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tekilochka [14]
3 years ago
6

You have an outdoor swimming pool that is 5.0 m wide and 12.0 m long. If weekly evaporation is 2.35 in, how many gallons of wate

r must be added to the pool each week (if it doesn't rain)?
Mathematics
1 answer:
kakasveta [241]3 years ago
7 0

Answer:

Water should be greater than 946.11 gallons per week to prevent the pool from drying.

Step-by-step explanation:

You have an outdoor swimming pool that is 5.0 m wide and 12.0 m long.

The height of water evaporated is = 2.35 inch

We will convert this to m.

1 inch = 0.0254 meter

So, 2.35 inch = 2.35\times0.0254=0.05969 meter

Now, volume of water in the pool = 5\times12\times0.05969=3.5814 cubic meter per week.

1 cubic meter = 264.172 gallons

So, 3.5814 cubic meter = 3.5814\times264.172=946.11gallons

Hence, the volume of the water that should be poured in the swimming pool should be greater than 946.11 gallons per week to prevent the pool from drying.

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an open rectangular cardboard box with a square base is to have a volume of 256cm^3. Find the dimensions of the box if the area
Anit [1.1K]
Let
x------> the length side of the square base of the box
y-------> the height of the box

we know that
volume of the box=b²*h
b=x
h=y
volume=256 cm³
so
256=x²*y------>y=256/x²-------->  equation 1

<span>The amount of material used is directly proportional to the surface area, so we will minimize the amount of material by minimizing the surface area.</span>

surface area of the cardboard=area of the base+perimeter of base*height
area of the base=x²
perimeter of the base=4*x
height=y
surface area=x²+4x*y-----> equation 2
substitute equation 1 in equation 2
SA=x²+4x*[256/x²]-----> SA=x²+1024/x

step 1 
find the first derivative of SA and equate to zero
2x+1024*(-1)/x²=0------> 2x=1024/x²----> x³=512--------> x=8 cm
y=256/x²------> y=256/8²-----> y=4 cm

the answer is
the length side of the square base of the box is 8 cm
the height of the box is 4 cm

5 0
3 years ago
Find each measure m&lt;1, m&lt;2,m&lt;3
Leno4ka [110]

Answer:

option 2.

m1 = 75    ,   m2 = 129   ,   m3 = 100

Step-by-step explanation:

with the rule that the internal angles of a triangle add up to 180 ° we can calculate the missing angles

x + 46 + 29 = 180

x = 180 - 46 -29

x = 105

a flat angle has 180 °

m1 + 105 = 180

m1 = 180 - 105

m1 = 75

46 + 54 + y = 180

y = 180 - 46 -54

y = 80

80 = z + 29

z = 80 - 29

z = 51

as they are two crossed lines the angle is reflected from the opposite side

with that principle and knowing that the angle of a turn is 360 °, if we subtract the 2 known angles and divide it by 2 we will obtain the missing angle (m2)

m2 * 2 = 360 - 51 * 2

m2 = 258/2

m2 = 129

m2 = 29 + m3

129 = 29 + m3

m3 = 129 - 29

m3 = 100

4 0
3 years ago
-4(2p + 5) + 8p = -11
sweet-ann [11.9K]

Answer:

There are no values of P to make it true

Step-by-step explanation:

6 0
2 years ago
The measure of angle 6 is 98°. What is the measure of angle 7?
otez555 [7]
Dude, it's impossible to solve without the pic
3 0
3 years ago
Read 2 more answers
Consider function f.
tekilochka [14]

Given:

The function is:

f(x)=\sqrt{7x-21}

To find:

The steps of finding the inverse function f^{-1}(x).

Solution:

We have,

f(x)=\sqrt{7x-21}

The steps of finding the inverse function are:

Step 1: Substitute f(x)=y.

y=\sqrt{7x-21}

Step 2: Interchange x and y.

x=\sqrt{7y-21}

Step 3: Taking square on both sides, we get

x^2=7y-21

Step 4: Adding 21 on both sides, we get

x^2+21=7y

Step 5: Divide both sides by 7.

\dfrac{1}{7}x^2+3=y

Step 6: Substitute y=f^{-1}(x).

\dfrac{1}{7}x^2+3=f^{-1}(x), where x\geq 0.

Therefore, the inverse of the given function is f^{-1}(x)=\dfrac{1}{7}x^2+3 and the arrangement of steps is shown above.

7 0
3 years ago
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