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3 years ago

494 divided by 14 is remainde

Mathematics

1 answer:

True [87]3 years ago

3 0

Answer:

494 divided by 14 = 35 with a remainder of 4.

Step-by-step explanation:

The remainder is the integer "left over" after dividing one integer by another to produce an integer quotient (integer division).

To calculate remainder, work the division in your calculator as normal. Once you have the answer in decimal form, subtract the whole number, then multiply the decimal value that's left by the divisor of your original problem. The result is your remainder.

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Find the exact values of the following,giving your answers as fractions

Vsevolod [243]

Answer:

(a) $3^{-2}=\frac{1}{9}$

(b) $4^{-3}=\frac{1}{64}$

Step-by-step explanation:

To find the exact value in fractions of the followings:

Exponents also called powers its a way of expressing a number multiplied by itself by a certain number of times.

Using $a^{-m}= \frac{1}{a^m}$ .......[1]

(a)

Fraction represents a part of a whole or more generally, any number of equal parts.

$3^{-2}$ = $\frac{1}{3^2}=\frac{1}{3\times 3}=\frac{1}{9}$ [ Using [1]]

(b)

$4^{-3}$ = $\frac{1}{4^3} =\frac{1}{4\times 4\times 4}=\frac{1}{64}$ [ Using [1]]

(c)

$2^{-6}$ = $\frac{1}{2^6} =\frac{1}{2\times 2\times 2\times 2\times 2\times 2}=\frac{1}{64}$ [ Using [1]]

8 0

3 years ago

Use the initial term and the recursive formula to find an explicit formula for the sequence an. Write your answer in simplest fo

Ipatiy [6.2K]

Answer:

$a_n = -11-14n$

Step-by-step explanation:

Given

$a_1 = -25$

$a_n = a_{n-1}-14$

Required

The explicit formula

First, calculate $a_2$

Set n=2; So:

$a_2 = a_{2-1}-14$

$a_2 = a_{1}-14$

Substitute -25 for $a_1$

$a_2 = -25-14$

$a_2 = -39$

Calculate the common difference (d)

$d = a_2 - a_1$

$d = -39 --25$

$d = -14$

So, the nth term is:

$a_n = a_1 + (n - 1)d$

$a_n = -25+ (n - 1)*-14$

Open bracket

$a_n = -25-14n + 14$

Collect like terms

$a_n = 14-25-14n$

$a_n = -11-14n$

4 0

3 years ago

Prove that T is one to one if and only if T carries linearly independent subsets of V onto linearly independent subsets of W.

balu736 [363]

Answer with Step-by-step explanation:

Suppose T is one-one

Let S be a linearly independent subset of V

We want to show that T(S) is linearly independent.

Suppose T(S) is linearly dependent.

Then there exist $v_1,v_2,...v_n\in S$ and some not all zero scalars $a_1,a_2,....a_n$ such that

$a_1T(v_1)+a_2T(v_2)+a_3T(v_3)+...+a_nT(v_n)=0$

T is linear therefore,

$T(a_1v_1+a_2v_2+..+a_nv_n)=0$

T is one-one therefore

N(T)=0

$a_v_1+....+a_nv_n=0$

S is linearly independent therefore,

$a_1=a_2=...a_n=0$

It is contradiction.Hence, T(S) is linearly independent.

Conversely, Suppose that T carries linearly independent subset of V onto linearly independent subsets of W.

Assume that T(x)=0 if the set x is linearly independent

Then, by assumption we conclude that {0} is linearly independent but {0} is linearly dependent.

It is contradiction .Hence, the set {x} is linearly dependent which implies that x=0

It means N(T)={0}.Therefore, T is one- one

4 0

3 years ago

Find, correct to four decimal places, the length of the curve of intersection of the cylinder 16x2 + y2 = 16 and the plane x + y

Yuri [45]

Let the curve C be the intersection of the cylinder

$16x^2+y^2=16$

and the plane

$x+y+z=1$

The projection of C on to the x-y plane is the ellipse

$16x^2+y^2=16$

To see clearly that this is an ellipse, le us divide through by 16, to get

$\frac{x^2}{1}+ \frac{y^2}{16}=1$

$\frac{x^2}{1^2}+ \frac{y^2}{4^2}=1$ ,

We can write the following parametric equations,

$x=cos(t), y=4sin(t)$

for

$0\le t \le 2\pi$

Since C lies on the plane,

$x+y+z=1$

it must satisfy its equation.

Let us make z the subject first,

$z=1-x-y$

This implies that,

$z=1-sin(t)-4cos(t)$

We can now write the vector equation of C, to obtain,

$r(t)=(cos(t),4sin(t),1-cos(t)-4sin(t))$

The length of the curve of the intersection of the cylinder and the plane is now given by,

$\int\limits^{2\pi}_0 {|r'(t)|} \, dt$

But

$r'(t)=(-sin(t),4cos(t),sin(t)-4cos(t))$

$|r'(t)|=\sqrt{(-sin(t))^2+(4cos(t))^2+(sin(t)-4cos(t))}$

$\int\limits^{2\pi}_0 {\sqrt{2sin^2(t)+32cos(t)-8sin(t)cos(t)} }\, dt=24.08778184$

Therefore the length of the curve of the intersection intersection of the cylinder and the plane is 24.0878 units correct to four decimal places.

6 0

4 years ago

Multiply (x +8)(x - 2) <br>i need awnsers asap

frozen [14]

Answer:

$x^{2}$ +6x-16

Step-by-step explanation:

(x+8)(x+−2)

=(x)(x)+(x)(−2)+(8)(x)+(8)(−2)

=x^2−2x+8x−16

=x^2+6x−16

4 0

3 years ago