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Step-by-step explanation:

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