Answer:
6.32 feets
Step-by-step explanation:
Given that:
Height of ramp = 2 feets
Length of base = 6 feets
Length of ramp = l
Using Pythagoras rule :
Hypotenus = sqrt(opposite² + adjacent²)
Length of ramp = sqrt(height of ramp² + length of base²)
l = sqrt(2² + 6²)
l = sqrt(4 + 36)
l = sqrt(40)
l = 6.3245
Length of ramp = 6.32 feets
Answer:
After 2009 the quality of the forests in this country improving.
Step-by-step explanation:
Consider the provided function.
Substitute f'(t)=0.
It is given that (0 ≤ t ≤ 10)
The test interval are (0,5) and (5,10)
For (0 < t < 5) the value of
For (5 < t < 10) the value of
Hence, the function is increasing from (5,10).
t = 0 corresponds to 2004.
Therefore, after 2009 the quality of the forests in this country improving.
Answer:
The system of equations is
Step-by-step explanation:
Let
x------> the number of videos of new releases
y-----> the number of classics videos
we know that
------> equation A
------> equation B
Using a graphing tool
Solve the system of equations
Remember that the solution of the system of equations is the intersection point both graphs
The intersection point is
see the attached figure
therefore
the number of videos of new releases is
the number of classics videos is
Answer:
The area of the triangle formed by origin, and the points (4,5) and (-2,5) will be 15 sq. units.
Step-by-step explanation:
The two parabolas are and y = x² - 2x - 3.
Now, solving those two equations we will get the points of intersection.
So,
⇒ - (x - 1)² + 24 = 3x² - 6x - 9
⇒ -x² + 2x - 1 + 24 = 3x² - 6x - 9
⇒ 4x² - 8x - 32 = 0
⇒ x² - 2x - 8 = 0
⇒ x² - 4x + 2x - 8 = 0
⇒ (x - 4)(x + 2) = 0
So, x = 4 or - 2.
Now, for x = 4 , y = 4² - 2(4) - 3 = 5 and the point of intersection is (4,5).
Or, for x = - 2, y = (- 2)² - 2(- 2) - 3 = 5 and the point of intersection is (-2,5).
Now, points (4,5) and (-2,5) make a straight line parallel to the x-axis at a perpendicular distance of 5 units from origin and its length is (4 - (- 2)) = 6 units.
So, the area of the triangle formed by origin, and the points (4,5) and (-2,5) will be = 0.5 × 5 × 6 = 15 sq. units. (Answer)
Answer:
-38 (You Should be Correct)
Step-by-step explanation:
-22 + (-16) is the same thing as -22-16.
Subtract -16 from -22.
We get -38.