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nikitadnepr [17]
3 years ago
10

To use a compass to find the midpoint of a line segment, Rebecca draws two arcs of equal radius from each of the two endpoints o

f the segment so that they also intersect on both sides of the segment. Identify the line that connects the two points where the arcs intersect.
a. radius of the arcs

b. diameter of the arcs

c. perpendicular bisector of the segment

d. angle bisector
Mathematics
1 answer:
DiKsa [7]3 years ago
3 0
We are given a line segment with two points on each end. Rebecca draws two arcs with equal radius from each point. Now, the intersection of the two arcs is the midpoint of the line. This can be explained by the radius of the arcs. Since they are equal, meaning they have the same distance from each point. Thus, the midpoint of the line. 
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From a thin piece of cardboard 30 in. by 30 in., square corners are cut out so that the sides can be folded up to make a box. Wh
Brilliant_brown [7]

Answer:

Dimensions 5in x 10in x 10in will yeild a box with a max. volume of  500 cubic inches

Step-by-step explanation:

Volume =  height x length x width

considering 'x' as the length of the square corners that has been cut out from the cardboard and also, that is height of the cardboard box.

square corners are cut out so that the sides can be folded up to make a box, cardboard sides would reduce by 2x

therefore,

V = x  (30-2x) (30-2x) ---> eq(1)

V=( 30x - 2x²) (30-2x)

V= 900x- 60x² - 60x² + 4x³

V=  4x³ - 120 x²+ 900x

Taking derivative w.r.t 'x'

dV/dx = 12x² - 240 x +900

dV/dx = 4 (3x² - 60x +225)

For maximum dV/dx, make it equal zero

dV/dx = 0

so,  4 (3x² - 60x +225)=0

3x² - 60x+225=0   (taking 3 common)

x² - 20x + 75 =0

Solving this quadratic equation

x² - 15x -5x + 75 =0

x(x-15) - 5(x-15) =0

Either (x-15)=0

x=15

Or x-5=0

x = 5

if we substitute x=15 in eq(1), volume becomes zero.

therefore, x cannot be 15

When x= 5

eq(1)=>V = 5  (30-2(5)) (30-2(5))

V= 5 (10) (10)

V= 500 cubic inches,

Therefore, Dimensions 5in x 10in x 10in will yeild a box with a max. volume of  500 cubic inches

7 0
3 years ago
8 x 6 = (4 x 6) (__x 6) <br> = 24 + __<br> =
guajiro [1.7K]

Answer:

8x6= (4x6) + (4x6)

= 24+24

= 48

Step-by-step explanation:

Hope this helps :)

8 0
3 years ago
Read 2 more answers
A teacher asks students to list the math lessons they learned on nine random school days in the past month. She evaluates the st
zysi [14]

Answer:

Simple random sampling

Step-by-step explanation:

Hope this work :)

5 0
2 years ago
400.0 ml of a gas are under pressure of 80.0 kpa what would the volume of the gas be at a pressure of 100.0 kpa
Ber [7]

Answer:

The final volume is 320 mL at pressure of 100 kPa.

Step-by-step explanation:

Boyle's law gives the relation between volume and pressure of a gas. It states that at constant temperature, volume is inversely proportional to its pressure such that,

V\propto \dfrac{1}{P}\\\\P_1V_1=P_2V_2

Let

V_1=40\ mL\\\\P_1=80\ kPa\\\\P_2=100\ kPa

We need to find V_2. Using above equation, we get :

V_2=\dfrac{P_1V_1}{P_2}\\\\V_2=\dfrac{400\times 80\times 10^3}{100\times 10^3}\\\\V_2=320\ mL

So, the final volume is 320 mL at pressure of 100 kPa.

6 0
3 years ago
Area and estimate helpp
Vikki [24]

Sorry. It's not clear. Plz tell me if there is 12 3/8in?

5 0
2 years ago
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