Step-by-step explanation:
initial speed = 272 ft/s
h = -16t² + 272t
a. 1120 = -16t² + 272t we change a bit into
16t² - 272t + 1120 = 0 then divide all with factor 16
t² - 17t + 70 = 0
(t - 10)(t - 7) = 0
t = 10 and t = 7
7 s when it goes up and 10 sec when the rocket goes down.
b. 1152 = -16t² + 272t we change a bit into
16t² - 272t + 1152 = 0 then divide all with factor 16
t² - 17t + 72 = 0
(t - 9)(t - 8) = 0
t = 9 and t = 8 sec
c. since the answer of a and b is:
7 sec and 8 sec the rocket goes up but at 9 sec and 10 sec the rocket goes down then we can take conclusion that the maximum height is reached at 8.5 s
so how long the rocket in the air?
goes up : 8.5 sec
goes down : 8.5 sec
total = 17 sec
Set up a proportional relationship:
xf/1n=(f/5)/(n/3)
xf/1n=3f/(5n) multiply both sides by 1n
xf=3f/5 so
x=3/5
Dave must mix in 3/5 of a cup of fruit with a single cup of nuts.
You could of also just noted that you need to multiply 1/5 times 3 because 1/5 mixes with just 1/3 of a cup of nuts...
Answer and Step-by-step explanation: Spherical coordinate describes a location of a point in space: one distance (ρ) and two angles (Ф,θ).To transform cartesian coordinates into spherical coordinates:
For angle θ:
- If x > 0 and y > 0:
;
- If x < 0:
; - If x > 0 and y < 0:
;
Calculating:
a) (4,2,-4)
= 6
For θ, choose 1st option:
b) (0,8,15)
= 17
The angle θ gives a tangent that doesn't exist. Analysing table of sine, cosine and tangent: θ = 
c) (√2,1,1)
= 2
= 
d) (−2√3,−2,3)
= 5
Since x < 0, use 2nd option:
Cilindrical coordinate describes a 3 dimension space: 2 distances (r and z) and 1 angle (θ). To express cartesian coordinates into cilindrical:
Angle θ is the same as spherical coordinate;
z = z
Calculating:
a) (4,2,-4)
= 
z = -4
b) (0, 8, 15)
= 8
z = 15
c) (√2,1,1)
= 
z = 1
d) (−2√3,−2,3)
= 4
z = 3
Answer:
Step-by-step explanation:
Keep 
and group -3x+8x which becomes 5x. Then keep -6.
Then it becomes the answer above.
Answer:
y = -3/2x - 15
Step-by-step explanation:
Use the slope intercept form y = mx + b to substitute the slope = -3/2 and the point (-8, -3).
y = mx + b
-3 = -3/2(-8) + b
-3 = 12 + b
-15 = b
y = -3/2x - 15
