The volume of a sphere is 2,240 yd^3. What will be the new volume in the dimensions are multiplied by 1/4?
1 answer:
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Answer:
The position vector of point C is <-3 , -17 , 8> or -3i - 17j + 8k
Step-by-step explanation:
* Lets revise how to solve the problem
- If the endpoints of a segment are (x1 , y1 , z1) and (x2 , y2 , z2), and
point (x , y , z) divides the segment externally at ratio m1 :m2, then
* Lets solve the problem
∵ AB is a segment where A = (3 , 1 , 2) and B = (1 , - 5 , 4)
∵ Point C lies on line AB such that AC : BC=3 : 2
∵ From the ratio AC = 3/2 AB
∴ C divides AB externally
- Lets use the rule above to find the coordinates of C
- Let Point A is (x1 , y1 , z1) , point B is (x2 , y2 , z2) and point C is (x , y , z)
and AC : AB is m1 : m2
∴ x1 = 3 , x2 = 1
∴ y1 = 1 , y2 = -5
∴ z1 = 2 , z2 = 4
∴ m1 = 3 , m2 = 2
- By using the rule above
∴
∴
∴
∴ The coordinates fo point c are (-3 , -17 , 8)
* The position vector of point C is <-3 , -17 , 8> or -3i - 17j + 8k
Niklas takes a dose of 25 micrograms of a certain supplement each day. The supplement has a half life of 4 hours, meaning that 1/64 of the supplement remains in the body after each day. How much of the supplement is in Niklas's body immediately after the 12th dose? Round your final answer to the nearest hundredth.
Answer:
The amount of the supplement in Niklas body immediately after the 12th dose is 430 micrograms to the nearest hundreth
Step-by-step explanation:
Half life is the time required for an element to decay into half of its initial size.
Given that :
The supplement has a half life of 4 hours, this implies that it decay to half of its size every 4 hours.
∴ there are 6 stages of division in a day.
i.e
The amount of the supplement in Niklas body after the first dose (first day) can be calculated as:
= × 25
= 0.390625 micrograms
It is said that he used the supplement daily for 12 days (12th dose),
As such ; we can estimate the amount of the supplement that is in his body immediately after the 12th dose; which is calculated as:
amount in his body per day × number of period for complete decay
= 0.390625 × 11
= 4.296875
≅4.30 micrograms
= 430 micrograms to the nearest hundreth
The amount of the supplement in Niklas body immediately after the 12th dose is 430 micrograms to the nearest hundreth