Q.6. The equation of the ellipse whose centre is at the origin and the x-axis, the major axis, which passes
through the points (-3, 1) and (2,-2) is
(A) 5x2 + 3y =32 (B) 3r? + 5y = 32 (C) 5x° - 3y2 = 32 (D) 3x* + 5y? + 32 = 0​

Answer:  Angle 3 and Angle 9

Step-by-step explanation:

Answer:

3 9

Step-by-step explanation:

Angles such that their terminal side passes through the origin and the point indicated on the circle are;

(3/4)·pi radian and (-5/4)·pi radians

An angle is the amount of rotation between two lines that intersect, which is measured in radians or degrees, indicated in the region close to the point of intersection of the lines.

The terminal side of an angle in standard position is the side indicating the degree of rotation from the initial side which is ion the positive x-axis.

The angular rotation to a point on a unit circle, such that the terminal side of the angle passes through the origin of the rectangular coordiinate, can be described by 2 angles, obtained by turning clockwise and anticlockwise.

The possible circle in a rectangular coordinate obtained from a similar question on the internet, created with MS Word is attached.

The rotation of the terminal side of a angle in standard position such that it coincides with the point is a rotation of 90° + 45°, anticlockwise from the initial side

90° + 45° = 135°

2·π radians = 360°

The angle of rotation of the terminal side clockwise from the initial side to the point is; -180° - 45° = -225°

The two angles terminal sides that passes through the point are therefore;

3·π/4 radians and -5·π/4 radians

Learn more about the unit circle here: https://brainly.com/question/28522971

#SPJ1

Answer:

-32 = 3x - 4y

Step-by-step explanation:

Let's first eliminate the fraactional coefficient by multiplying both sides by 4:

4y - 8 = 3x + 24

Next, combine the constants:  4y = 3x + 32

Finally, write this result in the form Ax + By = C:

-32 = 3x - 4y

In Q1, a 4-node quadrilateral isoparametric element is considered, and various calculations are performed. The Jacobian matrix is determined, followed by the computation of the stiffness matrix using both full Gauss integration scheme and reduced Gauss integration scheme. The differences between a rectangular element and the given element are discussed, focusing on where these differences arise. In addition, the stiffness matrix computed using full Gauss integration is compared to the exact integration computed using MATLAB's int command.

In Q2, the stiffness matrix of an 8-node quadrilateral isoparametric element is calculated using both full and reduced integration schemes. The same coordinates and material data from Q1 are used.

a) The Jacobian matrix is computed by calculating the derivatives of the shape functions with respect to the local coordinates.

b) The stiffness matrix using full Gauss integration scheme is obtained by integrating the product of the element's constitutive matrix and the derivative of shape functions over the element domain.

c) The stiffness matrix using reduced Gauss integration scheme is computed by evaluating the integrals at a reduced number of integration points compared to the full Gauss integration.

The differences between a rectangular element and the given element arise due to the variations in shape and location of the element nodes. These differences affect the computation of the Jacobian matrix, shape functions, and integration points, ultimately impacting the stiffness matrix.

In Q2, the same process is repeated for an 8-node quadrilateral isoparametric element, considering both full and reduced integration schemes.

The resulting stiffness matrices are compared to assess the accuracy of the numerical integration (full Gauss) compared to exact integration (MATLAB's int command). Any discrepancies between the two can provide insights into the effectiveness of the numerical integration method used.

To learn more about Gauss integration visit:

brainly.com/question/31157069

#SPJ11

On a 30-years mortgage, the monthly payment is $686.39, total cost of mortgage is $100,000 and total interest paid is $122,100.4.

By using formula, M =  [\(\frac{P [i(1+i)^{n} ]}{[(1+i)^{n-1} ] }\)

Where, M is the monthly payment

P is the principal amount

i is the interest rate

n is the number of payments

As per question,

1) Months in 30 years (n) =30x12= 360

i = 5.2%

P = $125,000

By using the formula mentioned above,

monthly payment = $686.39

2) total cost of mortgage = home price - down payment

= 125,000 - 25000

= $100,000

3) total interest paid = (M x n) - P

= (686.39 x 360) - 125,000

= $122,100.4

If you don't repay the loaned money for the purchase or refinancing of a home, the lender has the right to seize your property under the terms of a mortgage, which is a contract between you and the lender. The standard four components of a mortgage payment are principal, interest, taxes, and insurance. The primary component is the sum that is subtracted from your outstanding loan balance.

