Do a mental sum for 6 x 200 (1200) then subtract 6<span>x 2 (12) to give you 1188.</span>
Answer:
875 cm^3
Step-by-step explanation:
Here, we want to calculate the volume of the pyramid.
To do this, we need to calculate the area of the base and then multiply this by the height of the pyramid in question
Mathematically since the base is a square, formula for the base area would be ;
L^2 = 5^2 = 125 cm ^2
Now
using the height to get the volume , we have 125 * 7 = 875 cm^3
The factoring can be done similarly to a quadratic equation thanks to x^4 being the square value of x^2.
<span>x^4 + 6x^2 - 7
x^4</span><span> - x^2</span> + 7x^2 - 7
(x^4 - x^2) + (<span>7x^2 - 7)
</span>x^2(x^2 - 1) + 7(<span>x^2 - 1)
</span>(x^2 + 7)(x^2 - 1)
<span>(x^2 + 7)(x - 1)(x + 1)
</span>
Factored completely we get: <span>(x^2 + 7)(x - 1)(x + 1)</span>
Sin^6 x + cos^6 x =
= ( sin² x + cos² x ) ( sin^4 x - sin² x cos² x + cos^4 x ) =
= sin^4 x + 2 sin²x cos² x + cos^4 x - 2 sin² x cos² x - sin² x cos² x =
= ( sin² x + cos² x )² - 3 sin² x cos² x =
= 1 - 3 sin² x cos² x
After that:
1 - 3 sin² x cos² x = 5/8
1 - 5/8 = 3 sin² x cos² x
3/8 = 3 sin² x cos² x / : 3
1/8 = sin² x cos² x / * 4
1/2 = 4 sin² x cos² x
1/2 = ( 2 sin x cos x )²
√2 / 2 = 2 sin x cos x
sin 2 x = √ 2 / 2
2 x = π / 4, or x = 3 π / 4
Answer:
x 1 = π / 8, x 2 = 3 π / 8.
Call n the number of figure and w the number of white figures:
w = (n+2)^2 - n^2
w = n^2 + 4n + 4 - n^2 = 4n + 4
w = 4 (n+1)
All those formulas are equivalent.
