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3 years ago

Here is a linear equation: y = 1/4x +5/4

Mathematics

2 answers:

Sergeeva-Olga [200]3 years ago

8 0

Answer:

yes

Step-by-step explanation:

docker41 [41]3 years ago

3 0

Step-by-step explanation:

(1,1.5) is the solution but (12,4) is not the solution of given equation.

1.5=1/4×1+5/4(which is true)

4=1/4×12+5/4(which is false)

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What is the common ratio of 128,320,800,2000

Delicious77 [7]

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8 0

3 years ago

The department of transportation is repaving 3 1/3 miles of the interstate. If the workers can repave 2/3 of a mile per day, how

Crazy boy [7]

Answer:

5 days

Step-by-step explanation:

(3 1/3 miles)/(2/3 miles/day) = (10/3)/(2/3) days = 10/2 days = 5 days

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time = distance / speed

8 0

3 years ago

Write the integral in one variable to find the volume of the solid obtained by rotating the first-quadrant region bounded by y =

Dovator [93]

Answer:

V = π ∫₀² (y² − 8y + 6√(2y)) dy

V = π ∫₀² (6x − 5x² + x³) dx

Step-by-step explanation:

y₁ = 0.5x²

y₂ = x

First, find the intersections of the curves.

0.5x² = x

x² = 2x

x² − 2x = 0

x (x − 2) = 0

x = 0 or x = 2

So the points of intersection are (0, 0) and (2, 2).

When we revolve this region about the line x = 3, we get a hollow shape that looks like an upside-down funnel, or a volcano.

One option is to use washer method to find the volume, by cutting a thin horizontal slice of thickness dy, inner radius 3−x₁ = 3−√(2y), and outer radius of 3−x₂ = 3−y.

V = ∫₀² π [(3−y)² − (3−√(2y))²] dy

V = ∫₀² π (9 − 6y + y² − 9 + 6√(2y) − 2y) dy

V = π ∫₀² (y² − 8y + 6√(2y)) dy

Another option is to use shell method to find the volume, by cutting a thin vertical slice of thickness dx, radius 3−x, and height y₂−y₁ = x−0.5x².

V = ∫₀² 2π (3 − x) (x − 0.5x²) dx

V = ∫₀² 2π (3x − 1.5x² − x² + 0.5x³) dx

V = ∫₀² 2π (3x − 2.5x² + 0.5x³) dx

V = π ∫₀² (6x − 5x² + x³) dx

The second option is arguably easier to evaluate, but either one will get you the same answer (V = 8π/3).

7 0

3 years ago

Help me pls thank you alot!

damaskus [11]

Your answer will be -1/7

4 0

2 years ago

Read 2 more answers

Total world consumption of iron was approximately 900 million tons in 1993. If consumption had increased by 2.5% each year and t

Lilit [14]

Step-by-step explanation:

We can model the annual consumption of iron by the equation

c = 900 million tons x $1.025^n$ , where

n is the number of years after 1993 and

c is the consumption for that year.

An estimate for the total consumption of iron can now be obtained by integrating this equation with respect to a dummy variable, x from 0 to n.

$C = 900*10^6* \int\limits^n_0 {1.025^x} \, dx$

This equation simplifies to

C = 900 million tons x (1.025^n - 1) / ln(1.025), where

x is a dummy variable and

C is the total consumption of iron n years after 1993.

Let R be the amount of iron remaining at n years after 1993, so

R = 480 billion tons - C

R = 480 billion tons - 900 million tons x (1.025^n - 1) / ln(1.025)

We need to find the value of n when R is 0, so

0 = 480 billion tons - 900 million tons x (1.025^n - 1) / ln(1.025)

Simplify this equation to obtain

n = 107.4

So the iron will run out in the year 1993 + 107 = 2100

6 0

2 years ago