What is the weight of the piece of aluminum shown below at 0.0974 ​lb/​in^3? ​(Hint: Subtract the volume of the cylindrical​ hole.)

Answer:

[tex]\displaystyle \frac{dy}{dx} \bigg| \limits_{x = 6} = -9[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Calculus

Differentiation

Basic Power Rule:

Derivative Rule [Quotient Rule]:                                                                           [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle V = \frac{1}{3} \pi x^2y[/tex]

[tex]\displaystyle V = 324 \pi[/tex]

[tex]\displaystyle x = 6[/tex]

[tex]\displaystyle y = 27[/tex]

Step 2: Differentiate

Step 3: Evaluate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Let the number be x

ATQ

[tex]\\ \sf\longmapsto 5x+6=2x-3[/tex]

[tex]\\ \sf\longmapsto 5x-2x=-3-6[/tex]

[tex]\\ \sf\longmapsto 3x=-9[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{-9}{3}[/tex]

[tex]\\ \sf\longmapsto x=-3[/tex]

Answer:

13

5 - -8

When you subtract a negative number it changes to an addition so 5- -8 becomes 5 + 8 which equals 13.

Answer:

Option c.

Step-by-step explanation:

If we have a vector of N components (or variables), and we have K linear independent restrictions for these N components (such that K < N, we can't have more restrictions than components.)

The dimension of the vector will be given by N - K.

Here we know that we have a vector of 5 components, that can be written as:

[tex]v = \left[\begin{array}{ccc}v_1\\v_2\\v_3\\v_4\\v_5\end{array}\right][/tex]

And we have two restrictions, so we can expect that the dimension of the vector is:

5 - 2 = 3

But let's see it, the restrictions are:

"the first row is equal to the second row"

Then we can rewrite our vector as:

[tex]v = \left[\begin{array}{ccc}v_1\\v_1\\v_3\\v_4\\v_5\end{array}\right][/tex]

Notice that now we have only 4 variables, v₁, v₃, v₄, and v₅

We also know that the sum of the rows is equal to zero, thus:

v₁ + v₂ + v₃ + v₄ + v₅ = 0

we know that v₂ = v₁, so we can replace that to get:

2*v₁ + v₃ + v₄ + v₅ = 0

Now we can isolate one of the variables, to write it in term of the others, for example, let's isolate v₅:

v₅ = -2*v₁ - v₃ - v₄

Now if we replace that in our vector, we have:

[tex]v = \left[\begin{array}{ccc}v_1\\v_1\\v_3\\v_4\\-2*v_1 - v_3 - v_4\end{array}\right][/tex]

Notice that our vector depends on only 3 variables,  v₁, v₃, and v₄, so we can define our vector in a 3-dimensional space.

Then the correct option is c, the dimension of the vector space is 3.

Answer:

They look similar

Statistics is related to maths because we study, use and even consider statistic problems with reference to mathematics.

• It is mostly used to find the census, which is maths.

• It is used to find interest rates and other banking terms using statistics, which is again related to math.

• It is also used to find the average people living in a village or panchayat, which is also math.

Therefore I strongly believe that Statistics is Maths.

Thank You!

Answer:

[tex]A)58[/tex]

Step-by-step explanation:

[tex][Kindly\ refer\ the\ attachment]\\We\ are\ given:\\GH\ is\ the\ diameter\ of\ the\ circle.\\ Also,\\ GM=3\ units\ and\ MH=7\ units\\From\ the\ figure,\\GH\ subtends\ an\ angle\ at\ two\ points\ specifically\ M\ and\ N\ on\ the\\ arc.\\Now,\\We\ know\ that,\\'The\ Angle\ subtended\ by\ the\ diameter\ anywhere\ over\ the\ arc\ of\ the\\ circle\ is\ always\ 90\ degrees'.\\Hence,\\\angle GMH\ = \angle GNH=90\\[/tex]

