Please help with this question

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

a) The first 5 partial sums are listed in the table in the attachment.

__

b) Sigma notation makes use of the general term shown:

  [tex]\displaystyle\sum_{n=1}^\infty{\frac{3^n+(-2)^n}{6^n}}[/tex]

__

c) The sum appears to be close to 3/4. (For large n, a calculator cannot evaluate the terms of the series--they are too small.) The attachment shows the 100th sum to be rounded to 3/4 (from 12 significant digits).

QUESTION:- SOLVE EQUATION BY FACTORISATION

EQUATION:-

[tex] {x}^{2} + x - 72 = 0[/tex]

ANSWER:-

[tex] {x}^{2} + x - 72 = 0\\{x}^{2} + 9x - 8x - 72 = 0 \\ x(x + 9) - 8(x +9) = 0 \\ (x - 8)(x + 9) = 0 \\ [/tex]

NOW FOR VALUE OF X ->

[tex]x - 8 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x + 9 = 0\\ x = 8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = - 9[/tex]

9514 1404 393

Answer:

  C. 4 +√(x+5)

Step-by-step explanation:

The sign between the terms changes to form the conjugate. The radical contents are unchanged.

The conjugate of 4 -√(x+5) is 4 +√(x+5).

_____

Additional comment

The utility of a conjugate is that the product of a number and its conjugate is the difference of two squares. The squares are intended to remove an undesirable feature of the number, its imaginary part or its irrational part, for example. Here, the product of the number and its conjugate would be ...

  (a -b)(a +b) = a² -b²

  4² -(√(x+5))² = 16 -(x +5) = 11 -x . . . . no longer contains a root

Answer:

The number is 16

Step-by-step explanation:

Number : x

Procedure and resolution:

6x = 96

x = 96/6

x = 16

Answer:

[tex]\frac{dy}{dt}=304mi/h[/tex]

Step-by-step explanation:

From the question we are told that:

Height of Plane [tex]h=3mi[/tex]

Speed [tex]\frac{dx}{dt}=460mi/h[/tex]

Distance from station [tex]d=4mi[/tex]

Generally the equation for The Pythagoras Theorem is is mathematically given by

[tex]x^2+3^2=y^2[/tex]

For y=d

[tex]x^2+3^2=d^2[/tex]

[tex]x^2+3^2=4^2[/tex]

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

Therefore

[tex]x^2+3^2=y^2[/tex]

Differentiating with respect to time t we have

[tex]2x\frac{dx}{dt}=2y\frac{dy}{dt}[/tex]

[tex]\frac{dy}{dt}=\frac{x}{y}\frac{dx}{dt}[/tex]

[tex]\frac{dy}{dt}=\frac{\sqrt{7}}{4} *460[/tex]

[tex]\frac{dy}{dt}=304.2614008mi/h[/tex]

[tex]\frac{dy}{dt}=304mi/h[/tex]

9514 1404 393

Answer:

  x = 5.0

Step-by-step explanation:

The tangent relation is helpful:

  Tan = Opposite/Adjacent

  tan(50°) = x/4.2

  x = 4.2·tan(50°) ≈ 5.0054 . . . . multiply by 4.2

  x ≈ 5.0

Answer:

x = - 12/11

Step-by-step explanation:

Multiply by LCM (or LDC if you like that term better)

2 & 3 LCM = 6

6(3/2) x  + 6(1/3)x  + 5*6 = 3*6

9x + 2x + 30 = 18

11x = - 12

x = - 12/11

Answer:

Slope passes through (-6, 5) and (-2, 7)

[tex]m_1=\frac{y_2-y_1}{x_2-x_1} =m_1=\frac{7-5}{-2+6}[/tex]

[tex]m_1=\frac{2}{4} =\frac{1}{2}[/tex]

Slope passes through (4, 2) and (6, 6)

[tex]m_2=\frac{6-2}{6-4}[/tex]

[tex]\frac{4}{2} =2[/tex]

[tex]m_1\times m_2 \neq -1[/tex] [tex]m_1\neq m_2[/tex]

Answer:- A) neither perpendicular nor parallel.

