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Ivenika [448]
3 years ago
7

How do you verify this trigonometric identity? cos^2 θcot^2 θ = cot^2 θ - cos^2 θ

Mathematics
1 answer:
sattari [20]3 years ago
8 0
<h3>Explanation:</h3>

Replace cos^2(θ) with 1-sin^2(θ), and cot(θ) with cos(θ)/sin(θ).

  cos^2(θ)cot^2(θ) = cot^2(θ) - cos^2(θ)

  (1 -sin^2(θ))cot^2(θ) =  . . . . . replace cos^2 with 1-sin^2

  cot^2(θ) -sin^2(θ)·cos^2(θ)/sin^2(θ) = . . . . . replace cot with cos/sin

  cot^2(θ) -cos^2(θ) = cot^2(θ) -cos^2(θ) . . . as desired

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A car travels 17 miles on one gallon of gas
zmey [24]

When x =170, y =10, when x = 187, y = 1, when x = 204, y = 12, when x = 221, y = 13, when x = 238, y = 14, when x = 255, y = 15, when x = 272, y = 16, when x = 289, y = 17, when x = 306, y = 18, when x = 323, y = 19, when x = 340, y = 20,

Step-by-step explanation:

Step 1; Assume y is the gallons in the tank while x is the range of the car. We need to determine the equation relating the y to the x values in the given coordinates. x is the dependent value whereas y is the independent value i.e. the value of x depends on the value of y.

Step 2; As y increases, x also increases. For every extra gallon in the tank, the car can go another 17 miles. So with y as the amount of gas in the tank in gallons and x as the range of vehicle, we get;

x = 17y, this represents the relation between x and y.

To find the gallons in the tank, y = \frac{x}{17},

For x = 170, y = \frac{170}{17} = 10,

Similarly equating the values we get that when x = 187, y = 11,

when x = 204, y = 12,

when x = 221, y = 13,

when x = 238, y = 14,

when x = 255, y = 15,

when x = 272, y = 16,

when x = 289, y = 17,

when x = 306, y = 18,

when x = 323, y = 19,

when x = 340, y = 20,

8 0
2 years ago
How many milliliters are equal to 7 liters?
AlekseyPX

Answer:

7000

Step-by-step explanation:

5 0
3 years ago
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Solve this equation.<br> 2/3x−1/5x=x−1
KonstantinChe [14]

Answer:

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Step-by-step explanation:

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3 years ago
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Sue chooses a dress and necklace to wear when she performs at a violin recital. The probability that Sue selects a black dress i
Verizon [17]

Answer:

Sue has a 12% chance of choosing a black dress and a gold necklace (as a fraction: 3/25, and as a decimal: 0.12).

Step-by-step explanation:

To find the probability of two separate events both occurring (in this case, selecting a black dress and a gold necklace), the probabilities are multiplied usually as fractions or decimals.

<u>As fractions:</u>

40% = 4/10

30% = 3/10

4/10 * 3/10 = 12/100 = 3/25, 0.12, or 12%


<u>As decimals:</u>

40% = 0.4

30% = 0.3

0.4 * 0.3 = 0.12 = 3/25, 0.12, or 12%


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3 years ago
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Amanda [17]
Hello,

2.3 x 10^9 = ( 1 x 10^3) ( 2.3 x 10^n) 

Solution:

Take the logarithm of both sides of the equation to remove the variable from the exponent. 

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