Answer:
0.32km
Step-by-step explanation:
The speed that a tsunami can travel is modeled by the equation s = 356 StartRoot d EndRoot , where S is the speed in kilometers per hour and d is the average depth of the water in kilometers.
This is written mathematically as:
S = 356√d
What is the approximate depth of water for a tsunami traveling at 200 kilometers per hour?
S = 200km/hr
Hence:
200km/hr = 356√d
Divide both sides by 356
200/356 = 356√d/356
√d = 200/356
Square both sides
(√d)² = (200/356)²
d =(0.5617977528)²
d = 0.3156167151km
Approximately = 0.32km
Answer:
The lateral area is equal to
Step-by-step explanation:
In this problem the lateral area is equal to the area of one equilateral triangle multiplied by 
To find the area of one equilateral triangle calculate the height
The area of the triangle is equal to
we have
Applying the Pythagoras theorem
The area of one triangle is equal to
so
The lateral area is equal to
Answer:
(2, 11/2)
Step-by-step explanation:
This is a vertical parabola; we know that because x is squared here, while y is not. The standard equation of a vertical parabola with vertex (h,k) is
4p(y-k) = (x-h)^2, where p is the distance between the vertex and the focus. Comparing
4p(y-k) = (x-h)^2 to
10(y-3) = (x-2)^2, we see that 4p = 10. Therefore, p = 10/4 = 5/2, which is the vertical distance between the focus and the vertex.
Since the coordinates of the vertex are easily read from the given equation
(x-2)^2=10(y-3): (h,k) = (2, 3)
all we need to do is to add p (5/2) to the y-coordinate (3);
The focus is at (2, 3 + 5/2), or (2, 11/2).
I will rewrite the question for better understanding:
Ashley recently opened a store that uses only natural ingredients. She wants to advertise her products by distributing bags of samples in her neighborhood. It takes Ashley 2/3 of a minute to prepare one bag. It takes each of her friends 75% longer to prepare a bag. How many hours will it take Ashley and 4 of her friends to prepare 1575 bags of samples?
Answer:
- <em><u>5.3 hours</u></em>
Explanation:
<u>1) Time it takes Ashley to preprate one bag: </u>
<u>2) Time it takes each friend of Ashley: 75% more than 2/3 min</u>
- 75% × 2/3 min = 0.75 × 2/3 min = 3/4 × 2/3 min= 2/4 min = 1/2 min = 0.5 min
- 2/3 min + 1/2 min = 7/6 min
<u>3) Time it takes Ashley and the 4 friends working along to prepare one bag:</u>
- Convert each time into a rate, since you can set that the total rate of Ashley along with her four friends is equal to the sum of each rate:
- Rate of Ashley: 1 bag / (2/3) min = 3/2 bag/min
- Rate of each friend: 1 bag / (7/6) min = 6/7 bag/min
- Rate of Ashley and 4 friends = 3/2 bag/min + 4 × 6/7 bag/min = (3/2 +24/7) bag/min = 69/14 bag/min
<u>4) Time of prepare 1575 bags of samples:</u>
- time = number of bags / number of bags per min = 1,575 bags / (69/14) bags/min = 319.56 min
<u>5) Convert minutes to hours:</u>
- 356.56 min × 1 hour / 60 min = 5.3 hours
