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2 years ago

I'm confused on this

Mathematics

1 answer:

musickatia [10]2 years ago

6 0

Number 13 is c. Figure D
Number 14 is b. Figure D

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Question 2b only! Evaluate using the definition of the definite integral(that means using the limit of a Riemann sum

lara [203]

Answer:

Hello,

Step-by-step explanation:

We divide the interval [a b] in n equal parts.

$\Delta x=\dfrac{b-a}{n} \\\\x_i=a+\Delta x *i \ for\ i=1\ to\ n\\\\y_i=x_i^2=(a+\Delta x *i)^2=a^2+(\Delta x *i)^2+2*a*\Delta x *i\\\\\\Area\ of\ i^{th} \ rectangle=R(x_i)=\Delta x * y_i\\$

$\displaystyle \sum_{i=1}^{n} R(x_i)=\dfrac{b-a}{n}*\sum_{i=1}^{n}\ (a^2 +(\dfrac{b-a}{n})^2*i^2+2*a*\dfrac{b-a}{n}*i)\\$

$=(b-a)^2*a^2+(\dfrac{b-a}{n})^3*\dfrac{n(n+1)(2n+1)}{6} +2*a*(\dfrac{b-a}{n})^2*\dfrac{n (n+1)} {2} \\\\\displaystyle \int\limits^a_b {x^2} \, dx = \lim_{n \to \infty} \sum_{i=1}^{n} R(x_i)\\\\=(b-a)*a^2+\dfrac{(b-a)^3 }{3} +a(b-a)^2\\\\=a^2b-a^3+\dfrac{1}{3} (b^3-3ab^2+3a^2b-a^3)+a^3+ab^2-2a^2b\\\\=\dfrac{b^3}{3}-ab^2+ab^2+a^2b+a^2b-2a^2b-\dfrac{a^3}{3} \\\\\\\boxed{\int\limits^a_b {x^2} \, dx =\dfrac{b^3}{3} -\dfrac{a^3}{3}}\\$

4 0

2 years ago

Sam is building a model of an antique car the scale of his model to the actual car is 1 to 10 his model is 8 1/2 inches long how

rewona [7]

16 7/8

.......................................................

8 0

3 years ago

What is the answe ?????

mestny [16]

Answer:

1) The first option

2) -9, -7, 6, 8, 10

3) Rise by 10 degrees

Step-by-step explanation:

Ascending is from smallest to biggest therefore you start with the smallest negative number and end with biggest whole number.

8 0

2 years ago

A recipe for trail mix uses 7 ounces of almonds with 5 ounces of raisins. (Almonds and raisins are the only ingredients.) How ma

grin007 [14]

Answer:

x = 9 1/3 ounces of almonds

Step-by-step explanation:

Ounces of almonds : raisins

= 7 : 5

Total = 7 + 5

= 12

How many ounces of almonds would be in a one-pound bag (16 ounces) of this trail mix

Let

x = Ounces of almonds needed

x = 7 /12 × 16

= 112 /12

= 9 4/12

= 9 1/3

x = 9 1/3 ounces

3 0

2 years ago

4(8x - 3) - 6 = 5 + 2x<br><br> WHATS THE SOLUTION???

slamgirl [31]

Answer:

x = 23/30

Step-by-step explanation:

4(8x - 3) - 6 = 5 + 2x

32x - 12 - 6 = 5 + 2x

32x - 18 = 5 + 2x

32x - 2x = 5 + 18

30x = 23

x = 23/30

5 0

2 years ago

Read 2 more answers