Please answer this Calculus webwork question about differential equations:

Answer:

There were 30 8-points questions and 39 2-points question.

Process :-

Let the number of 8 points questions be x and 2 points questions be y.

Now,

8x+2y =318

x+y = 69

(according to the question)

x+y=69

x=69-y

plug in the value of x in the next equation 8x+2y=318,

8x+2y=318

or, 8(69-y)+2y=318

or, 552-8y+2y=318

or, -6y=318-552

or, -6y = -234

so, y = -234/-6

so, y = 39

Again,

x+y=69

or, x+y = 69

or, x+39 = 69

so, x = 30

Answer:

1,0

8/15,-7/25

Step-by-step explanation:

3x - 5y = 3

5y = 3x-3

y = (3x-3)/5

y= 3x² -4x +1

or, (3x-3)/5 = 3x²-4x +1

or, 3x-3 = 15x²-20x+5

or, 15x² - 23x +8 =0

or, 15x² - (15+8)x +8 =0

or, 15x² - 15x -8x +8 = 0

or, 15x (x - 1) -8(x-1) =0

or, (x-1)(15x-8)=0

Either,

x-1=0

x = 1

when x=1,

y= 0

or,

15x-8=0

x=8/15

when x= 8/15,

y= -7/25

Answer:

I guess that the geometric sequence is:

An = 2*5^(n - 2)

we usually have that that a geometric sequence is something like:

A*r^n.

so i will write the first two terms of our sequence separated, and i will calculate the summation of the first seven terms after n = 2.

A0 = 2*5^(-2) = 2/25

A1 = 2*5^-1 = 2/5

Then, the sum for a geometric sequence is:

SN = A(1 - r^N)/(1 - r)

in this case, A = 2 and r = 5, and i will use N = 7 for the sequence 2*5^n

S7 = 2*(1 - 5^7)/(1 - 5) = 39,062.

now we add the first terms that we obtained before and get:

S9 = 2/25 + 2/5 +  39,062 = 39,062.48

Answer:

The percent is 75%

Step-by-step explanation:

The value of n in the right triangle given is: 15.

Area of a triangle= 1/2 * width * height

We are given the following parameters for the right triangle:

Width = n + 3

Height = n + 3 - 8 = n - 5

Area of the triangle = 90 cm²

Substitute the values:

90 = 1/2 * (n - 5)(n + 3)

180 = n² - 2n - 15

n² - 2n - 15 - 180 = 0

n² - 2n - 195 = 0

Factorize:

(n - 15)(n + 13) = 0

n = 15 or n = -13

n = 15

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Answer:

Surface area of triangular pyramid = 48 inch²

Step-by-step explanation:

Given:

Base length of triangle = 6 inches

Height of triangle = 4 inches

Find:

Surface area of triangular pyramid

Computation:

Surface area of triangular pyramid = 4 x [Surface area of triangle]

Surface area of triangular pyramid = 4 x [(1/2)(b)(h)

Surface area of triangular pyramid = 4 x [(1/2)(6)(4)

Surface area of triangular pyramid = 4 x [(1/2)(24)]

Surface area of triangular pyramid = 4 x 12

Surface area of triangular pyramid = 48 inch²

Answer:

A. |12| > √80

B. √53 > |-5.3|

Step-by-step explanation:

A.  |12| > √80

The absolute value of 12 is 12, and the square root of 80 is 8.9442. This means the number sentence is true because it states that the absolute value of 12 is greater than the square root of 8.

B. √53 > |-5.3|

The square root of 53 is 7.2801 and the absolute value of -5.3 is 5.3. This means the number sentence is true because is states that the square root of 53 is greater than the absolute value of -5.3

have a nice day!

For the expression \(x^64 + ax^b + 25\) to be a perfect square for all integer values of x, b must be 64, and a must be a perfect square, written as a = \(y^2.\)

To determine the values of a and b such that the expression\(x^64 + ax^b\) + 25 is a perfect square for all integer values of x, we need to analyze the properties of perfect squares.

A perfect square is an expression that can be written as the square of another expression. In this case, we want the given expression to be in the form of\((x^n)^2,\) where n is an even integer.

Let's examine the given expression: \(x^64 + ax^b\) + 25

For it to be a perfect square, the quadratic term \(ax^b\)must have the same exponent as the leading term\(x^6^4.\) This means b must be equal to 64.

