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3 years ago

Find the 53" term of the following arithmetic sequence. 3, 11, 19, 27, ...

Mathematics

1 answer:

statuscvo [17]3 years ago

5 0

Answer:

419

Step-by-step explanation:

a=3

d=11-3=8

$a_{n}=a+(n-1)d\\n=53\\a_{53}=3+(53-1)*8\\=3+52*8\\=3+416\\=419$

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Point b has coordinates (-8,15) and lies on the circle whose equation is x^2+y^2=289. If an angles is drawn in standard position

Alenkinab [10]

Answer:

$\cos \theta=-\dfrac{8}{17}$

Step-by-step explanation:

Coordinates of Point b $=(-8,15)$

b lies on the circle whose equation is $x^2+y^2=289$

$x^2+y^2=17^2$

Comparing with the general form a circle with center at the origin: $x^2+y^2=r^2$

The radius of the circle =17 which is the length of the hypotenuse of the terminal ray through point b.

For an angle drawn in standard position through point b,

x=-8 which is negative

y=15 which is positive

Therefore, the angle is in Quadrant II.

$\cos \theta=\dfrac{Adjacent}{Hypotenuse} \\$Adjacent=-8\\Hypotenuse=17\\\cos \theta=\dfrac{-8}{17} \\\cos \theta=-\dfrac{8}{17}$

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3 years ago

Sin(x2 + y2) da r , where r is the region in the first quadrant between the circles with center the origin and radii 2 and 5

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Converting to polar coordinates gives

$\displaystyle\iint_R\sin(x^2+y^2)\,\mathrm dA=\int_{\theta=0}^{\theta=\pi/2}\int_{r=2}^{r=5}\sin(r^2)r\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle\pi\int_{r=2}^{r=5}2r\sin(r^2)\,\mathrm dr$
$=\displaystyle\pi\int_{r^2=4}^{r^2=25}\sin(r^2)\,\mathrm d(r^2)$
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3 years ago

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Rudik [331]

Answer:

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Step-by-step explanation:

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4 years ago

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Usimov [2.4K]

Answer:

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Step-by-step explanation:

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