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3 years ago

11

Solve the equation for all values of x. Not really sure how to do this? cos x = 3*cos x - 2

1 answer:

I am Lyosha [343]3 years ago

5 0

$\bf cos(x)=3cos(x)-2\implies 0=3cos(x)-2-cos(x)
\\\\\\
0=2cos(x)-2\implies 2=2cos(x)\implies \cfrac{2}{2}=cos(x)\implies 1=cos(x)
\\\\\\
cos^{-1}(1)=\measuredangle x\implies \measuredangle x=
\begin{cases}
0\\
2\pi 
\end{cases}$

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A bouncing ball reaches a height of 54 inches at its first peak, 36 inches at its second peak, and 24 inches at its third peak.

steposvetlana [31]

54, 36, 24 are the 1st 3 element of a geometric progression with 2/3 as a common ratio: PROOF:
the 1st term is 54, (a₁= 54) the 2nd term a₂ = 24, then
(a₂ = a₁.r) or 36 = 54.r → r= 36/54 = 2/3. Same logique for the 3rd term.
So 2/3 is common ratio. We know that :U(n) = a.(r)ⁿ⁻¹. Then if a =54 and r = x (given by the problem), then f(x) = 54.xⁿ⁻¹
n, being the rank of any element of this geometric progression

7 0

3 years ago

Read 2 more answers

Help with #9 linked above! Please help!

jasenka [17]

y = A(Bx - C)ⁿ + D

A is a vertical stretch (or shrink if |A| < 1)

B is a vertical shrink (or stretch if |B| < 1)

C is a shift to the right (or left if C is negative) → notice that Bx - C is "-C" so to take the opposite

D is a shift up (or down if D is negative)

when C = -3, it is a shift to the left 3 units

when D = -7, it is a shift down 7 units

Answer: B

6 0

3 years ago

Can some one please help me find the solution of the question

creativ13 [48]

Answer:

x=16°

Step-by-step explanation:

tanθ=opposite/adjacent

tan(<CAB)=BC/AB

<CAB=tan⁻¹(21/29)=35.9097308°

tanθ=opposite/adjacent

tan(<DAB)=BD/AB

<DAB=tan⁻¹((21/2)/29)=19.90374954°

<CAB=<DAB+x

x=<CAB-<DAB

=35.9097308-19.90374954

x=16.00598126°

8 0

2 years ago

Can someone please help?

riadik2000 [5.3K]

Answer:

I;m sorry if im wrong but i think it would be either b or d sorry if im wrong at least i tried that is all that matters

Step-by-step explanation:

8 0

3 years ago

A house worth $70,000 when purchased was worth $67,000 after the first year and $64,000 after the second year. If the economy do

Citrus2011 [14]

Answer:

a) The formula for the sequence is

$a_n = 67,000 -3,000(n-1)$

b) $a_7 = 49,000$

Step-by-step explanation:

Note that the difference between any two consecutive terms in the sequence is always equal to $3,000

$67,000-70,000= -3,000\\\\64,000-67,000=-3,000$

Then we have an arithmetic sequence where each term increases by a magnitude of 3,000 with respect to the previous term.

The explicit formula for an arithmetic sequence is:

$a_n = a_1 +d(n-1)$

Where d is the common difference between the consecutive terms of the sequence

$d = -3,000$

$a_1$ is the first term, or the value of the house after year 1 $a_1= 67,000$

n represents the number of years since the house was purchased

With

n={0, 1, 2, 3, 4, 5, 6, 7,.., n}

a) Then the formula for the sequence is

$a_n = 67,000 -3,000(n-1)$

With

n={0, 1, 2, 3, 4, 5, 6, 7,.., n}

---------------------------------------------------------------------------------------------

b) Now we can use the formula to find the price of the house after 7 years

$a_7 = 67,000 -3,000(7-1)$

$a_7 = 67,000 -3,000(6)$

$a_7 = 49,000$

3 0

3 years ago