Estimate the limit numerically or state that the limit does not exist. lim x → 0 4 x − 1 x Start by calculating the values of the function for the inputs listed in this table. x f ( x ) 0.01 0.001 0.0001 -0.0001 -0.001 -0.01 Based on the values in this table, it appears lim x → 0 4 x − 1 x = Give your answer accurate to 3 decimal places

Answer:

All you need to remember is the rules

Step-by-step explanation:

Let us remember

a to the m power x a to the nth power is = a to the m+n power. (add the exponents)

And

a to the m power ÷ a to the nth power is = a to the m-n power. (subtract the exponents) So

14 to the -4 power x 14 to the 7 power= 14 to the -4+7 which is equal to 14 to the 3rd power

Answer:

5.83

Step-by-step explanation:

Answer:

If x > 5, then y = 2x.

Step-by-step explanation:

If x > 5, then both expressions inside the absolute values are positive, so we can simplify the expression:

y = |x - 5| + |x + 5|

Since x > 5, we know that x - 5 > 0 and x + 5 > 0. Therefore, we can write:

y = (x - 5) + (x + 5)

Simplifying this expression, we get:

y = 2x

So, if x > 5, then y = 2x.

Hope this helped! Sorry if it's wrong. If you need more help, ask me! :]

Answer:

4-(2x+5) = 1/2(-4x-2)

4-2x-5=-2x-1

-1-2x-=-2x-1

Infinite solution

Step-by-step explanation:

Branliest pls

Answer:

the domain is -2 and the range is 0

Step-by-step explanation:

Answer:

Step-by-step explanation:

The domain of the graphed function is any value and the range is all positive numbers:

Answer:

9

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(y = 3x^2+9\)

Let x equal 0

\(y=3(0)^2 +9\\\\y= 3\times 0 +9\\\\y = 0+9\\\\y=+9\)

A price floor is a law that limits the minimum price at which a good, service, or factor of production can be sold while a price ceiling is a regulation that limits the maximum price at which a good, service, or factor of production can be sold

Price floors are commonly implemented to support producers, while price ceilings are typically put in place to protect consumers from higher prices that might result from shortages or monopolies.

Example of Price Floor:Agricultural subsidies are a common example of price floors. Government price floors ensure that farmers receive a minimum price for their crops.

If the market price of wheat falls below the government-established price floor, the government may buy the excess supply at the guaranteed price, ensuring that farmers are able to make a profit. If there is a price floor, the minimum price is set above the equilibrium price.

Learn more about price ceiling at:

https://brainly.com/question/2562066

#SPJ11

Answer:

10*2=20

-6*2=-12

20-12=8

Answer:

3

Step-by-step explanation:

The slope is rise/run and for this case, it is 3/1 which equals 3!!!

Problem

The difference of a number and 72 is 12. Find the number.​

Solution

Let x the number of intertest and we can write this:

x-72=12

And solving for x we got:

x= 72+12= 84

Answer:

Always true

Step-by-step explanation:

The definition of an interior or internal angle bisector is the the dividing line segment that splits the angle into two  equal angles (parts)

Therefore, given that the segment BD is the bisector of ∠ABC, then the formed angles m∡ABD and m∡DBC are, by definition of bisected ∠ABC, always congruent

Answer:

a=3.63

Step-by-step explanation:

Isolate the variable by dividing each side by factors that contain the variable.

Answer:

The missing monomial should be \(3b\).

Step-by-step explanation:

Given that,

\(( + 2a)^2 = + 12ab + 4\)

Let the missing monomial is x.

\(( x+ 2a)^2 = x^2+ 12ab + 4a^2\\\\( x+ 2a)^2=(3b)^2+ 2(2a)(3b) + (2a)^2\\\\So,\\\\( 3b+ 2a)^2=(3b)^2+ 2(2a)(3b) + (2a)^2\)

So, the missing monomial should be \(3b\).

While looking at the critical points of a function f(x) is a useful first step in finding its maxima and minima, it is not enough by itself to determine all of them.

The statement is partially correct. If a function f(x) is continuous on a closed interval, it is possible to find its absolute maxima and minima by looking at the points where f'(x) = 0, but this is not enough to guarantee that you have found all of them.

The reason why this is the case is because the condition f'(x) = 0 only identifies critical points, which are points where the function may have an extremum (either a maximum or a minimum). To determine whether a critical point is indeed a maximum or a minimum, you need to analyze the behavior of the function near the critical point.

One way to do this is by using the second derivative test, which states that if f(x) is twice differentiable and f''(x) > 0 at a critical point x, then f(x) has a local minimum at x. Similarly, if f''(x) < 0 at a critical point x, then f(x) has a local maximum at x.

You also need to use additional tools, such as the second derivative test, to verify whether the critical points are indeed extrema.

