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Jet001 [13]
2 years ago
15

Read this excerpt from a speech by televangelist Jerry Falwell, 1980.

Advanced Placement (AP)
1 answer:
IrinaVladis [17]2 years ago
6 0
Explanation is

in a file
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Use midpoints to approxiamte the area under the curve y=f(x) 5 sin(xx)!+ 2.5 cos(4xx) on the interval [0,1] using 10 equal subdi
alisha [4.7K]

Subdividing [0, 1] into 10 equally spaced intervals of length \Delta x=\frac{1-0}{10}=\frac1{10} gives the partition

[0,1] = \left[0,\dfrac1{10}\right] \cup \left[\dfrac1{10},\dfrac2{10}\right] \cup \cdots \cup \left[\dfrac9{10},1\right]

The i-th subinterval has left and right endpoints, respectively, given by

\ell_i = \dfrac{i-1}{10} \text{ and } r_i = \dfrac i{10}

where i\in\{1,2,3,\ldots,10\}.

The midpoint of the i-th interval is the average of these,

m_i = \dfrac{\ell_i+r_i}2 = \dfrac{2i-1}{20} \in \left\{\dfrac1{20},\dfrac3{20},\dfrac5{20},\ldots,\dfrac{19}{20}\right\}

We approximate the area under f(x) over [0, 1] by the Riemann sum,

\displaystyle \int_0^1 f(x) \, dx \approx \sum_{i=1}^{10} f(m_i) \Delta x \\\\ ~~~~~~~~ = \frac1{10} \sum_{i=1}^{10} \bigg(5\sin(\pi m_i) + 2.5 \cos(4\pi m_i)\bigg) \\\\ ~~~~~~~~ = \frac{\sin\left(\frac\pi{20}\right) + \sin\left(\frac{3\pi}{20}\right) + \cdots + \sin\left(\frac{19\pi}{20}\right)}2 \\\\ ~~~~~~~~~~~~ + \dfrac{\cos\left(\frac\pi5\right) + \cos\left(\frac{3\pi}5\right) + \cdots + \cos\left(\frac{19\pi}5\right)}4 \\\\ ~~~~~~~~ \approx 3.19623

(D)

6 0
2 years ago
what are the coordinates of the image of point (-1,-2) under a dilation of 3/2 with respect to the origin?
serious [3.7K]

Answer:

Point P '(-1,-2) is the image of point P(-2,3) under translation T

Explanation:

7 0
3 years ago
UUUU MVC
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Three strength training exercises that can be performed by adults at an average fitness level are:

Squats: Squats are particularly effective exercises because they allow you to work your legs, core and upper body simultaneously. They also allow you to add weight progressively through the use of dumbbells.

Planks: Planks are a type of exercise that accelerate strength training. They allow you to use your hands, sides and forearms. They also help you exercise your core, which is the basis for many everyday movements.

Rows: Rows are good exercises because they target the muscle groups that we do not engage often. These are our back muscles, which suffer greatly from sitting at a desk or hunching over a computer. Rows help improve posture and prevent back and shoulder problems.

Strength training leads to many benefits, including stronger muscles, bones and joints that help support your movement and reduced risk of injury during training.

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