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3 years ago

Find the 16th term of the arithmetic sequence whose common difference is d=6 and whose first term is a1=1.

Mathematics

1 answer:

sertanlavr [38]3 years ago

4 0

Answer:

The 16th term is 91

Step-by-step explanation:

The 16th term is U16 given by

U16=a+(n-1)d

U16=1+(16-1)×6

U16=1+(15×6)

U16=91

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Given that x=1+2tan theta and y=3sec theta - 4, by eliminating theta, determine a relationship between x and y only !

Naddik [55]

$x=1+2\tan\theta\\\\ 2\tan\theta=x-1\\\\ \tan\theta=\frac{1}{2}(x-1)\\\\\\ y=3\sec\theta-4\\\\ 3\sec\theta=y+4\\\\ \sec\theta=\frac{1}{3}(y+4)$

We'll use the formula below

$\tan^2\alpha+1=\sec^2\alpha\iff \sec^2\alpha-\tan^2\alpha=1$

So:

$\sec^2\theta-\tan^2\theta=1\\\\ (\frac{1}{3}(y+4))^2-(\frac{1}{2}(x-1))^2=1\\\\ \boxed{\dfrac{(y+4)^2}{9}-\dfrac{(x-1)^2}{4}=1}$

-----------------//----------------

$x=\sin\theta\\\\\\ y=\cos^2\theta-3\\\\ \cos^2\theta=y+3$

We'll use the formula below

$\sin^2\alpha+\cos^2\alpha=1$

So:

$\sin^2\theta+\cos^2\theta=1\\\\ x^2+(y+3)=1\\\\ \boxed{x^2+y=-2}$

7 0

3 years ago

What is the slope of the line represented by the equation y = 1/5x-3?

Romashka-Z-Leto [24]

Answer:

1/5

Step-by-step explanation:

Your equation is written in the form y=mx+b, where m is the slope and b is the y-intercept.

m=1/5, so the slope is 1/5

7 0

4 years ago

12,27,42,57

geniusboy [140]

A1=12, a2=27, a3=42, etc. The pattern is that you’re always adding 15 after starting with 12. So the general rule is...

an=12+15(n-1)

So then...

a18=12+15(18-1)
a18=12+15(17)
a18=267

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3 years ago

How many ounces are in 5 gallons?

Serhud [2]

Answer:

640

Step-by-step explanation:

there is 1 gallon for every 128 ounces

so 1 gal= 128z

to find 5gal= ?oz

you multiply 128 by 5 which gives u 640

which gives u 640 oz

hope this helps

6 0

4 years ago

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Which equation represents a line with a slope of zero?

dlinn [17]

Y = 4 is the answer.
Thanks (:

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3 years ago

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