Write the expression
using only positive exponents.
-3/x-4

Answer:

[tex]|R_n (x)| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]

Step-by-step explanation:

From the given question; the objective is to show that :

[tex]\lim_{n \to \infty} R_n (x) = 0[/tex] for all x in the interval of convergence f(x)=cos x, a= π/2

Assuming for the convergence f the taylor's series , f happens to be the derivative on an open interval I with a . Then the Taylor series for the convergence of f , for all x in I , if and only if  [tex]\lim_{n \to \infty} R_n (x) = 0[/tex]  

where;

[tex]\mathtt{R_n (x) = \dfrac{f^{(n+1)} (c)}{n+1!}(x-a)^{n+1}}[/tex]

is a remainder at x and c happens to be between x and a.

Given that:

a= π/2

Then; the above equation can be written as:

[tex]\mathtt{R_n (x) = \dfrac{f^{(n+1)} (c)}{n+1!}(x-\dfrac{\pi}{2})^{n+1}}[/tex]

so c now happens to be the points between π/2 and x

If we recall; we know that:

[tex]f^{(n+1)}(c) = \pm \ sin \ c \ or \ cos \ c[/tex] (as a result of the value of n)

However, it is true that for all cases that  [tex]|f ^{(n+1)} \ (c) | \leq 1[/tex]

Hence, the remainder terms is :

[tex]|R_n (x)| = | \dfrac{f^{(n+1)}(c)}{(n+1!)}(x-\dfrac{\pi}{2})^{n+1}| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]

If [tex]\lim_{n \to \infty} R_n (x) = 0[/tex]   for all x and x is fixed, Then

[tex]|R_n (x)| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]

Answer:

y - 1 = -2(x - 4).

Step-by-step explanation:

First, we need to find the slope. Two sets of coordinates are (-3, 3), and (-2, 1).

(3 - 1) / (-3 - -2) = 2 / (-3 + 2) = 2 / (-1) = -2.

The line will be parallel to the given line, so the slope is the same.

Now that we have a point and the slope, we can construct an equation in point-slope form.

y1 = 1, x1 = 4, and m = -2.

y - 1 = -2(x - 4).

Hope this helps!

The slope of the line passing  parallel to the given line and passes through the point (4, 1) is y = -2x + 9

The equation of a straight line is given by:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

The slope of the line passing through the points (-3,3) and  (-2,1) is:

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{1-3}{-2-(-3)} \\\\m=-2[/tex]

Since both lines are parallel, hence they  have the same slope (-2). The line passes through (4,1). The equation is:

[tex]y-y_1=m(x-x_1)\\\\y-1=-2(x-4)\\\\y=-2x+9[/tex]

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Answer:

10,000

Step-by-step explanation:

There are 2970 positive integers less than 1,000,000 have exactly one digit equal to 9 and have a sum of digits equal to 13

A number system is defined as a system of writing to express numbers.

We need to find

positive integers less than 1,000,000 have exactly one digit equal to 9 and have a sum of digits equal to 13

Let all 9 numbers ae

a+b+c+d+e+f+g+h+9=13

a+b+c+d+e+f+g+h=13-9

a+b+c+d+e+f+g+h=4

Then we use combinations

(n+k-1)Ck

¹¹C₄

11!/(11-4)!4!

11!/7!4!

330

Three hundred thirty times of nine is two thousand nine hundred seventy.

Now 330 ×9=2970

Hence there are 2970  positive integers less than 1,000,000 have exactly one digit equal to 9 and have a sum of digits equal to 13

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Answer:

Option 1: The terms in Pattern B is 4 times the corresponding terms of Pattern A

Step-by-step explanation:

Answer:

Pattern B has more then pattern A so option 2

Step-by-step explanation:

Answer:

[tex](\frac{4}{3},-\frac{10}{3})[/tex]

Step-by-step explanation:

If the extreme ends of a line segment AC are A[tex](x_1,y_1)[/tex] and C[tex](x_2,y_2)[/tex].

If a point B(x, y) divides the segment in the ratio of m : n

Then the coordinates of the point B are,

x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]

y = [tex]\frac{my_2+ny_1}{m+n}[/tex]

If the ends of AC are A(-2, 5) and C(2, -5) and a point B divides it in the ratio of m : n = 5 : 1

Therefore, coordinates of this point will be,

x = [tex]\frac{5\times (2)+1(-2)}{5+1}[/tex]

  = [tex]\frac{10-2}{5+1}[/tex]

  = [tex]\frac{8}{6}[/tex]

  = [tex]\frac{4}{3}[/tex]

y = [tex]\frac{5\times (-5)+1(5)}{5+1}[/tex]

  = [tex]\frac{-25+5}{6}[/tex]

  = [tex]-\frac{20}{6}[/tex]

  = [tex]-\frac{10}{3}[/tex]

Therefore, coordinates of the point B are [tex](\frac{4}{3},-\frac{10}{3})[/tex].

