Answer:
360 people
Step-by-step explanation:
Hope this helped! :)
Answer: the rate at which the distance between the boats is increasing is 68 mph
Step-by-step explanation:
The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.
Let x represent the length the shorter leg(south) of the right angle triangle.
Let y represent the length the longer leg(east) of the right angle triangle.
Let z represent the hypotenuse.
Applying Pythagoras theorem
Hypotenuse² = opposite side² + adjacent side²
Therefore
z² = x² + y²
To determine the rate at which the distances are changing, we would differentiate with respect to t. It becomes
2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1
One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that
dx/dt = 32
dy/dt = 60
Distance = speed × time
Since t = 0.5 hour, then
x = 32 × 0.5 = 16 miles
y = 60 × 0.5 = 30 miles
z² = 16² + 30² = 256 + 900
z = √1156
z = 34 miles
Substituting these values into equation 1, it becomes
2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60
68dz/dt = 1024 + 3600
68dz/dt = 4624
dz/dt = 4624/68
dz/dt = 68 mph
Answer:
3000 students
Step-by-step explanation:
If 48% of the students are female, and there are 1440 female students, we can set up a percentage proportion, assuming x is the total amount of students.
We can use the cross products property to find the value of x.
Hope this helped!
Answer:
$2.25
Step-by-step explanation:
Let "b" be the price of 1 brownie and "c" the price of 1 cookie.
At a bake sale, a student spent $11.00 buying 3 brownies and 5 cookies. Symbolicaly,
3 b + 5 c = 11.00 [1]
His friend spent $3.95 buying 1 brownie and 2 cookies. Symbolicaly,
1 b + 2 c = 3.95
b = 3.95 - 2c [2]
If we replace [2] in [1], we get
3 (3.95 - 2c) + 5 c = 11.00
11.85 - 6c + 5c = 11.00
c = 0.85
If we replace c = 0.85 in [2], we get
b = 3.95 - 2 (0.85) = 2.25
2x² + 5x -6x - 15 = 0
2x² - x - 15 = 0
2x² -x = 15
x = 3
3 x 3 = 9 x 2 = 18 - 3 = 15
i really don't know how i got 3 in the first place but that is your answer
hope this helps
