Question

need calc help ASAP

Answer 1

@kaylak post your question content when you can ok? :)

(Also please at least show effort in your questions, like your best guess. We can't do all the work for you)

Answer 2

I am and have a lot of the questions are already answered

Answer 3

are the above correct?

Answer 4

Okay let me check the first one.
Derivative of x = 10t + 5t^2 -0.8t^3
is x' = 10 + 10t - 2.4t^2
Your answer: When t = 5: 0 = 10 + 10(5) - 2.4(5^2)
= 10 + 50 - 2.4(25)
= 60 - 60 = 0

Yes the first one is correct

Answer 5

I want to say d for the first sone of the set and I know the derivative for the second just not sure how to factor it right

Answer 6

Second one:
derivative of y = 30t - 10t^2
y' = 30 - 20t

Maxiumum height is when the speed turns from positive to negative (when y' = 0)
0 = 30-20t
t = (-30)/(-20) = 1.5 seconds

Plugging that in
y = 30(1.5) - 10(1.5)^2
= 45 - 22.5 = 22.5.

I got a different answer.

Answer 7

oh the second to the set I put up is c nevermind

Answer 8

For the third one:

I don't think it's D.

The acceleration is just the derivative twice.

Velocity: 30 - 20t
Acceleration: -20
Magnitude of Acceleratoin: 20.

Answer 9

okay ty I think I understand it a bit more

Answer 10

so 4 is correct?

Answer 11

\(\color{#0cbb34}{\text{Originally Posted by}}\) @kaylak
I want to say d for the first sone of the set and I know the derivative for the second just not sure how to factor it right
\(\color{#0cbb34}{\text{End of Quote}}\)
c

Answer 12

give me a second for the 4th one

Answer 13

after these there are only 5 more questions

Answer 14

Yes. 4 is c. Although it's kinda complicated to get there. I used
https://www.symbolab.com/solver/step-by-step/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(sin%5E%7B2%7Dxcosx%5Cright)

Symbolab is like a step-by-step calculator

Answer 15

cool the next 4 above most should be answered

Answer 16

1 c?

Answer 17

2 b

Answer 18

okay for the next 4:

The first one:
the speed is 2cos(4t+1)(4) = 8cos(4t+1)

8cos(4(2)+1) = 8cos(9) = 7.3 ish.

Answer 19

You know how to take derivatives of sin right?

Answer 20

sin is cos I believe right?

Answer 21

the derivative

Answer 22

yeah

I assume for 2. The 'jerk' is acceleration

1/2sin(2t)
First derivative: cos(2t)
Second derivative: 2(-sin(2t)) = -2sin(2t)

Answer 23

no jerk is 3rd derivative

Answer 24

oh well then

Answer 25

I think I calculated that one in mathway so it's okay

Answer 26

Yeah you're right then for 2.

Answer 27

3 not sure

Answer 28

4 is d

Answer 29

So the slope would be the value of the first derivative.
Basically when is f'(x) = 2

f'(x) = 2cos(2x)*2 = 4cos(2x)

Basically solve for x: 4cos(2x) = 2

Answer 30

so e?

Answer 31

uh well
4cos(2x) = 2
cos(2x) = 1/2

We know cos(a) = 1/2 then a = pi/3

So 2x = pi/3
x = pi/6

I think b

Answer 32

okay fair enough and 4 is d?

Answer 33

Yes. I got the slope to be 6 square-root of 3.

So yah d

Answer 34

yay 5 more questions and I'm done!

Answer 35

okay holy crap.

For the first one there's division and we know
(a/b)' = (a'b-ab')/(b^2)

Answer 36

So in your problem that'll be
\[\frac{(x+a)'(x+b)-(x+a)(x+b)'}{(x+b)^2}\]

are you able to simplify that?

Answer 37

give me a sec

Answer 38

(x+a)' is literally just 1. It should be very quick to simplify it

Answer 39

yes I am just writing it down because I have to show my work lol

Answer 40

okay lol

Answer 41

wouldn't it be like 1/x^2 or something

Answer 42

hold on it is -a-b/(b+x)^2

Answer 43

@mhchen

Answer 44

I got b-a on the numerator

Answer 45

oh crap the fundamental definition not a regular derivative

Answer 46

\[\frac{(x+b)-(x+a)}{(x+b)^2} = \frac{b-a}{(x+b)^2}\]

Answer 47

nah just simplifying mistakes

Answer 48

oh I got it I was about to ask how but I understand now lol

Answer 49

For the 2nd picture. You go the same thing.

Find the derivative.

Plug in (1) for x to get the slope.

Then once you know the slope.

2 = (slope)(1) + b

solve for b

Answer 50

derivative is 3x^2-1/2xsquare root x

Answer 51

slope is 1 ?

Answer 52

I got something completely different.

\[\frac{(x^2+1)'(\sqrt{x})-(x^2+1)(\sqrt{x})'}{x}\]

you started here right?

Answer 53

\[\frac{(2x)(\sqrt{x})-(x^2+1)(\frac{1}{2}x^{-\frac{1}{2}})}{x}\]

Answer 54

Plug in x=1:

\[\frac{2-2*\frac{1}{2}}{1} = 2-1\]

well yeah slope is still 1 lol

Answer 55

lol and b is 1 I guess lol

Answer 56

my formula I use was similar but not the exact same but I still got the answer lol

Answer 57

so what's the equation of the tangent line lol?

Answer 58

y = (slope)x + b

y = 1x + 1

That's basically it

Answer 59

ah lol

Answer 60

3 more questions and then we are done

Answer 61

For the 3rd question:
It's asking what x is when the speed is -10

So first we find the derivative:
30 - 10t

And we find t when

-10 = 30 - 10t

What's t?

Answer 62

t=4

Answer 63

ye now we plug that back into the position function

x = 30t - 5t^2

Answer 64

-50

Answer 65

x = 30(4) - 5(4^2)
= 120 - 5(16)
= 120 - 80
= 40

Answer 66

crap I forgot the other x

Answer 67

let me fix that

Answer 68

2 more

Answer 69

okay so for the 4th picture.

It basically wants the derivative of the formula of a sphere.

but then rewrite it in a V/r form

this looks hard to me holy crap

Answer 70

okay I got.

First what is the derivative of

(4/3) * pi * r^3

Answer 71

4pir^2

Answer 72

yeah.

Now we need to get it in a * V/r form

To do that I did this:

\[4\pi r^2 * (\frac{V}{r}*\frac{r}{V}) = 4\pi r^2 * (\frac{r}{\frac{4}{3}\pi r^3}) \frac{V}{r}\]

Answer 73

Can you simplify that? Leave the V/r alone of course

Answer 74

I got r=3square root 6vpi/2pi but now I'm confused is the formula wrong?

Answer 75

you deleted your comment

Answer 76

I got 3

Answer 77

\[\frac{4\pi r^{3}}{\frac{4}{3}\pi r^3}\] = 3

Answer 78

oh okay

Answer 79

we are going to have a new curriculum where we are taught better lol have to finish the old curriculum first

Answer 80

so now we have to get it in the v/r form?

Answer 81

@mhchen

Answer 82

It's already in V/r form

3 V/r

Answer 83

I left the V/r alone when I simplified my equation.

So it's still there.

Answer 84

oh okay

Answer 85

last one!

Answer 86

alright last question:

take the derivative of sinx + cosx twice

and then plug pi/4 in it

Answer 87

-square root 2

Answer 88

?

Answer 89

@mhchen

Answer 90

ye

Answer 91

yay

Answer 92

ty so much!

Answer 93

np