To learn more about mortgage: https://brainly.com/question/23634190

#SPJ4

Answer:

The diameter of a sphere is twice its radius. Therefore, if the diameter of the sphere is 36, the radius of the sphere is 18 (half of 36).

The volume of a sphere is given by the formula V = (4/3)πr^3, where π is approximately 3.14159 and r is the radius of the sphere.

Substituting the value of the radius, we get:

V = (4/3) × π × 18^3

= (4/3) × π × 5832

≈ 9733.78 cubic units

Therefore, the volume of the sphere with a diameter of 36 is approximately 9733.78 cubic units.

(please could you kindly mark my answer as brainliest)

A child weighing 19 pounds should receive approximately 432.7 milligrams of cough medicine in one day, assuming a dosage of 5.0 milligrams of medicine per kilogram of body weight.

Step 1: Convert the weight from pounds to kilograms.

To convert pounds to kilograms, we multiply the weight in pounds by the conversion factor 0.4536.

19 pounds × 0.4536 = 8.6184 kilograms

Step 2: Calculate the amount of cough medicine based on the dosage.

Multiply the weight in kilograms by the dosage per kilogram.

8.6184 kilograms × 5.0 milligrams/kg = 43.092 milligrams

Therefore, a child weighing 19 pounds should receive approximately 43.092 milligrams of cough medicine in one day, using the given dosage of 5.0 milligrams of medicine per kilogram of body weight.

Learn more about kilograms here:

https://brainly.com/question/29761698

#SPJ11

Answer:

The linear equation for tip barista gets in a day is f(n)=0.5n+20.

Step-by-step explanation:

It is given, at a noon a barista notice that she has $20 in tip jar, if she makes an average of $0.50 from each customer,

It is required to find how much will she have in her tip jar if she serves n more customers during her shift. m=0.5. Bases on this write the equation for n more customers.

Step 1 of 1

It is given, at a noon a barista notice that she has $20 in tip jar, if she makes an average of $0.50 from each customer,

To solve this let f(n) is the total tip barista has in her tip jar after a day.

When n is equal to 0 , that barista has $20,

Then if barista make 0.5 from each customer, then for the linear function m=0.5,

Bases on this write the equation for n more customers,

\($$f(n)=0.5 n+20 .$$\)

Answer:

106,782,720

Step-by-step explanation:

84,480 pennies

There are 84,480 pennies in a mile. Yes, that is correct – 84,480 pennies! An interesting fact to know: 16 pennies laid side by side constitute 12 inches in length, or one foot, and since 5,280 feet equals one mile, that gives us 84,480 pennies in a mile.

84,480x1264=106,782,720

hope this helps!

Brainliest pls

Pls fully rate

Have a great day!

Answer: 4 exercises

Step-by-step explanation:

If we completed 87.5% of the math exercises before dinner, then we have completed 0.875 × total number of exercises.

Let "\(x\)" be the total number of exercises.

\(0.875x = 28\)

Solving for \(x\), we get:

\(\boxed{\begin{minipage}{4 cm}\text{\LARGE 0.875x = 28 } \\\\\\ \large $\Rightarrow$ $\frac{0.875x}{0.875}$ = $\frac{28}{0.875}$\\\\$\Rightarrow$x = 32\end{minipage}}\)

Therefore, the total number of exercises is 32.

We completed 28 exercises before dinner, so we have:  32 - 28 = 4 exercises left to do after dinner.

________________________________________________________

Answer:

Correct answer is D. ASA

Step-by-step explanation:

Let us first define ASA congruence rule:

2 triangles are called congruent according to ASA congruence rule if 2 angles of the triangle and the corresponding side between these two angles are equal to each other.

In the question figure, we can figure out following conclusions from Triangles \(\triangle SRT\text{ and }\triangle WXY\) respectively:

As per the definition of option d) ASA congruence, the triangles are congruent.

