PLEASE HELP !!!! ILL GIVE BRAINLIEST !!!

Natalija [7]

Split up the interval [2, 5] into $n$ equally spaced subintervals, then consider the value of $f(x)$ at the right endpoint of each subinterval.

The length of the interval is $5-2=3$ , so the length of each subinterval would be $\dfrac3n$ . This means the first rectangle's height would be taken to be $x^2$ when $x=2+\dfrac3n$ , so that the height is $\left(2+\dfrac3n\right)^2$ , and its base would have length $\dfrac{3k}n$ . So the area under $x^2$ over the first subinterval is $\left(2+\dfrac3n\right)^2\dfrac3n$ .

Continuing in this fashion, the area under $x^2$ over the $k$ th subinterval is approximated by $\left(2+\dfrac{3k}n\right)^2\dfrac{3k}n$ , and so the Riemann approximation to the definite integral is

$\displaystyle\sum_{k=1}^n\left(2+\frac{3k}n\right)^2\frac{3k}n$

and its value is given exactly by taking $n\to\infty$ . So the answer is D (and the value of the integral is exactly 39).

8 0

4 years ago

What is the measurement of ∠BAC and ∠ABC? Explain your process of solving.

Paraphin [41]

Answer:

<BAC = 78

<ABC = 68

Step-by-step explanation:

The remote angles theorem states that when one extends a side of a triangle, the angle formed between the extension and one of the sides of the triangle is equal to the sum of the two non-adjacent angles inside the triangle. One can apply this theorem here and state the following,

<BAC + <ABC = <ACD

Substitute,

(5y + 3) + (4y + 8) = (146)

Simplify,

9y + 11 = 146

Inverse operations,

9y + 11 = 146

-11 -11

9y = 135

/9 /9

y = 15

Now substitute this value back into the expressions to find the numerical measurement of (<BAC) and (<ABC),

<BAC = 5y + 3

5(15) + 3

78

<ABC = 4y + 8

4(15) + 8

68

5 0

3 years ago

Thomas happened to notice that at 4:00 p.m. on his uncle's farm, a fence post that was 5 feet tall cast a 3 foot shadow. he also

mash [69]

I used the proportion:
5:3=x:12
x=((12)(5))/3=20
20 feet

8 0

3 years ago

Read 2 more answers

Martin has a shoe box with the dimensions 4 inches, by 6 inches, by 10 inches. He wants to determine if a relay baton inches wil

kicyunya [14]

Answer:

10 inches.

Step-by-step explanation:

First we need to find what is the bigger dimension of the box, because the relay baton will occupy the box, and the larger dimension of the relay baton (that is, it's length) need to be less or equal than the larger dimension of the box.

The dimensions of the box are: 4 inches, 6 inches and 10 inches.

The larger dimension of the box is 10 inches. So, If we want the relay baton to fit in the box, the maximum length it can have is 10 inches.

8 0

3 years ago

In designing an experiment, the researcher can often choose many different levels of the various factors in order to try to find

artcher [175]

Answer:

a) 40 possible combinations

b) 8 possible combinations

Step-by-step explanation:

Given:

- Levels of temperature = 4

- Levels of catalysts = 2

- Levels of pressure = 5

Find:

To consider all possible combinations, how many experiments would need to be conducted?

With the three factors noted, how many experiments would need to be run to cover all possible combinations with each of the three factors at two levels?

Solution:

- We experiment each of the 3 factors to a certain level. So to conduct any experiment we have:

Temperature = 4C1 = 4 possibilities

Catalysts = 2C1 = 2 possibilities

Pressure = 5C1 = 5 possibilities.

- Hence, the total outcome for one particular experiment is a combination of all 3 factors possibility:

Total possible outcomes = 4*2*5 = 40 possible combinations

- Similarly if all factors are restricted to two levels only we have:

Temperature = 2C1 = 2 possibilities

Catalysts = 2C1 = 2 possibilities

Pressure = 2C1 = 2 possibilities.

- Hence, the total outcome for one particular experiment is a combination of all 3 factors possibility:

Total possible outcomes = 2*2*2 = 8 possible combinations

6 0

3 years ago