Answer:

∠PQR =  67.36° (Approx)

Step-by-step explanation:

Given:

PRQ is a right triangle

∠R = 90°

PQ = 13 cm

QR = 5 cm

PR = 12 cm

Find:

∠PQR = ?

Computation:

Using trigonometry application.

SinФ = 12 / 13

SinФ = 0.92

Sin 67.36° = 0.92

So,

∠PQR =  67.36° (Approx)

Answer:  [tex]\dfrac{(x+9)^2}{225}-\dfrac{(y+7)^2}{49}=1[/tex]

Step-by-step explanation:

The equation for a horizontal ellipse is: [tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex]  where

Given: major axis (diameter on x) is 30 --> x-radius (a) = 15  -->  a² = 225

           minor axis (diameter on y) is 14 --> y-radius (b) = 7   --> b² = 49

           center (h, k) is (-9, -7)

Input those values into the equation for a horizontal ellipse and simplify:

  [tex]\dfrac{(x-(-9))^2}{15^2}-\dfrac{(y-(-7))^2}{7^2}=1\\\\\\\large\boxed{\dfrac{(x+9)^2}{225}-\dfrac{(y+7)^2}{49}=1}[/tex]  

Answer:

  find the difference of points on the graph

Step-by-step explanation:

The cumulative frequency graph (CDF) represents the integral of the probability distribution function (PDF). You find the probability that X is in some interval by subtracting the value of the CDF at the low end of the interval from the CDF value at the high end of the interval.

  p(a < x < b) = cdf(b) -cdf(a)

Answer:

36.143

Step-by-step explanation:

143/1000=0.143

36+0.143=36.143

Answer:

wrong position of tan 64

Answer:

wat do u want me to do

Step-by-step explanation:

Answer:

I thinksomething is wrong.

I'm getting another proving it's-tan thita.

I hope this is the one you are searching for..

Step-by-step explanation:

f(x) = integral (-8x) dx = -4x^2 + C

f(1) = -3 = -4 + C

C = 1

f(x) = -4x^2 + 1

The particular solution of the differential equation f'(x) = -8x that satisfies the initial condition f(1) = -3 is: f(x) = -4x² + 1.

Here, we have,

To find the particular solution of the differential equation f'(x) = -8x that satisfies the initial condition f(1) = -3,

we can integrate the equation and use the initial condition to determine the constant of integration.

First, integrate both sides of the equation with respect to x:

∫ f'(x) dx = ∫ -8x dx

Integrating, we get:

f(x) = -4x² + C

Now, we can use the initial condition f(1) = -3 to find the value of the constant C.

Substituting x = 1 and f(x) = -3 into the equation, we have:

-3 = -4(1)² + C

-3 = -4 + C

C = -3 + 4

C = 1

Therefore, the particular solution of the differential equation f'(x) = -8x that satisfies the initial condition f(1) = -3 is:

f(x) = -4x² + 1

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Answer:

A. a line segment

Step-by-step explanation:

Answer:

The answer is

Step-by-step explanation:

To find the equation of the line we must first find the slope (m)

[tex]m = \frac{y2 - y1 }{x2 - x1} [/tex]

So the slope of the line using points

(-8,6) (-9,-9) is

[tex]m = \frac{ - 9 - 6}{ - 9 + 8} = \frac{ - 15}{ - 1} = 15[/tex]

So the equation of the line using point (-8,6) and slope 15 is

y - 6 = 15( x + 8)

y - 6 = 15x + 120

Writing the equation in the form

Ax+By=C

We have

15x - y = -120-6

The final answer is

Hope this helps you

Answer:

1:3

2:4

3:6

Step-by-step explanation:

we can divide both sides by 6 and get 1:2

we can divide both sides by 3 and get 2:4

we can divide both sides by 2 and get 3:6

Answer:

12:24, 3:6, 2:4

Step-by-step explanation:

What we are looking for here is a ratio that, when you divide/multiply the same constant on both parts of the ratio, you get 6:12.

6:12 is the same thing as 1:2, so we can find ratios equivalent to 1:2 (the first value will be half the second).

Hope this helped!

Answer:

17 miles

Step-by-step explanation:

4+5+5+3=17

Answer:

5/14

Step-by-step explanation:

You multiply the recripricoal in division problems:

5/2  ÷ 7/1 =

5/2 × 1/7 =

5/14

Answer:

5 / 14

Step-by-step explanation:

will make it simple... the technique is to flip the either 5/2 or 7/1

then multiply.

