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Answer:
See definition below
Step-by-step explanation:
Since we have to give a recursive definition, we must give a initial value f(0). Additionally, the value of f(n) must depend on the value of f(n-1) for all n≥1.
The required value of f(0) is (0+1)!=1!=1.
Now, the factorial itself is a recursive function, because (n+1)!=(n+1)n!. In terms of f, this means that f(n)=(n+1)f(n-1) for all n≥1.
Then, our definition is: f:N→N is defined by
- f(0)=1.
- For n≥1, f(n)=(n+1)f(n-1).
Answer:
The equation has no solution.
Step-by-step explanation:
Hi there!
First, let´s write the equation:
(√x + 3) + 6 = 3
To solve the equation, let´s subtract 6 to both sides of the equation:
√x + 3 = -3
subtract 3 to both sides of the equation:
√x = -6 (the square root of any number can´t be negative, but let´s solve it anyway and then check the solution).
Square both sides of the equation:
x = 36
Now, let´s check the solution:
(√x + 3) + 6 = 3
x = 36
(√36 + 3) + 6 = 3
(6 + 3) + 6 = 3
9 + 6 = 3
15 ≠ 3
Then, the equation has no solution.
Have a nice day!
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Answer:
- tan(A) = 7/24
- sin(A) = 7/25
- cos(A) = 24/25
Step-by-step explanation:
The mnemonic SOH CAH TOA can help you remember the trig ratios:
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
With respect to angle A, the sides are Adjacent = 24; Opposite = 7, Hypotenuse = 25. Then the desired trig ratios are ...
tan(A) = 7/24
sin(A) = 7/25
cos(A) = 24/25