695 is a hundred times smaller than

Answer:

See below for proof.

Step-by-step explanation:

Given:

[tex]y=\left(x+\sqrt{1+x^2}\right)^m[/tex]

First derivative

[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\If $f(g(x))$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=f'(g(x))\:g'(x)$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Differentiating $x^n$}\\\\If $y=x^n$, then $\dfrac{\text{d}y}{\text{d}x}=xn^{n-1}$\\\end{minipage}}[/tex]

[tex]\begin{aligned} y_1=\dfrac{\text{d}y}{\text{d}x} & =m\left(x+\sqrt{1+x^2}\right)^{m-1} \cdot \left(1+\dfrac{2x}{2\sqrt{1+x^2}} \right)\\\\ & =m\left(x+\sqrt{1+x^2}\right)^{m-1} \cdot \left(1+\dfrac{x}{\sqrt{1+x^2}} \right) \\\\ & =m\left(x+\sqrt{1+x^2}\right)^{m-1} \cdot \left(\dfrac{x+\sqrt{1+x^2}}{\sqrt{1+x^2}} \right)\\\\ & = \dfrac{m}{\sqrt{1+x^2}} \cdot \left(x+\sqrt{1+x^2}\right)^{m-1} \cdot \left(x+\sqrt{1+x^2}\right)\\\\ & = \dfrac{m}{\sqrt{1+x^2}}\left(x+\sqrt{1+x^2}\right)^m\end{aligned}[/tex]

Second derivative

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]

[tex]\textsf{Let }u=\dfrac{m}{\sqrt{1+x^2}}[/tex]

[tex]\implies \dfrac{\text{d}u}{\text{d}x}=-\dfrac{mx}{\left(1+x^2\right)^\frac{3}{2}}[/tex]

[tex]\textsf{Let }v=\left(x+\sqrt{1+x^2}\right)^m[/tex]

[tex]\implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{m}{\sqrt{1+x^2}} \cdot \left(x+\sqrt{1+x^2}\right)^m[/tex]

[tex]\begin{aligned}y_2=\dfrac{\text{d}^2y}{\text{d}x^2}&=\dfrac{m}{\sqrt{1+x^2}}\cdot\dfrac{m}{\sqrt{1+x^2}}\cdot\left(x+\sqrt{1+x^2}\right)^m+\left(x+\sqrt{1+x^2}\right)^m\cdot-\dfrac{mx}{\left(1+x^2\right)^\frac{3}{2}}\\\\&=\dfrac{m^2}{1+x^2}\cdot\left(x+\sqrt{1+x^2}\right)^m+\left(x+\sqrt{1+x^2}\right)^m\cdot-\dfrac{mx}{\left(1+x^2\right)\sqrt{1+x^2}}\\\\ &=\left(x+\sqrt{1+x^2}\right)^m\left(\dfrac{m^2}{1+x^2}-\dfrac{mx}{\left(1+x^2\right)\sqrt{1+x^2}}\right)\\\\\end{aligned}[/tex]

              [tex]= \dfrac{\left(x+\sqrt{1+x^2}\right)^m}{1+x^2}\right)\left(m^2-\dfrac{mx}{\sqrt{1+x^2}}\right)[/tex]

Proof

  [tex](x^2+1)y_2+xy_1-m^2y[/tex]

[tex]= (x^2+1) \dfrac{\left(x+\sqrt{1+x^2}\right)^m}{1+x^2}\left(m^2-\dfrac{mx}{\sqrt{1+x^2}}\right)+\dfrac{mx}{\sqrt{1+x^2}}\left(x+\sqrt{1+x^2}\right)^m-m^2\left(x+\sqrt{1+x^2\right)^m[/tex]

[tex]= \left(x+\sqrt{1+x^2}\right)^m\left(m^2-\dfrac{mx}{\sqrt{1+x^2}}\right)+\dfrac{mx}{\sqrt{1+x^2}}\left(x+\sqrt{1+x^2}\right)^m-m^2\left(x+\sqrt{1+x^2\right)^m[/tex]

[tex]= \left(x+\sqrt{1+x^2}\right)^m\left[m^2-\dfrac{mx}{\sqrt{1+x^2}}+\dfrac{mx}{\sqrt{1+x^2}}-m^2\right][/tex]

[tex]= \left(x+\sqrt{1+x^2}\right)^m\left[0][/tex]

[tex]= 0[/tex]

Based on the data recorded by Isabella, it can be concluded the cube is rather fair.