5/2 x 1/7 = 5 / 14

Answer:

1+5.3=6.3

Step-by-step explanation:

not sure what your asking for with the 2

explain what your looking for with the 2 and maybe we can help you further

(I have to do it the way I did it because the 2 in the question is confusing)

Answer:

For expression 1 + 5.32: 6.32

For expression 1 + 5.3 × 2: 11.6

Step-by-step explanation:

If the expression is 1 + 5.32:

If the expression is 1 + 5.3 × 2:

Answer:

Attachment 1 : Option C

Attachment 2 : Option A

Step-by-step explanation:

( 1 ) Expressing the product of z1 and z2 would be as follows,

[tex]14\left[\cos \left(\frac{\pi \:}{5}\right)+i\sin \left(\frac{\pi \:\:}{5}\right)\right]\cdot \:2\sqrt{2}\left[\cos \left(\frac{3\pi \:}{2}\right)+i\sin \left(\frac{3\pi \:\:}{2}\right)\right][/tex]

Now to solve such problems, you will need to know what cos(π / 5) is, sin(π / 5) etc. If you don't know their exact value, I would recommend you use a calculator,

cos(π / 5) = [tex]\frac{\sqrt{5}+1}{4}[/tex],

sin(π / 5) = [tex]\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}[/tex]

cos(3π / 2) = 0,

sin(3π / 2) = - 1

Let's substitute those values in our expression,

[tex]14\left[\frac{\sqrt{5}+1}{4}+i\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}\right]\cdot \:2\sqrt{2}\left[0-i\right][/tex]

And now simplify the expression,

[tex]14\sqrt{5-\sqrt{5}}+i\left(-7\sqrt{10}-7\sqrt{2}\right)[/tex]

The exact value of [tex]14\sqrt{5-\sqrt{5}}[/tex] = [tex]23.27510\dots[/tex] and [tex](-7\sqrt{10}-7\sqrt{2}\right))[/tex] = [tex]-32.03543\dots[/tex] Therefore we have the expression [tex]23.27510 - 32.03543i[/tex], which is close to option c. As you can see they approximated the solution.

( 2 ) Here we will apply the following trivial identities,

cos(π / 3) = [tex]\frac{1}{2}[/tex],

sin(π / 3) = [tex]\frac{\sqrt{3}}{2}[/tex],

cos(- π / 6) = [tex]\frac{\sqrt{3}}{2}[/tex],

sin(- π / 6) = [tex]-\frac{1}{2}[/tex]

Substitute into the following expression, representing the quotient of the given values of z1 and z2,

[tex]15\left[cos\left(\frac{\pi \:}{3}\right)+isin\left(\frac{\pi \:\:}{3}\right)\right] \div \:3\sqrt{2}\left[cos\left(\frac{-\pi \:}{6}\right)+isin\left(\frac{-\pi \:\:}{6}\right)\right][/tex] ⇒

[tex]15\left[\frac{1}{2}+\frac{\sqrt{3}}{2}\right]\div \:3\sqrt{2}\left[\frac{\sqrt{3}}{2}+-\frac{1}{2}\right][/tex]

The simplified expression will be the following,

[tex]i\frac{5\sqrt{2}}{2}[/tex] or in other words [tex]\frac{5\sqrt{2}}{2}i[/tex] or [tex]\frac{5i\sqrt{2}}{2}[/tex]

The solution will be option a, as you can see.

Answer:

C. H0 : p = 0.8 H 1 : p ≠ 0.8

The test is:_____.

c. two-tailed

The test statistic is:______p ± z (base alpha by 2) [tex]\sqrt{\frac{pq}{n} }[/tex]

The p-value is:_____. 0.09887

Based on this we:_____.

B. Reject the null hypothesis.

Step-by-step explanation:

We formulate null and alternative hypotheses as  proportion of people who own cats is significantly different than 80%.

H0 : p = 0.8 H 1 : p ≠ 0.8

The alternative hypothesis H1 is that the 80% of the  proportion is different and null hypothesis is , it is same.

For a two tailed test for significance level = 0.2 we have critical value  ± 1.28.

We have alpha equal to 0.2  for a two tailed test . We divided alpha with 2 to get the answer for a two tailed test. When divided by two it gives 0.1 and the corresponding value is ± 1.28

The test statistic is

p ± z (base alpha by 2) [tex]\sqrt{\frac{pq}{n} }[/tex]

Where p = 0.8 , q = 1-p= 1-0.8= 0.2

n= 200

Putting the values

0.8 ± 1.28 [tex]\sqrt{\frac{0.8*0.2}{200} }[/tex]

0.8 ± 0.03620

0.8362, 0.7638

As the calculated value of z lies within the critical region  we reject the null hypothesis.

