The numerical coefficient of -2pqr

Answer:

65/264 or 0.2462

Step-by-step explanation:

The given series is

(1/1.2.3) + (1/2.3.4) + (1/3.4.5) + ………………

If we denote the series by

u(1) + u(2) + u(3) + u(4) +……………..u(n),

where u(n) is the nth term, then

u(n) = 1/[n(n+1)(n+2)] , n = 1,2,3,4,………n.

which can be written as

u(n) = (1/2) [1/n(n+1) - 1/(n+1)(n+2)] ………………………(1)

In the question, the number of terms n =10, thereby restricting us only to first 10 terms of the series and we have to find the sum for this truncated series. Let S(10) denote the required sum. We have then from (1),

u(1) = (1/2) (1/1.2 - 1/2.3)

u(2) = (1/2) (1/2.3 - 1/3.4)

u(3) = (1/2) (1/3.4 - 1/4.5)

u(4) = (1/2) (1/4.5 - 1/5.6)

u(5) = (1/2) (1/5.6 - 1/6.7)

u(6) = (1/2) (1/6.7 - 1/7.8)

u(7) = (1/2) (1/7.8 - 1/8.9)

u(8) = (1/2) (1/8.9 - 1/9.10)

u(9) = (1/2) (1/9.10 - 1/10.11)

u(10) = (1/2) (1/10.11 - 1/11.12)

Let us now add the terms on LHS and the terms on RHS independently. The sum of LHS is nothing but the sum S(10) of the series up to 10 terms. On the RHS, alternate terms cancel and we are left with only the first and the last term. Therefore,

S(10) = (1/2) (1/1.2 - 1/11.12) = (1/2) (66–1)/132 = [65/(132.2)]

= 65/264

= 0.2462 (correct to four decimal places)

#carryonlearnig

Answer:

The complete question can be found online.

The missing information is:

Carson drove a total distance of 120km, he initially has 30L of fuel on his tank, and his car efficiency is 100 cm^3/km

Remember that 1000cm^3 = 1 L

then:

100cm^3 = 0.1L

This means that he uses 0.1 L per kilometer.

The equation that shows how many liters of fuel he will have is:

initial fuel - consumed fuel.

We know that the initial fuel is 30 liters.

And the consumed fuel will be the amount of fuel he used to drive the 120 km

Remember that for each km, he consumes 0.1 L of fuel.

Then for the 120km he used 120 times 0.1 L of fuel, so he used a total of:

120*0.1 = 12 L of fuel

Then the remaining fuel in the tank is:

30 L - 12 L = 18L

There are 18 L of fuel in the tank.

Answer:

Should be 30-100/1000*120

Step-by-step explanation:

answer is C. 252 ft^2

split the figure into two pieces and first figure out the rectangle (shown in turquoise).

If you multiply the width and length (18*6) you should get 108.

Then figure out the trapezoid (in magenta). the formula is (a+b)/2*h where a and b are the bases and h is the height. the bases are given, 6 and 18. to find the height, subtract the entire figure's height by 6, which is 18-6 and gives us 12. so the formula converted to this problem is (6+18)/2*12. simplify parenthesis and get 24/2*12. 24/2=12, so multiply 12*12. The area of the trapezoid is 144. Add the areas of both figures together and get 252.

Answer:

We know that the hypotenuse-leg theorem states that if the hypotenuse and one leg of a right triangle are congruent to hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. hypotenuse(AB) of △BDA equals to hypotenuse (CD) of △DBC.

Answer:

A. HL

Step-by-step explanation:

Answer:

(x-5)² + (y+4)² = 100

Step-by-step explanation:

The formula for calculating the equation of a circle is expressed as;

(x-a)² + (y-b)² = r² where:

(a,b) is the centre of the circle

r is the radius

Get the radius using the distance formula;

r = √(2-(-4))²+(-3-5)²

r = √6²+(-8)²

r = √36+64

r =√100

r² = 100

Since a = 5 and b = -4, on substituting into the formula;

(x-5)² + (y+4)² = 100

This gives the required equation

Answer:

(x-5)² + (y+4)² = 100

Step-by-step explanation:

Just got it correct on Edmentum test.

