# Tutor profile: Maryam S.

## Questions

### Subject: Trigonometry

George leans a 7ft long ladder against a wall x meters high. The base of the ladder is 2ft from the wall. How high is the wall?

This problem can be solved using Pythagoras theorem. let a=height of the wall =x b=distance from the wall to the ladder=2ft c=length of the ladder=7ft Therefore, a^2+b^2=c^2 Rearrange for a^2 a^2=c^2-b^2 a=sqrt(c^2-b^2) c=sqrt(49-4) c=sqrt(45) c=6.7ft Thus, the wall is 6.7ft high.

### Subject: Calculus

A rectangular box has the following dimensions: Length: x-2 Width: x+3 Height: x Stella wants to minimize the volume. Find the height (x) and the corresponding length and width for which the volume will be the minimum.

V=Length*Width*Height=(x-2)(x+3)(x) =(x^2+3x-2x-6)*x =x^3+x^2-6x To find the minimum volume, we must do the first-derivative test: V'=3x^2+2x-6 Equate V'=0 3x^2+2x-6=0 Apply quadratic formula x1=1.11 x2=-1.79 Since height cannot be a negative number, x=1.11 is the right answer. To check if the Volume is minimum at x=1.11, we do the second derivative test: V''=6x+2 V''(1.11)=6(1.11)+2, which is greater than (>) 0 Hence, the volume is minimum at x=1.11

### Subject: Algebra

The Busby family decides to go to the movies. The total number of members in the family is 7 (including adults and children). Moreover, their movie trip cost them $75 (excluding popcorn). Additional information for this problem: -Movie ticket price for adults: $10 per person -Movie ticket price per child (5 or younger): 50% of the adult price. How many adults are there in the Busby family?

The information in the question can be summarized into two equations. Let a=no. of adults and c=no. of children. Therefore, a+c=7 (*) and, 10a+5c=75 (**) (*) and (**) can be solved simultaneously. Make 'a' the subject of the formula in (*) a=7-c (***) Substitute (***) in (**) 10(7-c)+5c=75 Expand and solve for 'c' 70-10c+5c=75 5c=5 c=1 Substitute c=1 in (*) a+1=7 Therefore a=6 The Busby family has 6 adults.

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