Answer:
r = 1
Step-by-step explanation:
slope = change in y / change in x, so:
change in y / change in x = 2/3
5 - r / 7 - 1 = 2/3
5 - r / 6 = 2/3
now solve this equation.
first, multiply both sides by 6 to get rid of the fraction:
subtract 5 from both sides
multiply both sides by -1
Expression as a single natural logarithm is 2.48490664979.
<h3>What is natural logarithm?</h3>
ln 3+ ln 4
ln (3×4)
ln(12) =2.48490664979
The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.
The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).
To learn more about natural logarithm from the given link:
brainly.com/question/20785664
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Answer:
10!
Step-by-step explanation:
Exuse me if im wrong :')
Step-by-step explanation:
let us give all the quantities in the problem variable names.
x= amount in utility stock
y = amount in electronics stock
c = amount in bond
“The total amount of $200,000 need not be fully invested at any one time.”
becomes
x + y + c ≤ 200, 000,
Also
“The amount invested in the stocks cannot be more than half the total amount invested”
a + b ≤1/2 (total amount invested),
=1/2(x + y + c).
(x+y-c)/2≤0
“The amount invested in the utility stock cannot exceed $40,000”
a ≤ 40, 000
“The amount invested in the bond must be at least $70,000”
c ≥ 70, 000
Putting this all together, our linear optimization problem is:
Maximize z = 1.09x + 1.04y + 1.05c
subject to
x+ y+ c ≤ 200, 000
x/2 +y/2 -c/2 ≤ 0
≤ 40, 000,
c ≥ 70, 000
a ≥ 0, b ≥ 0, c ≥ 0.
X4-x2≥ 2x~~~2x≥ 2x True
Because " _ " is the same thing with "=" ; and because 2x=2x then 2x≥ 2x ~~~~~~Have a nice day!!! ★★
