need help please: show that 2^2020+2^2022=5.2^2020​

The best linear approximation to the function f(x) = e^x near x = 0 is L(x) = x + 1.

The given function is f(x) = e^x near x = 0.

To find the best linear approximation, L(x), we use the formula:

L(x) = f(a) + f'(a)(x-a),

where a is the point near which we are approximating.

Let a = 0, so that a is near the point x = 0.

f(a) = f(0) = e^0 = 1

f'(x) = d/dx (e^x) = e^x;

so f'(a) = f'(0) = e^0 = 1

Substituting these values into the formula: L(x) = 1 + 1(x-0) = x + 1

Therefore, the best linear approximation to f(x) = e^x near x = 0 is L(x) = x + 1.

For instance, linear approximation is used to approximate the change in a physical quantity due to a small change in another quantity that affects it.

To know more about linear approximation, visit:

https://brainly.com/question/1621850

#SPJ11

To find the radius of the crystal ball, we can use the formula for the volume of a sphere: V = (4/3) * π * r^3, where V is the volume and r is the radius.

Given that the volume of the crystal ball is 113.14 cm³, we can solve for r:

113.14 = (4/3) * π * r^3

To find the radius, we can rearrange the equation:

r^3 = (3/4) * (113.14 / π)

r = (3/4) * (113.14 / π)^(1/3)

Using a calculator, we can evaluate the expression to find the approximate value of the radius.

To find the volume of foam required to fill the vacant space inside the box, we need the volume of the box. However, the dimensions of the box are not provided in the question, so we cannot calculate the volume of foam accurately.

Learn more about radius here;

https://brainly.com/question/13449316

#SPJ11

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

Explanation:

For any triangle, the three angles always add to 180.

(angle1)+(angle2)+(angle3) = 180

(x+20)+(60)+(3x) = 180

x+20+60+3x = 180

(x+3x)+(20+60) = 180

4x+80 = 180

4x+80-80 = 180-80 .... subtracting 80 from both sides

4x = 100

4x/4 = 100/4 ... dividing both sides by 4

x = 25 ... is the answer

--------------------------

If you want to keep going to find the angles, then

angle 1 = x+20 = 25+20 = 45 degrees

angle 2 = 60 .... nothing to do here

angle 3 = 3x = 3*25 = 75 degrees

Then as a check, adding up the three angles should lead to 180

(angle1)+(angle2)+(angle3) = 45+60+75 = 180

This confirms our answer.

Answer:

D. All the terms are odd.

Step-by-step explanation:

\(\text{According to the image description provided:}\\\text{Term one starts with one dot. One is an odd number.}\\\text{If you add two to an odd number, the sum would be another odd number.}\\\text{This is what's happening with the pattern.}\\\text{For example:}\\3+2=5\\\text{Three is an odd number. If you add two to it, you would get five, which is}\\\text{another odd number.}\\\text{Term two has 3 dots, term three has 5 dots, term four has 7 dots.}\\\text{So, all terms should be odd.}\)

Answer:

4

Step-by-step explanation:

Using the rule of exponents

\(a^{0}\) = 1

Then

4\((57ab)^{0}\) = 1 and

4\((57ab)^{0}\) = 4 × 1 = 4

Answer:

4

Step-by-step explanation:

since 57ab has power 0 it is equal to 1

1×4 is 4

The motion of the baseballs under gravity are given by kinematic

equations of motion.

Response:

The height functions are;

\(1) \hspace{0.15 cm} h = 121 - \frac{1}{2} \times 9.81 \times t^2\)

\(2) \hspace{0.15 cm} h = 225 - \frac{1}{2} \times 9.81 \times t^2\)

According to the kinematic equations of motion, we have;

h = u·t + \(\mathbf{\frac{1}{2}}\)·g·t²

Where;

h = The height from which the ball is dropped

u = The initial velocity of each baseball = 0

g = Acceleration due to gravity ≈ 9.81 m/s²

t = The time taken

Which gives the following height functions

\(1) \hspace{0.15 cm} \underline{h = 121 - \frac{1}{2} \times 9.81 \times t^2}\)

\(2) \hspace{0.15 cm} \underline{h = 225 - \frac{1}{2} \times 9.81 \times t^2}\)

By comparison of the graphs of the height functions, we have that the

shapes of both graphs are parabolic.

