18 m 13m 13 m find the surface area
1 answer:
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Answer:
The correct option is 2.
Step-by-step explanation:
From the given graph it is noticed that the data points are located at (0,0), (1,0.25), (2,1), (3,2), (4,3), (5,4), (5.5,5), (6,6), (6.4,7), (6.7,7.8) and (7,9).
The rate of change from first two data points is
The rate of change from next two data points is
The rate of change it not constant, therefore the given data points are non linear.
The value of y increases as the value of x-increases. It means there is a positive relation between x and y.
Therefore the graph represent a Nonlinear positive association between x and y. Option 2 is correct.
We should choose mug 1 having volume of 71.24 inch³ ,with diameter 5.5 inches and height 3 inches holds the most !
<u>Step-by-step explanation:</u>
We have 2 mugs, One has a base that is 5.5 inches in diameter and a height of 3 inches. The other has a base of 4.5 inches in diameter and a height of 4 inches. Basically, mugs are cylinders so we will consider 2 cylinders .
To find which one holds the most we are supposed to find volume of both ,the one with maximum volume holds the most.
<u>Part 1: </u>
volume of cylinder 1 ()= πr₁²h₁ ,
r₁ = radius of cylinder ⇒
h₁ = height of cylinder ⇒ 3 inches
∴ = πr₁²h₁
⇒ 3.14×( 2.75 )²×3 ⇒ 71.24 inch³
<u>Part 2:</u>
volume of cylinder 2 ( )= πr₂²h₂
r₂ = radius of cylinder ⇒
h₂ = height of cylinder ⇒ 4 inches
∴ = πr₂²h₂
⇒ 3.14×( 2.25 )²×4 ⇒ 63.59 inch³
∵ ( 71.24 inch³ ) >
( 63.59 inch³ ), mug 1 with diameter 5.5 inches and height 3 inches holds the most.
The coefficients of the binomial expansion 
, where n is the row number, is given in the Pascal's triangle shown below.
First, to find the <span>coefficient of the fourth term of (x+2)^5 we look at row 5, term 4. The coefficient there is 10.
But, we must also remember that the term 2 also is taken to a certain power here. Mainly , for each term, the power of 2 is as follows:
2^0, 2^1, 2^2, 2^3=8.
So, in total we have: 10*8=80.
Second, to find </span><span> the coefficient of the third term of (3x-1)^5 we again go to the row 5, this time term 3 and we have 10 there. Now we must check how each of (3x) and 1 expand, now being careful about the sign as well.
we have:
(3x)^5 (1) -(3x)^4 (1) (3x)^3(1)=27x^3.
Thus, the coefficient of the third term is 27*10=270.
Third, we want to find </span><span>the coefficient of the third term of (a+5b^2)^4. We look at row 4, term 3. There we have 6.
The terms a and 5b^2 are as follows:
a^4 (5b^2)^0 </span> a^3 (5b^2)^1 a^2 (5b^2)^2=25a^2b^4
Thus, the coefficient is 25*6=150.
Answer:
80; 270; 150
First, to find the <span>coefficient of the fourth term of (x+2)^5 we look at row 5, term 4. The coefficient there is 10.
But, we must also remember that the term 2 also is taken to a certain power here. Mainly , for each term, the power of 2 is as follows:
2^0, 2^1, 2^2, 2^3=8.
So, in total we have: 10*8=80.
Second, to find </span><span> the coefficient of the third term of (3x-1)^5 we again go to the row 5, this time term 3 and we have 10 there. Now we must check how each of (3x) and 1 expand, now being careful about the sign as well.
we have:
(3x)^5 (1) -(3x)^4 (1) (3x)^3(1)=27x^3.
Thus, the coefficient of the third term is 27*10=270.
Third, we want to find </span><span>the coefficient of the third term of (a+5b^2)^4. We look at row 4, term 3. There we have 6.
The terms a and 5b^2 are as follows:
a^4 (5b^2)^0 </span> a^3 (5b^2)^1 a^2 (5b^2)^2=25a^2b^4
Thus, the coefficient is 25*6=150.
Answer:
80; 270; 150