Solve 1/25 = 5^x+4 ( all exponential)
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Answer: The "zero" is: " 2 " ; or, write as: " 2.92 " .
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→ " t = 2 " ; or, write as: " t = 2.92 " .
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Step-by-step explanation:
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Letting assume that this given function is supposed to be written as:
"distance as a function of time" ; that is:
d(t) = 70 - (2.4)t ;
→ since distance, "d" is the dependent variable (cannot be "manipulated or controlled") and as such, belongs on the "y-axis"—as the "dependent variable" ; whereas as time, "t" ; can be somewhat controlled (with respect to distance, at list as a starting point); and as such belongs on the "x-axis" as the "independent variable" .
Since no "specific units" are given to us in the problem for Either "distance" or "time" ; we shall use the term "units" to describe their values.
We have:
d(t) = 70 - (2.4)t ;
Let us rearrange this:
70 - (2.4)t ; ↔
= 70 + (- 2.4)t ; ↔
= (-2.4)t + 70 ;
And rewrite the function:
→ d(t) = (-2.4)t + 70 ;
To find the "zero" ; or "zeros" ; of this function; set "d(t)" equal to "zero" ; that is; "0" ; and solve for the value(s) for "t" when "d(t)" = 0 :
→ 0 = -2.4(t) + 70 ; ↔
Rewrite as:
→ -2.4(t) + 70 = 0 ;
For simplicity; let us multiply Each side of the equation by "10" ;
to get rid of the decimal value:
10*[ (-2.4)t) + 70 ] = 10 * [0] ;
From the left-hand side of the question:
Note the "distributive property" of multiplication:
a(b + c) = ab + ac ;
As such:
10* [-2.4(t) + 70 ] =
[10* -2.4(t)] + [10 * 70] =
-24t + 70 ;
From the "right-hand side" of the equation:
10 * 0 = 0 .
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So; we rewrite the equation as:
-24t + 70 = 0 ;
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Solve for " t " ;
-24t + 70 = 0 ;
Subtract "70" from Each Side of the equation;
-24t + 70 - 70 = 0 - 70 ;
to get:
-24t = -70 ;
Now, let's multiply each side of the equation by "-1" ;
to get rid of the "negative values" ;
-1* (-24t) = -1(-70) ;
to get:
24t = 70 ;
Now, let's divide Each Side of the equation by "24" ;
to isolate: "t" ; on one side of the equation; & to solve for "t" ;
24t / 24 = 70/24 ;
to get:
t = 70/24 ;
To simplify: either:
1) use calculator: 70 ÷ 24 = 2.916666666 ;
→ round to: 2.92 ;
→ t ≈ 2.92 ;
or: " ;
→ write as simplified improper fraction: " t = "
→ or: write as mixed number:
→ " = 35 ÷ 12 =
2 R 11
12 ⟌35
<u>- 24 </u>
1 1
→ write as: " 2 " ;
→ " t = 2 " .
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Hope this is helpful to you.
Wishing you the best!
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Answer:
Step-by-step explanation:
First, rewrite the equation (all terms should be in the left side):
In this equation,
Then the discriminant
Then