Determine the dimensions of the rectangle of largest area that can be inscribed in a semicircle of radius 4
Answers
Answer:
The length and width that maximize the area are:
W = 2*√8
L = 2*√8
Step-by-step explanation:
We want to find the largest area of a rectangle inscribed in a semicircle of radius 4.
Remember that the area of a rectangle of length L and width W, is:
A = L*W
You can see the image below to see how i will define the length and the width:
L = 2*x'
W = 2*y'
Where we have the relation:
4 = √(x'^2 + y'^2)
16 = x'^2 + y'^2
Now we can isolate one of the variables, for example, x'
16 - y'^2 = x^'2
√(16 - y'^2) = x'
Then we can write:
W = 2*y'
L = 2*√(16 - y'^2)
Then the area equation is:
A = 2*y'*2*√(16 - y'^2)
A = 4*y'*√(16 - y'^2)
If A > 1, like in our case, maximizing A is the same as maximizing A^2
Then if que square both sides:
A^2 = (4*y'*√(16 - y'^2))^2
= 16*(y'^2)*(16 - y'^2)
= 16*(y'^2)*16 - 16*y'^4
= 256*(y'^2) - 16*y'^4
Now we can define:
u = y'^2
then the equation that we want to maximize is:
f(u) = 256*u - 16*u^2
to find the maximum, we need to evaluate in the zero of the derivative:
f'(u) = 256 - 2*16*u = 0
u = -256/(-2*16) = 8
Then we have:
u = y'^2 = 8
solving for y'
y' = √8
And we know that:
x' = √(16 - y'^2) = √(16 - (√8)^2) = √8
And the dimensions was:
W = 2*y' = 2*√8
L = 2*y' = 2*√8
These are the dimensions that maximize the area.
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A number increased by seven is 15
B. 140 cm
C. 1,225 cm
D. 70 cm
Answers
Perimeter = 4 * S
Perimeter = 4 * 35 cm
Perimeter = 140 cm.
So the perimeter of a rhombus-shaped street sign that has a 35-cm side is equal to (B) 140 cm.
Answers
please give me brainliest! thanks
Answers
Answer:
The answer is
"She can read 216 words per minute because 72 divided by One-third is equal to 216."
Step-by-step explanation:
Given the statement
Susan can read 72 words in One-third of a minute ....pause
Whats is one-third of a minute
it is expressed as 1/3*60=20sec
so Susan can read 72 words in 20 second
this means that in a minute she can read
72+72+72 words= 216 word since 20sec*3 is 1 minute
alternatively
we then multiply 73 with the inverse of the denominator
=
=216 words
Answer:
is c then
Step-by-step explanation:
Answers
8 (2 + y) - 2y = 22
16 + 8y - 2y = 22
6y = 22 - 16
6y = 6
y = 1
And x = 2 + y = 2 + 1 = 3
Therefore, in (x, y) format . . . (3, 1)
Answer:answer is 3,1 on plato
Step-by-step explanation:trust me I literally just took it and it says correct
Discount Rate of 9%, with terms of 2/10 EOM, and FOB Shipping Point. The
seller has agreed to prepay the shipping charge of $80, which is not included in the
invoice amount. The invoice from the manufacturer is dated July 26.
Determine:
A)
By what date does Melissa have to pay in order to be able to take the cash
discount?
B)
What is the payment amount assuming that Melissa pays before the end of
the discount period?
Answers
Answer:
A) 10th of August
B) $1780.03
Step-by-step explanation:
A) From the payment terms of 2/10 EOM, Melissa is to receive a 2% discount if she pays within 10 days from the end of the month
From the date on the invoice, July 26, the date at which Melissa has to pay to take the cash discount is before the 10th of August
B) The payment amount will be 2% off the original payment amount
The total cost of the four new gas mowers less the trade discount = 499 × 4 × (100 - 9)/100 =$1816.36
The 2% discount will then be $1816.36 × (100 - 2)/100 = $1780.03
The payment amount assuming Melissa pays before the end of the discount period = $1780.03.
Answers
Answer:
4/3c^4 -it wont let me put it as it shows on your screen but the 4 is on top and under the line is 3c^4,
Step-by-step explanation:
Cancel the common factor of c^3 and z^7 -im not sure if this is what you were trying to get but its a answer-