A pyramid has a square base of length 4.8 m and a total surface area of 85 m². Find the volume of the pyramid.​

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)

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:

10.2

Step-by-step explanation:

195×2×3×π/360

= 13π/4

= 10.2 (rounded to the nearest tenth)

Answered by GAUTHMATH

what?

Step-by-step explanation:

I dont understand

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

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

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.

-----------

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:

(B)5 is the correct answer for the question

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:

Please check out the attachments below to get the answer

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]

if possible brainlist?

Step-by-step explanation:

A i think 3

and

B 3,999,805 will be left over

Answer:

10 is the correct answer.

Answer:

10

Step-by-step explanation:

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:

[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:

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:

[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:

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

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.

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:

5.1

Step-by-step explanation:

ik i am in the future

Step-by-step explanation:

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

2a/ 5a given fraction

2a-2/5a-2

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:

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).

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:

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