Answer:

Step-by-step explanation:

Answer:

1 11/24

Step-by-step explanation:

1 5/6- 3/8

= (1-0) + ( 5/6 - 3/8)

= 1 + 5x4/6x4 - 3x3/8x3

= 1 + 20/24 - 9/24

= 1 + 20 - 9/24

= 1 + 11/24

= 1 11/24

\(\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}\)

Given expression ,

\( \frac{1}{8} . \frac{1}{8} .y.y.y \\ \)

this can also be written as ,

\( \frac{1}{8} \times \frac{1}{8} \times y \times y \times y \\ \\ \longrightarrow \: \frac{y {}^{3} }{64} \)

hope helpful ~

Answer:

I=Prt

I/Pr=Prt/Pr

t=I/Pr

Answer:

90 times 3 is 270

270- 71 ( the average grade you have now)= 199

the 2 more report card average grade has to add up to 199 for you to get a 90.

Given function:\(f(x) = 3x³ - 3x² - 11x - 1\) We have to find the value of x for which f(x) has a tangent line of slope -3.Tangent to a curve at point P(x₁,y₁) is given by the equation,\(y - y₁ = m(x - x₁)\) where m is the slope of the tangent line.the value of x for which f(x) has a tangent line of slope -3 are\(x = 1 and x = -8/3.\)

So, we have to find the value of x for which the slope\(m = -3, i.e.,f '(x) = 9x² - 6x - 11 = -3\) Let's solve for x using the quadratic formula.\(9x² - 6x - 8 = 0\) Dividing throughout by

\(3,3x² - 2x - 8/3 = 0\)

Using the quadratic formula,\(x = [-(-2) ± √((-2)² - 4(3)(-8/3))]/(2)(3)x = [2 ± 10/3]/6x = 1 or -8/3\)

\(For x = 1,f(x) = 3(1)³ - 3(1)² - 11(1) - 1 = -12For x = -8/3,f(x) = 3(-8/3)³ - 3(-8/3)² - 11(-8/3) - 1 = -14.81\)

To know more about tangent visit:

https://brainly.com/question/27021216

#SPJ11

Answer:

principal (p)=$1895

time (t)=4years

rate(r)=7.9%

Step-by-step explanation:

Answer:

$598.82

yw:) jdbviusdbwsbndj

The quotient is 154. The remainder is 3.

What is a divisor?

In division, we multiply one number by any other number to produce a second number. Therefore, the dividend here refers to the number that is being divided. The divisor is the number that divides a given number. The quotient is the sum that we arrive at as a result. The remainder is the number that the divisor leaves after partially dividing the original number.

Given that 927 ÷ 6.

The dividend is 6 and the divisor is 927.

6) 927(100+50+4

   600

______

    327

    300

______

        27

        24

_______

            3

The remainder is 3. The quotient is 154.

To learn more about dividend, click on the below link:

https://brainly.com/question/27117855

#SPJ1

To divide two fractions, simply cross-multiply as following:

Answer:

y = 2x - 4

Step-by-step explanation:

To solve this problem, we must first calculate the slope of the line AB using the formula:

\(\boxed{m = \frac{y_2 - y_1}{x_2 - x_1}}\)

where:

m ⇒ slope of the line

(x₁, y₁), (x₂, y₂) ⇒ coordinates of two points on the line

Therefore, for line AB with points A = (2, 5) and B = (4, 4) :

\(m_{AB} = \frac{5 - 4}{2 - 4}\)

⇒ \(m_{AB} = \frac{1}{-2}\)

⇒ \(m_{AB} = -\frac{1}{2}\)

Next, we have to calculate the slope of the line BC.

We know that the product of the slopes of two perpendicular lines is -1.

Therefore:

\(m_{BC} \times m_{AB} = -1\)      [Since BC and AB are at right angles to each other]

⇒ \(m_{BC} \times -\frac{1}{2} = -1\)

⇒ \(m_{BC} = -1 \div -\frac{1}{2}\)      [Dividing both sides of the equation by -1/2]

⇒ \(m_{BC} = \bf 2\)

Next, we have to use the following formula to find the equation of line BC:

\(\boxed{y - y_1 = m(x - x_1)}\)

where (x₁, y₁) are the coordinates of a point on the line.

