This table shows some values of an exponential function.
What is the function?

Recall that the derivative of a function f(x) at a point x = c is given by

[tex]\displaystyle f'(c) = \lim_{x\to c} \frac{f(x) - f(c)}{x - c}[/tex]

By substituting h = x - c, we have the equivalent expression

[tex]\displaystyle f'(c) = \lim_{h\to0} \frac{f(c+h) - f(c)}h[/tex]

since if x approaches c, then h = x - c approaches c - c = 0.

The two given limits strongly resemble what we have here, so it's just a matter of identifying the f(x) and c.

For the first limit,

[tex]\displaystyle \lim_{h\to0} \frac{\sin\left(\frac\pi3 + h\right) - \frac{\sqrt3}2}h[/tex]

recall that sin(π/3) = √3/2. Then c = π/3 and f(x) = sin(x), and the limit is equal to the derivative of sin(x) at x = π/3. We have

[tex](\sin(x))' = \cos(x)[/tex]

and cos(π/3) = 1/2.

For the second limit,

[tex]\displaystyle \lim_{a\to0} \frac{e^{2a} - 1}a[/tex]

we observe that e²ˣ = 1 if x = 0. So this limit is the derivative of e²ˣ at x = 0. We have

[tex]\left(e^{2x}\right)' = e^{2x} (2x)' = 2e^{2x}[/tex]

and 2e⁰ = 2.

Answer:

√(137)

Step-by-step explanation:

First, you will need to find the other side length.....then you can use the Pythagorean Theorem to find the diagonal:

L x W = 44

4 x W = 44

W =11

Now the Pythag, Theorem:

 diagonal^2 = 4^2 + 11^2

        d^2 = 16+121

         d^2 = 137

          d = √(137)

Answer:

about 11.7 units (Pls mark me as brainy)

Step-by-step explanation:

Find the width:

length⋅width=  area

4w=44    Plug in known values.

4w/4=44/4    Divide both sides by 4

w=11

Find the diagonal:

(4)^2+(11)^2=  c^2   Use the Pythagorean Theorem.

16+121=  c^2   Simplify.

137=c^2   Simplify.

±√137​= √c^2   Square root both sides.

11.704699...= c   Simplify. Ignore the negative root, as the length must be positive.

11.7≈ c     Round to the nearest tenth.

The length of the diagonal is 11.7 units.

Answer:

.65 litres

Step-by-step explanation:

Answer: C. [tex]p = 2^{d}[/tex]

Step-by-step explanation:

The population rises exponentially, so the graph will have to go up. It also means the population is doubled directly in relation to days

Answer:

f=82.4

Step-by-step explanation:

f=9c/5+32

f=9x28/5+32

f=252/5+32

f=50.4+32

f=82.4

Horizontal shift of 1 unit to the left and a vertical shift downward of 2 units.

Transformation technique is a way of changing the position of an object on an xy-plane.

Given the parent function of a modulus function f(x) = |x|, the graph of the function g(x) = |x| - 2 shows a vertical translation of the parent function down by 2 units.

The resulting graph of the translated function is as shown below

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Answer:

Total area = 187.65 cm^2

Step-by-step explanation:

AREA of a triangle = 1/2 base * height

THREE sides    3     * 1/2 *9 *  11.3  = 152.55 cm^2

Bottom                       1/2 * 9 * 7.8  = 35.1 cm^2

  total = 187.65  cm^2

Using the combination formula, it is found that 35 different combination of teams can make it to the playoffs.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, 4 students are taken from a set of 7, hence the number of combinations is given by:

[tex]C_{7,4} = \frac{7!}{4!3!} = 35[/tex]

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solution

-4(327x-451)

Answer:

5) 22.95

6) 21.93

Step-by-step explanation:

Area of Triangle = BxH/2

= CxH/2

Answer:

The other length is 60m.

Step-by-step explanation:

If you look at the shape of a parallelogram, you will see that a parallelogram has two parallel sides. So, if the total perimeter is 220m, then 50m and 50m together would be 100m, so 220- 100= 120m left to fill in both sides left. so, 120÷2= 60m. 60m is the other length.

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the two integers, given that they are consecutive, and their sum is 65.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Let the first integer be x, and let the second integer be x+1.

Their sum is 65. Let's set up our equation:

[tex]\longmapsto\sf{x+x+1=65}[/tex]

Combine like terms:

[tex]\longmapsto\sf{2x+1=65}[/tex]

Subtract 1 from both sides of the equal sign:

[tex]\longmapsto\sf{2x=64}[/tex]

Divide both sides by 2:

[tex]\longmapsto\sf{x=32}[/tex]

To find the second integer, subtract the first integer from the sum of the two integers:

[tex]\longmapsto\pmb{65-32}[/tex]

[tex]\longmapsto\pmb{33}[/tex]

The integers are: 33 and 32.

Hope it helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

Answer:

21.25=4.25

Ms. Diaz buys 5 pounds of strawberrys

Step-by-step explanation:

The equation of line is x+2y+3=0.

The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term. It is an equation of degree one, with variables x and y.

Given:

x:-1  -5  1

y:-1  3  3

So,

m= 3-1/-5-(-1)

m= 2/-4

m=-1/2

Now, equation of line

(y-(-1))= m (x-(-1))

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

2y+2=-x-1

x+2y+3=0

Hence, the equation of line is x+2y+3=0.

