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2 years ago

What basic trigonometric identity would you use to verify that

Mathematics

1 answer:

Dafna1 [17]2 years ago

6 0

Given the equation:

$\frac{\sin^2x+\text{cos}^2x}{\cos x}=\sec x$

Let's determine the trigonometric identity that you could be used to verify the exquation.

Let's determine the identity:

Apply the trigonometric identity:

$\sin ^2x+\cos ^2x=1$

$\cos x=\frac{1}{\sec x}$

Replace cosx for 1/secx

Thus, we have:

$\begin{gathered} \frac{\sin^2x+\cos^2x}{\frac{1}{\sec x}} \\ \\ =(\sin ^2x+\cos ^2x)(\sec x) \\ \text{Where:} \\ (\sin ^2x+\cos ^2x)=1 \\ \\ We\text{ have:} \\ (\sin ^2x+\cos ^2x)(\sec x)=1\sec x=\sec x \end{gathered}$

The equation is an identity.

Therefore, the trignonometric identity you would use to verify the equation is:

$\cos ^2x+\sin ^2x=1$

ANSWER:

$\cos ^2x+\sin ^2x=1$

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Assignment: Compound Interest Investigation

sukhopar [10]

To help Tyler better understand how his money will increase in an account that uses simple interest and one that uses compound interest, we are going to use two formulas: a simple interest formula for the accounts that use simple interest, and a compound interest formula for the accounts that use compound interest.
- Simple interest formula: $A=P(1+rt)$
where:
$A$ is the final investment value
$P$ is the initial investment
$r$ is the interest rate in decimal form
$t$ is number of years
- Compound interest formula: $A=P(1+ \frac{r}{n} )^{nt}$
where:
$A$ is the final investment value
$P$ is the initial investment
$r$ is the interest rate in decimal form
$t$ is he number of years
$n$ is the number of times the interest is compounded per year

1.
a. This is a compound interest account, so we are going to use our compound interest formula. We now that $P=1500$ , $t=5$ , and since the interest is compounded annually (1 time a year), $n=1$ . To find the interest rate in decimal form, we are going to divide it by 100%: $r= \frac{4}{100} =0.04$ . Now that we have all the values lets replace them in our compound interest formula:
$A=1500(1+ \frac{0.04}{1}) ^{(1)(5)}$
$A=1824.98$
We can conclude that after 5 years he will have $1824.98 in this account.
b. Here we will use our simple interest formula. We know that $P=1500$ , $t=5$ , and $r= \frac{4}{100} =0.04$ . Lets replace those values in our simple interest formula:
$A=1500(1+(0.04)(5))$
$A=1800$
We can conclude that after 5 years he will have $1800 in this account.
c. The compound interest account from point a will yield more money than the simple account one from point b. The difference between the tow amounts is $1824.98-1800=24.98$

2.
a. Here we are going to use our compound interest formula. We know that $P=2000$ , $t=1$ and $r= \frac{8}{100} =0.08$ . We also know that the interest is compounded Quaternary (4 times per year), so $n=4$ . Now that we have all our values lets replace them into our formula:
$A=2000(1+ \frac{0.08}{4} )^{(4)(1)}$
$A=2164.86$
We can conclude that after 1 year he will have $2164.86 in this account.
b. Here we are going to use our simple interest formula. We know that $P=2000$ , $t=1$ , and $r= \frac{8}{100} =0.08$ . Once again, lets replace those values in our formula:
$A=2000(1+(0.08)(1))$
$A=2160$
We can conclude that after 1 year he will have $2160 in this account.
c. The compound interest account from point a will yield more money than the simple account one from point b. The difference between the tow amounts is $2164.86-2160=4.86$

3.
a. Since Bank A offers an account with a simple interest, we are going to use our simple interest formula. From the question we know that $P=3200$ , $t=3$ , and $r= \frac{3.5}{100} =0.035$ . Now we can replace those values into our formula to get:
$A=3200(1+(0.035)(3))$
$A=3536$
Now, to find the interest earned for Bank A we are going to subtract $P$ from $A$
$InterestEarned=3536-3200=336$
We can conclude that the interest earned for Bank A is $336
b. Since Bank B offers an account with a compound interest, we are going to use our compound interest formula. We know that $P=3200$ , $t=3$ , $r= \frac{3.4}{100} =0.034$ , and since the interest is compounded annually (1 time a year), $n=1$ . Now that we have all the values, lets replace them in our formula to get:
$A=3200(1+ \frac{0.034}{1} )^{(1)(3)}$
$A=3537.62$
Now, to find the interest earned for Bank A we are going to subtract $P$ from $A$ :
$InterestEarned=3537.62-3200=337.62$
We can conclude that the interest earned for Bank B is $337.62
c. Even tough the interest returns between the tow Banks are very similar, Bank B offers a slightly better interest over a period of time, which can make a big difference in the long run. If Tyler wants the earn more money, he definitively should deposit his money in Bank B.
d. The compound interest account from Bank B will yield more money than the simple account one from Bank A The difference between the tow amounts is $3537.62-3536=1.62$

6 0

4 years ago

7-3/8 <img src="https://tex.z-dn.net/?f=%20%20%20%3D%20%20%5C%5C%20%20" id="TexFormula1" title=" = \\ " alt=" = \\ "

serious [3.7K]

The answer is: " 6 $\frac{5}{8}$ " ;

or, write in decimal form; as: " 6.625 " .
________________________________________________
Note:
________________________________________________
7 - 3/8 = 56/8 - 3/8 = (56 - 3) / 8 = 53 / 8 ;
________________________________________________
$\frac{53}{8}$ = 53 ÷ 8 = " 6 $\frac{5}{8}$ " ;

or, write in decimal form; as: " 6.625 " .
________________________________________________________

5 0

4 years ago

Read 2 more answers

Identify the triangle

mr_godi [17]

Answer:

Step-by-step explanation:

i think

4 0

3 years ago

Read 2 more answers

One stack has 6 cups, and its height is 15 cm. The other one has 12 cups, and its height is 23 cm. How many cups are needed for

Ronch [10]

Answer:

Given

Number of stacks = 2

Stack 1 = 6 cups; h1 = 15cm

Stack 2 = 12 cups; h2 = 23cm

Let's first find the average:

With an average of 4/3, to obtain the number of cups needed to obtain a height of 50m, we have:

50 / (4/3)

= 50 * 3/4

= 150/4

= 37.5

From the answer, we can see that the number of cups is not really proportional to the height of the stack, because the average of stack one and stack 2 are different.

Step-by-step explanation:

7 0

3 years ago

If f(x)=2-x^1/2 and g(x)+x^2-9, what is the domain of g(x)/f(x)?

Dominik [7]

As far a domain, you only care about the denominator and radicals.

f(x) = 2 - √x is the denominator, so it can't be 0.
Also x is under a radical, so x can't be negative.
Set the denominator equal to 0 to find the excluded values.

2 - √x = 0
-√x = -2
√x = 2
x = 4, so 4 is an excluded value

The domain is all real numbers greater than or equal to 0, except 4.
[0, 4) U (4, ∞)
0 ≤ x < 4 U x > 4

6 0

4 years ago