[tex]Also,\\Pythagoras\ Theorem\ states\ that: 'In\ a\ right\ triangle,\ the\ sum\ of\ squares\\ \ of\ the\ legs\ is\ equal\ to\ the\ square\ of\ the\ hypotenuse'\\In\ \triangle GMH,\\Since\ \angle GMH=90,\\GM^2+MH^2=GH^2[Through\ Pythagoras\ Theorem]\\Hence,\\Substituting\ GM=3,\ MH=7:\\3^2+7^2=GH^2\\GH^2=9+49=58[/tex]

[tex]Similarly,\\In\ \triangle GNH,\\Since\ \angle GNH=90,\\GN^2+NH^2=GH^2\\Hence,\\Substituting\ GN=x\ and\ NH=y:\\x^2+y^2=GH^2\\x^2+y^2=58[/tex]

We are given the matrices A and B

[tex]A = \left[\begin{array}{ccc}2&3&-1\\0&2&5\\2&4&0\end{array}\right][/tex]

[tex]B = \left[\begin{array}{ccc}2\\1\\2\end{array}\right][/tex]

Multiplying these matrices:

We multiply matrices by taking the first column of the first matrix and the first row of the second matrix

we will multiply all the terms of the first column of the first matrix and multiply them by the terms of the first row of the second matrix, one by one

[tex]AB = \left[\begin{array}{ccc}2(2) + 3(1) + -1(2)\\0(2) + 2(1) + 5(2)\\2(2) + 4(1) + 0(2)\end{array}\right][/tex]

[tex]AB = \left[\begin{array}{ccc}5\\12\\8\end{array}\right][/tex]

9514 1404 393

Explanation:

Two matrices with dimensions (numbers of (rows, columns)) of (a, b) and (c, d) can only be multiplied if the number of columns in the left matrix is equal to the number of rows in the right matrix. That is, b=c. The dimensions of the product matrix will be (a, d).

For row i of the left matrix and column j of the right matrix, element a(i,j) of the product matrix is the dot-product of row i with column j. (The dot-product of two vectors is the sum of the products of corresponding elements.)

__

The example matrices have (row, column) dimensions (3, 3) and (3, 1), so can be multiplied with a result having dimensions (3, 1).

It is useful to refer to an element of a matrix by specifying the row and column in which it resides. An element of matrix 'A' in row 2 and column 3 can be referred to as A(2,3). Often, subscripts are used, as in ...

  [tex]A_{i,j}[/tex]

For matrix C = A·B, the element C(1,1) will be the sum ...

  A(1,1)B(1,1) +A(1,2)B(2,1) +A(1,3)B(3,1)

Calculators, apps, spreadsheets, and web sites are available that will perform this arithmetic for you. It can be a bit tedious to do by hand.

Here the product is ...

  [tex]A\cdot B=\left[\begin{array}{ccc}2&3&-1\\0&2&5\\2&4&0\end{array}\right] \cdot\left[\begin{array}{c}2&1&2\end{array}\right] =\left[\begin{array}{c}2(2)+3(1)+(-1)(2)&0(2)+2(1)+5(2)&2(2)+4(1)+0(2)\end{array}\right] \\\\=\left[\begin{array}{c}5&12&8\end{array}\right][/tex]

Answer:

x=3

Step-by-step explanation:

2x+1=7

2x=7-1

2x=6

x=6/2

x=3

Answer:

Solution,

2x + 1=7

or 2x = 7 - 1

or, 2x= 6

or, x = 6

2

or, x = 3

.:. x = 3

Answer:

-1 <x < 7

(-1,7)

Step-by-step explanation:

open circle on the left means the number is greater than

-1 <x

Open circle on the right means the number is less than

x < 7

Since both statements are true. we combine them

-1 <x < 7

open circles means parentheses, closed circles mean brackets

Answer:

14 nickels

Step-by-step explanation:

One nickel is worth 5 cents, so find the value of 14 nickels by multiplying 14 by 5:

14(5)

= 70

So, 14 nickels is equal to the 70 cents that she has in her purse.

