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siniylev [52]
2 years ago
12

Evaluate the expression x =5 for the given replacement

Mathematics
1 answer:
rewona [7]2 years ago
7 0

Answer:

x=5 is not a problem.

Step-by-step explanation:

x would be 5 thats it.

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Using mathematical induction prove whether or not the following statement is true for all positive integers n, or show why it is
aniked [119]

Base case: For n=1, the left side is 2 and the right is 2\cdot1^2=2, so the base case holds.

Induction hypothesis: Assume the statement is true for n=k, that is

2+6+10+\cdots+4k-2=2k^2

We want to show that this implies truth for n=k+1, that

2+6+10+\cdots+4k-2+4(k+1)-2=2(k+1)^2

The first k terms on the left reduce according to the assumption above, and we can simplify the k+1-th term a bit:

\underbrace{2+6+10+\cdots+4k-2}_{2k^2}+4k+2

2k^2+4k+2=2(k^2+2k+1)=2(k+1)^2

so the statement is true for all n\in\mathbb N.

5 0
3 years ago
A cylindrical beaker with diameter 10 in and height 12 in. is filled with water that is then poured into a rectangular
emmasim [6.3K]

Answer:

A. The volume of the cylindrical beaker = 942.5 in3.

B. Volume of the pan = 378 in3

C. The water in the cylindrical beaker will over flow the pan.

D. The height of the water in the beaker after the pan is filled is 7.2 in

Step-by-step explanation:

Data given from the question.

Diameter = 10 in

Height = 12 in

Dimension of the pan = 14 in x 9 in x 3 in

Determination of the volume of each solid.

A. Volume of the cylindrical beaker:

Volume = πr2h

Radius (r) = 10/2 = 5 in

Height (h) = 12 in

Volume (V) =?

V = πr2h

V = π x (5)^2 x 12

V = 942.5 in3.

The volume of the cylindrical beaker = 942.5 in3.

B. Volume of the rectangular pan

Volume = Length x Width x Height

The dimension for the rectangular pan = volume of the pan = 14 in x 9 in x 3 in

Volume of the pan = 378 in3

C. Since the volume of the cylindrical beaker is higher than that of the pan, the water in the cylindrical beaker will overflow the pan.

D. Determination of the height of the water in the cylindrical beaker after the pan is filled. This is illustrated below.

Let us calculate the volume of the water in the cylindrical beaker after the pan is filled

The volume of the cylindrical beaker = 942.5 in3.

Volume of the pan = 378 in3

Volume of water in the cylinder beaker after the pan is filled = 942.5 - 378 = 564.5 in3

With this new volume, we can calculate the new height of the water as follow:

Volume = 564.5 in3

Radius (r) = 5 in (the radius remains the same)

Height (h) =?

V = πr2h

h = V/πr2

h = 564.5/π(5)^2

h = 7.2 in

Therefore, the height of the water in the beaker after the pan is filled is 7.2 in

4 0
3 years ago
2x-3y=-14
dezoksy [38]
2x-3y=-14/×(-3) <=>-6x +9y=42
3x-2y=-6/×2<=>6x-4y=-12 se reduce -6x cu 6x si ne ramane 5y=30<=>y=6 , luom o ec care o vrem si inlocuim pe y cu 6 ...3x -2x=-6<=>3x-12=-6<=>3x=6<=>x= 2 , x-y=2-6=-4
8 0
3 years ago
Read 2 more answers
WIL MARK BRAINLYEST !
Tcecarenko [31]

Answer:

87%>0.25>21%>0.2

Step-by-step explanation:

87% converted to decimal form is 0.87 which is greater than 0.25 and 21% converted to decimal form is 0.21 which is also greater than 0.2 which can also be interpreted as 0.20! Hope this helps!

6 0
3 years ago
Read 2 more answers
Operations absolute value <br><br>|4 - 9| =<br><br>|4| -9 =
Lelu [443]
|4-9|
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5

|4|-9
4-9
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absolute value is the numbers distance from zero
6 0
3 years ago
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