Answer:
1) [tex]f'(t)=4t,\ g'(t)=3t^2+4[/tex]
2) [tex]p(t) =2t^5+8t^3[/tex]
[tex]p'(t)=10t^4+24t^2[/tex]
3) False
4)[tex]q(t) =\dfrac{1}{2}t+2t^{-1}[/tex]
[tex]q'(t)=\dfrac{1}{2}-\dfrac{2}{t^2}[/tex]
5) False
Step-by-step explanation:
Given that:
[tex]f(t) = 2t^2[/tex] and [tex]g(t) = t^3 + 4t[/tex]
Formula:
[tex]1. \dfrac{d}{dx}x^n=nx^{n-1}[/tex]
[tex]2. \dfrac{d}{dx}C.f(x)=C.f'(x)\ \{\text{C is a constant}\}[/tex]
1) Using above formula:
[tex]f'(t)=2\times 2 t^{2-1}=4t[/tex]
[tex]g'(t)=3t^{3-1}+4\times 1 t^{1-1}=3t^2+4[/tex]
2) [tex]p(t) =2t^2(t^3+4t)[/tex]
Rewriting the formula by distributing the [tex]2t^2[/tex] term:
[tex]p(t) =2t^2.t^3+2t^2.4t=2t^5+8t^3[/tex]
[tex]p'(t) = 10t^4+24t^2[/tex]
3) By using answers of part (1):
[tex]f'(t).g'(t)=12t^3+16t[/tex]
[tex]p'(t) = 10t^4+24t^2[/tex]
Therefore it is False that [tex]p'(t) = f'(t).g'(t)[/tex]
4) [tex]q(t)=\dfrac{t^3+4t}{2t^2}[/tex]
Writing by distributing:
[tex]q(t)=\dfrac{t^3}{2t^2}+\dfrac{4t}{2t^2}\\\Rightarrow q(t) =\dfrac{t}{2}+\dfrac{2}{t}\\\Rightarrow q(t) =\dfrac{1}{2}t+2t^{-1}[/tex]
Using the formula:
[tex]q'(t)=\dfrac{1}{2}t^{1-1}+2\dfrac{-1}{t^2}\\\Rightarrow q'(t)=\dfrac{1}{2}-\dfrac{2}{t^2}[/tex]
(5)By using answers in part (1):
[tex]\dfrac{g'(t)}{f'(t)}=\dfrac{3t^2+4}{4t}=\dfrac{3}{4}t+\dfrac{1}t[/tex]
[tex]q'(t)=\dfrac{1}{2}-\dfrac{2}{t^2}[/tex]
Therefore, it is False that:
[tex]q'(t)=\dfrac{g'(t)}{f'(t)}[/tex]
how many different choices of car does a person have if a particular model comes in 11 colors and 4 styles
Answer:
44 options
Step-by-step explanation:
In order to solve this problem you would simply need to multiply the options specifics together. In this scenario, these are the color and style. Therefore since the individual can choose from 11 colors and 4 styles you simply multiply 11 by 4. This is because every single color chosen has 4 styles to choose from, meaning that all 4 styles also have 11 colors to choose from and vice versa.
11 * 4 = 44
Therefore, we see that an individual looking to buy a car has a total of 44 options to choose from.
help me solve please.
Please help I’m in a hurry
Answer:
I believe it is A 20,
however id wait for another answer to confirm lol
Factor completely.
16-49x^2=16−49x
2
=
(Can someone help me plz)
Solve and show your work.
12-[2 + 6 ÷ (10 - 2³)]
Answer:
7
Step-by-step explanation:
[tex]2^{3} = 8[/tex] Plug 8 in: 12 - [2 + 6 ÷ (10 - 8)]10 - 8 = 2Plug 2 in: 12 - [2 + 6 ÷ (2)]6 ÷ 2 = 3Plug 3 in: 12 - [2 + 3]2 + 3 = 5Plug 5 in: 12 - 512 - 5 = 7I hope this helps!
Help me please I’m timed
Answer:
a=3 b=4
Step-by-step explanation:
a on the power of 3 is 8
3 on the power of 4 is 81
multiply them and you get 648
Find 6/11/-3. Write in simplest form
Answer:
Bit confusing but I'll try my best.
Step-by-step explanation:
6/11 diving by -3.
-2/11.
PLZ HELP THIS IS DUE SOON!!!!!!! Divide. Round to the nearest hundredth if necessary.
To the nearest hundredth, 80.88÷8.425 is_______
Answer:
10
Step-by-step explanation:
when you divide 80.88 by 8.425 you get 9.6
and since youre rounding, you can round up 6 because its higher than 5
and your final answer should be 10.
hoped this helped! :)
Solve the logarithmic equation by writing in exponential form or by graphing.
log (7 − 2x) = −1
Answer:
10^-1 = 7 - 2x
Step-by-step explanation:
17. Create an equation that requires distribution on both sides to solve and has a solution of -2.
Answer:
googl really helps sorry
Express this number in scientific notation. 53,010,00053,010,000
Answer:
[tex]5.30100005301 * 10^{15}[/tex]
Pls help i dont understand :( will give Brainliest + 25 Points
Answer:
A
Step-by-step explanation:
plug the points into the slope formula
slope = (y2 - y1)/(x2 - x1) Then you get the slope of -0.5
(5 - -1))/(-6-6)
6/-12
-0.5
Plug a point in to the equation of y = -0.5x + b
-1 = -0.5(6) +b
2 = b
Angle b= 61, angle c=57, and =2x what does x =
Answer:
can you provide more information
Step-by-step explanation:
faud's model racing care drives an average speed of 3 feet per second. Fuad records the distance and times in a table. At this rate, how long will it take the car to travel 21 feet?
