Pre-calc/trig

What is the first number greater than 106637 where it's tens and units digits are the same

sashaice [31]

The first number after that matching the criteria is 106644, as 33 is below so the closest one has to be at 44.

4 0

3 years ago

Wes works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate,

Dmitry [639]

Answer:

Correct answer: at 2 p.m. the population was 10,000

at 3 p.m. the population was 50,000

Step-by-step explanation:

At 1 p.m. population was 2,000

At 2 p.m. or after first hour, the population of bacteria increases

in this way 2,000 · k

At 3 p.m. or after second hour, the population of bacteria increases

2,000 · k²

At 4 p.m. or after third hour, the population of bacteria increases 2,000 · k³

2,000 · k³ = 250,000 => k³ = 250,000 / 2,000 = 125

k = ∛125 = 5 => k = 5

At 2 p.m. or after first hour, the population of bacteria was 2,000 · 5 = 10,000

At 3 p.m. or after second hour, the population of bacteria was 2,000 · 5² =

= 2,000 · 25 = 50,000

God is with you!!!

6 0

3 years ago

Find a formula for the inverse of the function f(x)=3x^3 + 2sinx + 4cosx

vitfil [10]

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 Problems1. 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.Local Linear Approximation formulaf(x) ≈ f(x₀) + f'(x₀)(x - x₀)
f(x₀ + ∆x) ≈ f(x₀) + f'(x₀)∆x when ∆x = x - x₀Local Linear Approximation from the Differential Point of View∆y ≈ f'(x)dx = dyError Propagation Variablesx₀ 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 yL'Hopital's RuleApplying L'Hopital's Rule1. 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).

5 0

4 years ago

(3,1) m=0 In standard form

diamong [38]

0x + y = 1 is the standard form of (3, 1) with m = 0

Solution:

We have been given a point and slope of an equation and have been asked to write it in the standard form.

The standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers. The standard form of a line is just another way of writing the equation of a line.

The given point is (3,1) and the slope is 0

To write in standard form we will first write it in point slope form and then rearrange it into a standard from.

The point slope form of line is given as:

$y-y_{1}=m\left(x-x_{1}\right)$

Where "m" is the slope of the line

Here in this problem, $m = 0 , x_1 = 3 and y_1 = 1$

y - 1 = 0(x - 3)

y - 1 = 0

y = 1

since the above equation doesn’t have an ‘x’ term we convert into a standard form as follows:

0x + y = 1

This is the standard form for the given point and slope of a line.

6 0

3 years ago

What is a square root?

gladu [14]

Answer:

A number multiplied by its self for ex 7 x 7 = 49 square root of 49 is 7

5 0

3 years ago

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