Brainliest..? thx
The kinetic energy k of an object in joules is given by the formula k = 1 mv2, where m is the object's mass in kilograms and v i
2 answers:
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Answer:
A. 7,348
Step-by-step explanation:
P = le^kt
intitial population = 500
time = 4 hrs
end population = 3,000
So we have all these variables and we need to solve for what the end population will be if we change the time to 6 hours. First, we need to find the rate of the growth(k) so we can plug it back in. The given formula shows a exponencial growth formula. (A = Pe^rt) A is end amount, P is start amount, e is a constant that you can probably find on your graphing calculator, r is the rate, and t is time.
A = Pe^rt
3,000 = 500e^r4
now we can solve for r
divide both sides by 500
6 = e^r4
now because the variable is in the exponent, we have to use a log
ln(6) = 4r
we can plug the log into a calculator to get
1.79 = 4r
divide both sides by 4
r = .448
now lets plug it back in
A = 500e^(.448)(6 hrs)
A = 7351.12
This is closest to answer A. 7,348
Therefore the maximum value of function f(x,y,z)= =1/27
And the minimum value is 0
<h3>What is function?</h3>function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable) (the dependent variable) (the dependent variable). Mathematics uses functions frequently, and functions are essential for specifying physical relationships in the sciences.
Here,
The function is given as:
f(x,y,z)=
=1
=>-1=0
Using Lagrange multiplies, we have:
L(x,y,z,λ)=f(x,y,z) +λ(0)
Substitute f(x,y,z)= and
-1=0
Differentiate
L(x)=+2λx
L(y)=+2λy
L(z)=+2λz
L(λ)=-1
Equating to 0
+2λx =0
+2λy = 0
+2λz = 0
-1 = 0
Factorize the above expressions
+2λx =0
2x(+λ)=0
2x=0 and (+λ)=0
x=0 and = -λ
+2λy = 0
2y(+λ)=0
2y=0 and (+λ)=0
y=0 and = -λ
+2λz = 0
2z(+λ)=0
2z=0 and (+λ)=0
z=0 and = -λ
So we have ,
x=0 and = -λ
y=0 and = -λ
z=0 and = -λ
The above expression becomes
x=y=z=0
This means that,
=1
x= ±1/
So,
y= ±1/
z= ±1/
The critic points are
x=y=z=±1/
x=y=z=0
Therefore the maximum value of function f(x,y,z)= =1/27
And the minimum value is 0
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