6y-1.5x=8
multiply both sides of the equation by 10
60y-15x=80
divide both sides
12y-3x=16
use the commutative property to reorder the terms
-3x+12y=16
change the signs on both sides of the equation
your answer will be : 3x-2y=-16
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:
A) Fill the blanks, Fail, 0.15, Success, 244, 0.61
B) 240 times
Step by-step explanation:
A) Void , 96, 0.24
Fail, 60, it should be 0.15 because 60/400
Success, 400 - 96- 60 or 244 and the relative frequency is 0.61.
B)
There is a total of 1000. If the relative frequency is 0.24, multiply 0.24 by 1000 to get the amount of times YOU would expect to be VOID.
Or in other words , 240 times
By proving it add all up
0.24 x 1000 + 0.76 x 1000 = 1000
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STEP - BY - STEP EXPLANATION
What to find?
An expression for the total number of books.
Given:
Number of shelves = 5
Number of books in each shelf = k
If Lucy has a bookcase with 5 shelves and each of this
shelf has k books, then the total number of books can be determine by multiplying the numbers of book by the numbers of shelves.
That is;
ANSWER
5K