So we have:\(x^64 + ax^64 + 25\)

Now, we can rewrite this as:\((x^32)^2 + 2(x^32) (\sqrt{a}) + (\sqrt{25})^2\)

By comparing this with the standard form of a perfect square, (\(x^n +\sqrt{k} )^2\), we can deduce that √a must be equal to x^32 and \(\sqrt{25}\) must be equal to \(\sqrt{k.}\)

Therefore, we have: \(\sqrt{a} = x^3^2\)and\(\sqrt{25} = \sqrt{k}\)

From the second equation, we know that k = 25.

Now, substituting the value of k back into the first equation, we have: \(\sqrt{a} = x^3^2\)

To satisfy this equation for all integer values of x, a must be a perfect square. Therefore, we can express a as a =\(y^2\), where y is an integer.

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The ordered pairs of the equation y = 3^x are (0,1), (1,3) and (2,9)

The equation is given as:

y = 3^x

Let x = 0, 1 and 2

y = 3^0 = 1

y = 3^1 = 3

y = 3^2 = 9

So, we have the following ordered pairs (0,1), (1,3) and (2,9)

Hence, the ordered pairs of the equation y = 3^x are (0,1), (1,3) and (2,9)

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The company should produce 235 units of Metakeb, 96 units of Mewesson, and 17 units of Metekem per month to use up all the available resources.

What is the Gaussian method?

The Gaussian method, also known as Gaussian elimination or row reduction, is a technique for solving systems of linear equations. It involves performing a sequence of operations on the rows of a matrix to transform it into an equivalent matrix that is in row echelon form or reduced row echelon form.

To use the Gaussian method, we need to set up a system of linear equations based on the given information. Let x, y, and z be the number of units of Metakeb, Mewesson, and Metekem produced per month, respectively. Then we have:

Machining department: 1200x + 1800y + 3000z = 1050(60)

Inspection department: 2400x + 1200y = 1160(60)

Assembly department: 600x + 3000y = 830(60)

Simplifying these equations, we get:

Machining department: 20x + 30y + 50z = 3150

Inspection department: 8x + 4y = 232

Assembly department: x + 5y = 139

Now we can use the Gaussian method to solve for x, y, and z:

Step 1: Write the augmented matrix:

| 20 30 50 | 3150 |

| 8 4 0 | 232 |

| 1 5 0 | 139 |

Step 2: Use row operations to get the matrix in row echelon form:

R2 → R2 - 4/5 R3

R1 → R1 - 20R3

| 0 -2 50 | 850 |

| 0 2 -4   | -28 |

| 1 5 0     | 139 |

R2→ -1/2 R2

R1 → R1 + R2

| 0 1 -25 | 407 |

| 0 1 -2 | 14 |

| 1 5 0 | 139 |

R1→ R1 - R2

| 0 0 -23 | 393 |

| 0 1 -2 | 14 |

| 1 5 0 | 139 |

R3→ R3 - 5R2

| 0 0 -23 | 393 |

| 0 1 -2 | 14 |

| 1 0 10 | 65 |

R1→ -1/23 R1

| 0 0 1 | -17 |

| 0 1 -2 | 14 |

| 1 0 10 | 65 |

R2 → R2 + 2R3

| 0 0 1 | -17 |

| 0 1 0 | 96 |

| 1 0 10 | 65 |

R3 → R3 - 10R1

| 0 0 1 | -17 |

| 0 1 0 | 96 |

| 1 0 0 | 235 |

Step 3: Read off the solution from the row echelon form:

z = -17

y = 96

x = 235

Therefore, the company should produce 235 units of Metakeb, 96 units of Mewesson, and 17 units of Metekem per month to use up all the available resources.

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The measure of side length EF in the right triangle is 24.

The Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c²  = a² + b²

From the diagram:

Hypotenuse DE = c = 26

Leg DF = a = 10

Leg EF = b = ?

Plug in the values and solve for b:

c²  = a² + b²

26²  = 10² + b²

676  = 100 + b²

b² = 676  - 100

b² = 576

b = +√576 ( we take the positive value since we are dealing with dimensions)

b = 24

Therefore, the length EF is 24.

Option C)24 is the correct answer.

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Answer:

with multiplying and dividing ratios you will need to either dividing or multiplying each of the terms in the ratios by the same number.

