Answer:
The standard form of the equation of the parabola is (y + 2)² = 8 (x - 3)
Step-by-step explanation:
The standard form of the equation of a parabola is (y - k)² = 4p (x - h), where
- The vertex of the parabola is (h , k)
- The focus is (h + p, k)
∵ The vertex of the parabola is (3 , -2)
∴ h = 3 and k = -2
∵ The focus is (5 , -2)
∴ h + p = 5
- Substitute h by 3 to find p
∵ 3 + p = 5
- Subtract 3 from both sides
∴ p = 2
∵ The standard form of the equation of the parabola is (y - k)² = 4p (x - h)
- Substitute the values of h , k , and p in the equation
∴ (y - -2)² = 4(2) (x - 3)
∴ (y + 2)² = 8 (x - 3)
The standard form of the equation of the parabola is (y + 2)² = 8 (x - 3)
Answer:
<u>The amount of money Lily had when she left the store, in terms of m, is 86 - 6m</u>
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
m = Milk Lily purchased
2m = Fruit Lily purchased (twice that amount on fruit)
3m - 6 = Bread Lily purchased (6 dollars less than 3 times the amount spent on milk for bread)
Amount of money Lily entered = $ 80
2. How much money did Lily have when she left? Write your answer in terms of m.
Let's write the equation to find out the money left in terms of m, this way:
Money left = 80 - m - 2m - (3m - 6)
Money left = 80 - m - 2m - 3m + 6
Money left = 86 - 6m
<u>The amount of money Lily had when she left the store, in terms of m, is 86 - 6m</u>
Answer:
= (√3+4√2)/2√6
Step-by-step explanation:
To evaluate cos45*/sec30*+cosec60*
First according to trigonometry identity
sec 30 = 1/cos30
cosec 60 = 1/sin60
Substitute
cos45*/sec30*+cosec60*
= cos45/(1/cos30) + 1/sin60
= cos45coss30 + 1/sin60
= 1/√2 * √3/2 + 1/(√3/2)
= √3/2√2 + 2/√3
= (√9+4√2)/2√6 +
= (√3+4√2)/2√6
<u>We are given:</u>Distance covered by the fastest man in 9 seconds = 100m
<u>To Find: </u>The distance covered in 1 min 2 seconds or 62 seconds
<u>Finding the Speed of the man:</u>
We know that:
speed = distance covered / time taken
Speed = 100 / 9 <em>(we are given that he travels 100 m in 9 seconds)</em>
Speed = 11.11 m/s
<u>Distance travelled in 62 seconds:</u>
We know that:
distance covered = speed * time
<em>replacing the value of speed and time</em>
Distance = 11.11 * 62
Distance = 688.82 m
