Determine the value of a.

Step-by-step explanation:

y-2=2(x-0)^2

Vertex: (0,2)

Axis of Symmetry is x=0

Opens upward

Hope that helps :)

Answer:

12 cents

Step-by-step explanation:

opportunity cost of the next best option forgone when one alternative is chosen over other alternatives

by loaning matt the money he forgoes the opportunity to earn 12 cents in interest. this is his opportunity cost

Answer:

So we'll use trig to solve this because it's a right triangle. The hypotenuse is the ladder (h) and the two smaller sides are the ground and the vertical wall (w).

That angle ladder makes with the ground = €

SOH: sin € = opposite/hypotenuse

No the ladder won't be safe!!!

Now let's make it safe:

The ladder's length (w) is constant, so stays 12

So now let's ask in an inequality what height will be safe (75° or less)

what does that mean?? well as long as you put the ladder against the wall so that the height from ground to top of the ladder is < 11.6 ft!!

Hope that helps! :-D

Step-by-step explanation:

Answer:

not safe it is 78.5 degrees

Step-by-step explanation:

Step-by-step explanation:

A can is a cylinder.

Volume of a can = Volume of Cylinder

[tex] = \pi {r}^{2} h[/tex]

Given Radius = 3.2 inches and height = 15 inches,

Volume of one olive oil can =

[tex]\pi( {3.2}^{2} )(15) \\ = 153.6\pi {in}^{3} [/tex]

Volume of 5 olive oil cans = 5 x volume of one olive can

[tex] = 5 \times 153.6\pi \\ = 768\pi {in}^{3} [/tex]

I will just leave the answer in terms of pi as I'm not sure if you need to round off your answers.

Answer:

(a) Yes, it does not matter if f is continuous or differentiable; every function satisfies the Mean Value Theorem.

(b) [tex]c =0.51995[/tex]

Step-by-step explanation:

Given

[tex]f(x) = e^{-4x};\ [0,2][/tex]

Solving (a); Does the function satisfy M.V.T on the given interval

We have:

[tex]f(x) = e^{-4x};\ [0,2][/tex]

The above function is an exponential function, and it is differentiable and continuous everywhere

Solving (b): The value of c

To do this, we use:

[tex]f'(c) = \frac{f(b) - f(a)}{b - a}[/tex]

In this case:

[tex][a,b] = [0,2][/tex]

So, we have:

[tex]f'(c) = \frac{f(2) - f(0)}{2 - 0}[/tex]

[tex]f'(c) = \frac{f(2) - f(0)}{2}[/tex]

Calculate f(2) and f(0)

[tex]f(x) = e^{-4x}[/tex]

So:

[tex]f(2) = e^{-4*2} = e^{-8} = 0.00033546262[/tex]

[tex]f(0) = e^{-4*0} = e^{0} = 1[/tex]

This gives:

[tex]f'(c) = \frac{0.00033546262 - 1}{2}[/tex]

[tex]f'(c) = \frac{-0.99966453738}{2}[/tex]

[tex]f'(c) = -0.4998[/tex]

Note that:

[tex]f'(x) = (e^{-4x})'[/tex]

[tex]f'(x) = -4e^{-4x}[/tex]

This implies that:

[tex]f'(c) = -4e^{-4c}[/tex]

So, we have:

[tex]f'(c) = -0.4998[/tex]

[tex]-4e^{-4c} =-0.4998[/tex]

Divide both sides by -4

[tex]e^{-4c} =\frac{-0.4998}{-4}[/tex]

[tex]e^{-4c} =0.12495[/tex]

Take natural logarithm of both sides

[tex]\ln(e^{-4c}) =\ln(0.12495)[/tex]

[tex]\ln(e^{-4c}) =-2.0798[/tex]

Apply law of natural logarithm

[tex]\ln(e^{ax}) =ax[/tex]

So:

[tex]-4c =-2.0798[/tex]

Solve for c

[tex]c =\frac{-2.0798}{-4}[/tex]

[tex]c =0.51995[/tex]

Answer:

78.46020384

Step-by-step explanation:

A=C^2/4π

A= 31.4^2/4π

A = 78.46020384

Answer:

The coefficients are 2 and -3

The exponents are 5 and 1

Step-by-step explanation:

Given

[tex]2x^5 - 3x[/tex]

Required

The coefficient and exponent

First, identify the terms.

