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Firdavs [7]
2 years ago
10

If f(x) = 4x - 3, then f '(x) is​

Mathematics
1 answer:
lord [1]2 years ago
8 0

Answer:

f'(x) = 4

Step-by-step explanation:

  • Derivative of 3 (constant number) is 0
  • Derivative of 4x is 4
  • f'(x) = 4 - 0 = 4
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What is the solution to the equation
Dafna11 [192]
\sqrt{4t+5}=3-\sqrt{t+5}\\\\D:4t+5\geq0\ \wedge\ t+5\geq0\ \wedge\ \sqrt{t+5}\leq3\\\\t\geq-\dfrac{5}{4}\ \wedge\ t\geq-5\ \wedge\ t\leq6

therefore
D:x\in\left< -\dfrac{5}{4};\ 6\right>

\sqrt{4t+5}=3-\sqrt{t+5}\ \ \ |^2\\\\(\sqrt{4t+5})^2=(3-\sqrt{t+5})^2\ \ \ |use:(a-b)^2=a^2-2ab+b^2\\\\4t+5=3^2-2\cdot3\cdot\sqrt{t+5}+(\sqrt{t+5})^2\\\\4t+5=9-6\sqrt{t+5}+t+5\ \ \ \ |-t\\\\3t+5=14-6\sqrt{t+5}\ \ \ \ |-14\\\\3t-9=-6\sqrt{t+5}\ \ \ \ |change\ signs
9-3t=6\sqrt{t+5}\ \ \ \ |:3\\\\3-t=2\sqrt{t+5}\ \ \ \ |^2\\\\(3-t)^2=(2\sqrt{t+5})^2\\\\3^2-2\cdot3\cdot t+t^2=4(t+5)\\\\9-6t+t^2=4t+20\ \ \ |-4t-20\\\\t^2-10t-11=0\\\\t^2+t-11t-11=0\\\\t(t+1)-11(t+1)=0\\\\(t+1)(t-11)=0\iff t+1=0\ \vee\ t-11=0\\\\t=-1\in D\ \vee\ t=11\notin D
Answer: t = -1.


7 0
3 years ago
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Tell whether the sequence is arithmetic. If it is, what is the common difference?
Ilya [14]
The answer is B. Yes; 4

Arithmetic sequence is the type of sequence of numbers which difference between each number will always remain constant
in the sequence above we could see the difference between one number with another is exactly 4:

15 + 4 = 19

19 + 4 = 23

23 + 4 = 27


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