y = tan^−1(x2/4) tan(y) = x2/4 sec2(y) = x/2 y′ = xcos^2(y)/2 cos^2(y) = 16x2+16 y′ = 8x/(x2+16)

let u be x2+16
du is 2x dx
dy = 4 du / u
y = 4 ln (x2 + 16)

y at x =0 = 4 ln (16) = 11.09

6 0

3 years ago

A can holds 4 golf balls. The diameter of each golf ball is 5 cm. What is the volume of the empty space inside the can?

forsale [732]

Answer:

Volume of the empty space in the can is 327.05 $cm^3$

Step-by-step explanation:

Given:

Number of golf ball the can holds = 4

Diameter of the golf ball = 5 cm

To Find:

Volume of the empty space in the can = ?

Solution:

Step 1: Finding the volume of one golf ball

Ball is shape of the sphere

So lets use the volume of the sphere formula

Volume of the golf ball = $\frac{4}{3}\pi r^3$

Radius = $\frac{5}{2}$ = 2.5 cm

Substituting the values

Volume of the golf ball

= $\frac{4}{3} \pi \times(2.5)^3$

= $\frac{4}{3} \pi \times (15.625)$

= $\frac{4}{3} \times 49.06$

= $\frac{196.24}{3}$

= 65.41

Step 2: Finding the volume of empty space of the can

volume of empty space of the can = volume of 5 golf ball

= 5 X 65.41

= 327.05

7 0

4 years ago

A total of 285 tickets were sold for the school play. they were either adult tickets or student tickets. the number of student t

Assoli18 [71]

Lets say the number of adult tickets is x. This means the number of student tickets is 2x. So, 2x + x = 285, or 3x =285. The means x = 95. So the number of adult tickets sold is 95.

8 0

3 years ago

Evaluate the expression when x = -4. 5(x – 6) + 3x – 2

SVETLANKA909090 [29]

Answer:

-64

Step-by-step explanation:

5(x – 6) + 3x – 2

Distribute

5x - 30 +3x -2

Combine like terms

8x -32

Let x = -4

8*-4 -32

-32 -32

-64

6 0

4 years ago