Imagine that you need to compute e^0.4 but you have no calculator or other aid to enable you to compute it exactly, only paper and pencil. You decide to use a third-degree Taylor polynomial expanded around x =0. Use the fact that e^0.4 < e < 3 and the Error Bound for Taylor Polynomials to find an upper bound for the error in your approximation.

|error| <= _________

Answer:

x = 2

Step-by-step explanation:

→ Simplify

x × ( 9 ) = 10 + 8

→ Further simplify

9x = 18

→ Divide both sides by 9

x = 2

Answer:

√9 × √6

√54

√27 × √2

Step-by-step explanation:

We can obtain the answer to the question given above as illustrated below:

3√6

Recall

a√b = √(a×a×b)

Thus,

3√6 = √(3×3×6)

3√6 = √(9 × 6)

Recall

√(a × b) = √a × √b

√(9 × 6) = √9 × √6

Therefore,

3√6 = √9 × √6

Recall

√9 × √6 = √(9 × 6)

√9 × √6 = √54

Thus,

3√6 = √54

Recall

√54 = √(27 × 2)

√54 = √27 × √2

Therefore,

3√6 = √27 × √2

Therefore,

3√6 = √9 × √6 = √54 = √27 × √2

Answer:

The length of each side of the city is 250b

Step-by-step explanation:

Given

[tex]a = 20[/tex] --- tree distance from north gate

[tex]b =14[/tex] --- movement from south gate

[tex]c = 1775[/tex] --- movement in west direction from (b)

See attachment for illustration

Required

Find x

To do this, we have:

[tex]\triangle ADE \sim \triangle ACB[/tex] --- similar triangles

So, we have the following equivalent ratios

[tex]AE:DE = AB:CB[/tex]

Where:

[tex]AE = 20\\ DE = x/2 \\ AB = 20 + x + 14 \\ CB = 1775[/tex]

Substitute these in the above equation

[tex]20:x/2 = 20 + x + 14: 1775[/tex]

[tex]20:x/2 = x + 34: 1775[/tex]

Express as fraction

[tex]\frac{20}{x/2} = \frac{x + 34}{1775}[/tex]

[tex]\frac{40}{x} = \frac{x + 34}{1775}[/tex]

Cross multiply

[tex]x *(x + 34) = 1775 * 40[/tex]

Open bracket

[tex]x^2 + 34x = 71000[/tex]

Rewrite as:

[tex]x^2 + 34x - 71000 = 0[/tex]

Expand

[tex]x^2 + 284x -250x - 71000 = 0[/tex]

Factorize

[tex]x(x + 284) -250(x + 284)= 0[/tex]

Factor out x + 284

[tex](x - 250)(x + 284)= 0[/tex]

Split

[tex]x - 250 = 0 \ or\ x + 284= 0[/tex]

Solve for x

[tex]x = 250 \ or\ x =- 284[/tex]

x can't be negative;

So:

[tex]x = 250[/tex]

Answer:

Step-by-step explanation:

Total amount = 200 mg + (13 days)×(180 mg)/day = 2620 mg

One 35 mL bottle contains (35 mL)×(10 mg)/mL) = 350 mg of medication.

(2620 mg)×(1 bottle)/(350 mg) ≈ 7.5 bottles

8 bottles are needed.

Answer:

20 km

Step-by-step explanation:

We can use ratios to solve

1 cm          4 cm

--------  = ------------

5 km          x km

Using cross products

1 * x = 4 * 5

x = 20

20 km

Answer:

1/5 = 4/x

Step-by-step explanation:

Each cm on the map represents 5 km. If it shows 4 cm apart of the map, you can use the proportion 1 cm : 5 km = 4 cm : x km.

Answer:

B. The question may not be directly stated.

We don't know what the exact p-value is, but we are told that it's as large as 0.005 which is smaller than alpha = 0.05

Since the p-value is smaller than alpha, this means we reject the null hypothesis.

The way you can remember this is "if the p-value is low, then the null must go". By "low", I mean "smaller than alpha".

Recall that the p-value is the probability of observing that specific test statistic, or larger. So the chances of chi-squared being 18.68 or larger is a probability between 0.0025 and 0.005; there's a very small chance of this happening. The p-value is based entirely on the assumption that the null is correct. But if the null is correct, then the chances of landing on this are very small. We have a contradiction that basically leads to us concluding the null must not be the case. It's not 100% guaranteed of course, but it's fairly strong evidence.

In short, the p-value being smaller than alpha = 0.05 means we reject the null.

In order to accept the null, the p-value must be 0.05 or larger.