To learn more about maxima here:

https://brainly.com/question/12982238

#SPJ4

Answer: 3/4, 5/8, 9/16, 31/32, etc.

Step-by-step explanation: Any fraction above the 1/2 ratio, but below the full number will work. (i.e. any number above 16 for 32nds, but below 32. So 17/32, 18/32, 19/32, etc.)

Answer:

M TO L

Step-by-step explanation:

Its right there.

Answer: L

Step-by-step explanation:

The value of x in the trapezoid is 117°.

A trapezoid is a quadrilateral a four-sided polygon with two parallel sides and two non-parallel sides. The parallel sides are most call the bases of the trapezoid, and the non-parallel sides are called the legs.

In a trapezoid, the opposite angles are supplementary. Therefore, we can set up an equation:

x + 63° = 180°

Solving for x, we get:

x = 180° - 63°

x = 117°

Therefore, the value of x in the trapezoid is 117°.

Full question "Find the value of x in the trapezoid below.

X

63°

X = = [?]°"

Read more about trapezoid here

brainly.com/question/26487711

#SPJ1

Answer:

The answer is $4.25

Step-by-step explanation:

Answer:

she would get 25 cents back or .25 dollars back :)

Step-by-step explanation:

Answer:

66 hours

Step-by-step explanation:

1.  1000 - 175 = 825

(He needs $825 left.)

2.  825/12.50=66

He needs to work 66 more hours before he can buy his new phone.

The percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second is  28.87%.

Given that the carrying capacity is directly proportional to the area, we can write:

C1 ∝ A1 = πr₁²

Since the carrying capacity is directly proportional to the area, we have:

C2 ∝ A2 = πr₂²

To find the percentage increase in diameter, we need to find the ratio of the increased area to the initial area and then express it as a percentage. Let's calculate this ratio:

(A2 - A1) / A1 = (πr₂² - πr₁²) / (πr₁²) = (r₂² - r₁²) / r₁²

We can also express the ratio of the increased carrying capacity to the initial carrying capacity:

(C2 - C1) / C1 = (60 - 36) / 36 = 24 / 36 = 2 / 3

Since the area and the carrying capacity are directly proportional, the ratios should be equal:

(r₂² - r₁²) / r₁² = 2 / 3

Now, let's substitute r = D/2 in the equation:

((D₂/2)² - (D₁/2)²) / (D₁/2)² = 2 / 3

(D₂² - D₁²) / D₁² = 2 / 3

Cross-multiplying:

3(D₂² - D₁²) = 2D₁²

3D₂² - 3D₁² = 2D₁²

3D₂² = 5D₁²

Dividing by D₁²:

3(D₂² / D₁²) = 5

(D₂² / D₁²) = 5 / 3

Taking the square root of both sides:

D₂ / D₁ = √(5/3)

To find the percentage increase in diameter, we subtract 1 from the ratio and express it as a percentage:

Percentage increase = (D₂ / D₁ - 1) × 100

Percentage increase = (√(5/3) - 1) × 100

Percentage increase = 28.87%

To learn more on Percentage click:

https://brainly.com/question/24159063

#SPJ1

The solutions to the equation are x = -1, x = -8, and x = 1/2.

The equation 4x³ + 32x² + 42x - 16 = 0 can be divided throuh by 2 as follows:

2x³ + 16x² + 21x - 8 = 0

We can test each of these possible roots by substituting them into the equation and seeing if we get 0. When we substitute -1, we get 0, so -1 is a root of the equation. We can then factor out (x + 1) from the equation to get:

(x + 1)(2x² + 15x - 8) = 0

We can then factor the quadratic 2x² + 15x - 8 by grouping to get:

(x + 8)(2x - 1) = 0

This gives us two more roots, x = -8 and x = 1/2.

Therefore, the solutions to the equation are x = -1, x = -8, and x = 1/2.

Learn more about equations on

https://brainly.com/question/2972832

#SPJ1

Answer: 0.7

Step-by-step explanation: 3/5 equals 0.6 which is less than 0.7, so 0.7 is the greater of the two.

The 16th term of the arithmetic sequence is -60.

To find the 16th term of an arithmetic sequence with a first term of 0 and a common difference of -4

we can use the formula for the nth term of an arithmetic sequence:

nth term = a + (n - 1)d

where:

a = first term

d = common difference

n = term number

Substituting the given values, we have:

16th term = 0 + (16 - 1) × (-4)

= 0 + 15(-4)

= 0 - 60

= -60

Therefore, the 16th term of the arithmetic sequence is -60.

To learn more on Sequence click:

https://brainly.com/question/21961097

#SPJ1

The correct pair of constraints that needs to be added to specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units is: P24 - P25 <= 80; P25-P24 <= 80. Therefore, the correct option is 5.

