Answer:
It is true, because the cosine function has a period of 2π
Step-by-step explanation:
Since, the period of the cos function is 360° ( or 2π radians ), it holds the property of:
Taking 
as 
, 
is equal to 
The equation is true!
<u>Note:</u> The cos function is even function
Hence, the equation is true, because the cosine function has a period of 2π, NOT because the cosine function is ODD, which it is not!!
Answer:
x = 1/2 and 3/2
Step-by-step explanation:
The given equation is logₓ (8x-3) - logₓ 4 = 2
Then we have to determine the value of x.
logₓ ![[\frac{(8x-3)}{4}]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B%288x-3%29%7D%7B4%7D%5D)
= 2 [ since log a - log b = log 
]
Now 
[if 
b = c then 
= b]
4x² = 8x -3
4x² - 8x + 3 = 0
(2x)² - 2(4x) + (4-4) + 3 = 0
[(2x)² - 2 (4x) + 4 ] - 1 = 0
(2x - 2)² = 1
(2x - 2)² = ± 1 ⇒
2x - 2 = 1 and 2x - 2 = -1
x = 3/2 2x = 1
x = 1/2
Therefore, x = 1/2 and 3/2 are the answers.
Answer:
The football team drank a total of 75 gallons of water.
Step-by-step explanation:
Half of 50 gallons is 25 gallons. 25 gallons + 50 gallons = 75 gallons.
Step-by-step explanation:
it seems we are dealing with subtraction, as the differences between the 1st and second, and between the 2nd and 3rd numbers are equal : -7
so, we can assume that the sequence is created by always subtracting 7.
a1 = 352
a2 = a1 - 7 = 352 - 7 = 345
a3 = a2 - 7 = a1 - 7 - 7 = 352 - 7 - 7 = 338
an = an-1 - 7 = a1 - 7(n-1) = 352 - 7(n-1)
a43 = 352 - 7(43-1) = 352 - 7×42 = 352 - 294 = 58
Since you only need two points to determine the slope, we use the first two, (0,15) and (2,9). The slope formula is (y2-y1)/(x2-x1), so (9-15)/(2-0)=(-6/2)=<em>-3</em>
