Consider the expression 3 * (10 * 2).
2 answers:
You might be interested in
9514 1404 393
Answer:
(a) x = (3 -ln(3))/5 ≈ 0.819722457734
(b) y = 10
Step-by-step explanation:
(a) Taking the natural log of both sides, we have ...
2x +1 = ln(3) +4 -3x
5x = ln(3) +3 . . . . . . . . add 3x-1
x = (ln(3) +3)/5 ≈ 0.820
__
(b) Assuming "lg" means "log", the logarithm to base 10, we have ...
log(y -6) +log(y +15) = 2
(y -6)(y +15) = 100 . . . . . . . taking antilogs
y^2 -9x -190 = 0 . . . . . . . . eliminate parentheses, subtract 100
(y -19)(y +10) = 0 . . . . . . . . factor
The values of y that make these factors zero are -19 and 10. We know from the first term that (y-6) > 0, so y > 6. That means y = -19 is an extraneous solution.
The solution is ...
y = 10
__
When solving equations using a graphing calculator, it often works well to define a function f(x) such that the solution is f(x) = 0, the x-intercept(s). That form is easily obtained by subtracting the right side of the equation from both sides of the equation. In part (a) here, that is ...
f(x) = e^(2x+1) -3e^(4-3x)
EXPLANATION:
-To formulate an equation, you must first know what data the exercise gives us to locate them correctly.
data:
-6 that must be added to a number.
-four times a number that is equal to 4x
-a result that is equal to 50
Now with these data we formulate the equation:
if we solve the equation we have:
Answer:
<em>The perimeter of the fencing is 44 feet (Option D)</em>
Step-by-step explanation:
<u>Area and Perimeter</u>
A square shape of side length (a) has an area given by:
And its perimeter is calculated as:
P = 4a
The area of Katrina's square garden is given as A=121 square feet. We need to calculate the side length by solving for a:
a = 11 feet
Once we know the value of a, then we calculate the perimeter:
P = 4*11 = 44
The perimeter of the fencing is 44 feet (Option D)