The terms are: [tex]2x^5[/tex] and [tex]- 3x[/tex]

The coefficient are the numbers written before the variables

The exponents are the power of the variables

So; for : [tex]2x^5[/tex]

[tex]Coefficient = 2[/tex]

[tex]Exponent = 5[/tex]

For [tex]- 3x[/tex]

[tex]Coefficient = -3[/tex]

[tex]Exponent = 1[/tex]

Answer: (i) 5/6

(ii) 1/6

Step-by-step explanation:

Her money spent in clothes = 2/3

her money spent in internet cafe = 1/6

total fraction spent =

2/3 + 1/6

= 4+1/6

= 5/6

fraction left with her =

1 - (5/6)

= 1/6

Answer:

I think its +10 above surface

Answer:

20% profit

Step-by-step explanation:

Hope this helps

9514 1404 393

Answer:

  $1686.05

Step-by-step explanation:

The amount with compound interest is ...

  A = P(1 +r/n)^(nt)

for principal P earning annual rate r compounded n times per year for t years.

  A = $1600(1 +0.0175/4)^(4·3) = $1686.05

The balance after 3 years is $1686.05.

Answer:

the answer is $1686.05

Step-by-step explanation:

:))

From the above, it can be seen that the nature of polynomial functions is dependent on its degree. Higher the degree of any polynomial function, then higher is its growth. A function which grows faster than a polynomial function is y = f(x) = ax, where a>1. Thus, for any of the positive integers n the function f (x) is said to grow faster than that of fn(x).

Thus, the exponential function having base greater than 1, i.e., a > 1 is defined as y = f(x) = ax. The domain of exponential function will be the set of entire real numbers R and the range are said to be the set of all the positive real numbers.

It must be noted that exponential function is increasing and the point (0, 1) always lies on the graph of an exponential function. Also, it is very close to zero if the value of x is mostly negative.

Exponential function having base 10 is known as a common exponential function. Consider the following series:

Derivative of logarithmic and exponential function 5

The value of this series lies between 2 & 3. It is represented by e. Keeping e as base the function, we get y = ex, which is a very important function in mathematics known as a natural exponential function.

For a > 1, the logarithm of b to base a is x if ax = b. Thus, loga b = x if ax = b. This function is known as logarithmic function.

Derivative of logarithmic and exponential function 2

For base a = 10, this function is known as common logarithm and for the base a = e, it is known as natural logarithm denoted by ln x. Following are some of the important observations regarding logarithmic functions which have a base a>1.

   The domain of log function consists of positive real numbers only, as we cannot interpret the meaning of log functions for negative values.

   For the log function, though the domain is only the set of positive real numbers, the range is set of all real values, i.e. R

   When we plot the graph of log functions and move from left to right, the functions show increasing behaviour.

   The graph of log function never cuts x-axis or y-axis, though it seems to tend towards them.

Derivative of logarithmic and exponential function 3

   Logap = α, logbp = β and logba = µ, then aα = p, bβ = p and bµ = a

   Logbpq = Logbp + Logbq

   Logbpy = ylogbp

   Logb (p/q) = logbp – logbq

Exponential Function Derivative

Let us now focus on the derivative of exponential functions.

The derivative of ex with respect to x is ex, i.e. d(ex)/dx = ex

It is noted that the exponential function f(x) =ex  has a special property. It means that the derivative of the function is the function itself.

(i.e) f ‘(x) = ex = f(x)

Exponential Series

Exponential Functions

Exponential Function Properties

The exponential graph of a function represents the exponential function properties.

Let us consider the exponential function, y=2x

The graph of function y=2x is shown below. First, the property of the exponential function graph when the base is greater than 1.

Exponential Functions

Exponential Function Graph for y=2x

The graph passes through the point (0,1).

   The domain is all real numbers

   The range is y>0

   The graph is increasing

   The graph is asymptotic to the x-axis as x approaches negative infinity

   The graph increases without bound as x approaches positive infinity

   The graph is continuous

   The graph is smooth

Exponential Functions

Exponential Function Graph y=2-x

The graph of function y=2-x is shown above. The properties of the exponential function and its graph when the base is between 0 and 1 are given.

