Find the volume of this sphere please help

Using the definition of the derivative,

[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{f(x) - f(-2)}{x - (-2)}[/tex]

[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{\dfrac6x + 3}{x + 2}[/tex]

[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{\dfrac{6+3x}x}{x + 2}[/tex]

[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{6+3x}{x(x + 2)}[/tex]

[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{3(x+2)}{x(x + 2)}[/tex]

[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{3}{x} = \boxed{-\dfrac32}[/tex]

Answer:

a)   [tex]s=482moh[/tex]

b)  [tex]s'=9mph[/tex]

Step-by-step explanation:

From the question we are told that:

Distance [tex]d=3930mi[/tex]

Time of flight [tex]T=8hr[/tex]

Flight back [tex]T_b=8.3hr[/tex]

Generally the equation for Time for flight with jet steam is mathematically given by

[tex]T=\frac{d}{s+s_1}[/tex]

[tex]8=\frac{3930}{s+s'}[/tex]

[tex]s+s'=491.3 ....equ1[/tex]

Generally the equation for Time for flight against jet steam is mathematically given by

[tex]T=\frac{d}{s-s_1}[/tex]

[tex]8.3=\frac{3930}{s-s_1}[/tex]

[tex]s+s'=473.5......equ 2[/tex]

Solving equ 1 and equ 2 simultaneously

[tex]s+s'=491.3[/tex]

[tex]s+s'=473.5[/tex]

Therefore

[tex]s=482moh[/tex]

[tex]s'=9mph[/tex]

Answer:

B

Step-by-step explanation:

2 units to the right -> -2 in the brackets next to x

4 units down -> -4 as a constant at the end of the equation

Answer:

72

The result is rational because it can be written as the ratio of two integers and its decimal expansion can terminate or repeat.

Answered by GAUTHMATH

Answer:

D. 1/16

Step-by-step explanation:

Evaluate: 2^-4

А. =100

В. -8ОО

С. -16

D. 1/16

Given

2^-4

= 1 / 2⁴

= 1 / (2 * 2 * 2 * 2)

= 1 / 16

Therefore,

2^-4 = 1/16

D. 1/16

Answer:

Please check out the attachments below to get the answer

Hi! I ran into a similar problem so i will try, but sorry if i get it wrong, so basically all you do i

Answer:

C

Step-by-step explanation  

The y-intercept is 1, the slope is -1/3, and the shaded area is under the graph because y is LESS than -x/3 + 1.

Answer:

5.1

Step-by-step explanation:

ik i am in the future

The partial fraction expansion will look like

(x - 2)/((x ² + 1) (x - 1)²) = (ax + b)/(x ² + 1) + c/(x - 1) + d/(x - 1)²

Get everything in terms of a common denominator, and compare the numerators on both sides:

x - 2 = (ax + b) (x - 1)² + c (x ² + 1) (x - 1) + d (x ² + 1)

Expand the right side:

x - 2 = (ax + b) (x - 1)² + c (x ² + 1) (x - 1) + d (x ² + 1)

x - 2 = (a + c) x ³ + (-2a + b - c + d) x ² + (a - 2b + c) x + b - c + d

Match up the coefficients and solve the resulting system of equations:

a + c = 0

-2a + b - c + d = 0

a - 2b + c = 1

b - c + d = -2

==>   a = -1, b = -1/2, c = 1, d = -1/2

So the expansion into partial fractions is

(x - 2)/((x ² + 1) (x - 1)²) = (-x - 1/2)/(x ² + 1) + 1/(x - 1) - 1/(2 (x - 1)²)

… = -(2x + 1)/(2 (x ² + 1)) + 1/(x - 1) - 1/(2 (x - 1)²)

Answers:

choice A)   y = 0x

choice D)  y = 0/x

========================================================

Explanation:

Choice A is the same as y = 0 because 0x turns into 0. Multiplying 0 with any number always leads to 0.

Similarly, choice D is the same as y = 0 as well. Dividing 0 over any nonzero value leads to 0. Note the key term "nonzero" here. We cannot have 0 in the denominator. So x = 0 is not allowed for choice D.

So for any nonzero x, we have 0x and 0/x result in the same thing.

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Extra info:

Choice B can be ruled out because something like x = 2 leads to y = 2.

Choice C is ruled out because we can never have 0 in the denominator.

Answer:

10 is the correct answer.

Answer:

10

Step-by-step explanation:

Answer:

160 chemistry books and 80 history books

Step-by-step explanation:

C=chemistry books sold, H=history books sold

C=2H

C+H=240, 3H=240, H=80, C=160

Answer:

22/5

Step-by-step explanation:

3m+18+2m=40

5m=40-18

5m=22

m=22/5

[tex] \bf \large \longrightarrow \: 3m \: + \: 18 \: + \: 2m \: = \: 40[/tex]

[tex] \bf \large \longrightarrow \:5m \: + \: 18 \: = \: 40[/tex]

[tex] \bf \large \longrightarrow \:5m \: = \: 40 \: - \: 18[/tex]

[tex] \bf \large \longrightarrow \:5m \: = \: 22[/tex]

[tex] \bf \large \longrightarrow \:m \: = \: \frac{22}{5} \\ [/tex]

[tex] \bf \large \longrightarrow \:m \: = \: \cancel\frac{22}{5} \: \: ^{4.4} \\ [/tex]

[tex] \bf \large \longrightarrow \:m \: = \: 4.4[/tex]

Answer:

The given graph is a function.

Step-by-step explanation:

There is only one given graph, and that graph is a function. In order to determine which graph is a function, conduct the vertical line test. Can a vertical line pass through the represented data set without crossing two y-values? (i.e. A 'sideways parabola' is not a function).

if possible brainlist?