OAmalOHopeO

Answer:

Step-by-step explanation:

1 km = 0.621 mi

1 hr = 60 min

(5 km)/(4.5 hr) × (0.621 mi)/km × (1 hr)/(60 min) = (0.0115 mi)/min

Step-by-step explanation:

SO, OT is parallel to the vector a+2b

Answer: 24 feet

Step-by-step explanation: i just guessed it on pluto and got it right. please leave a like if it worked

The length of another axis for the given ellipse will be around 25.6125 feet so none of the options will be correct.

a regular oval form produced when a cone is cut by an oblique plane that does not intersect the base, or when a point moves in a plane so that the sum of its distances from two other points remains constant.

In another word, an ellipse is a curve that becomes by a point moving in such a way that the sum of its distances from two fixed points is a closed planar curve produced.

General equation of an ellipse

(x 2 / a 2 )+ (y2 / b 2 )= 1

Given that

the plot of land is 40 feet across one axis

so  2a = 40 feet

a = 20 feet

The foci are 16 feet from the center so

c = 16

Now we know that

c = √(b² - a²)  

c² = b² - a²

16² = b² - 20²

b = 25.6125  

So, the length of the minor axis will be around 25.6125 feet.

To learn more about ellipse,

https://brainly.com/question/14281133

#SPJ2

Answer:

30

Step-by-step explanation:

Answer:

-13 degrees celcius.

Step-by-step explanation:

6 degrees are lowered every hour. 6*8 = 48 degrees, 48 degrees are lowered.

35-48 is -13. The room temperature will be -13 eight hours after the process begins.

Answer:

b)  [tex]c=1[/tex]

Step-by-step explanation:

From the question, we are told that:

Function

[tex]F(x)=2x^2-4x+9[/tex]

Given

Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.

Generally, the Function above is a polynomial that can be Differentiated and it is continuous

Where

-F(x) is continuous at (-1,3)

-F(x) Can be differentiated at (-1.3)

-And F(-1)=F(3)

Therefore

F(x) has Satisfied all the Requirements for Rolle's Theorem

Differentiating F(x) we have

[tex]F'(x)=4x-4[/tex]

Equating F(c) we have

[tex]F'(c)=0[/tex]

[tex]4(c)-4=0[/tex]

Therefore

[tex]c=1[/tex]

Answer:

(9,-2)

Step-by-step explanation:

5 is the x coordinate, and 4 is the y coordinate. When you go right a certain amount of units, you add those units to your x coordinate. If you were to go left a certain amount of units, you'd subtract them. Since we're going right, 5 + 4 = 9. When you go up a certain amount of units, you add those units to you y coordinate. If you were to go down a certain amount of units, you'd subtract them.  Since we're going up, -6 + 4 = -2. So, x = 9 and y = -2, or (9,-2)

Answer:

fourth root of 24 x cubed/16x to the power four

Answer:

see below

Step-by-step explanation:

The stems are in the middle and the leaves are on the left and right

Stems are 0,1,2,3,4,5

Answer:

a) 0

b) 2,3,4,5,6,7

c)3,4,6,7

Step-by-step explanation:

Answer:

26.75 units²

Step-by-step explanation:

This shape can be split into 3 triangles and a square. Find the area of each shape then add them all up.

[tex]A(Square)=2(2)=4\\\\A(Triangle)=\frac{1}{2}(2)(2)=2\\\\A(Triangle)=\frac{1}{2}(5)(2)=5\\\\A(Triangle)=\frac{1}{2}(9)(3.5)=15.75\\\\A(Shape)=4+2+5+15.75=26.75[/tex]

Therefore, the area of the shape is 26.75 units².

