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3 years ago

7z-18= -2z +19 solve for z. Show work .

Mathematics

1 answer:

Zanzabum3 years ago

4 0

Answer:

z=37/9

Step-by-step explanation:

move the variable to the left side and change its sign: 7z+2z-18=19

collect like terms, so add the 7 and 2: 9z=19+28

add the 28 and 19: 9z=37

divide both signs by 9: 37/9

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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

Kourtnie and kayla are sisters who are taking the same classes this semester: dre 098, chm 130/130a, and aca 122. if kourtnie ea

Volgvan

W are r are not valid grades. I have attached the table associated with this question

Answer:
GPA = 3.625

Explanation:
GPA stands for "Grade Point Average".
It can be easily calculated by dividing the total grade points with the total number of hours.
Taking a look at the table, we can find that:
Total grade points = 29
Total hours = 8
Therefore:
GPA = 29 / 8 = 3.625

Hope this helps :)

5 0

4 years ago

Factor x3 + 3x2 + 2x completely.<br> x(x2 + 3x + 2)<br> x(x + 1)(x + 2)<br> x(x - 1)(x - 2)<br> DONE

Natasha2012 [34]

$\text{To factor out the expression, all of the numbers have to have the same}\\\text{amount of variables}\\\\\text{You would see that in the expression}\,\, x^3 + 3x^2 + 2x\,\,\text{they all}\\\text{have "x"}\\\\\text{Factor out x:}\\\\x^3 + 3x^2+2x\\\\x(x^2+3x+2)\\\\\text{Factor}\,\, x^3 + 3x^2+2x\\\\x(x+1)(x+2)\\\\\boxed{\text{Answer:}\,x(x+1)(x+2)}}$

6 0

3 years ago

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Find a polynomial function f(n) such that f(1), f(2), ... , f(8) is the following sequence.

Irina18 [472]

Observing there is a difference of +8 between each f(x).
The slope of this sequence is 8.(y2-y1)/(x2-x1)
Using the point slope equation,
y-y1 = m(x-x1) yields

y = 8x -4 as the answer.

5 0

4 years ago

The volume of a cylinder is given by the formula <img src="https://tex.z-dn.net/?f=V%2B%20%5Cpi%20r%5E2h" id="TexFormula1" title

n200080 [17]

V = $\pi r^{2}h$ where r is radius and h is height

so when radius is (x+8) and height is (2x+3),

volume = $\pi (x+8)^{2}(2x+3)$

4 0

4 years ago

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