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3 years ago

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100 points What is the maximum volume of a square pryamid that can fit inside a cube with a side length of 24 cm? A) 2,304 cm3

B) 4,608 cm C) 6,912cm3 D) 13,824 cm3s

1 answer:

Aleonysh [2.5K]3 years ago

8 0

Answer:

B) 4,608.

Step-by-step explanation:

A square pyramid with the maximum volume that can fit inside a cube has a same base as a cube ( 24 cm x 24 cm ) . The height of the pyramid is also same as a side length of a cube ( h = 24 cm ).

The volume of the pyramid:

V = 1/3 · 24² · 24 = 1/3 · 576 · 24 = 4,608 cm³

Answer:

The maximum volume of the pyramid is 4,608 cm³.

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write an equation for the perpendicular bisector of the line joining the two points. PLEASE do 4,5 and 6

myrzilka [38]

Answer:

4. The equation of the perpendicular bisector is y = $\frac{3}{4}$ x - $\frac{1}{8}$

5. The equation of the perpendicular bisector is y = - 2x + 16

6. The equation of the perpendicular bisector is y = $-\frac{3}{2}$ x + $\frac{7}{2}$

Step-by-step explanation:

Lets revise some important rules

The product of the slopes of the perpendicular lines is -1, that means if the slope of one of them is m, then the slope of the other is $-\frac{1}{m}$ (reciprocal m and change its sign)
The perpendicular bisector of a line means another line perpendicular to it and intersect it in its mid-point
The formula of the slope of a line is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
The mid point of a segment whose end points are $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$
The slope-intercept form of the linear equation is y = m x + b, where m is the slope and b is the y-intercept

4.

∵ The line passes through (7 , 2) and (4 , 6)

- Use the formula of the slope to find its slope

∵ $x_{1}$ = 7 and $x_{2}$ = 4

∵ $y_{1}$ = 2 and $y_{2}$ = 6

∴ $m=\frac{6-2}{4-7}=\frac{4}{-3}$

- Reciprocal it and change its sign to find the slope of the ⊥ line

∴ The slope of the perpendicular line = $\frac{3}{4}$

- Use the rule of the mid-point to find the mid-point of the line

∴ The mid-point = $(\frac{7+4}{2},\frac{2+6}{2})$

∴ The mid-point = $(\frac{11}{2},\frac{8}{2})=(\frac{11}{2},4)$

- Substitute the value of the slope in the form of the equation

∵ y = $\frac{3}{4}$ x + b

- To find b substitute x and y in the equation by the coordinates

of the mid-point

∵ 4 = $\frac{3}{4}$ × $\frac{11}{2}$ + b

∴ 4 = $\frac{33}{8}$ + b

- Subtract $\frac{33}{8}$ from both sides

∴ $-\frac{1}{8}$ = b

∴ y = $\frac{3}{4}$ x - $\frac{1}{8}$

∴ The equation of the perpendicular bisector is y = $\frac{3}{4}$ x - $\frac{1}{8}$

5.

∵ The line passes through (8 , 5) and (4 , 3)

- Use the formula of the slope to find its slope

∵ $x_{1}$ = 8 and $x_{2}$ = 4

∵ $y_{1}$ = 5 and $y_{2}$ = 3

∴ $m=\frac{3-5}{4-8}=\frac{-2}{-4}=\frac{1}{2}$

- Reciprocal it and change its sign to find the slope of the ⊥ line

∴ The slope of the perpendicular line = -2

- Use the rule of the mid-point to find the mid-point of the line

∴ The mid-point = $(\frac{8+4}{2},\frac{5+3}{2})$

∴ The mid-point = $(\frac{12}{2},\frac{8}{2})$

∴ The mid-point = (6 , 4)

- Substitute the value of the slope in the form of the equation

∵ y = - 2x + b

- To find b substitute x and y in the equation by the coordinates

of the mid-point

∵ 4 = -2 × 6 + b

∴ 4 = -12 + b

- Add 12 to both sides

∴ 16 = b

∴ y = - 2x + 16

∴ The equation of the perpendicular bisector is y = - 2x + 16

6.

