The constant of variation is 5 because 4 multiplied by 5 equals 20.
Density (D) is calculated as mass (m) divided by volume (v).
D = m / v
The volume change is determined by measuring the water level before and after the object is introduced to the beaker,
v = 23.1 mL - 18.5 mL = 4.6 mL
Substituting into the density formula,
D = 8.24 g / 4.6 mL = 1.79 g/mL
Therefore, the density is roughly 1.79 g/mL.
Answer:
35.7 km and 248.3 °
Step-by-step explanation:
To clarify, I will include a diagram as an image.
We begin with the cosine law formula:
y² = 42² + 28² - (2 * 42 * 25 * cos 58 °)
y² = 2389 - 1112.83 = 1276.17
y = √1276.17
y = 35.72 km
Next, to find the bearing of the surveyor from her camp, we apply the sine law:
[(Sin 58 °) / y] = [(Sin A) / 42]
Here, A = (42 * sin 58 °) / 35.72
A = sin⁻¹ (0.9971)
A = 85.7 °
The bearing from the base camp now calculates to: 270 ° - (85.7 ° - 64 °) = 248.3 °
Answer:
- No, the second machine (function B) can produce an output of 0, while the first machine (function A) cannot.
Explanation
The functionality of each machine is dictated by the expression it operates under.
1) Function A:
To achieve an output of 0 with the equation y = x² + 3, one would need to resolve the equation x² + 3 = 0.
Given that x² is always non-negative for any real number, x² + 3 will always be at least 3, meaning an output of 0 is unattainable with the first machine.
2) Function B:
By solving 
Thus, utilizing x = 4 will yield an output of 0 with this machine.
Answer:
The prism's width is 2 cm
Step-by-step explanation:
The parameters provided are;
Volume of the prism = 170 cm³
Length of the prism = 5 cm
Height of the prism = 17 cm
The formula for the volume of the prism can be expressed as v = Length, l × Height, h × Width, w
Thus;
Volume = 5 cm × 17 cm × w = 170 cm³
Solving for width gives;
w = 170 cm³ / (5 cm × 17 cm) = 170 cm³ / (85 cm) = 2 cm
∴ Therefore, the prism's width = 2 cm.