First step is distribution:
-(6-5n)+12
-6+5n+12
5n+6=-6+5n+15
Second step combine like terms:
5n+6=5n+9
-6 -6
5n=5n+3
0=3
Can you please write the equation more clearly?
The derivative of y=cos(^7)base x is
<u> Dydx = (cos(7x))x⋅(ln(cos(7x))−7x(tan(7x)))
</u>
Step-by-step explanation:
step 1 :
y= (cos(7x))x
Take the natural logarithm of either side, bringing the t x down to be the coefficient of the right hand side we get the answer:
step 2 :
⇒ln y = xln (cos (7x))
Differentiate each side with respect to x. The rule of implicit differentiation: ddx (f(y)) = f'(y) ⋅ dydx
step 3 :
<u>∴1y ⋅ dydx = ddx (x) ⋅ln (cos(7x)) + ddx (ln (cos(7x)))⋅x
</u>
Use the chain rule for natural logarithm functions – ddx ( ln (f(x)) )= f'(x)f(x) - we can differentiate the ln (cos (7x))
step 4 :
<u>Ddx (ln (cos(7x))) = −7xsin (7x) cos( 7x 7tan (7x)
</u>
Returning to the original equation:
1y ⋅dydx = ln (cos(7x))−7xtan(7x)
Substitute the original y as a function of x value from the start back in.
Dydx = (cos(7x))x⋅(ln(cos(7x))−7x(tan(7x)))
(8,0) and (0,8) Using a website called desmos can help to visualize things like this.
We know that
We can write an Arithmetic Sequence as a rule:
<span>an = a1 + d(n−1)</span>
where
<span>a1 = the first term
<span>d =the "common difference" between terms
in this problem
a1=15 a2=7 a3=-1 a4=-9 ..... an=-225
d=a2-a1
d=7-15-----> d=-8
</span></span>an = a1 + d(n−1)
for
an=-225
d=-8
a1=15
find n
-225=15+(-8)*(n-1)--> (n-1)=[-225-15]/-8----> n-1=30---> n=30+1---> n=31
the answer is31
