Find the stationary point on the curve y=3x^4 +1 and determine its nature

Answers

Answer 1

Answer: $y=3x^4+1\ny'=12x^3\n\n12x^3=0\nx=0\leftarrow \text{stationary point}\n\n\forall x\in(-\infty,0)\ y'<0\Rightarrow y\searrow\n\forall x\in(0,\infty)\ y'>0\Rightarrow y\nearrow\n\Downarrow\ny(0)=y_(min)$

$y_(min)=3\cdot0^4+1=1$

Hello!

The answer is:

$MinimumNumberOfWeeks\geq5$

Why?

First, we need to find the money that Jarred needs including the money that he has already saved.

$MoneyNeeded=1200-400=800$

So, Jarred needs $800.

If he earns $160 a week, we can find the minimum weeks he has to work in order to earn $800 following the next steps:

$WeeksToWork=(MoneyNeeded)/(WeeklyEarn)=(800)/(160)=5$

So, if he has to work at least 5 weeks to earn the total amount of money, it can be expressed by the following inequality:

$MinimumNumberOfWeeks\geq5$

Have a nice day!

Final answer:

Jarred has to save $800 more to buy the go-cart, that is $1,200 minus the $400 he already saved. If he earns $160 per week, the inequality representing the minimal number of weeks he has to work is: 160w >= 800. If we solve this inequality for w, we find that w must be equal or greater than 5 weeks.

Explanation:

This question is about solving inequalities. The cost of the go-cart is $1,200 and Jarred has already saved $400. That leaves him with $800 he still needs to save.

His job pays him $160 a week. Therefore, we can identify the inequality as 160w + 400 ≥ 1,200.

To determine the minimum number of weeks Jarred needs to work, we solve for w

Steps to solve:

Subtract 400 from both sides of the equation to isolate the term with w: 160w ≥ 800.
Divide both sides by 160 to solve for w: w ≥ 5.
As you cannot work a fraction of a week, the minimum number of weeks he needs to work is 5.

Learn more about inequalities here:

brainly.com/question/32625151

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A hot air balloon can hold 90,000 cubic feet of air. It is being inflated at a rate of 6,000 cubic feet per minute. The total cubic feet of air a(t) is a function of the in minutes t. a. Identify the independent and dependent variables. b. What values of the domain and range make sense for this situation? Explain. c. Write a function to represent the total amount of air. Then determine the total amount of air in 6 minutes.

Answers

a. The independent variable is the variable whose variation does not depend on that of another, it is often denoted by x.
In our case independent variable is time in minutes
The dependent variable is the volume of air in the balloon.

b] The domain of the of this situation is:
[0≤t≤15]
this is because t will take 15 minutes for the balloon to get filled.

The range of the situation will be:
[0≤a(t)≤90000]

c]The function that represents this situation is a linear function given by:
y=ax+b
where:
a=rate/slope
b= initial amount of air in the balloon=0
Thus our function will be:
a(t)=6000t

d]
The total amount of air in the balloon after 6 minutes will be given by:
from
a(t)=6000t
a(6)=6000(6)
a(6)=36000 cubic feet

In order for two triangles to be similar, all corresponding pairs of angles must be __________.adjacent
congruent
proportional
supplementary

Answers

Supplementary idk if it’s this cuz I just started learning this and the teacher said all triangles equal 180 degrees so I hope this helped

hree different stocks were ordered. The purchase prices were 8 ⅜ dollars, 12 ⅛ dollars and 15 ⅜ dollars.how much was paid for all three stocks?

Answers

when you add all of the totals together your total amount will be $35.875

8 3/8 + 12 1/8 + 15 3/8

8 + 12 + 15 = 35
3/8 + 1/8 + 3/8 = 7/8

total = 35 7/8

-5v-6=3v+10 i really hate math but i need help

Answers

OK. We could have gotten along nicely without the comment.

-5v - 6 = 3v + 10

I think what you're trying to find is the number that ' v ' must be
in order to make the equation a true statement. That number
is called the 'solution' of the equation.

To find it, you have to massage and manipulate the equation around
until you have ' v ' and nothing else on one side. You can do anything
you want to a whole side of the equation, but whatever you do to one
side, you must immediately do to the other side. Here's one way you
could go about it:

-5v - 6 = 3v + 10

Add 5v to each side: -6 = 8v + 10

Subtract 10 from each side: -16 = 8v

Divide each side by 8 : -2 = v

Now, was that so painful ?

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