Answer: The answer is (c) 
Step-by-step explanation: Given that there are two functions f and g, defined by
We are to find f*g and also its domain.
Also, its domain will be all real numbers, since the function f*g is defined at all 'x' in real numbers.
Thus, the correct option is
Answer:
a. connect the point (0 , 3) with A
b. connect the origin (0 , 0) with B
c. For A: y = 0.5x +3
For B: y = 0.5x
Step-by-step explanation:
y = ax + b is the general rule for any straight line
a being the slope and b being the y intercept, a is given to be 0.5
y = 0.5x + b, substitute the coordinates of point A
4 = 0.5 *2 +b hence b = 4 - 0.5 *2 = 4 - 1 = 3
so y = 0.5 x + 3 is the equation of the line passing through A
since the second line that passes through B is parallel to the first, hence it has the same slope of 0.5
same procedure, substitute coordinates of B
2 = 0.5 * 4 + b hence b = 2 - 0.5 *4 = 2 - 2= 0
so y = 0.5 x is the equation of the line passing through B
6.5X + 9(30) = 8(30+X)6.5X +270 = 240 + 8X270-240 = 8X-6.5X1.5X = 30X = 30/1.5 =20 ounces of $6.50 alloy9 is within 1 of 86.5 is within 1.5 of 81.5 is 3/2 of 130 is 3/2 of 20You know you need more of $9 alloy since it's closer to $8You need exactly 3/2 or 1.5 times more of the $9 alloy30 is 1.5 times 20
Explicit Functiony = f(x) is said to define y explicitly as a function of x because the variable y appears alone on one side of the equation and does not appear at all on the other side. (ex. y = -3x + 5)Implicit FunctionAn equation in which y is not alone on one side. (ex. 3x + y = 5)Implicit DifferentiationGiven a relation of x and y, find dy/dx algebraically.d/dx ln(x)1/xd/dx logb(x) (base b)1/xln(b)d/dx ln(u)1/u × du/dxd/dx logb(u) (base b)1/uln(b) × du/dx(f⁻¹)'(x) = 1/(f'(f⁻¹(x))) iff is a differentiable and one-to-one functiondy/dx = 1/(dx/dy) ify = is a differentiable and one-to-one functiond/dx (b∧x)b∧x × ln(b)d/dx e∧xe∧xd/dx (b∧u)b∧u × ln(b) du/dxd/dx (e∧u)e∧u du/dxDerivatives of inverse trig functionsStrategy for Solving Related Rates Problems<span>1. Assign letters to all quantities that vary with time and any others that seem relevant to the problem. Give a definition for each letter.
2. Identify the rates of change that are known and the rate of change that is to be found. Interpret each rate as a derivative.
3. Find an equation that relates the variables whose rates of change were identified in Step 2. To do this, it will often be helpful to draw an appropriately labeled figure that illustrates the relationship.
4. Differentiate both sides of the equation obtained in Step 3 with respect to time to produce a relationship between the known rates of change and the unknown rate of change.
5. After completing Step 4, substitute all known values for the rates of change and the variables, and then solve for the unknown rate of change.</span>Local Linear Approximation formula<span>f(x) ≈ f(x₀) + f'(x₀)(x - x₀)
f(x₀ + ∆x) ≈ f(x₀) + f'(x₀)∆x when ∆x = x - x₀</span>Local Linear Approximation from the Differential Point of View∆y ≈ f'(x)dx = dyError Propagation Variables<span>x₀ is the exact value of the quantity being measured
y₀ = f(x₀) is the exact value of the quantity being computed
x is the measured value of x₀
y = f(x) is the computed value of y</span>L'Hopital's RuleApplying L'Hopital's Rule<span>1. Check that the limit of f(x)/g(x) is an indeterminate form of type 0/0.
2. Differentiate f and g separately.
3. Find the limit of f'(x)/g'(x). If the limit is finite, +∞, or -∞, then it is equal to the limit of f(x)/g(x).</span>
Answer:
decimal form is -21.44 and fractional form is -536/25
Step-by-step explanation:
