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lutik1710 [3]
3 years ago
10

00%7D%20" id="TexFormula1" title=" \sqrt{400 \times 400 - 24 \times 400 - 360 \times 400 - 200} " alt=" \sqrt{400 \times 400 - 24 \times 400 - 360 \times 400 - 200} " align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
max2010maxim [7]3 years ago
7 0

Answer:

\sqrt{400 \times 400 - 24 \times 400 - 360 \times 400 - 200} \\  \\  = \sqrt{160000 - 9600 - 144000 - 200} \\  \\  = \sqrt{160000 - 9600 - 144000 - 200} \\  \\ = \sqrt{160000 - 153,800} \\  \\  = \sqrt{6200} \\  \\  = 78.74 \\  \\

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-4x-3(-44-23)=13<br><br><br> please show the work, i’ll mark brainliest
pychu [463]

Answer:

47

Step-by-step explanation:

Let's solve your equation step-by-step.

−4x−3(−44−23)=13

Step 1: Simplify both sides of the equation.

−4x+201=13

Step 2: Subtract 201 from both sides.

−4x+201−201=13−201

−4x=−188

Step 3: Divide both sides by -4.

−4x

−4

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3 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
What’s the value of the 8 in 281480100
luda_lava [24]

We want to find the value of the 8 in 281,480,100

Let's find the place value of each of the numbers:

2 - hundred millions

8 - ten millions

1 - millions

4 - hundred thousands

8 - ten thousands

0 - thousands

1 - hundreds

0 - tens

0 - ones

I see there are two 8's so I wouldn't be too sure of which value to find, but just in case, we have the chart made above for place values.

There is one 8 at the ten millions value.

There is one 8 at the ten thousands value.

7 0
3 years ago
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Rufina [12.5K]
The answer is 72 hope that helped love :)<3
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3 years ago
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Which equation is a function of x?
lana [24]

Answer:

If you input a value of x then we get the output f(x) = y, which is the function of x. This is a function of x. Hence, x² = y is a function of x.

Step-by-step explanation:

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