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Illusion [34]
3 years ago
7

Sin^2x/cos^2 + sinxcscx = sec^2x Identify it, please explain so I know how you did it, thanks

Mathematics
1 answer:
max2010maxim [7]3 years ago
6 0

\frac{sin^2x}{cos^2x} + sin x *cscx\\ tan^2x + \frac{sin x}{sin x} \\ tan^2x + 1\\ sec^2x

\frac{sin^2x}{cos^2x} = tan^2x

csc x = \frac{1}{sinx}

tan^2x + 1 = sec^2x

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Calculate the new balance of an account that has been sitting for three years with a 1.5% interest rate and had an initial depos
maksim [4K]

Answer:

$5225

Step-by-step explanation:

Use the formula for the amount after simple interest: A = P(1 + rt)

"A" is the final amount, or balance.

"P" is the principal, or the starting amount.

"r" is the rate of interest in decimal form.

"t" is the time.

What we know:

P = 5000

t = 3

r = 1.5%

Convert the rate to decimal form by dividing by 100, or moving the decimal place two places to the left.

1.5% => 0.015 = r

Substitute what we know into the formula:

A = P(1 + rt)

A = 5000(1 + (0.015)(3))     <=simplify

A = 5000(1 + 0.045)

A = 5000(1.045)

A = 5225     <= new balance

The new balance of an account is $5225.

4 0
3 years ago
Which statements accurately describe the function f(x) = 3(18)*? Select three options.
Yanka [14]

Answer:

Step-by-step explanation:

Without the variable x, your "f(x) = 3(18)*" is not a function.  If you meant

f(x) = 3(18)^x, then the domain is "the set of all real numbers," and the range is (0, infinity).

the initial value is 3:  f(0) = 3(18)^0 = 3(1) = 3

7 0
3 years ago
The cost of Ms. Clark's restaurant meal is $25.50.
Ivan
With tip she paid a total of $30.60
5 0
3 years ago
Write 504 as a product of primes. Use index notation when giving your answer.
Sergio039 [100]

Prime Factors of 504: 2, 3, 7

23 × 32 × 71 where 2, 3, 7 are prime.

7 0
2 years ago
By driving 8 mph faster than Bob, John can make a 230 mile trip in one half hour less. How fast does Bob drive on the trip? Roun
____ [38]

Answer: The speed of Bob is 56.8 km/hr.

Step-by-step explanation:

Let the speed of Bob be 'x'.

Let the speed of John be 'x-8'.

Distance covered = 230 miles

time = 1\dfrac{1}{2}=\dfrac{3}{2}\ hr

According to question, we get that

\dfrac{230}{x}-\dfrac{230}{x+8}=\dfrac{3}{2}\\\\230\dfrac{x+8-x}{x(x+8)}=\dfrac{3}{2}\\\\\dfrac{230\times 8}{x^2+8x}=\dfrac{3}{2}\\\\\dfrac{1840}{x^2+8x}=\dfrac{3}{2}\\\\1840\times 2=3x^2+24x\\\\3680=3x^2+24x\\\\3x^2+24x-3680=0\\\\x\approx 56.8\ km/hr

Hence, the speed of Bob is 56.8 km/hr.

6 0
3 years ago
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