The y-intercepts are;

The x-intercepts (approximate values) are;

Baseball dropped from 121 feet; x-intercept (4.97, 0)

Baseball dropped from 225 feet; x-intercept (6.77, 0)

Learn more about functions here:

https://brainly.com/question/10010609

Answer: Y = 8

Step-by-step explanation: If x = to 0 then 0+y=8 therefore y=8

Hope this helps

Answer:

y = 8

Step-by-step explanation:

Given information,

→ x + y = 8

→ x = 0

Now the value of y will be,

→ x + y = 8

→ 0 + y = 8

→ y = 8 - 0

→ [ y = 8 ]

Hence, the value of y is 8.

Answer:

56.69

Step-by-step explanation:

Hope dis help

The cardinal number for the given set. A {21,23,25,27} sees; The given set has a cardinal number of 4.

This is further explained below.

Generally, cardinal numbers are an extension of the natural numbers that are used to assess the cardinality of sets. Cardinals are often referred to by their shorter form, cardinals. A finite set has a cardinality that is equal to a natural number, which is the number of items that are included inside the set.

A set of counting numbers is called its cardinal number. There is speculation that they are cardinals as well. Cardinal numbers are whole, non-fractional numerals, beginning with 1 and continuing in numerical order. Cardinal numbers include 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20.

In conclusion, The provided set A equals  {21,23,25,27}

The number of unique components that make up a set is referred to as the cardinal number.

The given set has a cardinal number of 4, which is denoted by the notation n(A).

Read more about cardinal numbers

https://brainly.com/question/13095210

#SPJ1

Answer:

X=28

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

A triangle always has 180° so that means 40° (2x+9)° and another angle add up to 180°.

We can find out two angles in order to find out the third, one of them is 40°  the other is 180°-105° because there are 180° on a line.

you get 75.

75°+40°=115°

180°-115°=65°

2x+9=65°

Make x the subject of the formula:

2x=56

(take away 9)

x=28

(divide both sides by 2)

Answer:

Step-by-step explanation:

y=-4x+13

if

the slope-intercept form of a linear equation is

where,m is slope and b is y-intercept

let's justify the first and second statement

our given equation is

y=-4x+13

where -4 is our slope or m

therefore,

1 and 2 statements are False

let's justify the third and fourth statement

our given equation is

y=-4x+13

where,13 is our y-intercept which means the line passes y-intercept when x=0

therefore,

third and fourth statements are False

The statement which is true regarding the line y = -4x + 13 is; The line passes through the point, (0, 13)

The equation of a straight line in slope-intercept form is usually of the form; y = mx + c

where m = slope and c is the y intercept with coordinate (0, c)

The statement which is true is therefore; The line passes through the point, (0, 13)

Read more:

https://brainly.com/question/1884491

Using Trigonometry, the values of the required side and angles are :

A.)

The value of b can be obtained thus:

b = √14² - 6²

b = 12.65

Therefore, b = 12.65

B.)

To obtain A

SinA = opposite/ hypotenus

SinA = 6/14

A = 25.38°

Hence, A = 25.38°

C.)

The sum of angles in a triangle = 180°

B + 25.38 + 90 = 180

B + 115.38 = 180

B = 64.62°

Hence, B = 64.62°

Learn more on trigonometry: https://brainly.com/question/24349828

#SPJ4

To solve for the angle a and b, we'll need to use the Pythagorean theorem.

It states that for any right triangle with legs of lengths a and b, and hypotenuse of length c, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

That is a² + b² = c²

Given right triangle with side B = 14 and side c = 6

Step 1: Calculate for the unknown side a using Pythagorean theorem.

a² + b² = c²

a² + 14² = 6²

a² = 6² - 14²

a² = 36 - 196

a = √(-160)

a is undefined. We can't proceed to solve for angle a.

Step 2: Calculate for the unknown angle b using the sine function.

sin b = opposite/hypotenuse sin b = a/c

a is undefined, so we can't solve for angle b as well.

Since we can't solve for angle a and b, we can't provide an answer for the given question. We need to have at least two sides or an angle and a side to solve for the other angle and side.

