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2 years ago

Translate the following verbal expression into an algebraic expression.

Mathematics

1 answer:

poizon [28]2 years ago

5 0

Answer:

3 * (x + 7)

Step-by-step explanation:

Mark number as x

Then the sum of a number and seven is x + 7

Three times x + 7 can be written as

3 * (x + 7)

Parentheses mean that we first add x and 7 and then multiply their sum by 3

Alternatively you can write it as 3x + 21, since

3 * (x + 7) = 3 * x + 3 * 7 = 3x + 21

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Given the Homogeneous equation x^2ydy+xy^2dx=0, use y=ux, u=y/x and dy=udx+xdu to solve the differential equation. Solve for y.

scZoUnD [109]

Answer:

$y=\frac{C}{x}$ .

Step-by-step explanation:

Given homogeneous equation

$x^2ydy+xy^2dx=0$

$\frac{\mathrm{d}y}{\mathrm{d}x}=-\frac{xy^2}{x^2y}$

Substitute y=ux , $u=\frac{y}{x}$

$\frac{\mathrm{d}y}{\mathrm{d}x}=-\frac{y}{x}$

Now,

$u+x\frac{\mathrm{d}u}{\mathrm{d}x}=\frac{\mathrm{d}y}{\mathrm{d}x}$

$u+x\frac{\mathrm{d}u}{\mathrm{d}x}=-u$

$\frac{\mathrm{d}u}{\mathrm{d}x}=-2u$

$\frac{du}{u}=-\frac{dx}{x}$

Integrating both side we get

lnu=-2lnx+lnC

Where lnC= integration constant

$lnu+ln{x}^2=lnC$

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Cancel ln on both side

$ux^2=C$

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xy=C

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2 years ago

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2 years ago

Depreciation is the decrease or loss in value of an item due to age, wear, or market conditions. We usually consider depreciatio

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Answer:The value of the bulldozer after 3 years is $121950

Step-by-step explanation:

We would apply the straight line depreciation method. In this method, the value of the asset(bulldozer) is reduced linearly over its useful life until it reaches its salvage value. The formula is expressed as

Annual depreciation expense =

(Cost of the asset - salvage value)/useful life of the asset.

From the given information,

Useful life = 23 years

Salvage value of the bulldozer = $14950

Cost of the new bulldozer is $138000

Therefore

Annual depreciation = (138000 - 14950)/ 23 = $5350

The value of the bulldozer at any point would be V. Therefore

5350 = (138000 - V)/ t

5350t = 138000 - V

V = 138000 - 5350t

The value of the bulldozer after 3 years would be

V = 138000 - 5350×3 = $121950

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3 years ago

Steve puts an 18-foot ladder against his house. The ladder reaches a height of 15 feet on the house. How far is the bottom of th

krek1111 [17]

Answer:

$3 \sqrt{11}$

Step-by-step explanation:

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${a}^{2} + {b}^{2} = c {}^{2}$