emmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmStep-by-step explanation:
Answer:
0.0830 radians per second
Step-by-step explanation:
If θ is the angle of elevation and h is the height of the balloon, then:
tan θ = h / 53
Take the derivative of both sides with respect to time:
sec² θ dθ/dt = 1/53 dh/dt
Use Pythagorean identity:
(1 + tan² θ) dθ/dt = 1/53 dh/dt
Substitute:
(1 + (h/53)²) dθ/dt = 1/53 dh/dt
Multiply both sides by 53²:
(53² + h²) dθ/dt = 53 dh/dt
Given dh/dt = 6 and h = 32:
(53² + 32²) dθ/dt = 53 (6)
dθ/dt = 318 / 3833
dθ/dt ≈ 0.0830
The angle of elevation is increasing at a rate of 0.0830 radians per second.
Answer:
C
Step-by-step explanation:
A: (0,__) (__ is the y-intercept)
In this case it is (0,3) so 3
B: y=mx+b (b is the y-intercept)
-4 is b so -4
C: y=2x+4
4 is b so 4
Let me know if you would like further explanation!!
9514 1404 393
Answer:
-4
Step-by-step explanation:
In a linear equation, the terms "unit rate", "rate of change", "constant of proportionality", and "slope" all refer to the coefficient of x (the independent variable).
Here, the coefficient of x is -4.
The slope is -4.
_____
<em>Additional comment</em>
Strictly speaking the "constant of proportionality" only refers to the x-coefficient (k) when the equation is of the form ...
y = kx . . . . . with no added constant
"Slope", "unit rate", and so on, can also refer to the x-coefficient (m) when the equation has a non-zero y-intercept (b):
y = mx + b
Answer:
2. 20
Step-by-step explanation:
2. The distance from one base of the prism to the other base of the prism, d = 10 mm
The thickness of each triangle to be used to fill the prism, t = 0.5 mm
The number of triangles needed, <em>n</em>, is therefore;
Where;
<em>d </em>represents the distance between the bases of the prism, <em>t</em>, represents the thickness of each triangle, and <em>n</em> represents the number of triangles it would take to fill up the prism
Therefore;
The number of triangles it would take to fill up the prism, n = 20
