If an object moves along a straight line, the distance traveled can be represented by a distance-time graph. In a distance-time graph, the gradient of the line is equal to the speed of the object. The greater the gradient (and the steeper the line) the faster the object is moving.

Step-by-step explanation:

6 0

3 years ago

Find dy/dx when y = Ln (sinh 2x). A. 2 cosh 2x B. 2 sech 2x C. 2 coth 2x D. 2 csch 2x

givi [52]

The function given is a composite function. Let's work from the outside in:
$y=(ln(sinh(2x)))$

First step:
$\frac{d}{dx}[y]= \frac{d}{dx}[ln(sinh(2x))]$

Now, let's work it out:
$\frac{dy}{dx} = \frac{1}{sinh(2x) } * \frac{d}{dx}[sinh(2x)]$

Next step:
$\frac{dy}{dx} = \frac{1}{sinh(2x) } * cosh(2x) * \frac{d}{dx}[2x]$

Next step:
$\frac{dy}{dx} = \frac{1}{sinh(2x) } * cosh(2x) *2$

Simplify:
$\frac{dy}{dx} = \frac{2cosh(2x)}{sinh(2x) }$

Simplify further:
$\frac{dy}{dx} = 2 (\frac{cosh(2x)}{sinh(2x)})$

Remember that:
${\frac{cosh(x)}{sinh(x)} = coth(x)$

So, your final answer is:
$\boxed{ \frac{dy}{dx} = 2coth(2x) }$

So, your answer is C. Hope I could help you!

8 0

4 years ago

Some students attend school 180 of the 365 Days in a year. About what percentage of the year do they attend school?

Galina-37 [17]

180/360=0.5
0.5*100=50%
hope it helps

4 0

3 years ago

-4(2x-3) A) 8x+12 B) 8x-12 C) -8x+12 D) -8x-12

Fofino [41]

Step 1: Multiply -4 and 2x. That would be -8x
Step 2: Multiply -4 and -3. That would be 12 because a negative number times a negative number results in a positive number.
Step 3: Put it all together (8x+12)
Answer: C

4 0

4 years ago