Based on the data, here are the results:

This implies, in total Isabella got the same number between five and seven times. For example, the number 2 was obtained 5 times, but the number 3 was obtained 7 times.

Even though Isabella did not get the same number of times each number, the dice is rather fair because by rolling the dice thirty six times you will obtain the same number at least five times.

Moreover, there is not a big difference in the number of times you obtain each number.

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Answer:

15 quarters and 10 nickels

Step-by-step explanation:

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

[tex]0.25q+0.05n=4.25[/tex]

multiply the first equation by -0.25 and add the second equation to it

[tex]-0.25q-0.25n=-6.25\\0.25q+0.05n=4.25[/tex]
________________
                [tex]-0.2n=-2[/tex]

[tex]n=\frac{-2}{-0.2} =10[/tex]   has 10 nickels

[tex]q=25-n=25-10=15[/tex]  has 15 quarters

10(.05) +15(0.25) = 0.5 + 3.75 = 4.25

Hope this helps

we just need to reflect the graph of g(x) around the y-axis, and then shift the whole graph 5 units upwards.

Here we have two functions:

[tex]g(x) = ln(x)\\\\f(x) = ln(-x) + 5[/tex]

Ok, let's start with g(x), which graph we know. If we reflect it around the y-axis, then the new function will be:

f(x) = g(-x)

If now we shift it up 5 units, then we get:

f(x) = g(-x) + 5

Replacing g(x):

f(x) = ln(-x) + 5

Which is our function

So we just need to reflect the graph of g(x) around the y-axis, and then move the whole graph 5 units upwards.

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Answer:

Step-by-step explanation:

The domain is the horizontal extent of the graph, the set of x-values for which the function is defined. The range is the vertical extent of the graph, the set of y-values defined by the function.

The given function is undefined where its denominator is zero, at x=1. Everywhere else, it can be simplified to ...

  [tex]\dfrac{3x^2+x-4}{x-1}=\dfrac{(x-1)(3x+4)}{(x-1)}=3x+4\quad x\ne 1[/tex]

The simplified function (3x+4) is defined for all values of x except x=1. The simplest description is ...

  x ≠ 1

In interval notation, this is ...

  (-∞, 1) ∪ (1, ∞)

The simplified function is capable of producing all values of y except the one corresponding to x=1: 3(1)+4 = 7. The simplest description is ...

  y ≠ 7

In interval notation, this is ...

  (-∞, 7) ∪ (7, ∞)

The value of tan 0 as given in question is 0

Trigonometric identities are equations involving the trigonometric functions that are true for every value of the variables involved. They are written in terms of sine, cosine and tangent.

According to the question, we are to find the value of tan0. This is as shown below;

tan 0 = 0

Note that the tangent angle is positive in the first and third quadrant. Hence the result of the given tangent expression will also be positive.

Hence the value of tan 0 as given in question is 0

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There are 5,040 different ways in which she can order the books.

We know that Donna has 9 books, but 2 of these books already have fixed positions (the first one and the last one).

So we only need to order the remaining 7 books in 7 positions.

And so on for the remaining positions.

The total number of different combinations in which she can order the books is given by the product between the numbers of options above, so we will get:

C = 7*6*5*4*3*2*1 = 5,040

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Answer:

A

Step-by-step explanation:

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

let's expand:

x - 4 / x² + 4x - 5

4 - 4 / 16 + 16 - 5 = 0 so answer is 4

Answer: 10204 millimeters

Step-by-step explanation: A gallon = 3875 mm. A quart is 946. 946x 3 = 2838. A pint is around 473 mm which, when multiplied by 7, is 3311. Finally, there are 6 ounces which are approximately 30 mm. 6x30 = 180. We add all of this up : 3875 + 2838+ 3311 + 180 = 10204.

Answer:

39

Step-by-step explanation:

In a triangle, the sum of any two side lengths must exceed the length of the remaining third side. Therefore these 3 inequalities must be true.

