a) w = 0.39
b) We know that a has to be between 1 and 10, so the only possibility is:
0.3862901=3.862901∗10−1
That means that k = -1.
c) Using the formula for percentage error, we get that:
ε=|va−veve|∗100%=|0.3862901−0.4270.427|∗100%=9.53
Closea)
p=8cos(45°)3x+2y+z=8cos(45°)3∗6+2∗9+4=8∗√2218+18=√29+4
b) Using GDC we can see that:
√29+4≈4.157
c) Since k = 2, we know that:
4.157=0.04157∗102
Closea) The volume of a cuboid can be calculated by multiplying the area of its base by its length, so:
4.8∗5.8∗9.1=253.344 cm3
b) As we know that 1dm=10cm, the conversion factor is 103=1000, so we get:
253.344 cm3=0.253344 dm3
c) 250 cm3
d) Let's start by calculating the area of the base:
Abase=4.8∗5.8=27.84 cm2
Now, the area of the larger side:
Alarge side=5.8∗9.1=52.78 cm2
Finally, the area of the smaller side
Asmall side=4.8∗9.1=43.68 cm2
We know that we have two of each side, so all of them have to be multiplied by two.
Let's calculate how much will be spent on the top and bottom of the cuboid. We know that it costs 0.15$ per cm2, so:
Ctop+bottom=27.84∗2∗0.15=$8.352
Now, the cost for the sides:
Csides=(52.78∗2+43.68∗2)∗0.12=$23.1504
So, the total cost is:
Ctotal=23.1504+8.352=31.5024≈$31.50
Closea)
q=12x2sin(α)5x2+2y=12∗9∗√3245+18=54√363=6√37
b)
6√37≈1.48
c) We know that k = 4, so:
1.48=0.000148∗104
Closea) To find the volume we need to apply the volume formula:
V=πr2∗h
As it can be seen from the figure, the radius will be a half of 8.4cm, so 4.2cm.
V=π4.22∗12.5=692.721...≈693cm3
b) The area of a cylinder is given by the formula:
A=2πrh+2πr2
We know that the top paert should not be paint, meaning that the formula we will actually use is:
A=2πrh+πr2
A=2π4.2∗12.5+π4.22=385.285...≈385cm2
c) To calculate the percentage error we first need to find the exact value, so the area will need to be multiplied by the dollar amount per each cm2. It is important to here take the exact value, not the rounding to 3 significant figures:
0.05∗385.285...≈19.26
Now, using the formula for percentage error, we get that:
ε=|va−veve|∗100%=|20−19.2619.26|∗100%=3.84%
Closea) By plugging the values into the formula, we get:
V=12(2.4+3.6)∗3.1∗8=74.4cm3
b)
V=74.4cm3≈74cm3
c) Knowing that a has to be between 1000 and 10000, we know that the only possible value it can take is 7440, so:
74.4=7440∗10−2
That means that k=−2
Closea)
Given: Point A: (3, 5), Point B: (6, 1)
Distance=√(x2−x1)2+(y2−y1)2
Substitute the coordinates of points A and B into the formula:
DistanceAB=√(6−3)2+(1−5)2
=√32+(−4)2
=√9+16
=√25
=5
So, the distance between points A and B is 5.
b)
We first need to find the distance between points C and D. So, given: Point C: (2, 4), Point D: (8, 9)
Using the distance formula:
Distance=√(x2−x1)2+(y2−y1)2
Substitute the coordinates of points C and D into the formula:
DistanceCD=√(8−2)2+(9−4)2
=√62+52
=√36+25
=√61
≈7.81
Now, let's check Alex's claim that the distance between points C and D is twice the distance between points A and B:
Alex's claim: DistanceCD=2×DistanceAB
7.81=2×5
Since 7.81≠10, Alex's claim is incorrect.
Closea)
Lower bound: 0.305−0.0005=0.3045meters
Upper bound: 0.305+0.0005=0.3055meters
b) The dimensions of the pyramid are:
- Base side length: 620feet
- Height: 27172=1358.5feet
To find the minimum possible volume, convert the bounds of 1foot into meters and calculate the volume:
Minimum side length: 620×0.3045=188.79meters
Minimum height: 1358.5×0.3045=413.53725meters
Volume of the pyramid:
V=13×(side length)2×height
V=13×(188.79)2×413.53725
V≈4913052m3
c) 4913052=4.913052×106
Close