Learn more about Pythagorean theorem from:

https://brainly.com/question/343682

#SPJ11

Answer:

Apply inverse law

a a⁻¹ = 1

The solution of the given linear equation is x = -6

Step-by-step explanation:

Step(i):-

Given equation -3 x-5=13

Adding '5' on both sides, we get

- 3 x - 5 + 5 = 13  + 5

- 3 x  = 1 8

step(ii):-

apply inverse law

a a⁻¹ = 1

(- 3)(-3)⁻¹ x = 18 (-3)⁻¹

x = 18/-3 = -6

(or)

Dividing '-3' on both sides , we get

                            \(\frac{-3 x}{ -3} = \frac{18}{-3}\)

                             x =- 6

The supply of average eggs is decreasing at a rate of approximately -550 cartons per week as the price decreases 7 cents per carton per week.

The equation given states that the weekly supply x (in thousands of cartons) of a certain brand of medium-sized eggs is related to the wholesale price p (in dollars/carton) by the following equation: 625p2 − x2 =100. In order to determine the rate at which the supply is changing, we must first calculate the value of p when x = 37,000, which is the number of cartons available at the beginning of the week. To do this, we can solve the equation for p when x = 37,000\(p = (100 + x2)1/2/625\). When x=37,000, p=3.65. Therefore, if the price is falling at the rate of 7¢/carton/week, then the new price p = 3.65 - 0.07 = 3.58. When we plug this new value of p into the supply equation, we get\(x^2\) = 4,225. Taking the square root of both sides gives us x = 65. Therefore, the supply is decreasing at a rate of approximately -550 cartons per week as the price decreases 7 cents per carton per week.

Learn more about average here

https://brainly.com/question/24057012

#SPJ4

Answer:

1. RQ

2. R, Y and V

3. T

4. No

Step-by-step explanation:

If we imagine a plane as a rectangle, we can easily see that planes RSTQ and RVUQ intersect in line RQ. Basically, if two planes intersect each other, that intersection is always a line.

Collinear points lie on the same line. Every two points make a line, so the third one also needs to lie along that line. On the diagram, R, Y and V are the only three points on the same line.

From the diagram, we can infer that QT and TX intersect in point T. Additionally, every two lines intersect in a point (of course, unless they're parallel).

Coplanar points lie in the same plane. Three points are enough to define a plane. Whichever three points (R, Q, W and U) we choose we'll have a plane, but the fourth point won't lie in it. This means they are not coplanar.

Answer:

1. 2.6(0.12)

Step-by-step explanation:

Answers 2. 3. and 4. are variations of equations that equal to 2.912. 1. Is incorrect because it equals to 0.312, which also cannot be correct because the kittens weight must increase.

The probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6 is 8.08%

The CLT states that the distribution of the sample means of a random variable with a finite mean and standard deviation approaches a normal distribution as the sample size increases.

In this case, the population mean is 0.5, and the population standard deviation is 0.7. Since we have a sample size of 50, the standard deviation of the sample means would be

=> 0.7 / √(50) = 0.099.

Next, we need to calculate the z-score, which measures the number of standard deviations from the mean.

In this scenario, we want to find the probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6. So, we would plug in x = 0.6, μ = 0.5, σ = 0.7, and n = 50 into the z-score formula. This gives us

=> (0.6 - 0.5) / (0.7 / √(50)) = 1.41.

Using a standard normal distribution table or calculator, we can find that the probability of a z-score of 1.41 or higher is approximately 0.0808. Therefore, the estimated probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6 is 0.0808 or about 8.08%.

To know more about standard deviation here.

https://brainly.com/question/16555520

#SPJ4

Complete Question:

The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. Each month, an SRS of 50 traps is inspected, the number of moths in each trap is recorded, and the mean number of moths is calculated. Based on years of data, the distribution of moth counts is discrete and strongly skewed, with a mean of 0.5 and a standard deviation of 0.7. Estimate the probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6.

Answer:

\(\sf f(-3) = 23\)

given:

\(\sf f(x) = 3x^2 -4\)

to find the output, replace x with the given integer.

solve:

\(\sf f(-3) = 3(-3)^2 -4\)

\(\sf f(-3) = 3(9) -4\)

\(\sf f(-3) = 27 -4\)

\(\sf f(-3) = 23\)

The 'nth' term is a formula with 'n' in it which enables you to find any term of a sequence without having to go up from one term to the next. 'n' stands for the term number so to find the 50th term we would just substitute 50 in the formula in place of 'n'.

