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3 years ago

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A,B, and C are polynomials, where a = n, b=2n+6, and c=n^2-1. What id AB - C in simplest form

1 answer:

Marina CMI [18]3 years ago

9 0

N^2 + 6n + 1
In simplest form

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How much does a glass cube with a side of 5-cm weigh if 1cm3 of glass weighs 2 2/5 grams?

PtichkaEL [24]

The weight of galss cube with side 5 cm is 300 grams

<em><u>Solution:</u></em>

A glass cube is of side length 5 cm

Let us first find the volume of glass cube

<em><u>The volume of cube is given as:</u></em>

$volume = (side)^3\\\\volume =5^3 = 125$

Thus volume of cube is 125 $cm^3$

Given that,

$1 cm^3 = 2\frac{2}{5} \text{ grams }\\\\1 cm^3 =\frac{12}{5} \text{ grams}$

So, weight of 125 cubic centimeter of glass cube is found by multiplying weight of 1 cubic centimeter of glass cube by 125

$\text{ Weight of 125 } cm^3 \text{ cube } = \text{ Weight of 1 } cm^3 \text{ cube } \times 125$

$\text{ Weight of 125 } cm^3 \text{ cube } = \frac{12}{5} \times 125 = 25 \times 12 = 300$

Thus weight of galss cube with side 5 cm is 300 grams

3 0

3 years ago

Read 2 more answers

Determine if the ordered pairs represent a function.<br> {(2,5),(4,7), (2,9), (6,10)}

zalisa [80]

Answer:

No it does not represent a function

Step-by-step explanation:

It fails the vertical line test..

5 0

2 years ago

Use the identity below to complete the tasks:

Gennadij [26K]

Answer:

a3+b3=(a+b)(a2-ab+b2)

4 0

3 years ago

A is an m×n matrix.Check the true statements below:A. The kernel of a linear transformation is a vector space.B. If the equation

Bess [88]

Answer:

Results are (1) True. (2) False. (3) False. (4) True. (5) True. (6) True.

Step-by-step explanation:

Given A is an $m\times n$ matrix. Let $T :U\to V$ be the corresponding linear transformationover the field F and $\theta$ be identity vector in V. Now if $x\in Ker( T)\implies T(x)=\theta$ .

(1) The kernel of a linear transformation is a vector space : True.

Let $x,y\in Ker( T)$ , then,

$T(x+y)=T(x)+T(y)=\theta+\theta=\theta\impies x+y\in Ker( T)$

hence the kernel is closed under addition.

Let $\lambda\in F, x\in Ker( T)$ , then

$T(\lambda x)=\lambda T(x)=\lambda\times \theta=\theta$

$\lambda x\in Ker(T)$ and thus Ket(T) is closed under multiplication

Finally, fore all vectors $u\in U$ ,

$T(\theta)=T(\theta+(-\theta))=T(\theta)+T(-\theta)=T(\theta)-T(\theta)=\theta$

$\implies \theta\in Ker(T)$

Thus Ker(T) is a subspace.

(2) If the equation Ax=b is consistent, then Col(A) is $\mathbb R^m$ : False

if the equation Ax=b is consistent, then Col(A) must be consistent for all b.

(3) The null space of an mxn matrix is in $\mathbb R^m$

: False

The null space that is dimension of solution space of an m x n matrix is always in $\mathbb R^n$ .

(4) The column space of A is the range of the mapping $x\to Ax$

: True.

(5) Col(A) is the set of all vectors that can be written as Ax for some x. : True.

Here Ax will give a linear combination of column of A as a weights of x.

(6) The null space of A is the solution set of the equation Ax=0.

: True

5 0

3 years ago

Which is closest to the volume of a cylinder with a height of 11 inches and

Veseljchak [2.6K]

Answer:

The closest to the volume of cylinder is <u>63 in.³</u>.

Step-by-step explanation:

Given:

Cylinder with a height of 11 inches and a circumference of 8 1/2 inches.

Now, to find the volume.

As circumference is given we get the radius by putting formula:

Circumference = 8 1/2 inches = 17/2 inches.

Let the radius be $r.$

$Circumference=2\pi r$

<em>Taking the value of π = 3.14.</em>

$\frac{17}{2}=2\times 3.14\times r$

$8.5=6.28\times r$

<em>Dividing both sides by 6.28 we get:</em>

$1.35=r$

So, radius = 1.35 inches.

Height = 11 inches.

Now, putting the formula to get the volume:

$Volume=\pi r^2h$

$Volume=3.14\times 1.35^2\times 11$

$Volume=3.14\times 1.8225\times 11$

$Volume=3.14\times 20.0475$

$Volume=62.949\ inches^3$

<u><em>Hence, the volume of cylinder = 63 inches³ (approximately).</em></u>

Therefore, the closest to the volume of cylinder is 63 in.³.

4 0

3 years ago