Answer:
Step-by-step explanation:
We have the equations
4x + 3y = 18 where x = the side of the square and y = the side of the triangle
For the areas:
A = x^2 + √3y/2* y/2
A = x^2 + √3y^2/4
From the first equation x = (18 - 3y)/4
So substituting in the area equation:
A = [ (18 - 3y)/4]^2 + √3y^2/4
A = (18 - 3y)^2 / 16 + √3y^2/4
Now for maximum / minimum area the derivative = 0 so we have
A' = 1/16 * 2(18 - 3y) * -3 + 1/4 * 2√3 y = 0
-3/8 (18 - 3y) + √3 y /2 = 0
-27/4 + 9y/8 + √3y /2 = 0
-54 + 9y + 4√3y = 0
y = 54 / 15.93
= 3.39 metres
So x = (18-3(3.39) / 4 = 1.96.
This is a minimum value for x.
So the total length of wire the square for minimum total area is 4 * 1.96
= 7.84 m
There is no maximum area as the equation for the total area is a quadratic with a positive leading coefficient.
Answer:
cubic units
Step-by-step explanation:
We are given that a region bounded by a curves 
x=4 and about y=5
We have to find the value of volume of the resulting solid
To find the volume of resulting solid we are using cylinder method
Substitute the values of x then we get
y-7=2 and y-7=-2
y=7+2=9 and y=-2+7=5
Radius of cylinder =r=y-5
and height =h=
Using cylinder method and integrate along y -axis from y=5 to y=9
Volume =
volume=
Volume =![2\pi[-\frac{y^4}{4}+19\frac{y^3}{3}-115\frac{y^2}{2}+225y]^9_5](https://tex.z-dn.net/?f=2%5Cpi%5B-%5Cfrac%7By%5E4%7D%7B4%7D%2B19%5Cfrac%7By%5E3%7D%7B3%7D-115%5Cfrac%7By%5E2%7D%7B2%7D%2B225y%5D%5E9_5)
Volume =![2\pi[-\frac{6561}{4}+\frac{625}{4}+19(\frac{729-125}{3})-115(\frac{81-25}{2})+225(9-5)]](https://tex.z-dn.net/?f=2%5Cpi%5B-%5Cfrac%7B6561%7D%7B4%7D%2B%5Cfrac%7B625%7D%7B4%7D%2B19%28%5Cfrac%7B729-125%7D%7B3%7D%29-115%28%5Cfrac%7B81-25%7D%7B2%7D%29%2B225%289-5%29%5D)
Volume=
Volume =
Volume =
Hence, volume of resulting solid = cubic units
Answer:
B
Step-by-step explanation:
The distance between the school and the library is less. Then the library is closer to school.
<h3>What is dilation?</h3>
Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
There is no effect of dilation on the angle.
On one map of a town, the scale from the town to the map is 12mi:3cm.
The school is 2.5cm from the grocery store on this map.
Then the distance between the school and the grocery store will be
⇒ (12 / 3) x 2.5
⇒ 10 miles
On a different map of the same town, the scale from the town to the make is 12mi: 2cm.
The school is 1.5cm from the library on that map.
Then the distance between the school and the library will be
⇒ (12 / 2) x 1.5
⇒ 9 miles
Thus, the distance between the school and the library is less.
Then the library is closer to school.
More about the dilation link is given below.
brainly.com/question/2856466
#SPJ1
Answer:
Step-by-step explanation:
They both (36 and 45) go into 9. Divide them both by 9.