6 less than "something" can be written as "something" - 6.

In this case, "something" is "the sum of y and x", which can be written as x + y

So, putting them togethre, we have:

i may be wrong but i think A. sorry if im wrong

Answer:

In standard form: 4x- 9y = 11

Explanation:

4x -9y -7 = 4

4x -9y = 4 + 7

4x- 9y = 11

Standard form: Ax+By = C...where the A, x coefficient should be positive.

543 cubic centimeters has 0.543 L approximate displacement

Engine displacement means the displacement of the piston inside cylinder from Bottom Dead Center into Top Dead Center in one cycle.

Basic formula to calculate engine displacement is

V = π/4 x \(D^{2}\) x H x N

Where :

D = Bore Diameter

H = Length of Stroke

N = Number of Cylinder

Since the question has already stated cubic centimeter, it has already show the displacement. So, we can ignore above formula and the 4 cylinder engine information.

First, we state what is known. It is the displacement at cubic centimeter

Cubic centimeter = 543 cc

Next, we change the unit of cubic centimeter ( cc ) into liter ( L )

Displacement = cc / 1000 L

                       = 543 / 1000 L = 0.543 L

Learn more about Displacement

https://brainly.com/question/11934397

#SPJ4

Answer:

The 95% confidence interval based on this sample is =

[6.41, 7.79]

Step-by-step explanation:

The formula for Confidence Interval =

Mean ± z × standard deviation/√n

Sample mean = 7.1 hours

Standard deviation = 5 hours

n = 200 students

z = 95% confidence interval z score

= 1.96

C.I = 7.1 ± 1.96 × 5/√200

C.I = 7.1 ± 0.693

Hence, Confidence Interval

= 7.1 - 0.693

= 6.407

Approximately = 6.41

= 7.1 + 0.693

= 7.793

Approximately = 7.79

Therefore, the 95% confidence interval based on this sample is

[6.41, 7.79]

Answer:

C

Step-by-step explanation:

Area = π\(r^{2}\)

r means radius

radius = d/2

d = diameter

8 /2 = 4

4 is radius

\(4^{2}\) = 16

^ ( its 4 x 4 ) ^

so then,

Area = 16π

Answer:

Step-by-step explanation:

\(A=\pi r^2,\ r=\frac{d}{2}\\ \\ A=\frac{\pi d^2}{4},\ d=8cm\\ \\ A=\frac{64\pi}{4}\\ \\ A=16\pi cm^2\)

In order to solve a radical equation, the radical must be isolated and then squared on both sides of the equation.

In order to solve a radical equation, what operation must be performed on both sides in order to remove the radical?The operation that must be performed on both sides of an equation in order to remove the radical is squaring it.To solve a radical equation, you must first isolate the radical expression on one side of the equation.

Then, the equation is solved by squaring both sides of the equation to eliminate the radical symbol.However, it is important to note that if you square both sides of an equation, you must verify the solution to the equation because squaring both sides of an equation can result in extraneous solutions. This means that the solutions found may not be valid for the original equation.

In conclusion, in order to solve a radical equation, the radical must be isolated and then squared on both sides of the equation. Finally, you must verify the solutions found to ensure that they are valid.

Learn more about radical equation here,

https://brainly.com/question/31941585

#SPJ11

your answer is second hope it's helpful to you

Hey there!

Yes

Is 4 - 4x and 4(1 - x) equivalent expressions? Why or why not?

If you want to know whether they are equivalent, let's first find the value of both of them.

\(4-4x\)

\(-4x+4\)

\(4(1-x)\)

Let's add parenthesis to 4 and (1-x) and add negative to x.

\((4)(1+-x)\)

Now separate all with parenthesis.

\((4)(1)+(4)(-x)=4-4x\\-4x+4(ANSWER)\)

Since both had the same value, they are equivalent.

Hope this helps!

\(\text {-TestedHyperr}\)

Answer:

2 1/3 meters

Step-by-step explanation:

You would simply divide 14 by 6 which gives you 2.3 repeating and 0.3 repeating is the fraction 1/3.