Step-by-step explanation:

A i think 3

and

B 3,999,805 will be left over

what?

Step-by-step explanation:

I dont understand

Answer:

[tex]{ \sf{ - 2 {a}^{5} + 4 {a}^{4} + 5 {a}^{3} + \frac{2}{3}a }}[/tex]

Answer:

D

Step-by-step explanation:

A polynomial is in standard equation when the degree of the polynomial are in descending order.

Answer:

D y=2/3 x +1

  y= -3/2 x+2

Step-by-step explanation:

Perpendicular lines have slopes that multiply to -1

The equations are written in slope intercept form

y = mx+b where m is the slope

A 1/5* 5 = 1  not perpendicular

B 2/3 * 3/2 = 1  not perpendicular

C -1/5 * -5 = 1  not perpendicular

D 2/3 * - 3/2 = -1   perpendicular

Answer:

y - intercept = 2.25

Step-by-step explanation:

y = mx + c

Where,

y = Total cost

x = additional cost

m = slope

c = y - intercept

y = 0.25x + 2.25

Relating with the above equation,

y - intercept = 2.25

Slope, m = 0.25

Answer:

Part 1; The volume of the box Thomas wants to make is 224 = 2·w² + 12·w

Part 2; The zeros for the equation of the function, are w = -14, or w = 8

Part 3

The width of the box is 8 inch

The length of the box, is 14 inches

The height of the box, is given as 2 inches

Part 4

Please find attached the graph of the function

Step-by-step explanation:

Part 1

The volume of the box Thomas wants to make, V = 224 in.³

The dimensions he cuts out from the length and width = 2 in² each

The length of the box = 6 inches + The width of the box

Let l represent the length of the box and let w represent the width of the box, we have;

l = 6 + w

The height of the box, h = The length of the cut out square = 2 inches

The volume of the box, V = Length, l × Width, w × Height, h

∴ V = l × w × h

l = 6 + w, h = 2

∴ V = (6 + w) × w × 2

V = 2·w² + 12·w,

The equation of the volume of the box, V = 2·w² + 12·w, where, V = 224

∴ 224 = 2·w² + 12·w

Part 2

The zeros of the equation for the volume of the box, V = 2·w² + 12·w, where, V = 224 are found as follows;

V = 224 = 2·w² + 12·w

∴ 2·w² + 12·w - 224 = 0

Dividing by 2 gives;

(2·w² + 12·w - 224)/2 = w² + 6·w - 112 = 0

∴ (w + 14) × (w - 8) = 0

The zeros for the equation of the function, are w = -14, or w = 8

Part 3

We reject the value, w = -14, therefore, the width of the box, w = 8 inch

The length of the box, l = 6 + w

∴ l = 6 + 8 = 14

The length of the box, l = 8 inches

The height of the box, h, is given as h = 2 inches

Part 4

The graph of the function created with MS Excel is attached

Answer:

solution,

(X1,y1)= (-4,5)

(X2,Y2)=(2,-3)

slope of the line(m)= y2-y1/x2-x1

=-3-5/2-(-4)

=-8/6

=-4/3

Answer:

[tex]\angle m + \angle t + \angle n = 180[/tex]

Step-by-step explanation:

Required

Show that:

[tex]\angle m + \angle t + \angle n = 180^o[/tex]

To make the proof easier, I've added a screenshot of the triangle.

We make use of alternate angles to complete the proof.

In the attached triangle, the two angles beside [tex]\angle m[/tex] are alternate to [tex]\angle t[/tex] and [tex]\angle n[/tex]

i.e.

[tex]\angle 1 = \angle t[/tex]

[tex]\angle 2 = \angle n[/tex]

Using angle on a straight line theorem, we have:

[tex]\angle 1 + \angle m + \angle 2 = 180[/tex]

Substitute values for (1) and (2)

[tex]\angle t + \angle m + \angle n = 180[/tex]

Rewrite as:

[tex]\angle m + \angle t + \angle n = 180[/tex] -- proved

Answer:

(B)5 is the correct answer for the question

Answer:

it is an rigjt angle triangle you shoult pythogores therom if you will know it it will be easy to you to understand this question

Answer:

Length = 10.435 inches

Step-by-step explanation:

Let the length be l

Let the width be w

Since the length is 9 inches more than half the width.

Then;

L = 0.5w + 9

Perimeter of a rectangle is;

P = 2Lw

Thus;

P = 2w(0.5w + 9)

Since perimeter = 60

Then;

2w(0.5w + 9) = 60

w² + 18w = 60

w² + 18w - 60 = 0

From quadratic formula;

w ≈ 2.87 in

L = 0.5(2.87) + 9

L = 10.435 in

The area of the slice of pie that was cut, rounded to the nearest hundredth is 22.08 square feet.

The slice of pie will form a sector as shown;

The area of the slice of pie will be expressed as:

[tex]A=\frac{\theta}{360}* \pi r^2[/tex]

[tex]\theta\\[/tex] is the central angle = 45 degrees

r is the radius

[tex]r=\frac{d}{2}\\r= \frac{15}{2}\\r= 7.5feet[/tex]

Substitute the given values into the formula above;

[tex]A=\frac{45}{360} * 3.14*7.5^2\\A=\frac{1}{8} * 176.625\\A=22.08ft^2[/tex]

Hence the area of the slice of pie that was cut, rounded to the nearest hundredth is 22.08 square feet.

The area of the slice of pie that was cut, rounded to the nearest hundredth is 22.08 square feet.

Learn more about an area of a sector here: https://brainly.com/question/12792310

Answer:

the guy on top is right

Step-by-step explanation:

i took the test

Step-by-step explanation:

according to question let 2a and 5a be the given rations

2a/ 5a given fraction

2a-2/5a-2