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larisa [96]
3 years ago
13

(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.

7 0
11 months ago
Pleaseeeeee I need help! <br><br> THANK YOU
amm1812

\:  \:  \:  \:  \:  \:  \:

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

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

<h2><u>hope</u><u> it</u><u> helps</u></h2>

4 0
2 years ago
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Which statement compares the limit as x approaches –4 for the two graphs? In both graph I and graph II, the limit is 5. In both
IceJOKER [234]
Selling . Recut read. Your graph 3
4 0
2 years ago
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2 to the power of negative 6
Alik [6]

Answer:

0.015625

Step-by-step explanation:

2^-6=0.015625

you can do it on any calculator to check

6 0
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 ;

299 mg

Step-by-step explanation:

General Continous growth rate equation :

A = Pe^rt

A = amount present, t years after year of initial amount.

Here,

P = 90 mg, amount in year 2000

r = rate = 12% = 0.12

t = years after 2000

Therefore,

A is written as ;

A(t) = 90e^0.12t

Amount present in year 2010 ;

t = 2010 - 2000 = 10

A(10) = 90e^0.12(10)

A(10) = 90 * e^1.2

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2 years ago
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