Answer:
Hope this helps
Step-by-step explanation:
Answer:
388.5yd²
Step-by-step explanation:
We have Triangle TUV
In the question, we are given already
Angle U = 32°
Angle T = 38°
Angle V = ???
Side t = 31yd
Side u = ?
Side v = ?
Area of the triangle= ?
Step 1
We find the third angle = Angle V
Sum of angles in a triangle = 180°
Third angle = Angle V = 180° - (32 + 38)°
= 180° - 70°
Angle V = 110°
Step 2
Find the sides u and v
We find these sides using the sine rule
Sine rule or Rule of Sines =
a/ sin A = b/ Sin B
Hence for triangle TUV
t/ sin T = u/ sin U = v/ sin V
We have the following values
Angle T = 38°
Angle U = 32°
Angle V = 110°
We are given side t = 31y
Finding side u
u/ sin U= t/ sin T
u/sin 32 = 31/sin 38
Cross Multiply
sin 32 × 31 = u × sin 38
u = sin 32 × 31/sin 38
u = 26.68268yd
u = 26.68yd
Finding side x
v / sin V= t/ sin T
v/ sin 110 = 31/sin 38
Cross Multiply
sin 110 × 31 = v × sin 38
v = sin 110 × 31/sin 38
v = 47.31573yd
v = 47.32yd
To find the area of triangle TUV
We use heron formula
= √s(s - t) (s - u) (s - v)
Where S = t + u + v/ 2
s = (31 + 26.68 + 47.32)/2
s = 52.5
Area of the triangle = √52.5× (52.5 - 31) × (52.5 - 26.68 ) × (52.5 - 47.32)
Area of the triangle = √150967.6032
Area of the triangle = 388.5454973359yd²
Approximately to the nearest tenth =388.5yd²
Answer: plants are same height in 30 days; Plant A is tallest in 6 weeks
Step-by-step explanation:
x = number of days
4 + (2/3)x = 9 + (1/2)x
(2/3)x - (1/2)x = 9 - 4
(1/6)x = 5
x = 30, number of days for Plant A and Plant B to be same height.
6 wks = 42 days
Plant A in 42 days: 4 + (2/3)(42) = 32 inches
Plant B in 42 days: 9 + (1/2)(42) = 30 inches
Answer:
36 cubic inches.
Step-by-step explanation:
Let the length, width and height of the rectangular prism are a, b, c respectively.
So, surface area, 2(ab + bc + ca) = 32 {Given} ............ (1)
Volume, abc = 12 {Given} ............ (2)
And, the sum of all the edges, 4(a + b + c) = 28 {Given} .......... (3)
Now, if the length width and height are increased by 1 inch, then the volume of the prism will be = (a + 1)(b + 1)(c + 1)
= abc + (ab + bc + ca) + (a + b + c) + 1
= 12 + 16 + 7 + 1 {From equations (1), (2) and (3)}
= 36 cubic inches. (Answer)
Answer:
18.25
Step-by-step explanation:
1/4 = 0.25
