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Dmitry_Shevchenko [17]
3 years ago
14

I am trying to figure this question: 1 + tan^2A = Sec^2A

Mathematics
1 answer:
chubhunter [2.5K]3 years ago
3 0

Answer:

see explanation

Step-by-step explanation:

Using the Pythagorean identity

cos²A + sin²A = 1 ( divide terms by cos²A )

\frac{cos^2A}{cos^2A} + \frac{sin^2A}{cos^2A} = \frac{1}{cos^2A} , that is

1 + tan²A = sec²A ← as required

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Kira owes Mark $5, and Mark owes Kira $7. Which statement means the same thing?
Mice21 [21]

Answer:

mark owes Kira $2

I think

5 0
3 years ago
T3=-6.5 and t5=-3.9 determine d
nekit [7.7K]
t_3=-6.5;\ t_5=-3.9\\\\t_5-t_3=2d\\\\2d=-3.9-(-6.5)\\\\2d=-3.9+6.5\\\\2d=2.6\ \ \ \ |divide\ both\ sides\ by\ 2\\\\\boxed{d=1.3}
4 0
3 years ago
Bob pays $2 to see a shoe if bob has $4 before the show how much will he have left after the show
SIZIF [17.4K]

Answer:

$2

Step-by-step explanation:

4 - 2 = 2

7 0
3 years ago
If your starting salary is $40,000 and you  receive a 4.2% raise every year, how much  TOTAL money will you make in 15 years?
Oliga [24]
The first year, the amount is 40,000

the second year is 40000 + 4.2% of 40000, or 0.042 * 4000, so 40000+(0.042*4000)
common factoring that  we get 40000(1 + 0.042), or just 40000(1.042)

in short, the starting amount is 40000, and to get the next term's value you'd use the "common ratio" of 1.042, namely the multiplier of 1.042.

for the third year it'll be 40000(1.042) + (0.042 *40000(1.042) ), again, common factoring that

40000(1.042)(1 + 0.042) or 40000(1.042)(1.042) or 40000(1.042)²

therefore,

\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=40000\\
r=1.042\\
n=15
\end{cases}
\\\\\\
S_{15}=40000\left( \cfrac{1-1.042^{15}}{1-1.042} \right)\implies S_{15}\approx 40000\left( \cfrac{-0.8536}{-0.042} \right)
\\\\\\
S_{15}\approx 812951.42
5 0
3 years ago
Twin Primes Conjecture A natural number is called a prime number if it has exactly two factors, 1 and itself. 1 is not a prime n
prohojiy [21]

Answer:

See explanation below.

Step-by-step explanation:

The prime numbers are bold:

1  2  3  4  5  6  7  8  9  10  11 12  13  14  15  16  17

18  19  20  21  22  23  24  25  26  27  28  29  30  31

a) We can see that as we go higher, twin primes seem less frequent but even considering that, there is an infinite number of twin primes. If you go high enough you will still eventually find a prime that is separated from the next prime number by just one composite number.

b) I think it's interesting the amount of time that has been devoted to prove this conjecture and the amount of mathematicians who have been involved in this. One of the most interesting facts was that in 2004 a purported proof (by R. F. Arenstorf) of the conjecture was published but a serious error was found on it so the conjecture remains open.

6 0
4 years ago
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