Answer:

1,000 defects

Step-by-step explanation:

Find how many defects that should be made by finding 1% of 100,000:

100,000(0.01)

= 1000

So, there should be 1,000 defects

Answer:

1. Negation

2. Equivalent

3. Neither

4. Neither

Step-by-step explanation:

p ^ ~q

~q → p~

~q ∨ p

~p ∨q

Answer:

A=1024 yd.^2

Step-by-step explanation:

A=s^2

Substitute,

A=32^2

So,

A=1024 yd.^2

Answer:

1024 yd²

Step-by-step explanation:

Since it's a square, the side lengths will all be the same length. Due to this, you can square the given value to find the area.

A(Square) = 32² = 1024

Answer:

0.5*sqrt33

Step-by-step explanation:

A(0,0,0) B(-4,1,-2), c(-4,2,-3)

Vector AB is (-4-0,-1-0, -2-0)= (-4,-1,-2)  The modul of AB is sqrt (4squared+

+(-1) squared+ (-2) squared)= sqrt (16+1+4)=sqrt21

Vector AC is (-4,2,-3) The modul of vector AC is equal to sqrt ((-4)squared+ 2squared+(-3)squared)= sqrt(16+4+9)= sqrt29

Vector BC is equal to (-4-(-4), 2-1, -3-(-2))= (0,1,-1)

The modul of BC is sqrt (1^2+(-1)^2)=sqrt2

Find the angle B

Ac^2= BC^2+AB^2-2*BC*AB*cosB

29= 2+21-2*sqrt2*sqrt21*cosB

29= 2+21-2*sqrt42*cosB

cosB= -3/ sqrt42

sinB= sqrt( 1-(-3/sqrt42)^2)=sqrt33/42= sqrt11/14

s=1/2* (sqrt2*sqrt21*sqrt11/14)=1/2*sqrt(42*11/14)= 0.5*sqrt33

Answer:

The 99% confidence interval for the true population mean turtle weight is between 77.76 and 82.24 ounces.

Step-by-step explanation:

We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a p-value of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575\frac{6.1}{\sqrt{49}} = 2.24[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 80 - 2.24 = 77.76 ounces.

The upper end of the interval is the sample mean added to M. So it is 80 + 2.24 = 82.24 ounces.

The 99% confidence interval for the true population mean turtle weight is between 77.76 and 82.24 ounces.

Answer:

3.5

Step-by-step explanation:

in order to find the maximum, we are basically solving to find the vertex of the graph. to find the vertex use :

-b/2a

the 'b' is 112

the 'a' is -16

so :

-112/-32 = 3.5

the answer is B, 3.5

Answer:

2.75 m²  

Step-by-step explanation:

From the information given:

the thickness of the paint = 0.07 cm = (0.07/100) m

= 0.0007 m thick

the diameter hemispherical dome = 50 m

∴

radius of the dome = 50m /2 = 25 m

The volume of a hemispherical dome is expressed as:

[tex]V = \dfrac{2}{3}\pi r^3[/tex]

Thus, the change in the volume now is:

[tex]\dfrac{dV}{dr} = \dfrac{2}{3}\pi *3 r^2[/tex]

[tex]{dV} = \dfrac{2}{3}\pi *3 r^2 (dr)[/tex]

[tex]{dV} = 2 \pi r^2 (dr)[/tex]

∴

dV = 2π × (25)² (0.0007)

where;

dr = 0.0007

dV = 2π × (25)² (0.0007)

dV = 2.75 m²  

Answer:

[tex]0.76d[/tex]

Step-by-step explanation:

Given

[tex]Formula = d - (0.24)d[/tex]

Required

Equivalent expression

We have:

[tex]Formula = d - (0.24)d[/tex]

Open bracket

[tex]Formula = d - 0.24d[/tex]

[tex]Formula = 0.76d[/tex]

Answer:

[tex]\displaystyle m = \frac{3}{4}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify points from graph.

Point (4, 0)

Point (0, -3)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m