Answer: Elizabeth and Manuel have a distance of 4 meters between them.
Step-by-step explanation: Please refer to the picture attached.
From the information given, Elizabeth is directly behind Hannah and directly left of Manuel. That means we have three points which are HEM, that is, we now have triangle HEM. The longest side (hypotenuse) which is the distance between Hannah and Manuel is given as 5 meters while the other side the distance between Hannah and Elizabeth is given as 3 meters.
We shall apply the pythagoras theorem in solving for the unknown side, EM.
The Pythagoras theorem states thus;
AC² = AB² + BC²
Where AC is the hypotenuse, and AB and BC are the other two sides.
Substituting for the known values, we now have;
5² = 3² + EM²
25 = 9 + EM²
Subtract 9 from both sides of the equation
16 = EM²
Add the square root sign to both sides of the equation
√16 = √EM²
4 = EM
Therefore the distance between Elizabeth and Manuel is 4 meters
Answer:
750 books
Step-by-step explanation:
Let there be "x" number of books in the 3rd room
Now,
2nd room has 3 times as 3rd room, so we can write:
Second Room = 3x
Also, there are 1960 MORE books in 1st room than 2nd room, so we can write:
First Room = 3x + 1960
In total there are 7210 books in all three rooms, thus we can write:
First Room + Second Room + Third Room = 7210
Now, replacing the first 2 equations in this, we get:
3x + 1960 + 3x + x = 7210
Solving for x:
"x" is indeed what we are looking for. Thus,
There are 750 books in the third room
Answer: nop
Step-by-step explanation:
Taking the derivative of 7 times secant of x^3:
We take out 7 as a constant focus on secant (x^3)
To take the derivative, we use the chain rule, taking the derivative of the inside, bringing it out, and then the derivative of the original function. For example:
The derivative of x^3 is 3x^2, and the derivative of secant is tan(x) and sec(x).
Knowing this: secant (x^3) becomes tan(x^3) * sec(x^3) * 3x^2. We transform tan(x^3) into sin(x^3)/cos(x^3) since tan(x) = sin(x)/cos(x). Then secant(x^3) becomes 1/cos(x^3) since the secant is the reciprocal of the cosine.
We then multiply everything together to simplify:
sin(x^3) * 3x^2/ cos(x^3) * cos(x^3) becomes
3x^2 * sin(x^3)/(cos(x^3))^2
and multiplying the constant 7 from the beginning:
7 * 3x^2 = 21x^2, so...
our derivative is 21x^2 * sin(x^3)/(cos(x^3))^2
Answer:
14
Step-by-step explanation:
56 divided by 7 = 8
14 divided by 7 = 2
hinting at 8/2