5 + 19 > x

5 + x > 19

19 + x > 5

We can ignore the third inequality because, for any positive value of x, the inequality is true.

x < 26

x > 14

Now we know that x, the length of the third side, must be greater than 14 but less than 26. Since we are asked for the smallest whole number possible, the third side would be length 15. Therefore the perimeter is 5 + 19 + 15 = 39.

well, we know that 25 pecks is 1/4% or namely 0.25%, less than 1%, and let's say the amount of pecks per day will be "x", which is 100% of that.

[tex]\begin{array}{ccll} pecks&\%\\ \cline{1-2} 25 & \frac{1}{4}\\[1em] x& 100 \end{array} \implies \cfrac{25}{x}~~=~~\cfrac{ ~~ \frac{1}{4} ~~ }{100}\implies 2500=x\cfrac{1}{4} \\\\\\ 2500=\cfrac{x}{4}\implies 10000=x[/tex]

Pila can peck a tree approximately 10,000 times per day.

Given that Pila can drill a small hole in a tree trunk with 25 pecks, which is only 1/4 % the average number of pecks that she can make each day.

We need to determine how many times per day can pila peck a tree.

Let's denote the average number of pecks Pila can make in a day as "x."

According to the information given, Pila can drill a small hole in a tree trunk with 25 pecks, which is only 1/4% (0.25%) of the average number of pecks she can make each day.

We can set up the following equation to represent the relationship:

0.25% of x = 25

To solve for x, we first convert 0.25% to decimal form by dividing by 100:

0.25% = 0.25/100 = 0.0025

Now, we can rewrite the equation:

0.0025x = 25

To isolate x, we divide both sides of the equation by 0.0025:

x = 25 / 0.0025

Simplifying the right side gives us:

x = 10,000

Therefore, Pila can peck a tree approximately 10,000 times per day.

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The first five terms of the recursive sequence are 5, 12, 19, 26 and 33.

In this question we have a linear recursive equation that requires the value of the immediately previous element to generate the next one. Then, we need to evaluate the expression for the first five elements:

i = 1

a₁ = 5

i = 2

a₁ = 5, a₂ = a₁ + 7

a₂ = 5 + 7

a₂ = 12

i = 3

a₂ = 12, a₃ = a₂ + 7

a₃ = 12 + 7

a₃ = 19

i = 4

a₃ = 19, a₄ = a₃ + 7

a₄ = 19 + 7

a₄ = 26

i = 5

a₄ = 26, a₅ = a₄ + 7

a₅ = 26 + 7

a₅ = 33

The first five terms of the recursive sequence are 5, 12, 19, 26 and 33.

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Answer: 2/6 2/3 11/12

Step-by-step explanation: if you do the common denominator, you will find the numbers 2/6= 4/12 11/12=11/12 2/3=8/12. So your answer should be 2/6 11/12 2/3

[tex]\frac{4}{7}(504)=\boxed{288}[/tex]

The arc length is given by the definite integral

[tex]\displaystyle \int_1^3 \sqrt{1 + \left(y'\right)^2} \, dx = \int_1^3 \sqrt{1+9x} \, dx[/tex]

since by the power rule for differentiation,

[tex]y = 2x^{3/2} \implies y' = \dfrac32 \cdot 2x^{3/2-1} = 3x^{1/2} \implies \left(y'\right)^2 = 9x[/tex]

To compute the integral, substitute

[tex]u = 1+9x \implies du = 9\,dx[/tex]

so that by the power rule for integration and the fundamental theorem of calculus,

[tex]\displaystyle \int_{x=1}^{x=3} \sqrt{1+9x} \, dx = \frac19 \int_{u=10}^{u=28} u^{1/2} \, du = \frac19\times\frac23 u^{1/2+1} \bigg|_{10}^{28} = \boxed{\frac2{27}\left(28^{3/2} - 10^{3/2}\right)}[/tex]

The simplified form of the given expression as a fraction is 7x/x-7

Fractions  are written as a ratio of two integers. For instance a/b is a fraction where a and b are integers.

