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3 years ago

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A rectangular solid measures 4.9 m by 8.3 cm by 6.8 dm. Express its volume in cubic meters, liters, cubic inches, and cubic feet

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1 answer:

Igoryamba3 years ago

7 0

Answer:

Part 1) The volume is 0.276556 m³

Part 2) The volume is 276.556 l

Part 3) The volume is 16,886.94 in³

Part 4) The volume is 9.68 ft³

Step-by-step explanation:

A rectangular solid measures 4.9 m by 8.3 cm by 6.8 dm

Part 1) Express its volume in cubic meters

<em>Convert the measures to meters</em>

Remember that

1 m=100 cm

1 m=10 dm

4.9 m

8.3 cm=8.3/100=0.083 m

6.8 dm=6.8/10=0.68 m

Find the volume

V=4.9*0.083*0.68=0.276556 m³

Part 2) Express its volume in liters

<em>Convert the measures to liters</em>

Remember that

1 m³=1,000 l

we have

V=0.276556 m³

so

Convert to liters

0.276556 m³=0.276556*1,000=276.556 l

Part 3) Express its volume in cubic inches

<em>Convert the measures to inches</em>

<em>we have</em>

4.9 m, 0.083 m, 0.68 m

Remember that

1 m= 39.3701 in

so

4.9 m=4.9*39.3701=192.91 in

0.083 m=0.083*39.3701=3.27 in

0.68 m=0.68*39.3701=26.77 in

Find the volume

V=192.91*3.27*26.77=16,886.94 in³

Part 4) Express its volume in cubic feet

<em>Convert the measures to feet</em>

<em>we have</em>

4.9 m, 0.083 m, 0.68 m

Remember that

1 m=3.28084 ft

so

4.9 m=4.9*3.28084=16.08 ft

0.083 m=0.083*3.28084=0.27 ft

0.68 m=0.68*3.28084=2.23 ft

Find the volume

V=16.08*0.27*2.23=9.68 ft³

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The factors of 5 that sum to 6 are 5 and 1. So, x^2 + 6 x + 5 = (x + 5) (x + 1):
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Factor -2 out of -4 x - 6:
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Factor the difference of two squares. x^2 - 5^2 = (x - 5) (x + 5):
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((x - 5) (x - 6) (x + 5) (x + 1))/((x - 5) (x + 5) (-2) (2 x + 3)) = ((x - 5) (x + 5))/((x - 5) (x + 5))×((x - 6) (x + 1))/(-2 (2 x + 3)) = ((x - 6) (x + 1))/(-2 (2 x + 3)):
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What is the multiplicative inverse of 5 in z11, z12, and z13? you can do a trial-and-error search using a calculator or a pc?

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A multiplicative inverse of an integer a is an integer x such that the product ax is congruent to 1 with respect to the modulus m.

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Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{4};$
$5\cdot 4=20=\overline{9};$
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The multiplicative inverse of 5 in $Z_{11}$ is 9.

2. $Z_{12}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11}\}.$

Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{3};$
$5\cdot 4=20=\overline{8};$
$5\cdot 5=25=\overline{1};$
$5\cdot 6=30=\overline{6};$
$5\cdot 7=35=\overline{11};$
$5\cdot 8=40=\overline{4};$
$5\cdot 9=45=\overline{9};$
$5\cdot 10=50=\overline{2};$
$5\cdot 11=55=\overline{7}.$

The multiplicative inverse of 5 in $Z_{12}$ is 5.

3. $Z_{13}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11},\overline{12}\}.$

Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{2};$
$5\cdot 4=20=\overline{7};$
$5\cdot 5=25=\overline{12};$
$5\cdot 6=30=\overline{4};$
$5\cdot 7=35=\overline{9};$
$5\cdot 8=40=\overline{1};$
$5\cdot 9=45=\overline{6};$
$5\cdot 10=50=\overline{11};$
$5\cdot 11=55=\overline{3};$
$5\cdot 12=60=\overline{8}.$

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Tema [17]

Answer:

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Step-by-step explanation:

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