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balu736 [363]
3 years ago
5

Please answer my question

Mathematics
1 answer:
Ghella [55]3 years ago
8 0

Interval notation uses parenthesis and brackets, while inequality notation uses inequality symbols.

a)

Interval notation: [-4, 8)

Inequality notation: -4\leq x

x >= -4, x < 8

---For inequality notation, it can also be written as two separate inequalities. I am not sure what your teacher is looking for, so I will provide both the compound and separate formats.

b)

Interval notation: (-infinity, 7)

Inequality notation: x < 7

c)

Interval notation: (-infinity, -6) U (0, infinity)

Inequality notation: -6> x \geq 0

x < -6, x >= 0

Hope this helps!

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Two boats leave a dock at the same time. One boat travels south at 32 mi divided by hr32 mi/hr and the other travels east at 60
TEA [102]

Answer: the rate at which the distance between the boats is​ increasing is 68 mph

Step-by-step explanation:

The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.

Let x represent the length the shorter leg(south) of the right angle triangle.

Let y represent the length the longer leg(east) of the right angle triangle.

Let z represent the hypotenuse.

Applying Pythagoras theorem

Hypotenuse² = opposite side² + adjacent side²

Therefore

z² = x² + y²

To determine the rate at which the distances are changing, we would differentiate with respect to t. It becomes

2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1

One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that

dx/dt = 32

dy/dt = 60

Distance = speed × time

Since t = 0.5 hour, then

x = 32 × 0.5 = 16 miles

y = 60 × 0.5 = 30 miles

z² = 16² + 30² = 256 + 900

z = √1156

z = 34 miles

Substituting these values into equation 1, it becomes

2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60

68dz/dt = 1024 + 3600

68dz/dt = 4624

dz/dt = 4624/68

dz/dt = 68 mph

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inna [77]

Answer:

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Step-by-step explanation:

2X+7=5X-8

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15=3X

5=X

5 0
3 years ago
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