Answer:

B, (-4,0)

Step-by-step explanation:

2(4x - 2y = -16)       8x - 4y = -32

   8x - 4y = -32

+  -3x + 4y = 12

  5x  = -20

x = -4

4(-4) - 2y = -16

-16 - 2y = -16

-2y = 0

y = 0

Answer:

$12.43

Step-by-step explanation:

Given :

Mean = $8.52

Standard deviation, = $2.38

Stock price which falls beyond 0.05 of the distribution is at the 95th percentile

The 95th percentile distribution has a Pvalue of 1.645 (standard normal table)

We obtain the value of x, with z = 1.645

Using the Zscore relation :

Zscore = (score - mean) / standard deviation

1.645 = (score - 8.52) / 2.38

Cross multiply :

1.645 * 2.38 = score - 8.52

3.9151 = score - 8.52

Score = 8.52 + 3.9151

Score = $12.4351

Stock price beyond 0.05 is $12.43

Answer:

Step-by-step explanation:

a). Total surface area of cylinder is defined by sum of curved surface area and surface area of the top and bottom.

Total surface area = 2πrh + 2πr²

Skateboarders use a half pipe structure which are not closed at the ends.

Therefore, curved surface of the half pipe = [tex]\frac{2\pi rh}{2}[/tex]

                                                                      = πrh

b). If r = 2.5 m and h = 9 m,

Curved surface area of the half pipe = π(2.5)(9)

                                                             = 70.69 m²

                                                              ≈ 71 m²

Answer:

f(k + 4) = -2k² - 13k - 28

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = -2x² + 3x - 8

Step 2: Evaluate

[tex]\displaystyle\Large \boldsymbol -2 \cdot \frac{3}{12} \cdot \frac{5}{10} \cdot \frac{7}{15} =-2 \cdot \frac{3 \!\!\!\!\diagup \cdot1}{3 \!\!\!\!\diagup\cdot 4} \cdot \frac{5 \!\!\!\!\diagup\cdot 1}{5 \!\!\!\!\diagup\cdot 2} \cdot \frac{7}{15} =\\\\\\-\frac{2 \!\!\!\!\diagup\cdot 7 }{2 \!\!\!\!\diagup\cdot 4 \cdot 15} =\boxed{-\frac{7}{60}}[/tex]

Answer:

The third one

Step-by-step explanation:

ANSWER :

- ( x+ 2 ) + 4

-x - 2 + 4

-x + 2

Answer:

−x+2

Step-by-step explanation:

-(x+2)+4 Distribute the negative sign (-) outside of the parenthesis with x and 2 and that will turn into -x-2+4.

Add -2 and 4 and that will turn into -x+2.

hypotenuse= 9²

so the distance between the 2 points is 81

4²+5²=c²

factor out the square which gives (4+5)²=c²

which makes c=9

answer=81

Answer:

I think album is another name of CD.

Answer:

8 - 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Given: [tex]\frac{26}{4 + \sqrt{3} }[/tex]

To express the given question in the form a + b[tex]\sqrt{3}[/tex], we first have to rationalize the denominator of the expression.

Rationalizing the denominator, we have;

[tex]\frac{26}{4 + \sqrt{3} }[/tex] * [tex]\frac{4 - \sqrt{3} }{4 - \sqrt{3} }[/tex]  = [tex]\frac{104 -26\sqrt{3} }{16 -4\sqrt{3} + 4\sqrt{3}- 3 }[/tex]

= [tex]\frac{104 - 26\sqrt{3} }{16 - 3}[/tex]

 = [tex]\frac{26(4 - \sqrt{3} }{13}[/tex]

= 2(4 - [tex]\sqrt{3}[/tex])

= 8 - 4[tex]\sqrt{3}[/tex]

The required form of the given question is therefore 8 - 4[tex]\sqrt{3}[/tex]

Answer:

a. 42

b. -12x-5

c. -60

d. -75

e. 66

f. -90

g. 144

h. -135

Answer:

12

Step-by-step explanation:

45-33 is 12

And I guess to check, make sure 12 < 18

Answer:

B. $20.00

Step-by-step explanation:

Step-by-step explanation:

triangle BCA=BAL bcoz Angle BCA= Angle BAL

Answer:

[tex]x = - 59[/tex]

Step-by-step explanation:

[tex](6x + 28) = (7x + 87)[/tex]

[tex]6x + 28 = 7x + 87[/tex]

[tex]6x - 7x = 87 - 28[/tex]

[tex]1x = - 59[/tex]

[tex]x = - 59[/tex]

Answer: [tex]75\ m[/tex]

Step-by-step explanation:

Given

The tower is 45 m high and Clinometer is set at 1.3 m above the ground

From the figure, we can write

[tex]\Rightarrow \tan 32^{\circ}=\dfrac{43.7}{x}\\\\\Rightarrow x=\dfrac{43.7}{\tan 32^{\circ}}\\\\\Rightarrow x=69.93\ m[/tex]

Similarly, for [tex]\triangle ACD[/tex]

[tex]\Rightarrow \tan 47^{\circ}=\dfrac{43.7+y}{x}\\\\\Rightarrow 69.93\times \tan 47^{\circ}=43.7+y\\\\\Rightarrow 74.99=43.7+y\\\Rightarrow y=31.29\ m[/tex]

Height of the tower is [tex]43.7+31.29\approx 75\ m[/tex]

Answer:

Brianna left home and drove 3 miles in 6 minutes. She then stopped for 4 minutes to pick up coffee. Finally, she traveled the last 4 miles in 6 minutes to arrive at her babysitting job.

Step-by-step explanation:

This answer is from Plato.

Answer:

Step-by-step explanation:

Vertices of ΔABC are,

A(-3, 6), B(2, 1) and C(9, 5)

Use the formula to get the distance between two points [tex](x_1,y_1)[/tex] and[tex](x_2,y_2)[/tex],

Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

By using the formula,

AB = [tex]\sqrt{(1-6)^2+(2+3)^2}[/tex]

     = [tex]\sqrt{50}[/tex] units

BC = [tex]\sqrt{(5-1)^2+(9-2)^2}[/tex]

     = [tex]\sqrt{65}[/tex] units

AC = [tex]\sqrt{(6-5)^2+(-3-9)^2}[/tex]

     = [tex]\sqrt{145}[/tex]

Use cosine rule to find the measure of ∠ABC.

AC² = AB² + BC²- 2(AB)(BC)cos(B)

[tex](\sqrt{145})^2=(\sqrt{50})^2+(\sqrt{65})^2-2(\sqrt{50})(\sqrt{65})\text{cosB}[/tex]

145 = 50 + 65 - 2(√3250)cosB

cos(B) = [tex]-(\frac{145-115}{2\sqrt{3250}})[/tex]

          = -0.26312

B = [tex]\text{cos}^{-1}(-0.26312)[/tex]

B = 105.26°

Answer:

(50,-30)

Step-by-step explanation:

Reflecting a point across the y axis is just like flipping a page on a book. The x  coordinate is flipped and the y coordinate stays the same.

Answer:

Step-by-step explanation:

-2y³ +  4 - (-3 - 2y³ - y - 5y²) = -2y³ + 4 + 3 + 2y³ + y + 5y²

                                             = -2y³ + 2y³  +5y² + y   + 4 + 3 {combine like terms}

                                             =  5y² +y + 7

Hello,

Let's say y= log(x) in base 10.

[tex]\\y=log(x)\\\\log^2(x)-3log(x)-4=0\\\\y^2-3y-4=0\\\\\Delta=9+16=5^2\\\\y=4\ or\ y=-1\\\\log(x)=4 \Longrightarrow x=10^4\\\\or\\\\log(x)=-1 \Longrightarrow x=10^{-1}=0.1\\[/tex]

Step-by-step explanation:

I solved it in the diagram

a) y=4.9x

b)y=63.7

c)x=13

Answer:

Value of expression = -3 / 4

Step-by-step explanation:

Given:

(12x + 8) + 4 = 3

Find:

Value of expression

Computation:

Given expression

(12x + 8) + 4 = 3

Step 1: Use Distributive property

12x + 8 + 4 = 3.

Step 2: By adding like terms.

12x + 12 = 3

Step 3: Transfer

12x = 3 - 12

Step 4: Subtract

12x = -9

Step 4: Divide both sides by 12

12x / 12 = -9 / 12

x = -3 / 4

Value of expression = -3 / 4