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2 years ago

Uuuuubhbjvykuhctkkhygtcykxmhfxg

Mathematics

1 answer:

vova2212 [387]2 years ago

7 0

The surface area of the spherical ball is given as follows:

$635.04\pi$ yd².

<h3>What is the surface area of a sphere?</h3>

The surface area of a sphere of radius r is given as follows:

$S = 4\pi r^2$ .

In this problem, the diameter is of 25.2 yd, hence the radius is given by:

r = 0.5 x 25.2 yd = 12.6 yd.

Then the surface area in yd² is:

$S = 4\pi (12.6)^2 = 635.04\pi$ .

More can be learned about the surface area of a sphere at brainly.com/question/21207980

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Which scale you would use on the coordinate plane to plot each set of points? A Select . (1.-6).(-7,-8), (-3, 7), (0.9) • (-20,

antoniya [11.8K]

Answer:qjs

Step-by-step explanation:

X= -7 to 1

Y= -8 to 9

X= -40 to 20

Y= -30 to 10

4 0

2 years ago

Calculate the perimeter of a triangle with the following measurements: 200 mm, 40 cm and 400 dm Please HELP

melisa1 [442]

Answer:

640 dm

Step-by-step explanation:

200+40+400=640dm

5 0

3 years ago

A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 6 L/min. The solution is mixed and drain

MissTica

Answer:

(a) 60 kg; (b) 21.6 kg; (c) 0 kg/L

Step-by-step explanation:

(a) Initial amount of salt in tank

The tank initially contains 60 kg of salt.

(b) Amount of salt after 4.5 h

$\text{Let A = mass of salt after t min}\\\text{and }r_{i} = \text{rate of salt coming into tank}\\\text{and }r_{0} =\text{rate of salt going out of tank}$

(i) Set up an expression for the rate of change of salt concentration.

$\dfrac{\text{d}A}{\text{d}t} = r_{i} - r_{o}\\\\\text{The fresh water is entering with no salt, so}\\ r_{i} = 0\\r_{o} = \dfrac{\text{3 L}}{\text{1 min}} \times \dfrac {A\text{ kg}}{\text{1000 L}} =\dfrac{3A}{1000}\text{ kg/min}\\\\\dfrac{\text{d}A}{\text{d}t} = -0.003A \text{ kg/min}$

(ii) Integrate the expression

$\dfrac{\text{d}A}{\text{d}t} = -0.003A\\\\\dfrac{\text{d}A}{A} = -0.003\text{d}t\\\\\int \dfrac{\text{d}A}{A} = -\int 0.003\text{d}t\\\\\ln A = -0.003t + C$

(iii) Find the constant of integration

$\ln A = -0.003t + C\\\text{At t = 0, A = 60 kg/1000 L = 0.060 kg/L} \\\ln (0.060) = -0.003\times0 + C\\C = \ln(0.060)$

(iv) Solve for A as a function of time.

$\text{The integrated rate expression is}\\\ln A = -0.003t + \ln(0.060)\\\text{Solve for } A\\A = 0.060e^{-0.003t}$

(v) Calculate the amount of salt after 4.5 h

a. Convert hours to minutes

$\text{Time} = \text{4.5 h} \times \dfrac{\text{60 min}}{\text{1h}} = \text{270 min}$

b.Calculate the concentration

$A = 0.060e^{-0.003t} = 0.060e^{-0.003\times270} = 0.060e^{-0.81} = 0.060 \times 0.445 = \text{0.0267 kg/L}$

c. Calculate the volume

The tank has been filling at 6 L/min and draining at 3 L/min, so it is filling at a net rate of 3 L/min.

The volume added in 4.5 h is

$\text{Volume added} = \text{270 min} \times \dfrac{\text{3 L}}{\text{1 min}} = \text{810 L}$

Total volume in tank = 1000 L + 810 L = 1810 L

d. Calculate the mass of salt in the tank

$\text{Mass of salt in tank } = \text{1810 L} \times \dfrac{\text{0.0267 kg}}{\text{1 L}} = \textbf{21.6 kg}$

(c) Concentration at infinite time

$\text{As t $\longrightarrow \, -\infty,\, e^{-\infty} \longrightarrow \, 0$, so A $\longrightarrow \, 0$.}$

This makes sense, because the salt is continuously being flushed out by the fresh water coming in.

The graph below shows how the concentration of salt varies with time.

3 0

3 years ago

A cuboid has a square base.

padilas [110]

The length of one side of the square base is 8.5 centimeters.

<u>Given the following data:</u>

Volume of cuboid = 867 cm

Height = 12 cm

To find the length of one side of the square base:

Mathematically, the volume of a cuboid is given by the formula:

$Volume = Base \; area$ × $Height$

Substituting the given values, we have:

$867 = Base \; area$ × $12$

$Base\;area = \frac{867}{12}$

Base area = 72.225 $cm^2$

Now, we can find the length by using the formula:

$Area \;of\;a \;square = length^2$

$72.25 = length^2$

$Length = \sqrt{72.25}$

<em>Length</em><em> = </em><em>8.5 centimeters</em>.

Therefore, the length of one side of the square base is 8.5 centimeters.

Find more information: brainly.com/question/11037225

8 0

2 years ago

Find all possible answers and check your solutions.Solve equation.

Bond [772]

A.
lxl=7
x=7 x=-7 (Take two cases, one as the others side negative and the other as positive)
B.
l2xl=32
2x=32 2x=-32
x=16 x=-16
C.
lx+7l=10
x+7=10 x+7=-10
x=3 x=-17
D.
lxl=53.1
x=53.1 x=-53.1

4 0

3 years ago

Read 2 more answers