Complete Question
Angela has constructed a wedge-shaped pillow for her TV watching needs. It contains 0.35 m³ of fluffy material. The pillow's base area measures 0.5m², and its height stands at 1m.
What is the length of the pillow?
Provide an exact answer (no rounding).
Answer:
1.4m
Step-by-step explanation:
A wedge can be defined as a Triangular prism. Thus,
The volume formula for a wedge (Triangular prism) is given by: 1/2 × B × H × L
b = 0.5m
h = 1 m
l =??
Volume of the wedge = 0.35 m³
0.35 = 1/2 × 0.5 × 1 × L
0.35 = 0.25 × L
Solving for L, we get: L = 0.35/0.25
L = 1.4m
Answer: 
Step-by-step solution:
Leon’s older brother’s height is 
feet
feet
Because Leon is 1/3 foot shorter than his brother,
Leon’s height = 
Convert to like fractions by multiplying numerator and denominator: multiply 3 for the first fraction and 4 for the second.
So, Leon’s height = 
feet
Therefore, Leon’s height is feet.
Applying the cosine law, we can determine:
<span>c</span>²<span> = a</span>²<span> + b</span>²<span> - 2abcos(C) </span>
<span>where: </span>
<span>a, b, and c represent the sides of the triangle and C indicates the angle opposite to side c</span>
<span>Thus, we have:</span>
<span>150</span>²<span> = 240</span>²<span> + 200</span>²<span> - 2(240)(200)cos(C) </span>
<span>Now we solve for C</span>
<span>22,500 = 57,600 + 40,000 - 96,000cos(C) </span>
<span>22,500 - 57,600 - 40,000 = -96,000cos(C)
</span>-75,100=-96,000cos (C)
cos (C)=0.7822916
C=arc cos(0.7822916)→ C=38.53°
<span>Therefore, the direction the captain should head towards island B is
180 - 38.53 </span><span>= 141.47 degrees</span>
The weight of an orangutan is 64.5 kilograms
Solution:
It is stated that the orangutan's weight is 142 pounds
Additionally,
1 kilogram is approximately 2.2 pounds
We will now convert 142 pounds into kilograms
1 kilogram = 2.2 pounds
As a result, 142 pounds translates to
When rounding to the nearest tenth, we obtain 64.5 kilograms
Therefore the mass of the orangutan is 64.5 kilograms
Let’s clarify this: the basketball moves faster, indicating the tennis ball won’t be able to catch up. Therefore, we utilize the formula:
Vr=Vb-Vt
<span>=0.5-0.25=0.25
</span>Thus, the relative speed is <span>0.25m/s.
I hope this is helpful.</span>
