Advanced Placement (AP), 11.10.2020 14:01 peoplearecoming

Which of the following is a characteristic shared by a weather satellite and an Earth observing satellite

Answers: 1

Show answers

Answers

Answer from: Quest

Answer: the interval on which the curve is concave up is (-∞, -1/2)====== $\displaystyle y = \int_{0}^x \frac{1}{1 + t + t^2} \; dt$ we find the interval where this curve is concave up by finding the interval in which the 2nd derivative is positive.differentiate the curve equation with respect to x $\begin{aligned} \frac{dy}{dx} & = \frac{d}{dx} \int_{0}^x \frac{1}{1 + t + t^2} \; dt \end{aligned}$ let the function f denote be the anti-derivative of the inside expression, i.e. a function such that $(d/dx)f(x) = 1/(1 + t + t^2)$ .then use the fundamental theorem of calculus: $\begin{aligned} \frac{dy}{dx} & = \frac{d}{dx} \int_{0}^x \frac{1}{1 + t + t^2} \; dt \\& = \frac{d}{dx} \big[ f(x) - f(0) \big] & & \text{\footnotesize apply ftc} \\ & = \frac{d}{dx}f(x) - 0 \\ & = \frac{1}{x + x + x^2} & & \text{\footnotesize since $\frac{d}{dx}f(x) = \frac{1}{1 + x + x^2}$ } \end{aligned}$ differentiate again to get second derivative. we can use chain rule with 1/x as the outside function and 1 + x + x² as the inside function $\begin{aligned} \frac{d}{dx} \left( \frac{dy}{dx} \right) & = \frac{d}{dx}\left(\frac{1}{1 + x + x^2} \right) \\ \frac{d^2y}{dx^2} & = \frac{-1}{\left(1 + x + x^2\right)^2} \cdot \tfrac{d}{dx}(1 + x + x^2) \\ & = \frac{-1}{\left(1 + x + x^2\right)^2} \cdot (1 + 2x) \\ & = \frac{-(1 + 2x)}{\left(1 + x + x^2\right)^2} \end{aligned}$ find critical numbers of the second derivative. these numbers are where the 2nd deriv. is undefined or zero.where the 2nd derivative is zero: set (d²y/dx²) to equal 0 and solve for x $\begin{aligned} 0 & = \frac{-(1 + 2x)}{\left(1 + x + x^2\right)^2} \\ 0 & = -(1+2x) \\ -1 & = 2x \\ x & = -1/2 \end{aligned}$ where the 2nd derivative is undefined: if the denominator is equal to zero, the derivative will be undefeined. attempting to solve the equation 1 + x + x² = 0results in a discriminant of $b^2 - 4ac = 1^2 - 4(1)(1) = -3$ meaning that the equal 1 + x + x² = 0 has no real solutions and therefore will never equal zero.======our only critical number is x = -1/2.this forms two intervals to test the sign for: (-∞, -1/2) and (-1/2, ∞)test values into the 2nd derivative for (-∞, -1/2)if we try x = -1, we get $\begin{aligned} \left.\frac{d^2y}{dx^2}\right|_{x = -1} & = \frac{-(1+2(-1))}{\left(1+(-1)+(-1)^2\right)^2} \\ & = \frac{-(1-2)}{1} \\ & = 1 \end{aligned}$ so the since the 2nd derivative of the curve is positive on the interval (-∞, -1/2), the curve is concave up on (-∞, -1/2)test values into the 2nd derivative for (-1/2, ∞)if we try x = 0, we get $\begin{aligned} \left.\frac{d^2y}{dx^2}\right|_{x = 0} & = \frac{-(1+2(0))}{\left(1+(0)+(0)^2\right)^2} \\ & = \frac{-(1)}{1} \\ & = -1 \end{aligned}$ so the since the 2nd derivative of the curve is positive on the interval (-∞, -1/2), the curve is concave down on (-∞, -1/2).the interval on which the curve is concave up is (-∞, -1/2)

Answer from: Quest

Ithink the answer is d

Answer from: Quest

It can the reader to have a broader understanding of the point or main idea of a passage/essay. if you use words with similar meanings throughout a written work, it can show the reader that the words reflect the key idea of a passage. this can really you to understand what is going on, and reflect on some key ideas and phrases that were mentioned in said written work.i hope this !

Answer from: Quest

answer:

i have the same question

Another question on Advanced Placement (AP)

Advanced Placement (AP), 23.06.2019 22:00

Amedical center’s rectangular parking lot currently has a length of 30 meters and a width of 20 meters. the center plans to expand both the length and the width of the parking lot by 2x meters. what polynomial in standard form represents the area of the expanded parking lot?

Answers: 2

Answer

Advanced Placement (AP), 24.06.2019 23:10

The use of a beat or a rhythm to remember something is

Answers: 1

Answer

Advanced Placement (AP), 25.06.2019 13:00

Which allows college students to work part time jobs to pay for educational expenses ?

Answers: 1

Answer

Advanced Placement (AP), 26.06.2019 03:30

Question 4 which was a foundation of the industrial revolution? a) large states held huge supplies of raw materials. b) coal replaced wood as the primary source of fuel. c) road infrastructure replaced waterways for transport. d) mercantilist policies drove down the price of goods. question 7 which was not a government response to the socialist challenges? a) establishing universal suffrage to all classes b) introducing medical insurance and pensions c) prohibiting underground employment for women d) restricting child labor for children under ten years old question 9 which was a cause of the boer war? a) movement and settlement of bantu peoples into afrikaner-populated states b) independence of northern afrikaner territories from british colonial authority c) evacuation of most afrikaner people out of south africa and back into europe d) british reconstitution of afrikaner-held territories into the union of south africa

Answers: 3

Answer

You know the right answer?

Which of the following is a characteristic shared by a weather satellite and an Earth observing sate...

Questions