What is c in (c+3)-2c-(1-3c)=2

1 answer:

7 0

<span>Simplifying (c + 3) + -2c + -1(1 + -3c) = 2 Reorder the terms: (3 + c) + -2c + -1(1 + -3c) = 2 Remove parenthesis around (3 + c) 3 + c + -2c + -1(1 + -3c) = 2 3 + c + -2c + (1 * -1 + -3c * -1) = 2 3 + c + -2c + (-1 + 3c) = 2 Reorder the terms: 3 + -1 + c + -2c + 3c = 2 Combine like terms: 3 + -1 = 2 2 + c + -2c + 3c = 2 Combine like terms: c + -2c = -1c 2 + -1c + 3c = 2 Combine like terms: -1c + 3c = 2c 2 + 2c = 2 Add '-2' to each side of the equation. 2 + -2 + 2c = 2 + -2 Combine like terms: 2 + -2 = 0 0 + 2c = 2 + -2 2c = 2 + -2 Combine like terms: 2 + -2 = 0 2c = 0 Solving 2c = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Divide each side by '2'. c = 0 Simplifying answer c = 0</span>

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12 is a common denominator of 1/4 and 1/3

viktelen [127]

True... both 3 and 4 are factors of 12 so it can be used as a common denominator.

1/3 × 4/4 = 4/12
1/4 × 3/3 = 3/12

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3 years ago

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A system for tracking ships indicated that a ship lies on a hyperbolic path described by 5x2 - y2 = 20. the process is repeated

zysi [14]

Answer:
The ship is located at (3,5)

Explanation:
In the first test, the equation of the position was:
5x² - y² = 20 ...........> equation I
In the second test, the equation of the position was:
y² - 2x² = 7 ..............> equation II
This equation can be rewritten as:
y² = 2x² + 7 ............> equation III

Since the ship did not move in the duration between the two tests, therefore, the position of the ship is the same in the two tests which means that:
equation I = equation II

To get the position of the ship, we will simply need to solve equation I and equation II simultaneously and get their solution.

Substitute with equation III in equation I to solve for x as follows:
5x²-y² = 20
5x² - (2x²+7) = 20
5x² - 2y² - 7 = 20
3x² = 27
x² = 9
x = <span>± </span>√9

We are given that the ship lies in the first quadrant. This means that both its x and y coordinates are positive. This means that:
x = √9 = 3

Substitute with x in equation III to get y as follows:
y² = 2x² + 7
y² = 2(3)² + 7
y = 18 + 7
y = 25
y = +√25
y = 5

Based on the above, the position of the ship is (3,5).

Hope this helps :)

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3 years ago

Can you help me please

Elena L [17]

Answer:

this is the ans

Step-by-step explanation:

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4 years ago

Find the values of e, a, b, and c for r = 24/(4 + 2sin theta)

Kaylis [27]

Answer:

Step-by-step explanation:

r=24/(4+2sin θ)

4r+2r sin θ=24

divide by 2

2r+r sin θ=12

2√(x²+y²)+y=12

2√(x²+y²)=12-y

squaring

4(x²+y²)=144-24y+y²

4x²+3y²+24y=144

4x²+3(y²+8y+16-16)=144

4x²+3(y+4)²-48=144

4x²+3(y+4)²=144+48

4x²+3(y+4)²=192

divide by 192

$\frac{x^2}{48}+\frac{(y+4)^2}{64}=1$

which is an ellipse with centre(0,-4) major axis on y-axis.

$a^2=64\\a=8\\major axis=2*8=16\\b^2=48\\b=4\sqrt{3}\\minor ~axis=2*4 \sqrt{3}=8 \sqrt{3}\\b^2=a^2(1-e^2)\\48=64(1-e^2)\\1-e^2=48/64=3/4\\e^2=1-3/4=1/4\\e=1/2\\c^2=a^2-b^2\\c^2=64-48=16\\c=4$