2 and 3 are the common factor of 24 and 60

Answer:

44

Step-by-step explanation:

1×5² + 3×5¹ +4×5⁰

25+15+4

44

Answer:

x = 1; y=6

Step-by-step explanation:

y = 2x +4

3x + y = 9

Substitute 2x+4 for y in 3x+y = 9

3x + y = 9

3x + 2x+4 = 9

5x + 4 = 9

5x = 9-4

5x = 5

5x/5 = 5/5

x = 1

Substitute 1 for  x in y = 2x +4

2(1) + 4

2 + 4

= 6

Answered by Gauthmath

Answer:

Plug -2 in for x of f(x)

--> -2^4 + 2(-2)^2 - 1

---> 23

f(-2) = 23

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..

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Answer:

[tex]13+19=n+25[/tex]

[tex]n+25=13+19[/tex]

Add 13+19= 32

[tex]n+25=32[/tex]

Now Subtract 25 from both sides

[tex]n+25-25=32-25[/tex]

[tex]n=7[/tex]

OAmalOHopeO

Answer:

x > -2

Step-by-step explanation:

14 <-7x

or, 14/-7=-7x/-7

or, -2 < x

The perimeter of a triangle is the summation of the three sides of the triangle. Base on the assumed values, the length of side BD is 2.

For [tex]\triangle ACD[/tex], the sides are: AC, AD and CD

So, the perimeter is:

[tex]P_{\triangle ACD} = AC + AD + CD[/tex]

For [tex]\triangle ABD[/tex], the sides are: AB, AD and BD

So, the perimeter is:

[tex]P_{\triangle ABD} = AB + AD + BD[/tex]

The difference in the perimeters is:

[tex]P_{\triangle ACD} - P_{\triangle ABD} =1 + \sqrt 3[/tex]

So, we have:

[tex](AC + AD + CD) - ( AB + AD + BD) =1 + \sqrt 3[/tex]

Open brackets

[tex]AC + AD + CD - AB - AD - BD =1 + \sqrt 3[/tex]

Evaluate like terms

[tex]AC + CD - AB - BD =1 + \sqrt 3[/tex]

Make BD the subject

[tex]BD = AC + CD - AB - (1 + \sqrt 3)[/tex]

The solution cannot be completed because the side lengths of [tex]\triangle ACD[/tex] and [tex]\triangle ABD[/tex] are not given; so, I will assume the following values.

[tex]AC =2; CD = 1; AB = \sqrt 3[/tex]

[tex]BD = AC + CD - AB - (1 + \sqrt 3)[/tex] becomes

[tex]BD = 2 + 1 + \sqrt 3 - (1 + \sqrt 3)[/tex]

Open bracket

[tex]BD = 2 + 1 + \sqrt 3 - 1 - \sqrt 3[/tex]

Evaluate like terms

[tex]BD = 2[/tex]

Base on the assumed values, the length of side BD is 2.

Read more about perimeters at:

https://brainly.com/question/6465134

Hi there!

[tex]\large\boxed{tanC = 40/9}[/tex]

tan = O / A, or the opposite side over the adjacent side.

From the diagram, we can see that the opposite side = 40 and the adjacent side = 9, so:

tan C = 40 / 9

Answer:

tan C = 40/9

Step-by-step explanation:

According to SOH - CAH - TOA, tan = opposite over adjacent.

In the picture, the opposite of tan C is 40 and the adjacent is 9.

So, tan C = 40/9

P.S. - Answer above is also correct.

The demand equation illustrates the price of an item and how it relates to the demand of the item.

From the question, we have:

[tex]Plates = 300[/tex]

[tex]Price = 20[/tex]

The number of plates (x) decreases by 10, while the price (y) increases by 5. The table of value is:

[tex]\begin{array}{cccccc}x & {300} & {290} & {280} & {270} & {260} \ \\ y & {20} & {25} & {30} & {35} & {40} \ \end{array}[/tex]

The slope (m) is calculated using:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, we have:

[tex]m = \frac{25-20}{290-300}[/tex]

[tex]m = \frac{5}{-10}[/tex]

[tex]m = -\frac{1}{2}[/tex]

The equation of the demand is as follows:

The initial number of plates (300) decreases by 10 is represented as: (300 - 10x).

Similarly, the initial price (20) increases by 5 is represented as: (20 + 5x).

