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ikadub [295]
3 years ago
12

A group of college students built a self-guided rover and tested it on a plane surface. They programmed the vehicle to move alon

g the path A–B–C–D–A represented on the coordinate plane. What distance will the rover cover if it completes one circuit?
A.
36 meters
B.
40 meters
C.
54 meters
D.
60 meters
E.
68 meters

Mathematics
1 answer:
makkiz [27]3 years ago
4 0

Answer:

B. 40 meters

Step-by-step explanation:

— Estimating

The rectangle enclosing the path has sides of length 9 m and 14 m, so its perimeter is 2(9+14) = 46 m. The distance covered will be shorter than that.

The distance from A to C is longer than the distance from D to C, so we know the distance will be longer than 2·14+9 = 37 m.

Only one answer choice fits in the range 37 < d < 46.

____

— Detailed calculation

The distance from B to C is the hypotenuse of a right triangle with sides 9 and 12. You will recognize that these side lengths are 3 times the side lengths of a 3-4-5 right triangle, so the hypotenuse distance is 3·5 = 15 meters.

The circuit length is ...

AB +BC +CD +DA = 2 + 15 + 14 + 9 = 40 . . . . meters

You might be interested in
Please help! Thank you so much!
igor_vitrenko [27]

Angle W:

180 = 90 + 57 + W

180 = 147 + W

W = 33 degrees

Using trigonometry functions to find the side lengths. (SOH CAH TOA)

Side XZ:

cos(57) = XZ / 18

XZ = cos(57) x 18

XZ = 9.8 units

Side XW:

sin(57) = XW / 18

XW = sin(57) x 18

XW = 15.1 units

Hope this helps!! :)

4 0
3 years ago
Find the perimeter of the pentagon MNPQR with vertices ​M(2​, 4​), ​N(5​, 8​), ​P(​8, 4​), ​Q(8​, 1​), and ​R(2​, 1​)
Gekata [30.6K]

Answer:

The pentagon MNPQR has a perimeter of 22 units.

Step-by-step explanation:

Geometrically speaking, the perimeter of the pentagon is the sum of the lengths of each side, that is:

p = MN + NP + PQ + QR + RM (1)

p = \sqrt{\overrightarrow{MN}\,\bullet \, \overrightarrow{MN}} + \sqrt{\overrightarrow{NP}\,\bullet \, \overrightarrow{NP}} + \sqrt{\overrightarrow{PQ}\,\bullet \, \overrightarrow{PQ}} + \sqrt{\overrightarrow{QR}\,\bullet \, \overrightarrow{QR}} + \sqrt{\overrightarrow{RM}\,\bullet \, \overrightarrow{RM}} (1b)

If we know that M(x,y) = (2,4), N(x,y) = (5,8), P(x,y) = (8,4), Q(x,y) = (8,1) and R(x,y) = (2,1), then the perimeter of the pentagon MNPQR is:

p =\sqrt{(5-2)^{2}+(8-4)^{2}} + \sqrt{(8-5)^{2}+(4-8)^{2}}+\sqrt{(8-8)^{2}+(1-4)^{2}}+\sqrt{(2-8)^{2}+(1-1)^{2}}+\sqrt{(2-2)^{2}+(4-1)^{2}}p = \sqrt{3^{2}+4^{2}} + \sqrt{3^{2}+(-4)^{2}}+\sqrt{0^{2}+(-3)^{2}}+\sqrt{(-6)^{2}+0^{2}}+\sqrt{0^{2}+3^{2}}

p = 22

The pentagon MNPQR has a perimeter of 22 units.

4 0
3 years ago
Options are 264 414 2487 9948
Brums [2.3K]
Find total area

area=pir^2
d/2=r
12=d, 12/2=6=r

area=pi6^2=36pi, pi=3.14
area=113.04 square inches

22 per square inch

113.04 times 22=2486.88
rounded
2487 calories
7 0
3 years ago
david has 212 feet of chain link fencing that he used to make a rectangular garden space in his backyard. the lengthof the garde
joja [24]

Answer:

calcium is in shells and bones

Step-by-step explanation:

4 0
3 years ago
What is the perimter of this figure?
alexira [117]

Answer:

30!

Step-by-step explanation:

Add all sides.

8 0
2 years ago
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