Answer:
Therefore the population will be maximum when x=30 inches.
Step-by-step explanation:
Given that, the mosquito population is a function of rainfall and can be approximated by the formula
where x is the number of inches of rainfall.
Differentiating with respect to x
Again differentiating with respect to x
Now we set N'(x)=0
Since at x=30, N''(x)<0, So at x=30, N(x) has maximum value.
Therefore the population will be maximum when x=30 inches.
16. 5x^3 y^-5 • 4xy^3
20x^4y^-2
20x^4 • 1/y^2
=20x^4/y^2
17. -2b^3c • 4b^2c^2
= -8b^5c^3
18. a^3n^7 / an^4 (a^3 minus a = a^2 same as n^7 minus n^4 = n^3)
=a^2n^3
19. -yz^5 / y^2z^3
= -z^2/y
20. -7x^5y^5z^4 / 21x^7y^5z^2 (divide -7 to 21 and minus xyz)
= -z / 3x^2
21. 9a^7b^5x^5 / 18a^5b^9c^3
=a^2c^2 / 2b^4
22. (n^5)^4
n ^5 x 4
=n^20
23. (z^3)^6
z ^3 x 6
=z^18
Answer:
P ≈ 48.89°(nearest hundredth)
Step-by-step explanation:
The triangle PQR forms a right angle triangle since angle R is 90°. The triangle has an hypotenuse , adjacent and opposite side.
Using the SOHCAHTOA principle one can find the sine ratio of angle P. Let us designate where each side represent.
opposite side(QR) = 55
adjacent side(PR) = 48
hypotenuse(PQ) = 73
sin P = opposite/hypotenuse
sin P = 55/73
P = sin⁻¹ 55/73
P = sin⁻¹ 0.75342465753
P = 48.8879095605
P ≈ 48.89°(nearest hundredth)
Answer:
d) angle 6 is alternate interior angle to angle 3
e) angle 2 is alternate exterior angle to angle 7
