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atroni [7]
3 years ago
14

How can I solve the following system of equations: -4x + y= 6, -5x -y =21. I know I can cancel out but I don't know where or whe

re to go from there.
Mathematics
1 answer:
matrenka [14]3 years ago
7 0
-4x + y = 6
-5x - y = 21

add both of them
-9x = 27
x = -3

(-4*-3) + y = 6
-12 + y = 6
y = 18
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rectangle

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This famous clock tower has a clock face with a diameter of 23 feet. What is the approximate area of this clock face
pashok25 [27]

Answer:

Therefore the approximate area of this clock face is 415.3 feet².

Step-by-step explanation:

Given:

Clock is of Circular Shape,

Diameter = 23 feet

Radius =r =\dfrac{diameter}{2}=\dfrac{23}{2}=11.5\ feet

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Area of Clock Face = ?

Solution:

Area of Circle having Radius 'r' is given as,

\textrm{Area of Circle}=\pi r^{2}

Substituting the values we get

\textrm{Area of Clock Face}=3.14\times (11.5)^{2}=415.265=415.3\ feet^{2}

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7 0
3 years ago
Find the coordinates of the vertex
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(2,8)

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4 0
3 years ago
Solve the following differential equations or initial value problems. In part (a), leave your answer in implicit form. For parts
shepuryov [24]

Answer:

(a) (y^5)/5 + y^4 = (t^3)/3 + 7t + C

(b) y = arctan(t(lnt - 1) + C)

(c) y = -1/ln|0.09(t + 1)²/t|

Step-by-step explanation:

(a) dy/dt = (t^2 + 7)/(y^4 - 4y^3)

Separate the variables

(y^4 - 4y^3)dy = (t^2 + 7)dt

Integrate both sides

(y^5)/5 + y^4 = (t^3)/3 + 7t + C

(b) dy/dt = (cos²y)lnt

Separate the variables

dy/cos²y = lnt dt

Integrate both sides

tany = t(lnt - 1) + C

y = arctan(t(lnt - 1) + C)

(c) (t² + t) dy/dt + y² = ty², y(1) = -1

(t² + t) dy/dt = ty² - y²

(t² + t) dy/dt = y²(t - 1)

(t² + t)/(t - 1)dy/dt = y²

Separating the variables

(t - 1)dt/(t² + t) = dy/y²

tdt/(t² + t) - dt/(t² + t) = dy/y²

dt/(t + 1) - dt/(t(t + 1)) = dy/y²

dt/(t + 1) - dt/t + dt/(t + 1) = dy/y²

Integrate both sides

ln(t + 1) - lnt + ln(t + 1) + lnC = -1/y

2ln(t + 1) - lnt + lnC = -1/y

ln|C(t + 1)²/t| = -1/y

y = -1/ln|C(t + 1)²/t|

Apply y(1) = -1

-1 = ln|C(1 + 1)²/1|

-1 = ln(4C)

4C = e^(-1)

C = (1/4)e^(-1) ≈ 0.09

y = -1/ln|0.09(t + 1)²/t|

8 0
3 years ago
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