Here, the given information is Pij = the production of product i in period j. We need to find the pair of constraints that will specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units. Thus, let the production of product 2 in period 4 and in period 5 be represented as P24 and P25 respectively.

Therefore, we can write the following inequalities:

P24 - P25 <= 80

This is because the production of product 2 in period 5 can be at most 80 units less than that of period 4. This inequality represents the difference being less than or equal to 80 units.

P25-P24 <= 80

This is because the production of product 2 in period 5 can be at most 80 units more than that of period 4. This inequality represents the difference being less than or equal to 80 units.

Therefore, we need to add the pair of constraints P24 - P25 <= 80 and P25-P24 <= 80 to specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units. Hence, option 5 is the correct answer.

Learn more about Constraints:

https://brainly.com/question/3469433

#SPJ11

Answer:

Step-by-step explanation:

\( \frac{x}{3} = - 9\)

Apply cross product property

\(x = - 9 \times 3\)

Calculate the product

\(x = - 27\)

Hope this helps...

Best regards!!

Answer:

x=-27

Step-by-step explanation:

The radius of convergence, R is (6cos(5)) / (s² + 36) + (sin(5)s) / (s² + 36).

To simplify the function f(t) = sin(6t + 5), we can utilize the trigonometric identity known as the sum-to-product formula, which states:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b).

In our case, a = 6t and b = 5, so we can rewrite f(t) as follows:

f(t) = sin(6t + 5) = sin(6t)cos(5) + cos(6t)sin(5).

Using this property, we can find the Laplace transform of f(t) by taking the Laplace transform of each term separately and adding them together.

L{f(t)} = L{sin(6t)cos(5)} + L{cos(6t)sin(5)}.

To find the Laplace transform of each term, we can use the standard Laplace transform pairs. The Laplace transform of sin(at) is given by:

L{sin(at)} = a / (s² + a²),

and the Laplace transform of cos(at) is given by:

L{cos(at)} = s / (s² + a²).

Applying these formulas to each term, we get:

L{f(t)} = L{sin(6t)cos(5)} + L{cos(6t)sin(5)}

= (6 / (s² + 6²)) * cos(5) + (s / (s² + 6²)) * sin(5).

Simplifying further, we have:

L{f(t)} = (6cos(5)) / (s² + 36) + (sin(5)s) / (s² + 36).

Thus, we have found the Laplace transform of f(t) in terms of s as:

L{f(t)} = (6cos(5)) / (s² + 36) + (sin(5)s) / (s² + 36).

This is the Laplace transform of the given function f(t) using a trigonometric identity to simplify it before applying the transform.

To know more about trigonometric identity here

https://brainly.com/question/12537661

#SPJ4

The interest rate is 10.89%

1. Given,С = 200+ 0.69YI = 80 - 1,000rG = 20NX = 850.09ee = 90M = 115YL = 0.5Y - 200rY = 300Using the equation for National Saving, we get,National Saving = Investment + Government Saving + Net exports(S – I) + (T – G) + (X – M) = 0T = 0, hence (S – I) + (X – M) = 0(1 – t)Y – C – (I + G) + NX = 0Where t = 0, we get,0.5Y – 200r – 200 – 69/100Y + 80 – 850.09e = 0.5Y – 200r – 970.09e – 120 = 0.5Y – 200r – 970.09e – 120 = 0Therefore, Y = 325.0454 - 0.5r + 4.851eThis is the equation for the IS curve.On the other hand, the equation for the LM curve is given by,Ms / P = YL(i)115 / 1 = 0.5Y - 200rTherefore, Y = 400 + 400rThis is the equation for the LM curve.The interest rate is given by the point of intersection of the two curves. Equating Y from both equations, we get,325.0454 - 0.5r + 4.851e = 400 + 400rSolving the above equation for r, we get r = 0.1089 or 10.89%..

The size of the nominal money supply in the new short-run equilibrium is 121.07.

2. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate.Flexible Exchange Rates:In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output.Real exchange rate will fall.Increase in output will be higher compared to the fixed exchange rate case.Fixed Exchange Rates:In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.Real exchange rate will remain unchanged.Increase in output will be less compared to the flexible exchange rate case.The nominal money supply in the new short-run equilibrium will change in the case of Fixed Exchange Rates. In the fixed exchange rate case, the domestic interest rate will increase, leading to an inflow of capital. This will increase the money supply and the LM curve will shift downwards until it intersects the IS curve at the new equilibrium point.

Real exchange rate will remain unchanged.

3. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate. Flexible Exchange Rates :In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output .Real exchange rate will fall. Value of the real exchange rate in the new equilibrium is 0.891.Fixed Exchange Rates: In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.

Know more about  interest rate here:

https://brainly.com/question/28236069

#SPJ11

Answer:

D

Step-by-step explanation:

It is the change in time