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3 years ago

Write an equation (y=mx+b) through the points: (3,-1) and (8,9)

Mathematics

1 answer:

Advocard [28]3 years ago

4 0

Answer:

y=2x-7

Step-by-step explanation:

m==2

y=mx+b

9=16-7

y=2x-7

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3 years ago

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3 years ago

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If asphalt pavement costs $0.70 per square foot, find the cost to pave the circular How much does it cost to pave this road?

Hunter-Best [27]

Answer:

Cost to pave the road = $4257

Step-by-step explanation:

Area of the pavement = Area of the outer circle - Area of the internal circle

Area of the outer circle = πr²

= π(55)²

= 3025π square feet

Area of the inner circle = π(33)²

= 1089π square feet

Area of the pavement = 3025π - 1089π

= 1936π

= 6082.12 square feet

Cost of pavement = $0.70 per square feet

Therefore, cost of 6082.12 square feet = 6082.12 × 0.70

= 4257.49

≈ $4257

Cost to pave the road = $4257

5 0

2 years ago

I guess I'm lacking in differential equations. I couldn't solve this question. Can you help me?

Sonja [21]

Answer:

See Explanation.

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Reciprocals

Algebra II

Log/Ln Property: $ln(\frac{a}{b} ) = ln(a) - ln(b)$

Calculus

Derivatives

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Chain Rule: $\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Derivative of Ln: $\frac{d}{dx} [ln(u)] = \frac{u'}{u}$

Step-by-step explanation:

Step 1: Define

$ln(\frac{2x-1}{x-1} )=t$

Step 2: Differentiate

Rewrite: $t = ln(\frac{2x-1}{x-1})$
Rewrite [Ln Properties]: $t = ln(2x-1) - ln(x - 1)$
Differentiate [Ln/Chain Rule/Basic Power Rule]: $\frac{dt}{dx} = \frac{1}{2x-1} \cdot 2 - \frac{1}{x-1} \cdot 1$
Simplify: $\frac{dt}{dx} = \frac{2}{2x-1} - \frac{1}{x-1}$
Rewrite: $\frac{dt}{dx} = \frac{2(x-1)}{(2x-1)(x-1)} - \frac{2x-1}{(2x-1)(x-1)}$
Combine: $\frac{dt}{dx} = \frac{-1}{(2x-1)(x-1)}$
Reciprocate: $\frac{dx}{dt} = -(2x-1)(x-1)$
Distribute: $\frac{dx}{dt} = (1-2x)(x-1)$