The correct answer is 14 nickels.

Answer:

3rd option

[tex]A) \frac{4-2}{2-1} =2[/tex]

[tex]B)\frac{1-0.5}{4-2} =0.25[/tex]

[tex]C)>2[/tex]

[tex]D) 1[/tex]

~OAmalOHopeO

Answer:

The third one is your answer

the answer is on the photo

Answer:

(cosB-1)(cosB+6)

Step-by-step explanation:

use u substitution . u = cosB

u^2+5u-6

factor

(u-1)(u+6)

put cosB back in for u

(cosB-1)(cosB+6)

Answer:

15÷39

Step-by-step explanation:

I hope it will help you

cos x = adjacent÷ hypotenuse

cos x =15÷39

cos x = 5÷13

Answer:

i believe it'll cost 200 dollars

Answer:

A=5h(B+b)

A/5h=B+b

A/5h - b= B

Answer:

55

Step-by-step explanation:

Any number that's ends with the digit 0 or 5 is divisible by 5.

Hi there!  

»»————-　★　————-««

I believe your answer is:  

D) 55

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Option A:}}\\\\108/5 = 21.6\\\\\boxed{\text{Option B:}}\\\\109/5 = 21.8\\\\\boxed{\text{Option C:}}\\\\69/5 = 13.8\\\\\boxed{\text{Option D:}}\\\\55/5 = \boxed{11}[/tex]

⸻⸻⸻⸻

55 is divisible by 5. You can also tell that it is divisible because it's last place digit is a '5'.

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

Reflection

Step-by-step explanation:

Because reflecting yourself in a mirror means pre image to image

Answer:

Step-by-step explanation:

dilation

Answer:

B. 13 units

Step-by-step explanation:

let

(x1 , y1) = (-4 , -6)

(x2 , y2) = (1 , 6)

distance between CD = root (x2 - x1)^3 + (y2 - y1)

= root {1 - ( -4)}^2 + {6 - ( -6)}^2

= root {1 +4}^2 + {6+6}^2

= root 5^2 + 12^2

= root 25 + 144

= root 169

= 13 units ans

9514 1404 393

Answer:

  100°

Step-by-step explanation:

The relevant relation for angle x is ...

  x = (AB +DE)/2

and for angle y, it is ...

  y =(AC -DE)/2

Using the second relation to write an expression for DE, we have ...

  DE = AC -2y

In the first equation, this lets us write ...

  x = (AB +(AC -2y))/2 = (AB +(2AB -2y))/2

  2x = 3AB-2y . . . . . . . . . . . . . . multiply by 2

  (2x +2y)/3 = AB = AC/2 . . . . . add 2y; divide by 3

  AC = (4/3)(x +y) = (4/3)(60° +15°) . . . . multiply by 2, substitute known values

  AC = 100°

Answer:

Step-by-step explanation:

A) 26*26*26 =17576

B)26*25*24=15600

C)26*26=676

D) 26

Answer:

55.55 and 45.55

Step-by-step explanation:

Let the car 1 speed be x km/hr and car 2 speed be x-10 km/hr.

Their relative velocity is 2x-10.

Distance covered in 9 hrs=9(2x-10).

18x-90=910, x=55.55 km/hr, x-10=45.55km/hr

Answer:

Simply because x=y2 doesn't imply that y=

√

x

.

Answer:

50.854 seconds

Step-by-step explanation:

24.98 + 25.874 = 50.854 seconds

Answer:

A,D,E,F

1,4.5,6

The experimental units are subjects.

There are three treatments.

One treatment is a circuit training class.

The factor is the type of class.

ED2021

Answer:

[tex] \frac{ \sqrt{3} }{3} [/tex]

Step-by-step explanation:

[tex]\frac{1}{3} \div \sqrt{3} [/tex]