So, the demand equation is:

[tex]R(x) = (300 - 10x) \times (20 + 5x)[/tex]

Open the brackets to calculate the maximum revenue

[tex]R(x) =6000 + 1500x - 200x - 50x^2[/tex]

[tex]R(x) =6000 + 1300x - 50x^2[/tex]

Equate to 0

[tex]6000 + 1300x - 50x^2 =0[/tex]

Differentiate with respect to x

[tex]1300 - 100x =0[/tex]

Collect like terms

[tex]100x =1300[/tex]

Divide by 100

[tex]x =13[/tex]

So, the price at maximum revenue is:

[tex]Price= 20 + 5x[/tex]

[tex]Price= 20 + 5 * 13[/tex]

[tex]Price= 85[/tex]

In conclusion:

Read more about demand equations at:

https://brainly.com/question/21586143

9514 1404 393

Answer:

  Yes, that distance is the hypotenuse of a right triangle whose sides are known

Step-by-step explanation:

The diagram seems to show the path of the ball as being two segments that are at right angles to each other. Then the direct-line distance to the hole from the tee is the hypotenuse (part A) of the triangle.

Since the leg lengths are known, the Pythagorean theorem can be used (part B) to find the length of the hypotenuse. (The answer to Part B is also the answer to Part C.)

Answer:

should be 192

Step-by-step explanation:

Answer:

The exact answer is 12*√2, if you need approximately answer it is 12*1.4= 16.8

Step-by-step explanation:

√50 + √98​ ​= √(25*2)+√(49*2)= √25√2+√49*√2= 5√2+7*√2=12*√2

Answer:

Step-by-step explanation:

First number is 1/10

Last letter is 1/26

The second digit is 1/9

The first letter is 1/25

1/10 * 1/26 * 1/9 * 1/25

0.00001709

This assumes no duplication is allowed,

If there are duplications

then 1/10 * 1/10 * 1/26 * 1/26

0.000014782

Answer:

7

This question is tying to introduce an idea that

eventually becomes a calculus question ....

(4^2 + 3(4)) - (0^2+3(0))

             4 - 0

28 - 0       = 7

   4

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

1. Approach

The average rate of change can simply be defined as the slope of a line that passes through any two points on a coordinate plane. In this situation, one is given a function, and one is asked to find the rate of change over an interval.

Given function: [tex]f(x)=x^2+3x[/tex]

Intervale, [tex][0, 4][/tex]

This can be done by evaluating the endpoints of the interval by substituting them into the function. Then writing the resulting the form of a point on the coordinate plane ([tex]x, y[/tex]). Finally, one can find the slope of the line that passes through the points by using the following slope formula,

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Where ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) are coordinate points.

2. Find the points

With the function (f(x)), substitute the end points of the itnerval ( [0, 4] ) into the function to generate coordinate points,

[tex]f(x)=x^2+3x[/tex]

[ 0, 4 ]

[tex]f(0)=(0)^2+3(0)\\=0 + 0\\ =0[/tex]

Point: (0, 0)

[tex]f(4)=(4)^2+3(4)\\= 16 + 12\\ = 28[/tex]

Point: (4, 28)

3. Find the average rate of change,

Now substitute the points the formula to find the slope, then simplify to evaluate

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

(0, 0), (4, 28)

Substitute,

[tex]\frac{y_2-y_1}{x_2-x_1}\\\\=\frac{28-0}{4-0}\\\\=\frac{28}{4}\\\\= 7[/tex]

The average rate of change is 7.

Answer:

√65

Step-by-step explanation:

you have to use the pythagoras theorem to find x which is the hypotenuse

x²=7²+4²

x²=49+16

√x²=√65

x=√65

I hope this helps

Answer: (7, 20)

Concept:

There are three general ways to solve systems of equations:

Since the question has specific requirements, we are going to use substitution to solve the equations.

Solve:

Given equations

y = 3x - 1

2x + 6 = y

Substitute the y value since both equations has isolated [y]

2x + 6 = 3x - 1

Add 1 on both sides

2x + 6 + 1 = 3x - 1 + 1

2x + 7 = 3x

Subtract 2x on both sides

2x + 7 - 2x = 3x - 2x

[tex]\boxed{x=7}[/tex]

Find the value of y

y = 3x - 1

y = 3(7) - 1

y = 21 - 1

[tex]\boxed{y=20}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

14 hours

Step-by-step explanation:

Take any two consecutive high tides and to find their x coordinatey and sub them..

both angles are 90 degrees

Answer:

D

Step-by-step explanation:

inverse just means opposite so if its shown dividing it first then adding, then the inverse is multiplying then subtracting

Answer:

55.41 feet

Step-by-step explanation:

Let the width be x.

ATQ, (x+50)*x=300, x=5*srt(37)-25=5.41. Length is 55.41 feet