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pantera1 [17]
3 years ago
5

what is the side length of the smallest square plate on which a 24-cm chopstick can fit along a diagonal without any overhang???

!!!!!!!
Mathematics
1 answer:
kumpel [21]3 years ago
3 0
A square is basically two triangles put together and since a square has four right angles you can use the Pythagorean Theorem to do this.

A squared +b squared <24
5 squared x 5 squared = 25

Sooooooo...... ;)
Get it?
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Two consecutive integers have a sum of 513. find the smaller of these two number
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513/2=256.5
which means 256 and 257 are the answers
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Which shows the expression below in simplified form?
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Answer:

B. 9x10^4

Step-by-step explanation:

\frac{4.5 \times  {10}^{8} }{5 \times  {10}^{3} }  \\  = 0.9 \times  {10}^{8 - 3}  \\  = 0.9 \times  {10}^{5}  \\  = 9 \times  {10}^{4}

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Which of the following is the correct simplified form of 16/56?
Leya [2.2K]

Answer:

B

Step-by-step explanation:

2/7 I Hope i helped

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Element X is a radioactive isotope such that every 51 years, its mass decreases by half. Given that the initial mass of a sample
pychu [463]

Answer: It will take 6 years for 7500 grams of X to reach 6900 grams.

Step-by-step explanation:

Expression for rate law for first order kinetics is given by:

t=\frac{2.303}{k}\log\frac{a}{a-x}

where,

k = rate constant  

t = age of sample

a = let initial amount of the reactant  

a - x = amount left after decay process  

a) for completion of half life:  

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

51=\frac{0.69}{k}

k=\frac{0.69}{51}=0.0135years^{-1}

b) for  7500 g to reach to 6900 g

t=\frac{2.303}{0.0135}\log\frac{7500}{6900}

t=6years

It will take 6 years for 7500 grams of X to reach 6900 grams.

5 0
2 years ago
Please help me, thank you!
dlinn [17]

Answer:

a. The first four terms are -4 , -4/3, -4/9 , -4/27

b. The series is converge

c. The series has sum to ∞ , the sum of the series is -6

Step-by-step explanation:

* Lets revise the geometric series

- Geometric series:

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)

# 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5)

* General term (nth term) of a Geometric Progression:

- U1 = a  ,  U2  = ar  ,  U3  = ar2  ,  U4 = ar3  ,  U5 = ar4

- Un = ar^n-1, where a is the first term , r is the constant ratio

 between each two consecutive terms  and n is the position of the

  number in the sequence

* In the problem

∵ The Un = -4(1/3)^n-1

∴ a = -4

∴ r = 1/3

a) To find the first four numbers use n = 1, 2 , 3 , 4

∴ U1 = a = -4

∴ U2 = -4(1/3)^(2 - 1) = -4(1/3) = -4/3

∴ U3 = -4(1/3)^(3 - 1) = -4(1/3)^2 = -4(1/9) = -4/9

∴ U4 = -4(1/3)^(4 - 1) = -4(1/3)^3 = -4(1/27) = -4/27

* The first four terms are -4 , -4/3, -4/9 , -4/27

b) If IrI < 1  then the geometric series is converge and if IrI > 1

   then the geometric series is diverge

∵ r = 1/3

∴ The series is converge  

c. The convergent series has sum to ∞

- The rule is: S∞ = a/(1 - r)

∴ S∞ = -4/(1 - 1/3) = -4/(2/3) = -4 × 3/2 = -6

* The sum of the series is -6

7 0
2 years ago
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