Answer:
See explanation
Step-by-step explanation:
We have to prove the identity
We will take right hand side of the identity
[ Tan θ will be positive since θ lies in 1st quadrant ]
Answer:
y = 13
Step-by-step explanation:
If it's a parallelogram then its consecutive angles are supplementary (add up to 180°).
6x - 12 + 132 - x = 180°,
5x + 120 = 180
5x = 60
x = 12
6x - 12 = 6(12) - 12 = 72 - 12 = 60
Parallelogram, opposite angles are equal
so
6y + 18 = 6x - 12
6y - 18 = 60
6y = 78
y = 13
Answer:
<u>The Eastbound train speed is 76.5 miles per hour and the Westbound train speed is 79.5 miles per hour.</u>
Step-by-step explanation:
1. Let's review all the information provided for solving this question:
Eastbound train speed = x
Westbound train speed = x + 3 miles per hour (The speed of the westbound train is 3mph greater than the speed of the eastbound train)
Duration of trip = 3 hours
Distance between trains after 3 hours = 468 miles
2. Let's find the speed of each train, using the following equation:
3x + 3(x + 3) = 468
3x + 3x + 9 = 468
6x + 9 = 468
6x = 468 - 9 (Subtracting 9 at both sides)
6x = 459
x = 459/6 (Dividing by 6 at both sides)
x = 76.5 miles per hour
<u>The Eastbound train speed is 76.5 miles per hour and the Westbound train speed is 79.5 miles per hour.</u>
3. Proof that x = 76.5 is correct
3x + 3(x + 3) = 468
3 (76.5) + 3 (76.5 + 3) = 468
229.5 + 238.5 = 468
<u>468 = 468</u>
<u>The value of x = 76. 5 is correct. And now we know that the Eastbound train has traveled 229.5 miles since the departure from Cleveland and the Westbound train 238.5 miles.</u>
The length of arc of the given circle, to the nearest hundreth, is: 2.41 units.
<h3>What is the Length of an Arc?</h3>
Length of arc = ∅/360 × 2πr, where the radius of the circle is r, and the reference angle is ∅.
We are given the following:
Radius (r) = 3 units
Reference angle (∅) = 46°
Plug in the values into the length of arc formula:
Length of arc = 46/360 × 2π(3)
Length of arc = 2.41 units.
Therefore, the length of arc of the given circle, to the nearest hundreth, is: 2.41 units.
Learn more about length of arc on:
brainly.com/question/2005046
6 and 30 camd be simplified with 6
the result will be 1:5
so the question mark is 5