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3 years ago

(m3 - 6m2 - 16m + 63) divided by (m - 7)

Mathematics

1 answer:

Arlecino [84]3 years ago

3 0

Therefore( $m^3 -6m^2-16m +63$ )÷ (m-7) $= (m^2 +m-9)$

Step-by-step explanation:

$m^3 -6m^2-16m +63$

$=m^3 -7m^2$ $+m^2 -7m$ $-9m+63$

$= m^2(m-7)$ $+m(m-7)$ $-9(m-7)$

$= (m-7 ) (m^2 +m-9)$

Therefore( $m^3 -6m^2-16m +63$ )÷ (m-7) $= (m^2 +m-9)$

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1. The figure shows the regular triangular pyramid SABC. The base of the pyramid has an edge AB = 6 cm and the side wall has an

Musya8 [376]

Given:

• AB = 6 cm

• SM = √15 cm

Let's solve for the following:

• 1) the base elevation AM.

Given that we have a regular triangular pyramid, the length of the three bases are equal.

AB = BC = AC

BM = BC/2 = 6/2 = 3 cm

To solve for AM, which is the height of the base, apply Pythagorean Theorem:

$\begin{gathered} AM=\sqrt{AB^2-BM^2} \\ \\ AM=\sqrt{6^2-3^2} \\ \\ AM=\sqrt{36-9} \\ \\ AM=\sqrt{27} \\ \\ AM=5.2\text{ cm} \end{gathered}$

The base elevation of the pyramid is 5.2 cm.

• (2)., The elevation SO.

To find the elevation of the pyramid, apply Pythagorean Theorem:

$SO=\sqrt{SM^2-MO^2}$

Where:

SM = √15 cm

MO = AM/2 = 5.2/2 = 2.6 cm

Thus, we have:

$\begin{gathered} SO=\sqrt{(\sqrt{15})^2-2.6^2} \\ \\ SO=\sqrt{15-6.76} \\ \\ SO=2.9\text{ cm} \end{gathered}$

Length of SO = 2.9 cm

• (3). Area of the base:

To find the area of the triangular base, apply the formula:

$A=\frac{1}{2}*BC*AM$

Thus, we have:

$\begin{gathered} A=\frac{1}{2}*6^*5.2 \\ \\ A=15.6\text{ cm}^2 \end{gathered}$

The area of the base is 15.6 square cm.

• (4). Area of the side surface.

Apply the formula:

$SA=\frac{1}{2}*p*h$

Where:

p is the perimeter

h is the slant height, SM = √15 cm

Thus, we have:

$\begin{gathered} A=\frac{1}{2}*(6*3)*\sqrt{15} \\ \\ A=34.86\text{ cm}^2 \end{gathered}$

• (5). Total surface area:

To find the total surface area, apply the formula:

$TSA=base\text{ area + area of side surface}$

Where:

Area of base = 15.6 cm²

Area of side surface = 34.86 cm²

TSA = 15.6 + 34.86 = 50.46 cm²

The total surface area is 50.46 cm²

• (6). Volume:

To find the volume, apply the formula:

$V=\frac{1}{3}*area\text{ of base *height}$

Where:

Area of base = 15.6 cm²

Height, SO = 2.9 cm

Thus, we have:

$\begin{gathered} V=\frac{1}{3}*15.6*2.9 \\ \\ V=15.08\text{ cm}^3 \end{gathered}$

The volume is 15.08 cm³.

ANSWER:

• 1.) 5.2 cm

• 2.) 2.9 cm

• 3.) 15.6 cm²

• 4.) 34.86 cm²

• (5). 50.46 cm²

• 6). 15.08 cm³.

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11 months ago

Pleaseeeeee I need help! THANK YOU

amm1812

$\: \: \: \: \: \: \:$

$\frac{3}{10} \\ \\ or \: in \: alternate \: \: form \\ \\ 0.3$

<h2>refer to the attachment for explanation</h2>

<h2>hope it helps</h2>

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IceJOKER [234]

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2 years ago

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2 to the power of negative 6

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Answer:

0.015625

Step-by-step explanation:

2^-6=0.015625

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3 years ago

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A radioactive substance decays at a continuous rate of 12% per year, and 90 mg of the substance is present in the year 2000. (a)

Alla [95]

Answer:

A(t) = 90e^0.12t ;

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Step-by-step explanation:

General Continous growth rate equation :

A = Pe^rt

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Here,

P = 90 mg, amount in year 2000

r = rate = 12% = 0.12

t = years after 2000

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A is written as ;

A(t) = 90e^0.12t

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t = 2010 - 2000 = 10

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