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4 years ago

What are the first and second steps performed in solving the inequality 2(4w + 8) – 2w + 42 > 78? Name the property used.

1 answer:

6 0

Hello :
<span>2(4w + 8) – 2w + 42 > 78
8w+16-2w+42 </span>> 78......(<span>distributivity × for + )
6w </span>> 20
w > 20/6

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The circumference of a sphere was measured to be 82 cm with a possible error of 0.5 cm. (a) Use differentials to estimate the ma

NeTakaya

Answer:

The Maximum error is $26cm^2$

Step-by-step explanation:

Given that the circumference of a sphere was measured to be 82 cm with a possible error of 0.5 cm

<h3>To find :</h3><h3>(a) Use differentials to estimate the maximum error in the calculated surface area. (Round your answer to the nearest integer.) $cm^2$ </h3>

Given circumference of a sphere=82 cm and possible error =0.5 cm

Error of the surface area is dA

Error of circumference is dC = 0.5 cm

We know that the formula for Circumference of a sphere is C=2πr units

Differentiating with respect to r

$dC = 2\pi dr$

$dr =\frac{dC}{2π}$

$=\frac{0.5}{2\pi}$ (∵ dC = 0.5 cm)

<h3>Since Area $A = 4\pi r^2$ square units</h3>

Differentiating with respect to r

$dA = 8\pi rdr$ square units

Since given C = 82 cm.and also C=2πr we have

$r=\frac{C}{2π}$

$=\frac{82}{2π}$

$r=\frac{41}{π}$

From that $dA = 8\pi rdr$

Substituting the values of r and dr in the above equation we get

$dA = 8\pi (\frac{41}{\pi}) (\frac{0.5}{2\pi})$

$=4(41)\times (\frac{0.5}{3.14})$

$=26.1146$

$dA=26cm^2$

∴ Maximum error is $26cm^2$

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4 years ago

What is a symmetric matrix?

horsena [70]

Answer:

symmetric matrix is the square matrix and it is equal to its transpose

Step-by-step explanation:

solution

a symmetric matrix is the square matrix and it is equal to its transpose

As A is symmetric matrix then

A = $A^{T}$

here only square matrices will be symmetric

and matrix A is symmetric its mean its matrices have equal dimension

and every square diagonal matrix is also symmetric when all off diagonals element is zero

symmetric matrix for all indices i and j

A = aij = aji

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