It appears that you have a derivative and want to integrate...
dy/dx=1+3√x
y(x)=x+(2/3)x^(3/2)+C you are given that f(4)=25 so we can solve for the constant of integration...
y(4)=25=4+16/3+C
21=16/3+C
(63-16)/3=C
47/3=C so
f(x)=x+(2/3)x^(3/2)+47/3
f(x)=(3x+2x^(3/2)+47)/3
The product is 60.
We start out with the information we have. This forms a right triangle, with one leg being 24, the other leg x, and the hypotenuse 30. Using the Pythagorean theorem we have
x²+24²=30²
x²+576=900
Subtract 576 from both sides:
x²+576-576 = 900-576
x²=324
Take the square root of each side:
√x²=√324
x=18
We know that the formula for the volume of a triangular prism is V=(1/2bh)H, where b is the base of the triangle, h is the height of the triangle, and H is the height of the prism. Substituting our known information we have:
720=(1/2*18*24)y
720=216y
Divide both sides by 216:
720/216 = 216y/216
3 1/3 = y
This means the product of x and y would be:
18(3 1/3)
18(10/3)
180/3
60
Answer:
sqrt(10) *x
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2
x^2 + (3x)^2 = hypotenuse ^2
x^2 + 9x^2 = hypotenuse ^2
10x^2 = hypotenuse ^2
Take the square root of each side
sqrt( 10x^2) = sqrt(hypotenuse ^2)
sqrt(10) * x = hypotenuse
Answer:
0.075 inches per year
Step-by-step explanation:
The average rate of change is measured as
( difference in diameter ) ÷ ( difference in years )
= ( 251 - 248 ) ÷ ( 2005 - 1965 )
= 3 inches ÷ 40 years
= 0.075 inches per year