Answer:
well 3 × 7 = 21
Step-by-step explanation:
1. 0+3=3
2. 3+3=6
3. 6+3=9
4. 9+3=12
5. 12+3=15
6. 15+3=18
7. 18+3=21
So the answer is 7
Can anyone solve this please ?
The list price of a toolbox is $127.35. The chain discount is 10/5. What is the final net price?
Answer:
[tex]125.35[/tex]
Step-by-step explanation:
[tex]The \: final \: net \: price \:is \: 127.35 - \frac{10}{5} =\\ 127.35 - 2 = 125.35[/tex]
16) 56 is what percent of 40?
%
140
Step-by-step explanation:
56:40*100 =
(56*100):40 =
5600:40 = 140
$20.00, 10% tax, 15% tip
Urgently helpp!
Answer:
Tax=$2
15% before tax= $3
15% after= $3.30
Answer:
I know the tip but can't help with tax
Write a number that has a 5 that is 1/10 the value of the 5 in 5.348
Answer:
0.5
Step-by-step explanation:
5.348
5 is in ones place
5/10=0.5
A radio station requires DJs to play 2 commercials for every 14 songs they play. What is the unit rate of songs to commercials? songs The unit rate is 1 commercial
The correct answer for this question is that the unit rate is 5:1. We can work this out by simplifying down the 2 commercials to every 10 songs ration, so that 10:2 becomes 5:1. We can work this out by halving the original ratio to simplify it.
Can someone help please
in abook 5/8 of the pages have pictures on them given that 70 pages have at least one picture on them work out the total numb in the pages
Answer:
112 pages
Step-by-step explanation:
Setup a ratio of 5/8 to 70/x and use the butterfly method to solve the equation and get 112. (I know I'm late)
347 is what in expanded form
Answer:
300+40+7
Step-by-step explanation:
if you gave someone an apple if you had 500 apples and then another 2x apples and then 3x apples next 456x how much left man?????????????????????????
Answer:
31
Step-by-step explanation:
Hope this helps!!!
Segment addition pleas help in struggling
Answer:
x = -8
Step-by-step explanation:
using what's given, you can make the following equation:
3 + 2x + 22 = x + 17
3 + 22 + 2x - x = 17
25 + x = 17
x = 17 - 25
x = -8
Answer:
Step-by-step explanation:
3 + 2x + 22= x + 17
2x + 25 = x + 17
x + 25 = 17
x = -8
3 + 2(-8) + 22 = -8 + 17
25 - 16 = 9
9 = 9
Alex would like to buy one pack of colored pencils
Answer:
good for alex
Step-by-step explanation:
Shakira is baking cookies to put in packages for a fundraiser. Shakira has made 86 chocolate chip cookies and 42 sugar cookies.
Shakira wants to create identical packages of cookies to sell, and she must use all of the cookies.
What is the greatest number of identical packages that Shaquira can make?
Answer:
she can make 42 identical packages
Step-by-step explanation:
Answer:
Assuming there can only be 2 cookies per identical package, She can make 42 identical packages which contains 2 chocolate chip cookies and 1 sugar cookie.
86 / 2 = 43 chocolate chips cookies
42 / 1 = 42 sugar cookies
With the sugar cookies not having the capability to match the requirements we will assume for this answer that an "Identical Package" is composed of 2 chocolate chip cookies, and a single sugar cookie.
-I hope this is the answer you are looking for, please feel free to post your questions of brainly.com in the future.
Select the term that is suggested by the fugure
Answer:
im pretty sure its line segment if
Step-by-step explanation:
if its not im so sorry!!
determine the slope of the line given this two points (-2,4) and (1,6) with solution
Answer:
Slope = y2 - y1/x2 - x1
Slope = 6-4 / 1--2
Slope = 2/3
Step-by-step explanation:
hope that will help you
The slope of the line will be 2/3.
The formula for the slope will be:
= (y2 - y1) / (x2 - x1)
where,
y2 = 6
y1 = 4
x2 = 1
x1 = -2
We will slot the values into the equation which will be:
= (y2 - y1) / (x2 - x1)
= (6-4) / (1- -2)
= 2/(1+2)
= 2/3
Therefore, the slope is 2/3.
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Ray OJ bisects Angle LOK.
Measurement of Angle LOK = 82 degrees.
Solve for x.
Answer:
x = 14
Step-by-step explanation:
<LOJ = 3x
<KOJ = (2x + 12)°
<LOK = 82°
m<LOJ + m<KOJ = m<LOK (angle addition postulate)
3x + 2x + 12 = 82 (substitution)
5x + 12 = 82
5x = 82 - 12 (Subtraction property of equality)
5x = 70
x = 70/5 (division property of equality)
x = 14