Step-by-step explanation:

Examples

12:14

you would divide by 2 and you would get

6:7

hope this helps

Answer:

a) 263,158

b) $164,500

c) Ethical issues companies face when deciding to move operations: job loss for employees, poor working conditions and exploitation of workers, negative environmental impact,...

Step-by-step explanation:

a)

Total cost = (0.25 + 0.02 + 0.03 + 0.15) x + 250,000

Total revenue = 1.40x

Setting the two equations equal to each other and solving for x, we get:

(0.45)x + 250,000 = 1.40x

0.95x = 250,000

x ≈ 263,158

b)

If the company sells 270,000 candy bars at $1.40 each, the total revenue generated is:

270,000 * $1.40 = $378,000

The total cost of producing 270,000 candy bars is:

(0.25 + 0.02 + 0.03 + 0.15) * 270,000 + $250,000 = $213,500

Therefore, the company's profit is:

$378,000 - $213,500 = $164,500

c)

Ethical issues companies face when presented with the decision to move operations: job loss for employees, poor working conditions and exploitation of workers, negative environmental impact,...

Answer:

y = -5/2x

Step-by-step explanation:

y = mx + b

y = -5/2x

Answer:

Answer:

Solution given:

\((x_1,y_1)=(-4,10)\)

\((x_2,y_2)=(-6,15)\)

now

slope:\(\frac{y_2-y_1}{x_2-x_1}=\frac{15-10}{-6+4}=\frac{5}{-2}\)

Slope: -5/2

9.  The stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. The stamp duty payable on a property with a purchase price of K150,000 is K7,500.

To calculate the stamp duty payable on properties with a purchase price of K45,000 and K150,000, we need to apply the corresponding rates of stamp duty based on the given information.

Given:

Value of Property:

Up to K35,000: Stamp Duty Rate - 2%

K35,000 to K70,000: Stamp Duty Rate - 3%

K70,000 to K140,000: Stamp Duty Rate - 4%

Over K140,000: Stamp Duty Rate - 5%

9. Calculate the stamp duty payable on properties whose purchase price is K45,000:

Since the purchase price of K45,000 falls within the range of K35,000 to K70,000, the stamp duty rate applicable is 3%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K45,000 * 3%

= K45,000 * 0.03

= K1,350

Therefore, the stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. Calculate the stamp duty payable on properties whose purchase price is K150,000:

Since the purchase price of K150,000 is above K140,000, the stamp duty rate applicable is 5%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K150,000 * 5%

= K150,000 * 0.05

= K7,500

Therefore, the stamp duty payable on a property with a purchase price of K150,000 is K7,500.

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Answer:

  x = 31.2

Step-by-step explanation:

You want the solution to the proportion 12/x = 5/13.

You can eliminate the fractions by multiplying this equation by the least common denominator. That value is 13x, the product of these denominators. Multiplying by 13x, we have ...

  \(\dfrac{12}{x}\times13x=\dfrac{5}{13}\times13x\\\\\\12\cdot13=5\cdot x\qquad\text{simplified}\)

Now, the value of x is found by dividing both sides by its coefficient.

  \(\dfrac{12\cdot13}{5}=\dfrac{5x}{5}\\\\\\\dfrac{156}{5}=x\\\\\boxed{31.2=x}\)

__

Additional comment

The first step we did, multiplying by 13x, is also sometimes called "cross multiplication." The result of that step is that each numerator is multiplied by the opposite denominator.

Multiplying both sides of the equation by the same value (13x) is supported by the multiplication property of equality. The term "cross multiplication" is descriptive of the result, but is not a recognized property of equality. It is a good idea to keep the math operations you do grounded in the properties of equality.

You will notice that the steps we did were "multiply by 13x" and "divide by 5". These can be done at once by "multiply by 13x/5". Of course, that operation is done to both sides of the equation.

Any proportion can be written 4 ways:

  \(\dfrac{12}{x}=\dfrac{5}{13}\qquad\dfrac{x}{12}=\dfrac{13}{5}\qquad\dfrac{x}{13}=\dfrac{12}{5}\qquad\dfrac{13}{x}=\dfrac{5}{12}\)

These can be thought of as "upside down" and "sideways." We like the versions with the variable on top of a fraction, because the solution to that is simply multiplication by the variable's denominator.

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Answer:

1) How many bottles can you buy for $3?

Answer : 4

2) What is the cost per bottle of water?

