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3 years ago

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Questions 8-12 are 2 points each.)

1 answer:

Makovka662 [10]3 years ago

5 0

Idk I’m so srry I dumb

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Help! Given that tanθ=-1, what is the value of secθ, for 3π/2<θ<2π?

user100 [1]

Answer: Choice B) $\sqrt{2}$

Work Shown:

$\sec^2(\theta) = \tan^2(\theta) + 1\\\\\sec^2(\theta) = (\tan(\theta))^2 + 1\\\\\sec^2(\theta) = (-1)^2 + 1\\\\\sec^2(\theta) = 2\\\\\sec(\theta) = \sqrt{2}\\\\$

Note: secant is positive in quadrant Q4, when theta is between 3pi/2 radians and 2pi radians (270 degrees and 360 degrees). So that's why we don't consider the minus form of the plus minus.

5 0

2 years ago

If S_1=1,S_2=8 and S_n=S_n-1+2S_n-2 whenever n≥2. Show that S_n=3⋅2n−1+2(−1)n for all n≥1.

Snezhnost [94]

You can try to show this by induction:

• According to the given closed form, we have $S_1=3\times2^{1-1}+2(-1)^1=3-2=1$ , which agrees with the initial value <em>S</em>₁ = 1.

• Assume the closed form is correct for all <em>n</em> up to <em>n</em> = <em>k</em>. In particular, we assume

$S_{k-1}=3\times2^{(k-1)-1}+2(-1)^{k-1}=3\times2^{k-2}+2(-1)^{k-1}$

and

$S_k=3\times2^{k-1}+2(-1)^k$

We want to then use this assumption to show the closed form is correct for <em>n</em> = <em>k</em> + 1, or

$S_{k+1}=3\times2^{(k+1)-1}+2(-1)^{k+1}=3\times2^k+2(-1)^{k+1}$

From the given recurrence, we know

$S_{k+1}=S_k+2S_{k-1}$

so that

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 2\left(3\times2^{k-2}+2(-1)^{k-1}\right)$

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 3\times2^{k-1}+4(-1)^{k-1}$

$S_{k+1}=2\times3\times2^{k-1}+(-1)^k\left(2+4(-1)^{-1}\right)$

$S_{k+1}=3\times2^k-2(-1)^k$

$S_{k+1}=3\times2^k+2(-1)(-1)^k$

$\boxed{S_{k+1}=3\times2^k+2(-1)^{k+1}}$

which is what we needed. QED

6 0

2 years ago

Whats the diffrence of 2 2/3 - 1 2/5 write answer in simplest form

Fofino [41]

$2 \frac{2}{3}-1 \frac{2}{5}=2 \frac{2 \times 5}{3 \times 5}-1 \frac{2 \times 3}{5 \times 3}=2 \frac{10}{15}-1 \frac{6}{15}=\boxed{1\frac{4}{15}}$

3 0

3 years ago

Read 2 more answers

HELP ASAP MARKING AS BRINLIST

weeeeeb [17]

Answer:

Because they are equal (Right angle)

Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

8 0

3 years ago

Read 2 more answers

Show how to use the distributive property to simplify 4(5+x).

VladimirAG [237]

Answer:

Step-by-step explanation:

Ur mom

8 0

3 years ago