Point B = (4, 4) is on line BC, and its slope is 2. Therefore:

\(y - 4 =2 (x - 4)\)

⇒ \(y - 4 = 2x - 8\)         [Distributing 2 into the brackets]

⇒ \(y = 2x-4\)

Therefore, the equation of line BC is y = 2x - 4.

On solving the provided question we can say that - the answer of the quadratic equation is S(x) = ( 2 ) + ( 1 ) =3  \(P(x) = ( 2 ) * ( 1 ) =2\)

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. A quadratic equation is referred to as an equation of degree two in mathematics. As a result, this function's highest exponent is 2. Y = ax2 + bx + c, where a, b, and c are integers and a must be 0, gives the typical form of a square. These are all examples of quadratic equations: y = x2 + x3 + x + 1.

S(x) = (  ) + (  ) =3

\(P(x) = ( ) * ( ) =2\)

S(x) = ( 2 ) + ( 1 ) =3

\(P(x) = ( 2 ) * ( 1 ) =2\)

To know more about quadratic equation visit:
https://brainly.com/question/17177510

#SPJ4

Answer:

y(5y +2) -3a²

Step-by-step explanation:

that is the solution above

There are 168 positive integers that are there less than 1000 that are relatively prime to 100 with no common factor.

Prime numbers are numbers that have only two factors, that are, 1 and the number itself, and any whole number greater than 1 that is divisible only by 1 and itself, is defined as a prime number.

There are some properties of prime numbers:

To find the prime number, first, we have to find the factors of the given number. If the number of factors is more than two, then the number is not a prime number otherwise it is a prime number.

To know more about Prime numbers:

https://brainly.com/question/881160

#SPJ4

The combination of meters (m) and seconds (s) is used to measure speed or distance.

Here are the completed statements using the appropriate metric units: My friend is 2 METERS tall. My water bottle has a volume of 1.5 LITERS. My thumb is 2 CENTIMETERS wide. I bought 3 KILOGRAMS of apples at the store. A penny weighs about 3 GRAMS. I can run 60 METERS in 10 seconds. Explanation: Meters (m) is the metric unit used to measure length or height. Liters (L) is the metric unit used to measure volume or capacity. Centimeters (cm) is the metric unit used to measure small distances or widths.

Kilograms (kg) is the metric unit used to measure mass or weight. Grams (g) is a smaller metric unit used to measure mass or weight. The combination of meters (m) and seconds (s) is used to measure speed or distance. These metric units provide standardized measurements that are widely used across the world, making it easier to communicate and compare quantities.

To learn more about distance click here: brainly.com/question/15256256

#SPJ11

Answer

Sum of the first 13 terms = 8191

Explanation

The sum of terms in a geometric term is given as

where

a = first term = 1

r = common ratio = ratio of consecutive terms = (Second term)/(First term) = (2/1) = 2

n = number of terms = 13

Hope this Helps!!!

A function f such that f '(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f is f(x) = 3x^4/4 + 729/4.

In the given question, we have to find a function f such that f'(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f.

The given function is f'(x) = 3x^3.

No integrating on both side,

f(x) = \(\int3x^3dx\) + C

f(x) = 3x^4/4 + C

As given, the line 81x + y = 0 is tangent to the graph of f.

So, slope at point of tangent; f'(x) = -81

So, 3x^3 = -81

Divide by 3 on both side, we get

x^3 = -27

Taking cube root on both side, we get

x = -3

So putting the value of x in 81x + y = 0, we get

y = 243

Thus, f(x) passes through (-3, 243).

So, 243 = 3/4(81) + C

Multiply by 4 on both side, we get

972 = 243 + 4C

Subtract 243 on both side, we get

4C = 729

Divide by 4 on both side, we get

C = 729/4

So, f(x) = 3x^4/4 + 729/4

To learn more about function link is here

brainly.com/question/21145944

#SPJ4

Answer:

It would be 2/5

Step-by-step explanation:

It would originally be 8/20 but you would simplify it to 2/5.

Answer:

y = -4

Step-by-step explanation:

y = 6 is line that is parallel to x-axis

So, the required is also parallel to x -axis

The equation of line parallel to x-axis , y = c, where c is y-intercept

y = - 4