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trasher [3.6K]
3 years ago
9

8) Solve for x. -3x - 8 = 10 A) -54 B) -6 C) 6 D) 5 54

Mathematics
1 answer:
lakkis [162]3 years ago
3 0

Answer:

X= -6 (B)

Step-by-step explanation:

-3x=18

X=18/-3

X= -6

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3 years ago
Derivative of tan(2x+3) using first principle
kodGreya [7K]
f(x)=\tan(2x+3)

The derivative is given by the limit

f'(x)=\displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}h

You have

\displaystyle\lim_{h\to0}\frac{\tan(2(x+h)+3)-\tan(2x+3)}h
\displaystyle\lim_{h\to0}\frac{\tan((2x+3)+2h)-\tan(2x+3)}h

Use the angle sum identity for tangent. I don't remember it off the top of my head, but I do remember the ones for (co)sine.

\tan(a+b)=\dfrac{\sin(a+b)}{\cos(a+b)}=\dfrac{\sin a\cos b+\cos a\sin b}{\cos a\cos b-\sin a\sin b}=\dfrac{\tan a+\tan b}{1-\tan a\tan b}

By this identity, you have

\tan((2x+3)+2h)=\dfrac{\tan(2x+3)+\tan2h}{1-\tan(2x+3)\tan2h}

So in the limit you get

\displaystyle\lim_{h\to0}\frac{\dfrac{\tan(2x+3)+\tan2h}{1-\tan(2x+3)\tan2h}-\tan(2x+3)}h
\displaystyle\lim_{h\to0}\frac{\tan(2x+3)+\tan2h-\tan(2x+3)(1-\tan(2x+3)\tan2h)}{h(1-\tan(2x+3)\tan2h)}
\displaystyle\lim_{h\to0}\frac{\tan2h+\tan^2(2x+3)\tan2h}{h(1-\tan(2x+3)\tan2h)}
\displaystyle\lim_{h\to0}\frac{\tan2h}h\times\lim_{h\to0}\frac{1+\tan^2(2x+3)}{1-\tan(2x+3)\tan2h}
\displaystyle\frac12\lim_{h\to0}\frac1{\cos2h}\times\lim_{h\to0}\frac{\sin2h}{2h}\times\lim_{h\to0}\frac{\sec^2(2x+3)}{1-\tan(2x+3)\tan2h}

The first two limits are both 1, and the single term in the last limit approaches 0 as h\to0, so you're left with

f'(x)=\dfrac12\sec^2(2x+3)

which agrees with the result you get from applying the chain rule.
7 0
3 years ago
What is the equation for the line on the graph​
____ [38]

Answer:

x = -1

Step-by-step explanation:

7 0
3 years ago
Mai, Eric, and Dean served a total of 103 orders on Monday. Mai served 8 more orders than Eric. Dean served 3 times as many orde
mel-nik [20]
Let the number of orders Eric served be x

Eric = x
Mai =  x+ 8         [Mai served 8 more than Eric]
Dean = 3x           [Dean served 3 times as many as Eric]

Given that the total is 103
x + x + 8 + 3x = 103  
5x + 8 = 103
5x = 103 - 8
5x = 95
x = 19


x = 19
x + 8 = 19 + 8 = 27
3x = 19 x 3 = 57

Eric served 19
Mai served 27
Dean served 57





3 0
3 years ago
100 bombbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
Over [174]

Answer:

SJNSIWBJBEHDH

Step-by-step explanation:

HJSJSJJSNS

5 0
3 years ago
Read 2 more answers
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