Answer:
1. <u>Average velocity</u>
When t=4
i. [4, 4.1]
= y(4.1) - y(4) / 4.1 - 4
= 275 - 16(4.1)^2 - 275 - 16(4)^2 / 0.1
= 275 - 16*16.81 - 275 - 16(16) / 0.1
= 6.04 - 19 / 0.1
= -12.96 /0.1
= -129.6
ii. [4, 4.05]
= y(4.05) - y(4) / 4.05 - 4
= 275 - 16(4.05)^2 - 275 - 16(4)^2 / 0.05
= 275 - 16*16.40 - 275 - 16(16) / 0.05
= 12.6 - 19 / 0.05
= -6.4 / 0.05
= -128
iii. [4, 4.01]
= y(4.01) - y(4) / 4.01 - 4
= 275 - 16(4.01)^2 - 275 - 16(4)^2 / 0.01
= 275 - 16*16.08 - 275 - 16(16) / 0.01
= 17.72 - 19 / 0.01
= -1.28 / 0.01
= -128
b. Instantaneous velocity
y = 275 - 16t^2
dy/dx = -32t
Considering t = 4
Instantaneous velocity after 4 seconds = -32(4)
Instantaneous velocity after 4 seconds = -128
21/64 × 100% = 32.81%
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<h3>
Answer: (3,-4)</h3>
Explanation:
The vertex of f(x) is (3,-6)
The vertex of g(x) is (3,-4). We keep the x coordinate the same, but add 2 to the y coordinate. This shifts the vertex 2 units up.
Answer:
272 cm²
Step-by-step explanation:
Step 1
We have to find the scale factor
When given the volume of two solids, the formula for the scale factor is
V1/V2 = (Scale factor)³
The volume of Pyramid A is 704 cm³ and the volume of Pyramid B is 297 cm³
V1 = Pyramid A
V2 = Pyramid B
704/297 = (scale factor)³
We simplify the left hand side to simplest fraction
The greatest common factor of 704 and 297 = 11
704÷11/297÷11 = (scale factor)³
64/27 = (scale factor)³
We cube root both sides
cube root(scale factor)³ = cube root (64/27)
scale factor = (4/3)
Step 2
(Scale factor)² = S1/S2
S1 = Surface area of Pyramid A =?
S2 = Surface area of Pyramid B = 153 cm²
Hence,
(4/3)² = S1/153
16/9 = S1/153
Cross Multiply
S1 × 9 = 16 × 153
S1 = 16 × 153/9
S1 = 272 cm²
Therefore, the Surface Area of Pyramid A = 272 cm²
Answer:
There is no solution (since none has side length of 4 units)
Step-by-step explanation:
If V (-1,1) is one of vertex of a square, then the next vertex to V distance must be the known value of 4
VA: V to (-3,3) = √(-1 - -3)² + (1 - 3)² = √8 = 2.8
VB: to (-5,-3) = √(-1 - -5)² + (1 - -3)² = √32 = 5.7
VC: o (3,3) = √(-1 -3)² + (1 - 3)² = √20 = 4.47
VD: to (-5,3) = √(-1 - -5)² + (1 - 3)² = √20 = 4.47
VE: to (4,5) = √(-1 - 4)² + (1 - 5)² = √41 = 6.4