Given the expression below;

(1/7+1/x)/(1/49+1/x²)

Find the LCM to have:

(x+7/7x)/(x²-49)/49x²

Divide to have:

x+7/7x * 49x²/(x²-49)

(x+7) * 7x/(x+7)(x-7)

Cancel out the like terms to have:

1 * 7x/x-7

= 7x/x-7

Hence the simplified form of the given expression as a fraction is 7x/x-7

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An airplane is heading north at an airspeed of 640 km/hr, but there is a wind blowing from the southwest at 90 km/hr. degrees off course will be 6.25°

Generally, the equation for the velocity of the plane with reference to the ground is  mathematically given as

Vp=  velocity of the plane with reference to wind+  velocity of the wind with reference to ground

Therefore

Vp=Vp'+Vw

[tex]mVp=\sqrt{(640)^2+(90)^2-2*640*90cos45}[/tex]

mVp=579.8km/h

where

[tex]\frac{sintheta}{90}=\frac{sin45}{Vp'}[/tex]

[tex]sin \theta=\frac{90}{579.8}*sin45[/tex]

sin[tex]\theta=0.109[/tex]

[tex]\theta=sin^{-1}(0.109)=6.25[/tex]

In conclusion,  degrees off course will be 6.25

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Answer:

soln,

write the question

=9x^2+1-6x-2×9x^2+25+9x^2+25

=9x^2+1-6x-18x^2+25+9x^2+25

=9x^2-18x^2+9x^2+1+25+25-6x

=51-6x

if(3x+1)^2 mean that (3x+1)has power of 2 and u don't have to use the formula this is the answer

Step-by-step explanation:

it's just BODMAS method

The chance or probability of landing on a number divisible by 2 is 1/2.

The likelihood of an event occurring is defined by probability. By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

According to the question,

Total number of outcomes = 6

Favorable number of outcomes = 3

Thus, the required Probability = 3/6 =1/2

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The borrower owes $14,760.82  at the end of 8 years

What is compounding interest?

Compounding interest means that earlier interest would earn more interest in the future alongside the loan principal.

Note that in this case the loan continues to accumulate interest because there no repayments, in other words, the loan balance after 8 years, which comprises of the principal and interest for 8 years can be computed using the future value formula of a single cash flow(the single cash flow is the principal) as shown thus:

FV=PV*(1+r/n)^(n*t)

FV=loan balance after 8 years=unknown

PV=loan amount=$5,000

r=annual interest=14%

n=number of times in a year that interest is compounded=2(twice a year)

t=loan period=8 years

FV=$5000*(1+14%/2)^(2*8)

FV=$5000*(1.07)^16

FV=$5000*2.95216374856541

FV=loan balance after 8 years=$14,760.82

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Answer:

Step-by-step explanation:

6x-6>y

put y=6

6x-6>6

6x>12

x>12/6

x>2

(3,6) is one solution.

Answer:

Mean 7.4

Median 7

Mode 7, 11

Step-by-step explanation:

Let me know if this is correct!

Answer: 7.4, 7, 7 and 11

Step-by-step explanation:

The mean is the sum of all the numbers divided by the number of numbers. In this case, there are 10 numbers.

[tex]Mean=\frac{6+7+11+5+8+7+4+13+11+2}{10}=\frac{74}{10}=7.4[/tex]

The median is the number (or the average of the two numbers) in the middle of the set when it is ordered in ascending order. Let's first order it from least to greatest.

[tex]2,4,5,6,7,7,8,11,11,13[/tex]

The two middle numbers are 7 and 7. The median is the mean of these two numbers.

[tex]Median=\frac{7+7}{2}=\frac{14}{2}=7[/tex]

The mode is the number that is most repeated number in the set. The numbers 7 and 11 are repeated twice. Hence, the modes are 7 and 11.

Answer:

Step-by-step explanation:

1.733707699

could you brainlyest me?

Answer:

120

Step-by-step explanation:

The angle below x is 40 degree cause alternate angle. Then you get,

20+x+40=180

60+x=180

x=180-60

x=120

12x² + 102x² + 114x - 84

Answer:

Solution Given:

1st term: 6x²+39x-21

Taking common

3(2x²+13x-7)

doing middle term factorization

3(2x²+14x-x-7)

3(2x(x+7)-1(x+7))

3(x+7)(2x-1)

2nd term: 6x²+54x+84

taking common

6(x²+9x+14)

doing middle term factorization

6(x²+7x+2x+14)

6(x(x+7)+2(x+7))

2*3(x+7)(x+2)

Now

Least common multiple = 2*3(x+7)(2x-1)(x+2)

2(x+2)(6x²+39x-21)

(2x+4)(6x²+39x-21)

2x(6x²+39x-21)+4(6x² + 39x-21)

