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3 years ago

In which

Mathematics

1 answer:

MrRa [10]3 years ago

7 0

The orthocenter is outside the triangle if it's an obtuse triangle.

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Ketch the bounded region enclosed by y=e2x,y=e4xy=e2x,y=e4x and x=1x=1. decide whether to integrate with respect to xx or yy, an

slamgirl [31]

A) See the attached graph. The purple area appears to be what you want to find.

b) Integrating with respect to x seems much easier. If one were to integrate over y, there would need to be two regions of integration: [1, e^2] and [e^2, e^4].

c) $\int\limits^1_0 {(e^{4x}-e^{2x})} \, dx =\frac{1}{4}(e^{4}-1) -\frac{1}{2}(e^{2}-1) \approx 10.2050094588$

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3 years ago

The Controlled Substances Act of 1970 categorized drugs such as morphine and cocaine as Schedule ________ drugs.

givi [52]

B. II Schedule 2: Examples of Schedule 2 drugs include Cocaine and Morphine.

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4 years ago

AP Calculus redo! I know the answer but can't figure out exactly how to get there. Thank you! I want to work through the steps.

Monica [59]

You're approximating

$\displaystyle\int_1^5 x^2\,\mathrm dx$

with a Riemann sum, which comes in the form

$\displaystyle\int_a^b f(x)\,\mathrm dx=\lim_{n\to\infty}\sum_{i=1}^nf(x_i)\Delta x_i$

where $x_i$ are sample points chosen according to some decided-upon rule, and $\Delta x_i$ is the distance between adjacent sample points in the interval.

The simplest way of approximating the definite integral is by partitioning the interval into equally-spaced subintervals, in which case $\Delta x=\dfrac{b-a}n$ , and since $[a,b]=[1,5]$ , we have

$\Delta x=\dfrac{5-1}n=\dfrac4n$

Using the right-endpoint method, we approximate the area under $f(x)$ with rectangles whose heights are determined by their right endpoints. These endpoints are chosen by successively adding the subinterval length to the starting point of the interval of integration.

So if we had $n=4$ subintervals, we'd split up the interval of integration as

$[1,5]=[1,2]\cup[2,3]\cup[3,4]\cup[4,5]$

Note that the right endpoints follow a precise pattern of

$2=1+\dfrac44$
$3=1+\dfrac84$
$4=1+\dfrac{12}4$
$5=1+\dfrac{16}4$

The height of each rectangle is then given by the values above getting squared (since $f(x)=x^2$ ). So continuing with the example of $n=4$ , the Riemann sum would be

$\displaystyle\sum_{i=1}^4\left(1+\dfrac{4i}4\right)^2\dfrac44$

For $n=5$ ,

$\displaystyle\sum_{i=1}^5\left(1+\dfrac{4i}5\right)^2\dfrac45$

and so on, so that the definite integral is given exactly by the infinite sum

$\displaystyle\lim_{n\to\infty}\sum_{i=1}^n\left(1+\dfrac{4i}n\right)^2\dfrac4n$

4 0

3 years ago

List 3 terms in the expression 4x + 5y - 12 - x + 3y A. B. C.

adell [148]

Answer:

A. 3x

B. 8y

C. -12

Step-by-step explanation:

Combine like terms. Same variable raiased to the same exponent.

3 0

4 years ago

In triangle OPQ, p = 38 cm, q = 29 cm and Angle O=39º. Find the length of o, to the nearest

Lisa [10]

Answer:

The length of o is 24 centimeters

Step-by-step explanation:

In Δ OPQ

∵ Side p is opposite to ∠P

∵ Side q is opposite to ∠Q

∵ Side o is opposite to ∠O

→ To find side o we must use the cosine rule

∴ o = $\sqrt{p^{2}+q^{2}-2(p)(q).cos(O) }$

∵ p = 38 cm

∵ q = 29 cm

∵ m∠O = 39°

→ Substitute them in the rule to find o

∴ o = $\sqrt{(38)^{2}+(29)^{2}-2(38)(29).cos(39)}$

∴ o = 23.92008154

→ Round it to the nearest centimeter (whole number)

∴ o = 24 centimeters

∴ The length of o is 24 centimeters

6 0

3 years ago