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Oxana [17]
2 years ago
14

Help please...........

Mathematics
1 answer:
Bumek [7]2 years ago
5 0

Answer:

it is 130 degrees

Hope this helps!! ;)

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a. Verify that the given point lies on the curve. b. Determine an equation of the line tangent to the curve at the given point.
xxMikexx [17]

Answer:

y = 13*( -x/9 + 1/5)

Step-by-step explanation:

Given:

- The curve has an equation as follows:

                               44 = 5x^2 + 3xy + 3y^2

Find:

a. Verify that the given point (2​,2​) lies on the curve.

b. Determine an equation of the line tangent to the curve at the given point.

Solution:

- To verify whether the point lies on the given curve we will substitute the coordinates of the point into the equation as follows:

                              44 = 5*(2)^2 + 3*(2)(2) + 3*(2)^2

                              44 = 20 + 12 + 12

                              44 = 44 ......Hence proven.

- The equation of the line tangent to the curve is expressed as a linear function as follows:

                              y = m*x + C

Where, m is the gradient of the line.

            C is the y-intercept.

                              m = Δy / Δx = dy/dx

- We will take the derivative of the given curve with respect to x as follows:

                             0 = 10x + 3*( y + xy' )  + 6y*y'\\\\-10x - 3y = y' ( 3x + 6y)\\\\ y' = - \frac{10x + 3y}{3x + 6y}

- Evaluate y' at the point (2,2) we get:

                            y' = - ( 10(2) + 3(2) ) / ( 3(2) + 6(2) )

                            y' = - ( 26 ) / (18)

                            y'= m = - 13/9

- To evaluate C, we will use the point (2,2) for linear expression above with m as follows:

                            y = -13*x/9 + C

                            2 =-13*(2)/9 + C

                            C = 13 / 5

- The equation of the tangent is as follows:

                            y = 13*( -x/9 + 1/5)  

8 0
3 years ago
Natalie drinks 2 pints of milk each day. How many days does it take her to drink 1 gallon of milk? PLZ HELP
Lostsunrise [7]

Answer:

4 days

Step-by-step explanation:

4 0
3 years ago
An inflatable figure is a decoration on Gabriella's lawn. A rope 42 in. long secures the top of the figure to the ground at an a
Mekhanik [1.2K]

Answer:

41.4 in

Step-by-step explanation:

(sin 80) <u>opposite</u>      =    <u>x</u>

          hypotenuse        42

x = 42 * sin (80)  = 41.4 in

7 0
2 years ago
. Asking 100 students at a large university for their opinions on campus life is an example of measuring a _____.
Slav-nsk [51]

Answer:

B

Step-by-step explanation:

I am assuming that the university has much more than 100 students so 100 people is just a small sample.

3 0
3 years ago
Read 2 more answers
The sales tax rate for the state of Washington was 7%.
sladkih [1.3K]

Answer:

Total cost of the car including tax=$4,066

Step-by-step explanation:

Sales tax rate=7%

Price of the car=$3800

Sales tax=7% of 3800

=7/100×3800

=$266

Total cost of the car=price of the car+ sales tax

=$3800+$266

=$4,066

5 0
3 years ago
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