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3 years ago

Solve the equation 3cosx = 5sinx for x in the interval 0 smaller than equal to x smaller than equal to 360 degrees.

Mathematics

1 answer:

Artist 52 [7]3 years ago

5 0

The equation is false, because 3 $\neq$ 4.794579

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Kate currently has an account balance of $7,194.66. She opened the account 21 years ago with a deposit of $2,978.41. If the inte

jolli1 [7]

Use the attached formula.
exp = [log (total / principal) / n*years]
where "n" is compounding periods per year
exp = [log (7,194.66 / 2,978.41) / (365*21)
exp = log ( 2.4156042989 ) / 7,665
exp = log ( 2.4156042989 ) / 7,665
exp = 0.38302579382 / 7,665
exp = 0.00004997074935681670 

rate = (10^exp -1)* n
rate = (10^0.00004997074935681670 -1) * n
rate = (1.0001150685 -1) * 365
rate = (.0001150685) * 365
rate = 0.0420000025 
rate = 4.20000025 %
rate = 4.2 %

Yes, it's just that easy. LOL

5 0

3 years ago

Read 2 more answers

If the sum of the even integers between 1 and k, inclusive, is equal to 2k, what is the value of k?

Alisiya [41]

If $k$ is odd, then

$\displaystyle\sum_{n=1}^{\lfloor k/2\rfloor}2n=2\dfrac{\left\lfloor\frac k2\right\rfloor\left(\left\lfloor\frac k2\right\rfloor+1\right)}2=\left\lfloor\dfrac k2\right\rfloor^2+\left\lfloor\dfrac k2\right\rfloor$

while if $k$ is even, then the sum would be

$\displaystyle\sum_{n=1}^{k/2}2n=2\dfrac{\frac k2\left(\frac k2+1\right)}2=\dfrac{k^2+2k}4$

The latter case is easier to solve:

$\dfrac{k^2+2k}4=2k\implies k^2-6k=k(k-6)=0$

which means $k=6$ .

In the odd case, instead of considering the above equation we can consider the partial sums. If $k$ is odd, then the sum of the even integers between 1 and $k$ would be

$S=2+4+6+\cdots+(k-5)+(k-3)+(k-1)$

Now consider the partial sum up to the second-to-last term,

$S^*=2+4+6+\cdots+(k-5)+(k-3)$

Subtracting this from the previous partial sum, we have

$S-S^*=k-1$

We're given that the sums must add to $2k$ , which means

$S=2k$
$S^*=2(k-2)$

But taking the differences now yields

$S-S^*=2k-2(k-2)=4$

and there is only one $k$ for which $k-1=4$ ; namely, $k=5$ . However, the sum of the even integers between 1 and 5 is $2+4=6$ , whereas $2k=10\neq6$ . So there are no solutions to this over the odd integers.

5 0

3 years ago

Jonah is making a model house. The real house is 22 feet tall. His model is 10 inches tall. What is the foot : inch ratio for hi

Bumek [7]

Answer:

11: 5

Step-by-step explanation:

22 feet: 10 inches Reduce. 22/10 = 11/5

6 0

2 years ago

The force of gravity on the moon is approximately one sixth that of earth. the direct variation equation for weight on earth com

Inga [223]

Plug in 180 for e and solve for m

8 0

2 years ago

Anit [1.1K]

Answer:

-1/3

Step-by-step explanation:

(-2, 5) and (1, 4)

Slope:

m=(y2-y1)/(x2-x1)

m=(4-5)/(1+2)

m=(-1)/3

m= -1/3

5 0

2 years ago