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Gemiola [76]
3 years ago
9

Use skip counting and the number line to find the missing number. 3X__=12

Mathematics
1 answer:
loris [4]3 years ago
7 0

Answer:


Step-by-step explanation:

3 times 4 is 12. you can solve this by dividing 12 by 3, or by skip counting and using repeated addition.

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Yakvenalex [24]

Answer:

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Step-by-step explanation:

4 0
2 years ago
A cable television compan is laying cable in an area with underground utilities. Two subdivisions are located on opposite sides
Schach [20]

Answer:

Step-by-step explanation:

Given:

Point Q = Q is on the north bank 1200 m east of P $40/m to lay cable underground and $80/m way to lay the cable.

Lets denote T be a point on north bank, therefore, point T is t m east and 100m north of P.

Note that 0 < t < 1200

Distance from P to T using Pythagoras theorem:

PT^2 = PQ^2 + QT^2

PT = √(t²+100²) = √(t²+10,000)

Distance from T to Q:

TQ = 1200 - t

From above, Cable from P to T is underwater, and costs $80/m to lay.

Cable from T to Q is underground, and costs $40/m to lay.

Total cost of the cable:

C(t) = 80√(t²+10,000) + 40(1200 - t)

Cost is at its minimum: when dC/dt = C'(t) = 0 and d^2C/dt^2 = C''(t) > 0

dC/dt = C'(t)

= 80 * 1/2 (t² + 10,000)^(-1/2) × 2t + 40 × (-1)

dC/dt = C'(t)

= 80t/√(t² + 10,000) - 40 = 0

80t/√(t² + 10,000) = 40

80t = 40√(t² + 10,000)

2t = √(t² + 10,000)

square both sides:

4t² = t² + 10,000

3t² = 10,000

t² = 10,000/3

t = 100/√3

≈ 57.735

d^2C/dt^2 =

C''(t) = [80√(t² + 10,000) - 80t × t/√(t²+10,000)] /√(t²+10,000)

C''(t) = [(80(t²+10,000) - 80t²) / √(t²+10,000)] /√(t²+10,000)

C''(t) = 800,000 / (t² + 10,000)^(3/2)

C''(t) > 0 for all t

Therefore C(t) is minimized at t = 100/√3

C(100/√3) = 80√(10,000/3 + 10,000) + 40 × (1200 - 100/√3)

= 80 √(40,000/3) + 48,000 - 4000/√3

= 16000/√3 + 48,000 - 4000/√3

= 48,000 + 12,000/√3

= 48,000 + 4,000√3

= 4000 (12 + √3)

≈ 54,928.20

Minimum cost is $54,928.20

This occurs when cable is laid underwater from point P to point T(57.735 m east and 100m north of P) and then underground from point T to point Q (1200 - 57.735)

= 1142.265 m

5 0
3 years ago
The next four digits in the number 0.3435363738394041 are
Vera_Pavlovna [14]
<h3>The pattern is 0.01+</h3>

<u>So the next 4 digits are:</u>

<h3>0.4243</h3><h3></h3>

0.34353637383940414243

3 0
3 years ago
How many 16-ounce bottles would be needed to hold the same total amount of water 56 bottles that each holds 20 ounces
snow_lady [41]

70 bottles will hold 16 ounces amount same as 56 bottles hold 20 ounces.

Step-by-step explanation:

Given,

56 bottles hold 20 ounces each.

Total amount 56 bottles hold= 56x20

Total amount hold by 56 bottles= 1120 ounces

Let the number of 16 ounces bottles be = x

Total amount hold by x bottles = 16x

According to the given statement both amounts are same;  

16x=1120\\Dividing\ both\ sides\ by\ 16\\\frac{16x}{16} = \frac{1120}{16} \\x=70

70 bottles will hold 16 ounces amount same as 56 bottles hold 20 ounces.

Keywords: Division, Multiplication

Learn more about division at:

  • brainly.com/question/2035523
  • brainly.com/question/2088305

#LearnwithBrainly

6 0
3 years ago
Help me with question number 3 please!!!
grin007 [14]

Answer: please mark brainlyest

Step-by-step explanation:

5 0
2 years ago
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