   The line passes through the point (0,1)

   The domain includes all real numbers

   The range is of y>0

   It forms a decreasing graph

   The line in the graph above is asymptotic to the x-axis as x approaches positive infinity

   The line increases without bound as x approaches negative infinity

   It is a continuous graph

   It forms a smooth graph

Exponential Function Rules

Some important exponential rules are given below:

If a>0, and  b>0, the following hold true for all the real numbers x and y:

       ax ay = ax+y

       ax/ay = ax-y

       (ax)y = axy

       axbx=(ab)x

       (a/b)x= ax/bx

       a0=1

       a-x= 1/ ax

Exponential Functions Examples

The examples of exponential functions are:

   f(x) = 2x

   f(x) = 1/ 2x = 2-x

   f(x) = 2x+3

   f(x) = 0.5x

Solved problem

Question:

Simplify the exponential equation 2x-2x+1

Solution:

Given exponential equation: 2x-2x+1

By using the property: ax ay = ax+y

Hence, 2x+1 can be written as 2x. 2

Thus the given equation is written as:

2x-2x+1 =2x-2x. 2

Now, factor out the term 2x

2x-2x+1 =2x-2x. 2 = 2x(1-2)

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

2x-2x+1 = – 2x

Answer:

I think its y-x, if y >x.

Step-by-step explanation:

what

is the quistion cause can't nobody see that

Answer:

566

Step-by-step explanation:

566

Answer:

ask in English then only I will answer

[tex]533 {?}^{2} \times \frac{?}{?} [/tex]

Answer:

53

Step-by-step explanation:

jddhhevehevevegejwkwveehjebebsjsbs

Answer:

(-14)-(-53) = 39

18-(-2)=20

(-84)/(12)=-7

25*2=50

Step-by-step explanation:

two minuses are plus

when numbers are on the minuses which number is higher their sign will have an answer

Answer:

A. 39

B. 20

C. -7

D. 50

Step-by-step explanation:

A. ( -14) - ( -53) =

53 - 14 = 39

B. (18) - ( -2) =

18 + 2 = 20

C. ( -84) / ( 12) =

-84/12 = -7

D. (25) * (2) =

25(2) = 50

Answer:

not sure but i think the answer is a)

Answer:

it should be the graph on the bottom right

Step-by-step explanation:

The income should be more than the cost in order to make a profit and that happens for Leanne when she sells 8 quilts, so the 8 should be on the x-axis (the axis named "Quilts Sold")

The income should be 0 in the beginning bc when she sells 0 quilts she will be earning 0.

after selling 8 quilts her income will be higher than her costs

(Though naming the y-axis as "profit" is not accurate bc when she sells 0 quilts she will lose money since she will be spend money to make the quilts but not earn the money to compensate for the cost).

with all of these reasons combined the correct should be the one on the bottom right

Answer:

(20,24) (17,20) and (8,8)

Hope this helps

Step-by-step explanation:

Given:

The sequence is:

[tex]17,-\dfrac{17}{8},\dfrac{17}{27},-\dfrac{17}{64},\dfrac{17}{125},...[/tex]

To find:

The formula for the nth term in the given sequence.

Solution:

We have,

[tex]17,-\dfrac{17}{8},\dfrac{17}{27},-\dfrac{17}{64},\dfrac{17}{125},...[/tex]

The given sequence can be written as

[tex]\dfrac{17}{1^3},-\dfrac{17}{2^3},\dfrac{17}{3^3},-\dfrac{17}{4^3},\dfrac{17}{5^3},...[/tex]

The sign are alternative and the absolute value of each term can be defined by the expression [tex]\dfrac{17}{n^3}[/tex], where n is a natural number.

So, the required formula is:

[tex]a_n=(-1)^{n+1}\dfrac{17}{n^3}[/tex]

Therefore, the formula for nth term in the given sequence is [tex]a_n=(-1)^{n+1}\dfrac{17}{n^3}[/tex].

Answer:

x² - 12x + 36

factored: (x - 6)(x - 6)

Answer:

272

Step-by-step explanation:

u do 68*4 because it said 4 times as  henery

Hope this helps

Answer:

272

Step-by-step explanation:

4 times 68 = 272

Answer:

£16:£144

Step-by-step explanation:

1+9=10

160/10=16

1×16=16

9×16=£144

Answer:

16£ and 114£

Step-by-step explanation:

add the ratios

1 + 9 = 10

for the first ratio

(1/10) × 160

= 16£

for the second ratio

(9/10) × 160

= 114£

Answer:

C : x=2

Step-by-step explanation:

Edge 2022