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Andre45 [30]
2 years ago
8

Talia is packing a moving box. She has a square-framed poster with an area of 4 square feet. The cube-shaped box has a volume of

14 cubic feet. Will the poster lie flat in the box? Explain?
Mathematics
1 answer:
yan [13]2 years ago
3 0

Answer:

Length of sides of poster = 2 Ft

Length of sides of box = 2.41 Ft

Since the box has a longer side than the poster, the poster will lie flat when placed in the box.

Step-by-step explanation:

In order to determine if the poster will lie flat in the box or not, we will determine the length of the sides of the poster and the box, if the length of the side of the square poster is smaller than that of the box, it will lie flat. This is calculated as follows:

Area of poster = 4 square feet

Area of poster =  (Length)²

4 = (Length)²

∴ Length = √(4)

Length of poster = 2 Ft

Volume of box = 14 cubic feet

Volume of box = (Length)³

14 = (Length)³

∴ Length = ∛(14)

Length = 2.41 Ft

∴ Length of sides of poster = 2 Ft

Length of sides of box = 2.41 Ft

Since the box has a longer side than the poster, the poster will lie flat when placed in the box.

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A shop sells chocolate, vanilla and strawberry ice creams. 45% of the ice creams sold are vanilla, and 1/4 are strawberry. What
labwork [276]

Answer:

30% of ice cream are chocolate

Step-by-step explanation:

45% = vanilla

1/4 = strawberry

(1/4)×100 = 25%

chocolate = 100%-45%-25%

= 30%

8 0
2 years ago
Read 2 more answers
Prove that a line that divides two sides of a triangle proportionally is parallel to the third side. Be sure to create and name
sattari [20]

Answer:

Given: A triangle ABC and a line DE parallel to BC.

To prove: A line parallel to one side of a triangle divides the other two sides proportionally.

Proof: Consider ΔABC and DE be the line parallel to Bc, then from ΔABC and ΔADE, we have

∠A=∠A (Common)

∠ADE=∠ABC (Corresponding angles)

Thus, by AA similarity, ΔABC is similar to ΔADE, therefore

AB/AD= AC/AE

⇒AD+DB/AD = AE+EC/AE

⇒1+DB/AD = 1+ EC/AE

⇒DB/AD = EC/AE

Therefore, a line parallel to one side of a triangle divides the other two sides proportionally.

⇒Therefore Proved

Hope this helps!!!

3 0
2 years ago
Define f(0,0) in a way that extends f to be continuous at the origin. f(x, y) = ln ( 19x^2 - x^2y^2 + 19 y^2/ x^2 + y^2) Let f (
kirill115 [55]

Answer:

f(0,0)=ln19

Step-by-step explanation:

f(x,y)=ln(\frac{19x^2-x^2y^2+19y^2}{x^2+y^2}) is given as continuous function, so there exist lim_{(x,y)\rightarrow(0,0)}f(x,y) and it is equal to f(0,0).

Put x=rcosA annd y=rsinA

f(r,A)=ln(\frac{19r^2cos^2A-r^2cos^2A*r^2sin^2A+19r^2sin^2A}{r^cos^2A+r^2sin^2A})=ln(\frac{19r^2(cos^2A+sin^2A)-r^4cos^2Asin^a}{r^2(cos^2A+sin^2A)})

we know that cos^2A+sin^2A=1, so we have that

f(r,A))=ln(\frac{19r^2-r^4cos^2Asin^a}{r^2})=ln(19-r^2cos^2Asin^2A)

lim_{(x,y)\rightarrow(0,0)}f(x,y)=lim_{r\rightarrow0}f(r,A)=ln19

So f(0,0)=ln19.

8 0
2 years ago
A carousel has eight evenly spaced seats shaped like animals. During each ride, the carousel makes between 8 and 9 clockwise rev
Yakvenalex [24]

Answer:

2931 + 51.4n/7 degrees where n is the number of animal from the lion to the zebra in the clockwise direction.

Step-by-step explanation:

We don't have details on the positions of the lion and the zebra prior to revolution but suppose the zebra is n animal away from the lion where n could be in the range of 0 to 6 in the clockwise direction. If n = 0, the zebra is next to the lion in line, and if n = 6, the zebra is right behind the lion.

In angular term, since all 8 animals are evenly spaced, there are 7 space in between them, each of them would span an angle of 360/7 degrees

Then the angular distance between the zebra and the lion is (n+1)360/7 degrees

If the carousel makes between 8 and 9 revolutions then the total angular distance is 8*360 + (n+1)360/7 = 2931 + 51.4n/7 degrees

3 0
2 years ago
Read 2 more answers
Divide 794.1 by 7.61. Round off your answer to two decimal places. A. 104.35 B. 786.49 C. 95.83 D. 1,043.50
VikaD [51]
Answer: 
A. 104.35

Explanation: 
794.1 ÷ 7.61 = 104.34954 
Round off to two decimal places: 
104.349 
round 4 up to 5 because the next number is greater than 5: 
9 > 5 
So 
104.35
3 0
2 years ago
Read 2 more answers
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