The height of a tower is measured as 16.6 m. What is the shortest possible height of the tower?

Henry received $500 for his birthday which he intends to invest in an account that pays simple interest at the rate of 12% per y

Mila [183]

Answer:

$560

Step-by-step explanation:

Given that :

Principal, P= $500

Interest rate, r = 12% per year

Amount in account after 1 year

Time = 1 year

Using the relation :

A = P(1 + rt)

A = final amount in account

A = $500(1 + 0.12(1))

A = $500(1 + 0.12)

A = $500(1.12)

A = $560

3 0

2 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

2 years ago

What’s the area all sides meet at right angles

Marina86 [1]

Answer: 54

Step-by-step explanation: I separated it into 3 areas in my head and then added up 21+21+12 to get 54

7 times 3 is 21

and

3 times 4 is 12

sorry if i am wrong i just did this in my head

8 0

2 years ago

HELP I WILL MARK BRAINLIEST

gulaghasi [49]

Answer:

https://quizlet.com/141193969/mirrors-and-lenses-flash-cards/ i dont know

Step-by-step explanation:

7 0

2 years ago

What is the answer to 4/5 x 3/4

Furkat [3]

3/4 x 4/5

= 3 · 4/4 · 5

= 12/20

= 3 · 4/5 · 4

= 3/5

4 0

2 years ago

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