Answer:
y=sin(ln(x))
Step-by-step explanation:
First, we have to order the terms as follows and express y' as dy / dx:
Then, we have to integrate
with this solution after integration:
Then, we have to reorder
and applied Sin function on both sides
To define the value of C, we use the known point y(1)=0 and replace in the equation
The function that proves that differential equation is
Esecially the problem is 3x +x < 160
To find this out we first need to combine like terms
4x<160
Then get rid of the coefficient. In this problem, we divide by 4
x<40
So Rachel has to be less then 40, and Stephanie has to be less than 120.
Any questions?
Answer:
- 8
Step-by-step explanation:
Note that 
is the slope of the tangent at x = a
Differentiate using the power rule
(a
) = na
Given
y = 3x² - 2x + 5, then
= 6x - 2
x = - 1 : = 6(- 1) - 2 = - 6 - 2 = - 8
<span>A rancher wants to create two rectangular pens, as shown in the attached figure
Let the side parallel to the </span><span>existing fence line = y
And the sides which is perpendicular to </span><span>existing fence line = x
</span><span>The pens need to have a total area of 972 square feet
</span>∴ x y = 972
∴ y = 972/x
Let the length of needed fence = L
∴ L = y + 3x
substituting with the value of y
∴
differentiating the length with respect to x and equating with zero
∴
solve for x
∴ x = 18
substituting to find y
∴ y = 54
<span>The dimensions should be used to minimize the amount of fence used
is 18 , 54 feet </span>
Answers:
What is the ratio? 120:2
What is the unit rate? 60:1
What is the rate? 60 jumping jacks per minute
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Further Explanation:
To find the ratio of jumping jacks to minutes, you just write the two values 120 and 2 separated by a colon. That's how we get 120:2 as our first answer.
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Once we have 120:2, we divide both parts by 2 to get 60:1
120/2 = 60
2/2 = 1
The reason why we do this is so that the "2 minutes" turns into "1 minute". A unit ratio has the time value in unit increments so we can see how many jumping jacks Samuel can do. Writing "60:1" means "60 jumping jacks in 1 minute"
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Saying "60 jumping jacks in 1 minute" is the same as saying "60 jumping jacks per minute", which is similar to a car's speed of something like 60 miles per hour. The unit "X per Y" is the template for speed, where X is the number of items you get done and Y is the unit of time. In this case, X = 60 jumping jacks and Y = 1 minute.
