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snow_tiger [21]
3 years ago
13

Suppose that f(1=9, f(4=?3, f?(1=9, f?(4=?5, and f?? is continuous. find the value of ?41xf??(xdx.

Mathematics
1 answer:
Over [174]3 years ago
8 0
Some characters in your question are not displayed properly, so I'm guessing at what it says.

"Suppose that f(1)=9, f(4)=-3, f'(1)=9, f'(4)=-5, and f'' is continuous. Find the value of \displaystyle\int_1^4xf''(x)\,\mathrm dx."

(Correct me if I'm wrong!)

Integrate by parts, letting u=x and \mathrm dv=f''(x)\,\mathrm dx, so that \mathrm du=\mathrm dx and v=f'(x). Then you have

\displaystyle\int_1^4xf''(x)\,\mathrm dx=xf'(x)\bigg|_{x=1}^{x=4}-\int_1^4f'(x)\,\mathrm dx

Integrating once more gives

\displaystyle\int_1^4xf''(x)\,\mathrm dx=xf'(x)\bigg|_{x=1}^{x=4}-f(x)\bigg|_{x=1}^{x=4}
=(4f'(4)-1f'(1))-(f(4)-f(1))
=(-20-9)-(-3-9)=-17
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If matrix A has dimensions m x n and matrix B has dimensions n x p where m, n, and p are distinct positive integers, which of th
mel-nik [20]

You probably already have an idea of what a matrix is; it's a rectangular array of numbers. What they represent is a bit complicated to explain. There's a whole subject about it (see "linear algebra" for more info). Whatever they represent isn't important though, you don't need to know everything about matrices to compute their product (or whether it's even possible).

A quick definition: A matrix of dimension r-by-c is a matrix with r rows and c columns.

Matrix multiplication all comes down to an operation called the "dot product". It's defined by the sum of component-wise products of elements between two lists. What this means is, if x=\{1,2,0\} and y=\{-1,0,3\}, then the dot product of x and y is

x\cdot y=(1)(-1)+(2)(0)+(0)(3)=-1+0+0=-1

What we did was take the first elements of each list and multiplied them, and the same for the other two elements, then added them all together. Notice that the product can't be computed if x and y don't thave the same number of elements.

We write this product in matrix form as

\begin{bmatrix}1&2&0\end{bmatrix}\begin{bmatrix}-1\\0\\3\end{bmatrix}

Notice the pattern here: on the left, a matrix with 1 row and 3 columns; on the right, a matrix with 3 rows and 1 column. The number of columns of the first matrix have to match the number of rows of the second.

The orientation makes a big difference. The product above returns a 1-by-1 matrix (or simply a scalar number):

\begin{bmatrix}1&2&0\end{bmatrix}\begin{bmatrix}-1\\0\\3\end{bmatrix}=\begin{bmatrix}(1)(-1)+(2)(0)+(0)(3)\end{bmatrix}=\begin{bmatrix}-1\end{bmatrix}=-1

On the other hand, the alternate orientation would result in a 3-by-3 matrix.

\begin{bmatrix}1\\2\\0\end{bmatrix}\begin{bmatrix}-1&0&3\end{bmatrix}=\begin{bmatrix}(1)(-1)&(1)(0)&(1)(3)\\(2)(-1)&(2)(0)&(2)(3)\\(0)(-1)&(0)(0)&(0)(3)\end{bmatrix}=\begin{bmatrix}-1&0&3\\\-2&0&3\\0&0&0\end{bmatrix}

So the number of rows of the first matrix and number of columns of the second matrix determine the number of rows and columns, respectively, of the matrix product.

I think we have enough information about matrix multiplication to answer this question. If A has dimensions m\times n and B has dimensions n\times p, then the matrix product AB exists (n columns in A, n rows in B), but the matrix product BA does not (p columns in B, m rows in A, but m\neq p). So I is not true.

We know AB exists, and with m rows in A and p columns in B, we expect AB to have m rows and p columns, so AB has dimensions m\times p. So II is true.

With dimensions r\times c, a matrix would contain rc elements. m,n,p are distinct, so mp\neq n^2. So III is not true.

3 0
3 years ago
Read 2 more answers
What is 7x-2= <br><img src="https://tex.z-dn.net/?f=7x%20-%202%20%3D%2011x%20-%2034" id="TexFormula1" title="7x - 2 = 11x - 34"
Rufina [12.5K]
7x-2=11x-34\ \ \ |+2\\\\7x=11x-32\ \ \ |-11x\\\\-4x=-32\ \ \ \ |:(-4)\\\\x=8
3 0
3 years ago
Find the exact values of x and r
NemiM [27]

Answer:

Below

Step-by-step explanation:

You can use sine law to solve this : sina / A = sinb / B

We will first find side x

We know that since this is a special triangle that side will = 28, but we can prove this mathematically :

sin(45) / 28 = sin(45) / x

= 28 sin(45) / sin(45)

x = 28

Now to find side r just use Pythagorean theorem a^2 + b^2 = c^2 :

c^2 = 28^2 + 28^2

      = 1568

Square root this number

r = 39.597

The just round to however your teacher wants

If you didn't already know about special triangles, an isosceles right triangle like this one has a ratio which is the two legs will equal each other, while the hypotenuse is √2a . You could have also used this to solve.

Hope this helps! Best of luck.  

3 0
3 years ago
<img src="https://tex.z-dn.net/?f=8m2%2B30m%2B7." id="TexFormula1" title="8m2+30m+7." alt="8m2+30m+7." align="absmiddle" class="
Mariulka [41]

It is already simplified I'm pretty sure:

8m^2 + 30m + 7

3 0
2 years ago
16. Risa wants to order business cards. A print-
s344n2d4d5 [400]

Answer:

A - $214.40

Step-by-step explanation:

Since b is the number of boxes of cards and n is the number of ink colors, and we're given the number of boxes of cards, and number of ink colors, we plug in:

4= b

and

3 = n

into the given equation to solve for C.

Using the order of operations we start inside our parentheses and work from there:

C= $25.60*4 + $14.00*4(3 - 1)

C= $25.60*4 + $14.00*4(2)

C= $102.40 + $112

C= $214.40

5 0
2 years ago
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