Find the area of the region bounded by the hyperbola 25x2 − 4y2 = 100 and the line x = 3. (using trigonometric substitution)

23.92

Step-by-step explanation:

We solve for y:

use trig substitution:

The derivative of x is:

when x=2

when x=3

The area is defined as 2xarea:

The area is the integral of the equation:

for range 0 to sec-1(3/2)

Substitute x=2secu

We know that sec²-1 = tan²u

After simplifying

For the range

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!