Step-by-step explanation:
When a negative number is placed within a modulus function, the result will be positive. For instance, |-3| equals 3, |-6| equals 6, and |5| equals 5, etc.
A modulus function, expressed as |x|, is always positive unless x is zero, in which case it equals zero.
Consequently, |x| cannot be less than -4 because |x| is always non-negative. Thus, the statement is inaccurate.
The formula for the volume of a sphere can be derived as follows. We will approach this through calculus, utilizing the concept of a solid of revolution; this is a three-dimensional shape formed by rotating a two-dimensional curve around a straight line (the axis of revolution) that lies within the same plane. From calculus, we know that we will generate a shape by rotating the specified circumference. Next, we isolate y and utilize certain limits for this integral.
Hello! C and D aren't correct answers, as they fall downward due to gravity. The object accelerates downward at -10 m/s, resulting in an increasing speed as it descends, going beyond 10 m/s, which indicates that speed isn't steady. Hence, the correct answer is A.
Respuesta:
Por lo tanto, la integral de superficie es 
.
Explicación paso a paso:
La función dada es,
Para encontrar,
donde S=A=superficie del cilindro elíptico debemos aplicar el teorema de divergencia, así que,
- Si el vector unitario
está dirigido en dirección positiva (hacia afuera), entonces z=c y,
- Si el vector unitario está dirigido en dirección negativa (hacia adentro), entonces z=-c y,
Por lo tanto, la integral de superficie sin el vector unitario de la superficie es,
The salt enters at a rate of (5 g/L)*(3 L/min) = 15 g/min.
The salt exits at a rate of (x/10 g/L)*(3 L/min) = 3x/10 g/min.
Thus, the total rate of salt flow, represented by 
in grams, is defined by the differential equation,
which is linear. Shift the 
term to the right side, then multiply both sides by 
:
Next, integrate both sides and solve for :
Initially, the tank contains 5 g of salt at time 
, so we have
The duration required for the tank to contain 20 g of salt is 
, such that
