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3 years ago

Simplify and write the trigonometric expression in terms of sine and cosine:

Mathematics

1 answer:

kicyunya [14]3 years ago

6 0

Answer:

f(x) = + cosx or - cosx

Step-by-step explanation:

(2+tan^2x/sec^2x) -1 =(f(x))^2

=(( 1 + sec^2x)/sec^2x) -1

= 1 / sec^2x + 1 - 1

= 1 / sec^2x

= cos^2x

(f(x))^2 = cos^2x

f(x) = + cosx or - cosx

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Vern sold his 1964 Ford Mustang for $55,000 and wants to invest the money to earn him 3.6% interest per year. He will put some o

noname [10]

Answer: He should invest $44000 in fund A and $11000 in fund B.

Step-by-step explanation:

Let x represent the amount which he invested in fund A.

Let y represent the amount which he invested in fund B.

Vern sold his 1964 Ford Mustang for $55,000 and wants to invest the money to earn him 3.6% interest per year. He will put some of the money into Fund A that earns 2% per year and the rest in Fund B that earns 10% per year.. This means that

x + y = 55000

The formula for determining simple interest is expressed as

I = PRT/100

Considering fund A,

P = $x

T = 1 year

R = 2℅

I = (x × 2 × 1)/100 = 0.02x

Considering fund B,

P = $y

T = 1 year

R = 10℅

I = (y × 10 × 1)/100 = 0.1y

The interest that he wants to earn on the total amount in a year is 3.6%. The interest would be

I = (55000 × 3.6 × 1)/100 = 1980

Therefore,

0.02x + 0.1y = 1980 - - - - - - - - - -1

Substituting x = 55000 - y into equation 1, it becomes

0.02(55000 - y) + 0.1y = 1980

1100 - 0.02y + 0.1y = 1980

- 0.02y + 0.1y = 1980 - 1100

0.08y = 880

y = 880/0.08

y = 11000

x = 55000 - y = 55000 - 11000

x = 44000

4 0

3 years ago

Determine whether the following series converge or diverge

Mars2501 [29]

An alternating series $\sum\limits_n(-1)^na_n$ converges if $|(-1)^na_n|=|a_n|$ is monotonic and $a_n\to0$ as $n\to\infty$ . Here $a_n=\dfrac1{\ln(n+1)}$ .

Let $f(x)=\ln(x+1)$ . Then $f'(x)=\dfrac1{x+1}$ , which is positive for all $x>-1$ , so $\ln(x+1)$ is monotonically increasing for $x>-1$ . This would mean $\dfrac1{\ln(x+1)}$ must be a monotonically decreasing sequence over the same interval, and so must $a_n$ .

Because $a_n$ is monotonically increasing, but will still always be positive, it follows that $a_n\to0$ as $n\to\infty$ .

So, $\sum\limits_n(-1)^na_n$ converges.

5 0

3 years ago

Which migonometric rates are comect for mangle<br> ABC? Select three options

aleksklad [387]

Answer:

semoga jawapan ini dapat membantu

6 0

3 years ago

Evaluate 10 + 8÷4 - 12

Kryger [21]

Answer:

Step-by-step explanation:

evaluate 10 + (8÷4) - 12

3 0

1 year ago

Read 2 more answers

Youre purchasing a new television with a 32" screen. the 32" measurement represents the diagonal measurement of the screen. You

Nonamiya [84]

Answer:

B. 28 inches

Step-by-step explanation:

We can use the Pythagorean theorem to solve this problem.

a^2 +b^2 =c^2 where a and b are the legs and c is the hypotenuse (diagonal)

16^2 + b^2 = 32^2

256 + b^2 =1024

Subtract 256 from each side

256-256 + b^2 =1024-256

b^2 = 768

Take the square root of each side

sqrt(b^2) = sqrt(768)

b = 27.7128129

Rounding to the nearest inche

b = 28 inches

3 0

2 years ago