∵ The line passes through (6 , 1) and (0 , -3)

- Use the formula of the slope to find its slope

∵ $x_{1}$ = 6 and $x_{2}$ = 0

∵ $y_{1}$ = 1 and $y_{2}$ = -3

∴ $m=\frac{-3-1}{0-6}=\frac{-4}{-6}=\frac{2}{3}$

- Reciprocal it and change its sign to find the slope of the ⊥ line

∴ The slope of the perpendicular line = $-\frac{3}{2}$

- Use the rule of the mid-point to find the mid-point of the line

∴ The mid-point = $(\frac{6+0}{2},\frac{1+-3}{2})$

∴ The mid-point = $(\frac{6}{2},\frac{-2}{2})$

∴ The mid-point = (3 , -1)

- Substitute the value of the slope in the form of the equation

∵ y = $-\frac{3}{2}$ x + b

- To find b substitute x and y in the equation by the coordinates

of the mid-point

∵ -1 = $-\frac{3}{2}$ × 3 + b

∴ -1 = $-\frac{9}{2}$ + b

- Add $\frac{9}{2}$ to both sides

∴ $\frac{7}{2}$ = b

∴ y = $-\frac{3}{2}$ x + $\frac{7}{2}$

∴ The equation of the perpendicular bisector is y = $-\frac{3}{2}$ x + $\frac{7}{2}$

8 0

3 years ago

Allana used Fraction 3 over 5 yard of fabric to make a scarf. Can she make 2 of these scarves with Fraction 1 and 7 over 10 yard

Paul [167]

(1 7/10) / (3/5)
(17/10) / (3/5) =
17/10 * 5/3 =
85/30 =
2 5/6........yes, because 1 7/10 divided by 3/5 = 2 5/6...answer C

5 0

3 years ago

I need the answers for these pls help

DanielleElmas [232]

Answer:

1)

A. m arc QRS = 100°

B. m arc QRT = 255°

C. m arc UTS = 180°

D. m arc UTR = 205°

2)

1] The major arc CA = 255°

2] The minor arc AB = 90°

Step-by-step explanation:

In a circle:

The measure of an central angle is equal to the measure of its subtended arc
The measure of a circle is 360°
Any chord divides a circle into two arcs, a minor arc its measure is < 180° and a major arc its measure is > 180°, the sum of the measures of the minor and major arcs is 360°
If the measures of the minor and major arcs are equal, then each arc represents a semi-circle

1)

In circle O

A.

∵ m∠QOR = 75°

∵ ∠QOR subtended by arc QR

- By using the 1st note above

∴ m of arc QR = m∠QOR

∴ m of arc QR = 75°

∵ m∠ROS = 25°

∵ ∠ROS subtended by arc RS

∴ m of arc RS = m∠ROS

∴ m of arc RS = 25°

The measure of arc QRS is the sum of the measures of arcs QR and RS

∴ m arc QRS = 75° + 25° = 100°

B.

∵ m∠SOT = 155°

∵ ∠SOT subtended by arc ST

∴ m of arc ST = m∠SOT

∴ m of arc ST = 155°

The measure of arc QRT is the sum of the measures of arcs QR, RS and ST

∴ m arc QRT = 75° + 25° + 155 °= 255°

C.

∵ m∠UOT = 25°

∵ ∠UOT subtended by arc UT

∴ m of arc UT = m∠UOT

∴ m of arc RUT = 25°

The measure of arc UTS is the sum of the measures of arcs UT and TS

∴ m arc UTS = 25° + 155° = 180°

D.

The measure of arc UTR is the sum of the measures of arcs UT, TS and SR

∴ m arc UTR = 25° + 155° + 25 = 205°

2)

1]

∵ The sum of the measures of the minor and major arcs is 360°

∵ m of minor arc AC = 105°

- Subtract 105 from 360° to find the measure of the major arc CA

∴ m of major arc CA = 360° - 105°

∴ m of major arc CA = 255°

2]

∵ m of major arc AB = 270°

- Subtract 270° from 360° to find the measure of the minor arc AB

∴ m of minor arc AB = 360° - 270°

∴ m of minor arc AB = 90°

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Answer:

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