Answer:
24%
Step-by-step explanation:
The number of kilograms, y, of original oxygen that remain in the body after t hours can be modeled by the equation y = 0.32(0.76)^t . What is the rate of decrease of original oxygen?
The formula for Exponential Decrease is given as:
y = a(1 - r)^t
Where
y = Amount after time t
a = Original amount
r = Rate of decrease
t = Time
Comparing both Equations
y = 0.32(0.76)^t = y = a(1 - r)^t
We know that
0.76 = 1 - r
Solving for r
Collect like terms
r = 1 - 0.76
r = 0.24
Converting to Percentage
= 0.24 × 100
= 24%
Therefore, the rate of decrease of original oxygen is 24%
Answer:
7
Explanation:
−
2
x
+
10
=
−
4
take 10 from both sides
−
2
x
=
−
14
divide both sides by -2 to find x
x
=
7
Step-by-step explanation:
This is the concept of application of quadratic expressions. Given that the height of the ball is modeled by the equation;
h=-7.3t^2+8.25t+2.1+5
The time taken for the ball to hit the ground will be given as falls;
-7.3t^2+8.25t+7.1=0
to solve for t we use the quadratic formula;
t=[-b+/-sqrt(b^2-4ac)]/(2a)
a=-7.3, b=8.25, c=2.1
t=[-8.25+/-sqrt[8.25^2+4*7.3*7.1]/(-2*7.3)
t= -0.572
or
t=1.702
since there is not negative time we take the time taken for the ball to hit the ground will be: t=1.702 sec
Answer:
False
Step-by-step explanation:
Lets call the three prime divisors of n p, q, and r, being r the largest, we know:
Now, if
then
So:
Also, for every natural greater than one, we know:
![\sqrt[3]{n}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bn%7D%3C%5Csqrt%7Bn%7D)
so
![\sqrt[3]{n}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bn%7D%3C%5Csqrt%7Bn%7D%20%3C%20r)
from which:
![\sqrt[3]{n} < r](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bn%7D%20%3C%20r)
So, we see, this means the preposition is false, we can find a particular counterexample:
q=2
p=3
p*q = 6
We need to choose a prime greater than 6
r=7
n= 2 * 3 *7 = 42
![\sqrt[3]{42} = 3.4760 < 7](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B42%7D%20%3D%203.4760%20%3C%207)
