MATHEMATICS COLLEGE

Divide. Give the Divide. Give the quotient and remainder.254 divided 8

Quotient:

Remainder:
Divide. Give the Divide. Give the quotient and remainder. 254 - 1

Answers

Answer 1
Answer:

Step-by-step explanation:

254 = 8 * 30 + 8 * 1 + 6

= 8(30 + 1) + 6

= 8 * 31 + 6.

Hence the quotient is 31 and the remainder is 6.
Answer 2
Answer:

Answer:

254/8=31.75

Step-by-step explanation:

The remainder of 254 divided by 8 is 6

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Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.y = e^x^2 ln 4x^3

Answers

(d(lnx))/(dx)=(1)/(x)

Answer:

(dy)/(dx)=e^(x^2)((2x^2ln(4x^3)+3)/(x))

Step-by-step explanation:

We are given that a function

y=e^(x^2)ln(4x^3)

We have to differentiate w.r.t x

(dy)/(dx)=e^(x^2)* 2xln(4x^3)+e^(x^2)* (1)/(4x^3)* 12x^2

By using formula

(d(lnx))/(dx)=(1)/(x)

(d(e^x))/(dx)=e^x

(dy)/(dx)=e^(x^2)(2xln(4x^3)+(3)/(x))

(dy)/(dx)=e^(x^2)((2x^2ln(4x^3)+3)/(x))

Hence, the derivative of function

(dy)/(dx)=e^(x^2)((2x^2ln(4x^3)+3)/(x))

I keep getting the same answer and I know I am using the right formula. don't know where I am going wrong.

Answers

From March 10 to May 12 = 63 days.

63 days / 365 days = 0.1726 years.


Simple interest formula = Interest = Principal X interest rate x time


Interest = 15305.50 - 15000 = 305.50

Principal = 15000

Time = 0.1726 years


Replace the values into the formula:

305.50 = 15000 x Interest rate x 0.1726

Simplify:

305.50 = 2589.041 x interest rate

Solve for interest rate:

interest rate = 305.50 / 2589.041

interest rate = 0.11799 x 100

Rate = 11.80%

Determine whether [1 0 3 , −3 1 −7 , 5 −1 13] is a basis for set of real numbers R cubed 3. If the set is not a​ basis, determine whether the set is linearly independent and whether the set spans set of real numbers R cubed 3.

Answers

Answer:

The set is not a basis. It is not linearly independent and doesn't span the given vector space

Step-by-step explanation:

Let u = (1,0,3), v = (-3,1,-7) and w=(5,-1,13). We want to check if the set {u,v,w} is a basis for \mathbb{R}^3. By definition, a basis is a linearly independent set that spans the vector space. So, if it is a basis, it automatically is linearly independent and spans the whole space. Since we have 3 vectors in

A=\left[\begin{matrix}1 & -3 & 5 \n 0 & 1 & -1 \n 3 & -7 & 13 \end{matrix}\right]

which is the matrix whose columns are u,v,w. To check that the set {u,v,w} is linearly independent,it is equivalent to check that the row-echelon form of A has 3 pivots.

The step by step calculation of the row-echelon form of A is ommited. However, the row-echelon form of A is

A=\left[\begin{matrix}1 & 0 & 2 \n 0 & 1 & -1 \n 0 & 0 & 0 \end{matrix}\right]

In this case, we have only 2 pivots on the first and second column. This means that the columns 1,2 of matrix A are linearly independent. Hence, the set {u,v,w} is not linearly independent, and thus, it can't be a basis for \mathbb{R}^3. Since it is not a basis, it can't span the space.

The coordinates for the vertices of a polygon are (1, 4), (6, 4), and (6,1). What type of polygon is formed by these points?A) square
B) quadrilateral
C) right triangle
D) scalene triangle

Answers

C) right triangle; there are 3 coordinates so it is a triangle, and when you graph it there is a right angle
it is a right triangle

Evaluate the expression 2x-4y if x=3 and y=(1/2)

Answers

Answer:

Step-by-step explanation:

2(3) - 4(1/2)

6 - 2 = 4

Find the number of positive integers not exceeding 108 that are not divisible by 5 or by 7.

Answers

Answer:

75

Step-by-step explanation:

The set of positive integer not exceeding 108 divisible by 5 is

D_5=\{5 \quad 10 \quad 15 \quad 20 \quad 25 \quad 30\quad 35 \quad 40 \quad 45 \quad 50 \quad 55 \quad 60 \quad 65\n \quad 70 \quad 75 \quad 80 \quad 85 \quad 90 \quad 95 \quad100 \quad 105\}

and the set of positive integer not exceeding 108 divisible by 7 is

D_7=\{7 \quad 14 \quad 21 \quad 28 \quad 35 \quad 42 \quad 49 \quad 56 \quad 63 \quad 70 \quad 77 \quad 84 \quad 91 \quad 98 \quad 105\}

Moreover, there are exactly three positive numbers not exceedng 108 that are divisible by both 5 and 7, i.e,

D_5 \cap D_7=\{37 \quad 70 \quad 105\}.

Also note that the size of D_5 is \#D_5=21 , the size of D_7 is \#D_5=15 and \# D_7 \cap D_5 = 3.

On the other hand, If a positive integer not exceding 108 is not divisible by 5 or 7, then it doesn't belong to any of this sets. Therefore, the number of positive interges not exceding 108 that are not divisible by 5 or 7 is equal to

108 -(\#D_7 + \# D_5 - \# D_7 \cap D_5)=108 -(21+15-3)=75
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