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Natalka [10]
2 years ago
12

1+ cos^4 x-sin^4 x = 2 cos² x​

Mathematics
1 answer:
Mariana [72]2 years ago
7 0

\text{L.H.S}\\\\=1+ \cos^4 x - \sin^4 x\\\\=1+ (\cos^2 x)^2 - (\sin^2 x)^2\\\\=1+(\cos^2 x + \sin^2 x)(\cos^2 x- \sin^2 x)\\\\=1+1\cdot(\cos 2x)\\\\=1+\cos 2x\\\\=2\cos^2 x\\\\=\text{R.H.S}\\\\\text{Proved.}

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A truck rental company rents a moving truck One Day by charging $39 + 0.09 per mile write a linear equation that relates the cos
Ivanshal [37]

Answer:

(a)\ c(x) = 39 + 0.09 x

(b)\ \$53.4

Step-by-step explanation:

Given

Base\ Charge = \$39

Rate = 0.09 per mile

Solving (a): Linear Equation

The total charges (c(x)) is: the base charge + the rate * number of miles (x).

So, we have:

c(x)= 39 + 0.09 * x

c(x) = 39 + 0.09 x

Solving (b): Cost of rent, if miles = 160

This implies that x = 160

So, we have:

c(x) = 39 + 0.09 x

c(160) = 39 + 0.09 *160

c(160) = 39 + 14.4

c(160) = 53.4

7 0
3 years ago
Will give 25 points and brainliest answer if correct
Norma-Jean [14]
Let d be the common difference between terms in the sequence \{a_n\}_{n\ge1}. Then

a_{19}=-58
a_{20}=a_{19}+d
a_{21}=a_{19}+2d
\implies-164=-58+2d\implies d=-53

The first term in the sequence, a_1, satisfies

a_2=a_1+d
a_3=a_1+2d
a_4=a_1+3d
...
a_{19}=a_1+18d
\implies-58=a_1+18(-53)\implies a_1=896

So the explicit formula for the n-th term in the sequence is

a_n=a_1+(n-1)d\implies a_n=896-53(n-1)
5 0
4 years ago
Which equation represents “nine less than k is three”?
evablogger [386]

Answer:

k - 9 = 3

And k = 12

5 0
3 years ago
Read 2 more answers
Can someone help please
Ira Lisetskai [31]
Hello there! I can help you! The formula for compound interest is P(1 + r)^t, where P= principal (initial amount), r = interest rate (in decimal form), and t = time (in years). Let's do this step by step. First off, we add the rate into 1. 4% is the interest rate (0.04 in decimal form). 1 + 0.04 is 1.04. Now, what we will do is raise that number to the 2nd power, because the time that elapses is 2 years. 1.04² is 1.0816. That's that. Now, multiply 7,500 to find the total amount of money. 1.0816 * 7,500 is 8,112. There. Toby's savings account balance in 2 years is £8,112.

Note: To solve for compound interest questions like it, add 1 to the percentage rate in decimal form, raise that number to a power based on the number of years (for example, raise the number to the 7th power if we are looking for the balance after 7 years), and then multiply that number by the starting amount. After you raise the number by a power, there may be a lot of numbers behind it. Whatever you do, DO NOT delete the number. Keep it there and multiply it by the principal.
5 0
3 years ago
If AB=x and x=4, then the transitive property states
Anarel [89]

Answer:

4. AB=4

Step-by-step explanation:

Transitive property is like substitution, or that's how I like to think of it. Since we have 2 common variables and 2 equations, we can "link them together". Replacing x with 4, you get AB=4.

8 0
3 years ago
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