MATHEMATICS HIGH SCHOOL

Use the method of quadrature to estimate the area under the curve y=-x^2+5 and above the x-axis from x=0 to x=2.

Answers

Answer 1

Answer:

Answer:

Area = $(22)/(3)$

Step-by-step explanation:

Given is a curve

$y=-x^2+5$

we have to find the area of this curve above x axis from 0 to 2

By method of quadrature we know that area of a curve above x axis is given by,

$\int\limits^a_bf( {x} )\, dx$

Here a= 0 and b =2

Substitute to get

Area = $\int\limits^0_2 {-x^2+5} \, dx \n=(-x^3)/(3) +5x$

Substituting limits

Area = $(-8)/(3) +10 =(22)/(3)$

Answer 2

Answer: I'm a calculus teacher at the high school level and I have never heard of quadrature. I teach from an AP approved college-level text so...I'll do it using the antiderivative! Setting that up to integrate we have $- \int\limits^2_0 { (x^2-5)} \, dx$ . If you notice, I pulled the negative out in front of the integral and changed the signs in the function. So it could really be rewritten as $-1 \int\limits^2_0 {(x^2-5)} \, dx$ . Integrating we have $-1[ (x^3)/(3) -5x]$ from 0 to 2. Subbing in those bounds, we have $-1[( (2^3)/(3)-5(2))-( (0^3)/(3)-5(0))]$ which simplifies to $-1( (8)/(3)-10)$ . Distributing the -1 in gives us $10- (8)/(3)= (22)/(3)$

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Complete the following statements by writing the missing word (s).16. If two lines intersect, then their intersection is exactly ________________.

17. _____________ line can be drawn through two points.

18. If two planes intersect, then their intersection is ________________.

19. Through any three non-collinear points there exists exactly ______________.

Answers

16. one point, and only one

17. one, and only one

18. a line

19. one and only one plane

16 a point
17 one
18 a line
19 one plane

Consider the sequence 51, 43, 35, 37, 19 which function describes the sequence.

Answers

The function f(n) = 8n - 5 + (-1)ⁿ × 3 indeed generates the given sequence 51, 43, 35, 37, 19.

The given sequence is 51, 43, 35, 37, 19. To identify the underlying function describing this sequence, let's analyze the pattern between the terms.

Subtraction: If we look at the differences between consecutive terms, we get the following sequence of differences: -8, -8, 2, -18.

Alternating Behavior: The differences between terms seem to alternate between subtracting 8 and adding 2.

Possible Linear Function: The alternating behavior suggests that this sequence might be generated by a linear function with some sort of periodic or alternating component.

Linear Function with Alternating Component: A possible function to describe this sequence could be:

f(n) = 8n - 5 + (-1)ⁿ × 3

Here, n represents the position in the sequence (starting from n = 1), and (-1)ⁿ introduces the alternating component. When n is even, (-1)ⁿ becomes 1, and when n is odd, (-1)ⁿ becomes -1.

Now, let's test this function with the given values:

- For n = 1: f(1) = 8(1) - 5 + (-1)¹ × 3 = 8 - 5 + (-1) × 3 = 3 - 3 = 0

- For n = 2: f(2) = 8(2) - 5 + (-1)² × 3 = 16 - 5 + 1 × 3 = 11 + 3 = 14

- For n = 3: f(3) = 8(3) - 5 + (-1)³ × 3 = 24 - 5 - 3 = 19 - 3 = 16

- For n = 4: f(4) = 8(4) - 5 + (-1)⁴ × 3 = 32 - 5 + 3 = 27 + 3 = 30

- For n = 5: f(5) = 8(5) - 5 + (-1)⁵ × 3 = 40 - 5 - 3 = 35 - 3 = 32

For similar questions on sequence

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Max scored 9 runs on Monday and 11 runs on Tuesday. How many runs did he score in all?

Answers

The totalrun he scored in all would be 20.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We have been given that max scored 9 runs on Monday and 11 runs on Tuesday.

We need to find the total number of scores he runs in all.

The run scored on Monday = 9

The run scored on Tuesday= 11

The total = run scored on Monday + run scored on Tuesday

The total = 9 + 11 = 20

The totalscore he runs in all would be 20.

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Out of those two days ? 20 runs

In the number 1,934 , is the value of the 9 in hundreds place ten times as great as the value of 3 in the tens place?

Answers

Answer:

No, the value of the 9 in the hundreds place in the number 1,934 is not ten times as great as the value of the 3 in the tens place.

Step-by-step explanation:

The value of the 9 in the hundreds place is 9 multiplied by 100, which is 900.

The value of the 3 in the tens place is 3 multiplied by 10, which is 30.

So, no the value of the 9 in the hundreds place in the number 1,934 is not ten times as great as the value of the 3 in the tens place.

What is the radius of a circle circumscribed about a rectangle with a length of 8 centimeters and a width of 6 centimeters?

Answers

if we think about it, the touching parts of the rectangle and circle are the corners

the distance between opposite corners is the diameter of the circle
the radius would be 1/2 diameter
so we just use the pythagorean theorem to find the legnth of the diagonal and thus the diameter then halve that to get radtius

a^2+b^2=c^2
c=hypotonuse
a and b are legs

8^2+6^2=c^2
64+36=c^2
100=c^2
10=c

10=diameter
10/2=5=radis

5 centimeters

Find the value of c that makes each trinomial a perfect square.

Answers

Answer:

The answer to your question is the letter a.

Step-by-step explanation:

Data

x² + 12x + c

If this trinomial is a perfect square trinomial, the third term must be half the second term divided by the square root of the first term, and to the second power.

-Get half the second term

12x/2 = 6x

-Divide by the square root of the first term

6x/x = 6

-Express the result to the second power

6² = 36

-Write the perfect square trinomial

(x² + 12x + 36) = (x + 6)²

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