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2 years ago

5(0.04y-0.08) >3(0.2y-0.05-0.4y)

Mathematics

1 answer:

MAXImum [283]2 years ago

3 0

0.08(y + -1) + 0.12y = 0.14 + -0.05(10)

Reorder the terms:

0.08(-1 + y) + 0.12y = 0.14 + -0.05(10)

(-1 * 0.08 + y * 0.08) + 0.12y = 0.14 + -0.05(10)

(-0.08 + 0.08y) + 0.12y = 0.14 + -0.05(10)

Combine like terms: 0.08y + 0.12y = 0.2y

-0.08 + 0.2y = 0.14 + -0.05(10)

Multiply -0.05 * 10

-0.08 + 0.2y = 0.14 + -0.5

Combine like terms: 0.14 + -0.5 = -0.36

-0.08 + 0.2y = -0.36

Solving

-0.08 + 0.2y = -0.36

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '0.08' to each side of the equation.

-0.08 + 0.08 + 0.2y = -0.36 + 0.08

Combine like terms: -0.08 + 0.08 = 0.00

0.00 + 0.2y = -0.36 + 0.08

0.2y = -0.36 + 0.08

Combine like terms: -0.36 + 0.08 = -0.28

0.2y = -0.28

Divide each side by '0.2'.

y = -1.4

Simplifying

y = -1.4

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For a display, identical cubic boxes are stacked in square layers. Each layer consists of cubic boxes arranged in rows that form

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Answer:

285 boxes are in the display

Step-by-step explanation:

Given data

top layer box = 1

last row box = 81

to find out

how many box

solution

we know that every row is a square so that if the bottom layer has 81 squares it mean this is 9² and every row has one lesser box

so that next row will have 8^2 and than 7² and so on till 1²

so we can say that cubes in the rows as that

Sum of all Squares = 9² + 8² +..........+ 1²

Sum of Squares positive Consecutive Integers formula are

Sum of Squares of Consecutive Integers = (1/6)(n)(n+1)(2n+1)

here n = 9 so equation will be

Sum of Squares of Consecutive Integers = (1/6) × (9) × (9+1) × (2×9+1)

Sum of Squares of Consecutive Integers = 285

so 285 boxes are in the display

7 0

2 years ago

10 x 3 tens - unit form and standard form

vfiekz [6]

10X3 tens in unit form is written:
10*3 tens = 30 tens = 300 units

10X3 tens in standard form:
10 x 3 tens = 10 x 30 = 300

6 0

2 years ago

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A map of a rectangular park has a length of 4 inches and a width of 6 inches. It uses a scale of 1 inch for every 30 Miles. What

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Answer:

The actual area 21600 miles²

Step-by-step explanation:

* Lets explain how to solve the problem

- A drawing that shows a real object with accurate sizes reduced or

enlarged by a certain amount called the scale

- Drawing scale is a ratio between the drawing length and the

actual length

- To find the actual dimensions from the drawing dimensions use the

scale drawing

* Lets solve the problem

- A map of a rectangular park has a length of 4 inches and a width

of 6 inches

∴ The drawing dimensions are:

# length = 4 inches

# width = 6 inches

- The scale of the map is 1 inch foe every 30 miles

∴ The scale drawing is 1 : 30

- To find the actual area find the actual dimensions

∵ The scale drawing is 1 : 30

∵ The length = 4 inches and the width = 6 inches

- By using cross multiplication

∴ 1 : 30

4 : actual length

6 : actual width

∴ Actual length = (4 × 30)/1 = 120

∴ Actual length = 120 miles

∴ Actual width = (6 × 30)/1 = 180

∴ Actual Width = 180 miles

∴ The actual dimensions are 120 miles and 180 miles

∵ The area of any rectangle = length × width

∴ The actual area = 120 × 180 = 21600

∴ The actual area 21600 miles²

5 0

2 years ago

A common assumption in modeling drug assimilation is that the blood volume in a person is a single compartment that behaves like

mixas84 [53]

Answer:

a) $\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) $\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) the steady state mass of the drug is 2000 mg

d) t ≅ 153.51 minutes

Step-by-step explanation:

From the given information;

At time t= 0

an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 500

The inflow rate is 0.06 L/min.

Assume the drug is quickly mixed thoroughly in the blood and that the volume of blood remains constant.

The objective of the question is to calculate the following :

a) Write an initial value problem that models the mass of the drug in the blood for t ≥ 0.

From above information given :

$Rate _{(in)}= 500 \ mg/L \times 0.06 \ L/min = 30 mg/min$

$Rate _{(out)}=\dfrac{x}{4} \ mg/L \times 0.06 \ L/min = 0.015x \ mg/min$

Therefore;

$\dfrac{dx}{dt} = Rate_{(in)} - Rate_{(out)}$

with respect to x(0) = 0

$\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) Solve the initial value problem and graph both the mass of the drug and the concentration of the drug.

$\dfrac{dx}{dt} = -0.015(x - 2000)$

$\dfrac{dx}{(x - 2000)} = -0.015 \times dt$

By Using Integration Method:

$ln(x - 2000) = -0.015t + C$

$x -2000 = Ce^{(-0.015t)$

$x = 2000 + Ce^{(-0.015t)}$

However; if x(0) = 0 ;

Then

C = -2000

Therefore

$\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) What is the steady-state mass of the drug in the blood?

the steady-state mass of the drug in the blood when t = infinity

$\mathbf{x = 2000 - 2000e^{-0.015 \times \infty }}$

x = 2000 - 0

x = 2000

Thus; the steady state mass of the drug is 2000 mg

d) After how many minutes does the drug mass reach 90% of its stead-state level?

After 90% of its steady state level; the mas of the drug is 90% × 2000

= 0.9 × 2000

= 1800

Hence;

$\mathbf{1800 = 2000 - 2000e^{(-0.015t)}}$

$0.1 = e^{(-0.015t)$

$ln(0.1) = -0.015t$

$t = -\dfrac{In(0.1)}{0.015}$

t = 153.5056729

t ≅ 153.51 minutes

4 0

1 year ago

A glass bead has the shape of a rectangular prism with a smaller rectangular prism removed. What is the volume of the glass that

olganol [36]

The volume of the removed portion is 35 cm³.

Step-by-step explanation:

Given,

The length× width× height (L×B×H) of the outer part = 3 cm×3 cm×7 cm

The length× width× height (l×b×h) of the inner part = 2 cm×2 cm×7 cm

To find the volume of the removed portion.

Formula

The volume of the removed portion = volume of outer part - volume of inner part

Volume of rectangular prism = l×b×h

Now,

Volume of outer part = 3×3×7 cm³ = 63 cm³

Volume of inner part = 2×2×7 cm³ = 28 cm³

Hence,

The volume of the removed portion = 63-28 cm³ = 35 cm³

4 0

2 years ago

Read 2 more answers