Answer:

5

Step-by-step explanation:

a^2 + b^2 = c^2

4^2 + 3^2 = c^2

16 + 9 = c^2

25 = c^2

c = 5

Answer:

Step-by-step explanation:

[tex]Hypotenuse = ?\\Opposite = 4\\Adjacent = 3\\\\Pythagoras \: Theorem ;\\\\Hypotenuse^2 =Opposite^2+Adjacent ^2\\\\Hypotenuse^2 = 4^2 +3^2\\\\Hypotenuse^2 = 16+9\\\\Hypotenuse^2 = 25\\\\\sqrt{Hypotenuse^2}=\sqrt{25} \\Hypotenuse = 5[/tex]

Answer:

Step-by-step explanation:

Formula for area of a triangle:

Height x Base /2

Base (b) = h +4

Height = h

h + 4 x h /2 = 30cm

=> h +4 x h = 60

=> h+4h =60

=> 5h = 60

=> h = 12

Height = 12

Base = 12 +4 = 16

Answer:

Those two are 0.25

4/16 = 1/4

5/20 = 1/4

Answer: Please Give Me Brainliest, Thank You!

4/16 = 5/20 = 1/4

Step-by-step explanation:

Because If you divide 4 and 16 by 4 you get 1/4 and if you divide 5 and 20 with 5 you get 1/4

Answer:

3 years

Step-by-step explanation:

A = P(1 + r)^t

A = I + P

A = 14,000 + 4,634 = 18,634

18,634 = 14,000(1 + 0.1)^t

18,634/14,000 = 1.1^t

log (18,634/14,000) = log 1.1^t

log (18,634/14,000) = t * log 1.1

t = [log (18,634/14000)]/(log 1.1)

t = 3

Answer:

2.086

Step-by-step explanation:

Log 122 is equal to 2.086

Answer:

7(n + 4)

Step-by-step explanation:

Represent the number by n.  Then the verbal expression becomes

7(n + 4).

Answer:

[tex]\Large \boxed{\sf 17 \ and \ 18}[/tex]

Step-by-step explanation:

The product means multiplication.

There are two positive consecutive integers.

Let the first positive consecutive integer be x.

Let the second positive consecutive integer be x+1.

[tex](x) \times (x+1) =306[/tex]

Solve for x.

Expand brackets.

[tex]x^2 +x =306[/tex]

Subtract 306 from both sides.

[tex]x^2 +x -306=306-306[/tex]

[tex]x^2 +x -306=0[/tex]

Factor left side of the equation.

[tex](x-17)(x+18)=0[/tex]

Set factors equal to 0.

[tex]x-17=0[/tex]

[tex]x=17[/tex]

[tex]x+18=0[/tex]

[tex]x=-18[/tex]

The value of x cannot be negative.

Substitute x=17 for the second consecutive positive integer.

[tex](17)+1[/tex]

[tex]18[/tex]

The two integers are 17 and 18.

The product of two consecutive positive integers is 306.

We need to find the integers

solution : Let two consecutive numbers are x and (x + 1)

A/C to question,

product of x and (x + 1) = 306

⇒x(x + 1) = 306

⇒x² + x - 306 = 0

⇒ x² + 18x - 17x - 306 = 0

⇒x(x + 18) - 17(x + 18) = 0

⇒(x + 18)(x - 17) = 0⇒ x = 17 and -18

so x = 17 and (x +1) = 18

Therefore the numbers are 17 and 18.

Hope it helped u if yes mark me BRAINLIEST

TYSM!

Answer:

Perimeter=60.18cm

Area=215.495cm^2

Step-by-step explanation:

Given:

Length of book=18.34cm

Breadth=11.75cm

Solution:

Perimeter=2(l +b)

P=2(18.34+11.75)

P=2 x 30.09

P=60.18cm

Area=l x b

A=18.34 x 11.75

A=215.495 cm^2

Thank you!

Answer:

500,000

Step-by-step explanation:

(2.1 * 10^8)/(4.2 * 10^2) =

= 2.1/4.2 * 10^8/10^2

= 0.5 * 10^6

= 500,000

The division of 2.1 × 10⁸ and 4.2 × 10² thus the exponent 2.1 × 10⁸ is 500000 times the exponent 4.2 × 10².

The number system is a way to represent or express numbers.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

As per the given exponents 2.1 × 10⁸

Let's assume 2.1 × 10⁸ is x times 4.2 × 10².

2.1 × 10⁸ = x (4.2 × 10²)

x = 2.1 × 10⁸/4.2 × 10²

x = 500000

Hence "The division of 2.1 × 10⁸ and 4.2 × 10² thus the exponent 2.1 × 10⁸ is 500000 times the exponent 4.2 × 10²".

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