12x³+78x² - 42x+4(6x² + 39x-21)

12x³+78x² - 42x + 24x² + 156x-84

12x³ + 102x²-42x + 156x - 84

12x² + 102x² + 114x - 84

Answer:

[tex]12x^3+102x^2+114x-84[/tex]

Step-by-step explanation:

Given polynomials:

[tex]\begin{cases} 6x^2+39x-21\\6x^2+54x+84 \end{cases}[/tex]

Factor the polynomials:

Polynomial 1

[tex]\implies 6x^2+39x-21[/tex]

[tex]\implies 3(2x^2+13x-7)[/tex]

[tex]\implies 3(2x^2+14x-x-7)[/tex]

[tex]\implies 3[2x(x+7)-1(x+7)][/tex]

[tex]\implies 3(2x-1)(x+7)[/tex]

Polynomial 2

[tex]\implies 6x^2+54x+84[/tex]

[tex]\implies 6(x^2+9x+14)[/tex]

[tex]\implies 6(x^2+7x+2x+14)[/tex]

[tex]\implies 6[x(x+7)+2(x+7)][/tex]

[tex]\implies 6(x+2)(x+7)[/tex]

[tex]\implies 2 \cdot 3(x+2)(x+7)[/tex]

The lowest common multiplier (LCM) of two polynomials a and b is the smallest multiplier that is divisible by both a and b.

Therefore, the LCM of the two polynomials is:

[tex]\implies 2 \cdot 3(x+7)(x+2)(2x-1)[/tex]

[tex]\implies (6x^2+54x+84)(2x-1)[/tex]

[tex]\implies 12x^3+108x^2+168x-6x^2-54x-84[/tex]

[tex]\implies 12x^3+102x^2+114x-84[/tex]

Let [tex]n[/tex] be the total number of stickers. If she puts 21 stickers on a page, she will fill up [tex]p[/tex] pages such that

[tex]n = 21p + 14[/tex]

Suzanna has between 90 and 100 stickers, so

[tex]90 \le n \le 100 \implies 76 \le n - 14 \le 86[/tex]

[tex]n-14[/tex] is a multiple of 21, and 4•21 = 84 is the only multiple of 21 in this range. So she uses up [tex]p=4[/tex] pages and

[tex]n-14 = 4\cdot21 \implies n = 4\cdot21 + 14 = \boxed{98}[/tex]

stickers.

Applying the Chords of a Circle Theorem, the length of AD is: 1.6 units.

The theorem states that if the radius of a circle is perpendicular to a chord, it divides the chord into two equal halves.

Therefore, we have:

CD = DE = 11/2 = 5.5.

AB = BE = 10

Find DB using the Pythagorean theorem

DB = √(BE² - DE²)

DB = √(10² - 5.5²)

DB = 8.4

AD = AB - DB

AD = 10 - 8.4

AD = 1.6 units.

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Answer:

Step-by-step explanation:

A graphing calculator makes finding or verifying the zeros of a polynomial function as simple as typing the function into the input box.

The attachment shows the function zeros to be x ∈ {-2, 3, 7}, as required.

The leading coefficient of this odd-degree polynomial is positive, so the value of f(x) tends toward infinity of the same sign as x when the magnitude of x tends toward infinity.

__

Additional comment

The function is entered in the graphing calculator input box in "Horner form," which is also a convenient form for hand-evaluation of the function.

We know the x^2 coefficient is the opposite of the sum of the zeros:

  -(7 +(-2) +3) = -8 . . . . x^2 coefficient

And we know the constant is the opposite of the product of the zeros:

  -(7)(-2)(3) = 42 . . . . . constant

These checks lend further confidence that the zeros are those given.

(The constant is the opposite of the product of zeros only for odd-degree polynomials. For even-degree polynomials. the constant is the product of zeros.)

Answer: Look in step-by-step explanation

Step-by-step explanation:

Area has a unit of cm^2 or m^2, whilst Volume has a unit of cm^3 or m^3

Using this information, we can see that we have to square both sides of the similarity ratio for the area ratio and cube both sides of the similarity ratio for the volume ratio
For example, question 2 states that the similarity ratio is 3:6, so the area ratio is 3^2:6^2 or 9:36 and the volume ratio is 3^3:6^3 = 27:216

You can do the rest from here