Which is correct: To who did you give the book? To whom did you give the book?
It should be: To whom did you give the book? Who is a subject, while whom is an object. Think of the difference in how you would answer the question. Who is similar to he, while whom is similar to him. Which would you say? I gave the book to he. or I gave the book to him. It should be the second option. I like to remember that whom is like him because they both end in m.
The admission fee at a fair is $2.00 for children and $5.00 for adults. One day, 3,000 people enter the fair and $12,000 is collected. How many children and how many adults were at the fair that day?
Let adults be represented by a and children be represented by c. We know that the total number at the fair is 3,000, so a+c=3000. We also know the total income is $12,000, so 2c+5a=12,000. Now we can use substitution. Looking at our first equation, a+c=3000, we can solve for the number of adults by subtracting c from each side. a+c-c=3000-c or a=3000-c Now we can use that value for a in our second equation. 2c+5a=12,000 or 2c + 5(3000-c)=12,000 When multiplied out, it looks like this: 2c + 15,000 + -5c=12,000 2c-5c + 15,000= 12,000 -3c + 15,000=12,000 Now we can subtract 15,000 from both sides. -3c +15,000-15,000=12,000-15,000 -3c= -3,000 Divide both sides by -3 -3c/-3= -3,000/-3 c=1,000 Now we have c, we can plug it back into our first equation to solve for a. a+c=3000 or a+1000=3000 Subtract 1000 from both sides. a+1000-1000=3000-1000 a+2000 There were 2000 adults and 1000 children.
A force of 100 N acting on a body for 8 seconds reaches a velocity of 30 m/s. Find its mass and its momentum at the end of the 8 seconds.
We know the force is 100 N, or F=100 N. The time is 8 seconds, or t=8 s. The initial velocity is 0 m/s, or u=0 m/s. The final velocity is 30 m/s, or v=30 m/s. We need to find the mass, which can be found with this equation: m=F/a. a is acceleration, which we do not yet have. To solve for acceleration we need this equation: a=(v-u)/t. We do have all these components. a=(v-u)/t or a=(30 m/s - 0 m/s)/8 s a= 3.75 m/s^2 Now we can solve for the mass. m=F/a or m=100 N/3.75 m/s^2 m=26.67 kg Now we need to find momentum at the end of the 8 seconds. Momentum (known as p) is mass times velocity, or p=mv. We now have both the mass and velocity. p=mv or p=(26.67 kg)x(30 m/s) p=800 kg m/s