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Using implicit differentiation, it is found that the radius is increasing at a rate of 0.0081 cm per minute.

The volume of a sphere of radius r is given by:

[tex]V = \frac{4\pi r^3}{3}[/tex]

Applying implicit differentiation, the rate of change is given by:

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]

In this problem, we have that:

[tex]\frac{dV}{dt} = 500, r = 70[/tex]

Hence the rate of change of the radius is given as follows:

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]

[tex]19600\pi\frac{dr}{dt} = 500[/tex]

[tex]\frac{dr}{dt} = \frac{500}{19600\pi}[/tex]

[tex]\frac{dr}{dt} = 0.0081[/tex]

The radius is increasing at a rate of 0.0081 cm per minute.

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its that one dudee!!!!!

Answer:

  3103 calories

Step-by-step explanation:

We presume the number of calories is proportional to the area of the pizza. The ratio of areas is the square of the ratio of the linear dimensions, so the number calories in the larger pizza is ...

  (14/6)² × 570 calories = 3103 1/3 calories

There are about 3103 calories in the 14-inch pizza.

Answer:

Step-by-step explanation:

Q1

A graph which uses horizontal or vertical bars with no gaps to represent data is called bar graph.

Q2

Data plotted against the frequency in a histogram is class interval.

Q3

The data plotted against the frequency in an ogive is cumulative frequency.

Q4

A score of 50 under the column > c.f. with the boundaries 23.5 - 28.5 means 50 students got a score greater than 23.5.

Q5

Mean = 2(2) + 3 + 4 + 7(3) + 10 + 11 + 2(12) / 11

Mean = 4 + 7 + 21 + 21 + 24 / 11

Mean = 77/11

The mean is 7

Q6

The median is the middle term.

The median of the distribution is 7

Answer:

yes there is a correlation

Step-by-step explanation:

here's how I found this by looking up all key words.

Answer:

y = (-1/4)x + (13/4)

Step-by-step explanation:

The general structure of an equation in slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept.

Remember that in a point (-3,4) you have an "x" and "y" value. As such, you have been given values for the "x", "y", and "m" variables. Therefore, you can plug these values into the general structure to find the value of "b".

y = mx + b                              <---- General structure

y = (-1/4)x + b                         <---- Plug (-1/4) in "m"

4 = (-1/4)(-3) + b                      <---- Plug in values from point

4 = (13/4) + b                          <---- Multiply (-1/4) and -3

(13/4) = b                               <---- Subtract (13/4) from both sides

Now that you know the value of "m" and "b", you can determine the formula.

y = (-1/4)x + (13/4)

Step-by-step explanation:

width= x (let)

length= x+5

Area=50 cm

Now ,

area = l ×b

50 = (X×X+5)

50 = (2X + 5)

50÷ 2= X+5

25 -5 = X

X=20

LENGTH = X+5

20+5

=25

Answer:

y = - 2 | x - 2 | + 4

Step-by-step explanation:

the general equation of an absolute value function is

y = a|x - h| + k

where (h, k ) are the coordinates of the vertex and a is the stretch factor

here (h, k ) = (2, 4 ) , then

y = - 2|x - 2| + 4

Answer:

See below ~

Step-by-step explanation:

Formula for absolute value function :

y = a |x - h| + k

==============================================================

Given :

⇒ a = -2

⇒ Vertex = (h, k) = (2, 4) [based on graph]

=============================================================

Solving by substitution :

⇒ y = -2|x - 2| + 4

Answer: Coordinate (1,6)

Step-by-step explanation: Because it is located on one of the corners already if you count the spaces! I hope this helped!! :D

Answer:

the person above me is right its (1,6) its the only one thats located on a corner

Step-by-step explanation:

The median of the data is 5 if the all class widths are 1, option (C) is correct.

A median is a middle number in a series of numbers that have been arranged to lift, and it might be more informative of the set of data than the average. When there are extremes in the sequences that might affect the average of the numbers, the median is sometimes employed instead of the mean.

In the histogram, 15 data values are given:

1, 2, 2, 3, 3, 3, 4, 5, 6, 6, 7, 7, 7, 8, 9

The mid-value is 5 which is on the 8th place

Thus, the median of the data is 5 if the all class widths are 1, option (C) is correct.

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Answer:

C (3,6)

Step-by-step explanation:

So the zeroes are the points that the loop goes through on the x-axis

so three and six

Answer:

You should raise one side 14 inches

Step-by-step explanation:

I used a right angle triangle calculater at this sight

https://www.calculator.net/right-triangle-calculator.html

The value of the [tex]\rm 6x^5y^3[/tex] is 35 if the value of [tex]\rm 2x^2y = 5[/tex] and [tex]\rm 3x^3y^2 = 7[/tex]

It is defined as the combination of constants and variables with mathematical operators.

We have:

[tex]\rm 2x^2y = 5\\\\\rm 3x^3y^2 = 7[/tex]

We have to find the value of [tex]\rm 6x^5y^3[/tex]

[tex]=\rm 6x^5y^3\\\\= \rm 6(x^2y)(x^3)(y^2)[/tex]

=6(5/2)(7/3)

= (5)(7)

= 35

Thus, the value of the [tex]\rm 6x^5y^3[/tex] is 35 if the value of [tex]\rm 2x^2y = 5[/tex] and [tex]\rm 3x^3y^2 = 7[/tex]

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