1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
maks197457 [2]
3 years ago
13

Let r(t)=⟨t2,1−t,4t⟩. calculate the derivative of r(t)⋅a(t) at t=5, assuming that a(5)=⟨−4,4,−5⟩ and a′(5)=⟨−5,9,3⟩

Mathematics
1 answer:
erastovalidia [21]3 years ago
6 0
\mathbf r(t)=\langle t^2,1-t,4t\rangle
\implies\mathbf r'(t)=\langle 2t,-1,4\rangle

\dfrac{\mathrm d(\mathbf r(t)\cdot\mathbf a(t))}{\mathrm dt}\bigg|_{t=5}=\mathbf r'(5)\cdot\mathbf a(5)+\mathbf r(5)\cdot\mathbf a'(5)
=\langle10,-1,4\rangle\cdot\langle-4,4,-5\rangle+\langle25,-4,20\rangle\cdot\langle-5,9,3\rangle
=(-40-4-20)+(-125-36+60)
=-165
You might be interested in
Reduce to simplest form​
lisov135 [29]

Answer: 4/15

Step-by-step explanation:

-1/3 - -3/5

Two negative signs become positive so it's

-1/3+3/5

Taking the LCM as 15,

-1/3= -5/15

3/5= 9/15

-5/15 + 9/15

= (-5+9)/15

= (9-5)/15 ( just changing the order without changing the sign)

= 4/15

This is the simplest form

(If you need it in decimal form is 0.26666... or 0.267)

Hope it helps

3 0
3 years ago
Read 2 more answers
find rodrigos percent increase or decrease in sales each week. week 1, is 17 wwek 2, is 25 week 3, is 18 and week 4, is 27. his
sveticcg [70]
<span>Answer: The multiplication factor of increase should be inverse of the multiplication factor of decrease.

    e.g. Say you have a number 100. You increase it by 25%. The multiplication factor is 5/4 i.e. when you multiply 100 by 5/4, you get 100*5/4 = 125. This is 25% more than 100. Now you want to decrease it by a certain % such that you get 100 back. Basically, 100*5/4 * x = 100 So x = 4/5 (inverse of 5/4) Hence, you decrease by 20% (the multiplication factor of 20% is 4/5) or Use this formula: cumulative % change = a + b + ab/100 You want the cumulative change to be 0. a + b + ab/100 = 0 If you know that you are increasing by 25% and want to find the % by which you should decrease to get the same number, 25 + b + 25b/100 = 0 5b/4 = -25 b = -20 So you need to decrease (hence you get the -ve sign) by 20%.</span>
3 0
3 years ago
What is the answer to 5.06 by 47.058
IRINA_888 [86]
If you multiply 5.06 by 47.058 you will get  238.11348
3 0
3 years ago
A certain cold remedy has an 88% rate of success of reducing symptoms within 24 hours. Find the probability that in a random sam
Hitman42 [59]

Answer:

The probability of cured people in who took the remedy is 8/9.

Step-by-step explanation:

Success rate of the cold remedy = 88%

The number of people who took the remedy = 45

Now, 88% of 45 = \frac{88}{100}  \times 45 = 39.6

and 39.6 ≈ 40

So, out of 45 people, the remedy worked on total 40 people.

Now, let E: Event of people being cured by cold remedy

Favorable outcomes = 40

\textrm{Probability of Event E}  = \frac{\textrm{Total number of favorable outcomes}}{\textrm{Total outcomes}}

or, \textrm{Probability of people getting cured}  = \frac{\textrm{40}}{\textrm{45}}  = \frac{8}{9}

Hence, the probability of cured people in who took the remedy is 8/9.

3 0
3 years ago
Can someone please tell me how to show work for this so I can get an answer I din't understand this!!! :,(
pav-90 [236]

Answer:

100% I looked it up and red an article

3 0
2 years ago
Read 2 more answers
Other questions:
  • Write in slope-intercept form of the equation of the line through the given point. Through: (-3,-3) and (4,0)
    13·2 answers
  • 9. Solve the equation for x.<br> 3x + y = 2<br> Z
    5·1 answer
  • If 3/4 of a pie is being split between 6 people, how big of a slice would each person get?
    11·1 answer
  • Simplify.
    14·1 answer
  • Subtract the polynomials (7.8x - 3.4y + z) and (-9.2x + 4.8y - 2.1z), then place the answer in the proper location on the grid.
    9·1 answer
  • A Broadway theater has 600 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $50, main seats fo
    12·1 answer
  • Please help me with this problem will give branlyiest.
    10·1 answer
  • The sum of two numbers is 10. Their difference is 6. What are the two numbers? ​
    14·2 answers
  • A six dice is rolled 150 times.Which of the following best describes how many times it is likely to land on a odd number
    15·1 answer
  • 50 points!!
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!