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3 years ago

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Mathematics

2 answers:

Helga [31]3 years ago

6 0

Answer:

(-8) ^4

Step-by-step explanation:

The base is the number being multiplied

-8

The exponent is the number of times it is multiplied

(-8) ^4

prohojiy [21]3 years ago

3 0

Answer:

(-8)^4

Step-by-step explanation:

-8• -8 • -8 • -8 = 4,096

So:

-8^4 = - 4,096
(-8)^4 = 4,096
-(8^4) = - 4,096

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A builder purchases 600 bricks for a new residential construction. The dimensions of each brick are 5.1 cm by 10.2 cm by 20.3 cm

Blababa [14]

<h3>Answer:</h3>

1165.83 kg

<h3>Explanation:</h3>

The total mass is the product of volume of one brick, the number of bricks, and the density. For this problem, it is convenient to use dimensions in meters.

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4 years ago

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The volume of a cylinder is 252π252π cm3 and its height is 7 cm.

kirill [66]

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3 years ago

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4 years ago

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = e^−2

Mekhanik [1.2K]

Answer:

x=1

y=s

z=1

Step-by-step explanation:

(x, y, z)=(1, 0, 1)

Substitute 0 for y

$y = e^{-2t} *sin 4t\\0 = e^{-2t} *sin 4t\\\\0 = e^{-2t} *(\frac{e^{4t}-e^{-4t}}{2j} )\\0 = e^{-2t} *(e^{4t}-e^{-4t} )\\0 = e^{-2t} *e^{4t}*(1-e^{-8t} )\\\\0 = e^{2t}*(1-e^{-8t} )\\\\\\Either \\0 = e^{2t}\\t = -inf\\or\\0 = (1-e^{-8t} )\\(e^{-8t} ) = 1\\ -8t = ln(1) =0\\t=0\\\\$

Confirming if t=0 satisfy the other equation

x = e^−2t cos 4t = e^−2(0)cos(4*0)

= e^(0)cos(0) = 1

z = e^−2t = e^−2(0) = 0

Therefore t=0 satisfies the other equation

Finding the tangent vector at t=0

$\frac{dx}{dt}=-2te^{-2t} cos4t + e^{-2t}(-4sin4t)=-2(0)e^{-2(0)} cos4(0) + e^{-2(0)}(-4sin4(0))=0\\\\ \frac{dy}{dt} =-2te^{-2t} sin4t + e^{-2t}(4cos4t)=-2(0)e^{-2(0)} sin4(0)+ e^{-2(0)(4cos4(0)) }= 1\\\\\frac{dz}{dt} = -2te^{-2t} = -2(0)e^{-2(0)} = 0$

The vector equation of the tangent line is

(1, 0, 1) +s(0,1,0)= (1, s, 1)

The parametric equations are:

x=1

y=s

z=1

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3 years ago

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