Answer: $0.75

Step-by-step explanation:

Cost of 12 bottles = $9

we have to find cost of 1 bottle so lets divide LHS and RHS by 12

Cost of 12/12 bottles = $9/12

Cost of 1 bottle = $3/4 = $0.75

Thus,  Answer to

2) What is the cost per bottle of water?

Answer : $0.75

____________________________________

1) How many bottles can you buy for $3?

let the number of bottles that can be bought for $3 is x

cost of 1 bottle = $0.75

cost of x bottles = cost of 1 bottle*x = $0.75x

cost of x bottles is also $3

therefore,

$0.75x = $3

x = $3/$0.75 = 4

Thus, 4 bottles can be bought for $3 -----answer

Answer:

The domain for the interval of decrease is 3 ≤ x ≤ 5

The given triangle is a trigonometry identity . The value of the unknown variable 'x' is 3√2

The given triangle is a trigonometry identity with the following sides and angles

Opposite = x

Hypotenuse = 6

Angle = 45 degrees

According to the trigonometry identity

sin 45 = opposite/hypotenuse

sin 45 = x/6

x = 6sin45

x = 6(1/√2)

x = 6√2/2

x = 3√2

Hence the value of x in radical form is 3√2

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Answer:

K5.60.

Step-by-step explanation:

Answer:

A and C

Step-by-step explanation:

Since it is isosceles two sides should be equal and we already know the perimeter is 21in.

5+5+11=21in

5+8+8=21in

Answer:

A and C

Step-by-step explanation:

Since it is isosceles two sides should be equal and we already know the perimeter is 21in.

5+5+11=21in

5+8+8=21in

Note that in the prompt above, the value of x is given as: 16°

To answer the issue, we will first name all of the points supplied to us on the isosceles triangle, then identify O, and last discover the value of x. See the attached image.

As a result, an isosceles triangle has two equal sides and two equal angles. The term is derived from the Greek words iso (same) and skelos (skull) (leg). An equilateral triangle has all of its sides equal, whereas a scalene triangle has none of its sides equal.

In ΔAOB

OA =  OB = R, the radius of the circle O,

therefore, the ΔAOB is an isosceles triangle, with OA, OB as the congruent sides and AB as the base of the triangle.

Thus, ∠OAB = ∠OBA = 53°

Sum of all the angles of a triangle = 180°

∠O + ∠AOB + ∠OBA = 180°

We know ∠AOB = ∠OBA, therefore,

∠O + 2(∠AOB) = 180°

∠O + 2(53°) = 180°
∠O = 180 - 106

∠O = 74°

In ΔOBC,

BC is the tangent to the circle O, therefore,

∠OBC = 90°

Sum of all the angles of a triangle = 180°

∠O + ∠OBC + ∠OCB = 180°

74° + 90° + ∠OCB = 180°

∠OCB = 180° - 74° - 90°

∠OCB = 16°

Hence, the value of x is 16°.

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Answer:

(10, -18)

Step-by-step explanation:

midpoint formula: (sum of both x-values/2, sum of both y-values/2)

(0 + x)/2 = 5

x = 10

(4 + y)/2 = -7

y = -18

Answer:

domain : - ∞ < x < 1

Step-by-step explanation:

the function is increasing on the upward part of the curve. that is

from negative infinity to the vertex at (1, 3 )

domain : - ∞ < x < 1

Answer: 10/40 or 1/4

Step-by-step explanation:

Add up all the amount of rolls, so 10+6+4+8+6+6=40

then add the probability of rolling a 3 or 6 = 10

divide that quantity out of the whole

answer is 10/40 and simplified is 1/4

hope it helps

Answer:

A number multiplied by a variable.

Step-by-step explanation:

For example, 4 is a coefficient.

\(4x\)

The additional wire, in feet, that the factory needs in order to wrap the deliveries would be = 37.6 feet

That is option B.

The total length of wire needed in the factory to wrap up all the deliveries for the house project = 175 ft.

The lengths of wires available = 2 × 12 yrd = 24 yrd.

But 1 yard = 3 foot

24 yards = X

Make X the subject of formula;

X = 24×3 = 72 ft

The second wire available = 65.4 ft

To calculate the remaining wire first add all the available wire. That is;

= 72+65.4 = 137.4ft

Subtract fro the total wire;

= 175-137.4 = 37.4 feet.

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The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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