Answer:
(a)
>install.packages("air4")
>library(air4)
>attach(UN11)
>plot(ppgdp, fertility)
Check attachments for the plots
90 inches 18 times 5 is 90 and 30 times 3 is 90 so the lowest point which they will be at the height is 90 inches
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)))
Answer:
-3
Step-by-step explanation:
the y intercept is the number that does not have a variable behind it (3)
the slope is the number that does have a variable behind it (4)
Use ratio and proportion
5.25/x= 82/100
cross multiply
82 x= 525
x= 6.4 miles
Hope this helps