Answer:
The altitude of the climber is 1.40 miles
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
<em>In the right triangle BCD</em>
tan(22°)=h/(x-0.5)
h=tan(22°)*(x-0.5) ----> equation A
<em>In the right triangle ACD</em>
tan(15°)=h/x
h=tan(15°)*(x) ----> equation B
Equate equation A and equation B and solve for x
tan(22°)*(x-0.5)=tan(15°)*(x)
tan(22°)*x-tan(22°)*0.5=tan(15°)*x
x[tan(22°)-tan(15°)]=tan(22°)*0.5
x=tan(22°)*0.5/[tan(22°)-tan(15°)]
x=1.48 miles
Find the value oh h
h=tan(15°)*(1.48)=0.40 miles
therefore
The altitude of the climber is equal to
0.40+1=1.40 miles
Answer:
16428 oranges
Explanation:
Total yield = number of trees × number of oranges in each tree
Initial yield = 600×24= 14400 oranges
To find the equation needed, let x = additional trees and y= total yield
Number of trees = 24 +x
Number of oranges in each tree = 600-12x
Equation of total yield y= (24+x)(600-12x)
y= 14400-288x+600x-12x²
y= -12x²+312x+14400
Using a graphing calculator, from the graph drawn for this quadratic equation, we notice that it is a parabola. Therefore to find the maximum value, we should find the maximum point which is at the vertex of the parabola, we use the formula x= -b/2a
A quadratic equation is such: ax²+bx+c
Therefore x =-312/2×-12
x= -312/-24
x= 13
So we can conclude that in order to maximise oranges from the trees, the person needs to plant an additional 13 trees. Substituting from the above:
24+x=24+13= 37 trees in total
y= -12x²+312x+14400= -12×13²+312×13+14400= -2028+4056+14400
=16428 oranges in total yield
Answer:
x-intercept = 17/4 and y = -17/3
Step-by-step explanation:
To find the intercepts: set x = 0 for the y-intercept and solve the equation and set y =0 for the x- intercept and solve the equation.
To
4x - 3y = 17
4(0) - 3y = 17
0 - 3y = 17
y = 17 /-3
y = -17/3 = -5 2/3 y-intercept = -5 2/3.
The ordered pair on the graph is (0, -17/3)
4x - 3(0) = 17
4x - 0 = 17
4x = 17
x = 17/4 x-intercept = 17/4
The ordered pair on the graph is (17/4, 0)
Answer:
2a + 10
Step-by-step explanation:
the number = 2(a + 5)
= 2a + 10
