Answer:
Step-by-step explanation:
The question to be solved is the following :
Suppose that a and b are any n-vectors. Show that we can always find a scalar γ so that (a − γb) ⊥ b, and that γ is unique if 
. Recall that given two vectors a,b a⊥ b if and only if 
where 
is the dot product defined in 
. Suposse that 
. We want to find γ such that 
. Given that the dot product can be distributed and that it is linear, the following equation is obtained
Recall that 
are both real numbers, so by solving the value of γ, we get that
By construction, this γ is unique if 
, since if there was a 
such that 
, then
Answer:
576
Step-by-step explanation:
First off, we can use the area of a kite formula, (D1*D2)/2 to get the area of one side of the kite, which is simplified to 18 * 32 : which gets us 288. But because we are looking for the area of the front and back side, we multiply 288 by 2- getting the final answer of <u>576</u>.
From the calculation, the growth rate is 0.88.
<h3>What is the growth rate?</h3>
To find the relative growth rate
P1 = Poe^rt
P2 = Poe^rt
Thus;
1920 = Poe^4r ------ (1)
1966080 =Poe^12r -------(2)
P2/P1 gives;
1966080/1920 = Poe^12r/Poe^4r
1024 = e^12r/e^4r
1024 =e^8r
1024 = (e^r)^8
2^10 = (e^r)^8
e^r = 2^1.25
e^r = 2.38
r = ln(2.38)
r = 0.88
The initial size of the culture is;
1920 = Poe^(0.88 * 4)
Po = 1920/e^(0.88 * 4)
Po = 57
The expression for the exact number of bacteria after t hours is
P(t) = 57e^0.08t
The growth (in bacteria per hour) after 9.5 hours is
P(t) = 57e^(0.88 * 9.5)
P(t) = 243544
For the number to reach 72,000;
72,000 = 57e^0.88t
72,000/57 = e^0.88t
ln 126 = ln[e^0.88t]
4.8 = 0.88t
t = 4.8/0.88
t = 5.5 hours
Learn more about exponential growth;brainly.com/question/13674608
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Answer:
yes
Step-by-step explanation:
Answer:
There is 18% left of the pie.
Step-by-step explanation:
There is only 100% of a pie. If she at 82% then there is 18% left. 100-82=18
