Answer:
the interest amount totals $240
Step-by-step explanation:
I hope this is helpful.
Response:
55 mph. All options are incorrect.
Detailed explanation:
When speed changes inversely with the time taken, it can be expressed as v ∝ 1/t, where:
v represents speed,
t refers to the time taken.
This leads to;
v = k/t, with k being a constant of proportionality.
Given that Kris takes 5 hours traveling at 55 mph, we replace v with 55 mph and t with 5 hours in the equation to find k as follows:
55 = k/5
Cross-multiplying yields:
k = 55 * 5
k = 275
To determine the speed Martin needs to drive for 5 hours, we substitute k = 275 and t = 5 back into the original equation v = k/t as follows:
v = 275/5
v = 55 mph
Thus, we conclude that in order to travel for 5 hours, Martin must also drive at 55 mph.
The volume of a cylinder can be determined using the formula pi*h*d^2/4, which leads us to V = pi*(39 mm)(39 mm)^2 / 4 = 46,589 mm^3. Dividing the mass of 1 kg by the volume of 46,589 mm^3 results in a density of 2.1464 x 10^-5 kg/mm^3. Typically, density is expressed in kg/m^3, so we convert this by multiplying by 1x10^9, yielding a density of 21,464 kg/m^3.
Answer:
To find the number of genuine solutions for a system of equations consisting of a linear equation and a quadratic equation
1) With two variables, say x and y, rearrange the linear equation to express y, then substitute this y in the quadratic equation
After that, simplify the resulting equation and determine the number of real roots utilizing the quadratic formula, 
for equations of the type 0 = a·x² - b·x + c.
When b² exceeds 4·a·c, two real solutions emerge; if b² equals 4·a·c, there will be a single solution.
Step-by-step explanation:
The tension does not approach infinity.
<span>Let's analyze free body diagrams (FBDs) for each mass, considering the direction of motion of m₁ as positive.
For m₁: m₁*g - T = m₁*a
For m₂: T - m₂*g = m₂*a
Assuming a massless cord and pulley without friction, the accelerations are the same.
From the second equation: a = (T - m₂*g) / m₂
Substitute into the first:
m₁*g - T = m₁ * [(T - m₂*g) / m₂]
Rearranging:
m₁*g - T = (m₁*T)/m₂ - m₁*g
2*m₁*g = T * (1 + m₁/m₂)
2*m₁*m₂*g = T * (m₂ + m₁)
T = (2*m₁*m₂*g) / (m₂ + m₁)
Taking the limit as m₁ approaches infinity:
T = 2*m₂*g
This aligns with intuition since the greatest acceleration m₁ can have is -g. The cord then accelerates m₂ upward at g while gravity acts downward, leading to a maximum upward acceleration of 2*g for m₁.</span>
