MATHEMATICS MIDDLE SCHOOL

The straight line with equation y = 11x - 28
is a tangent to the curve
y = {x}^(3) - a {x}^(2) + bx - 1
at the point (3,5). Find A, the coefficient of
{x}^(2)
​

Answers

Answer 1
Answer:

Answer:

a=3

Step-by-step explanation:

The equation of the curve is

y=x^3-ax^2+bx-1.

The gradient function is given by

(dy)/(dx)=3x^2-2ax+b

The gradient of this curve at the point (3,5) is equal to the gradient of the tangent y=11x-28 which is 11.

\Rightarrow 11=3(3)^2-2a(3)+b

\Rightarrow 11=27-6a+b

\Rightarrow b-6a=-16...(1)

The given point, (3,5) also satisfies the equation of the curve.

\Rightarrow 3^3-a(3)^2+b(3)-1=5

\Rightarrow 27-9a+3b-1=5

\Rightarrow3b-9a=-21

\Rightarrow b-3a=-7...(2)

Equation (2) minus equation (1) gives

-3a+6a=-7+16

3a=9

This implies that;

a=3

Related Questions

Below are the numbers of fish each person on a fishing trip caught. Which measure or measures of central tendency best reflect the data? Explain your reasoning.3 6 10 8 9 10 11 10 8 4 9 10 1 10 9 8 6 9
Ned is training for a biathlon. He will swim every sixth day and bicycle every eighth day. On what days will he both swim and bicycle?? Specified answers please!!
At the beach cleanup, Maya's group collected 14.8 pounds of trash on Saturday and 12.5 pounds on Sunday. Will's group collected the same total amount of trash as Maya's group but collected only 11.8 pounds on Saturday. HELP PEALSE!!!!!How much trash did Will's group collect on Sunday?A.3.0 poundsB.12.5 poundsC.15.5 poundsD.27.3 pounds
At camp, Miriam learned how to use a pottery wheel. She can make 3 bowls in 2 hours. How long will it take her to make a set of 12 bowls?
Three times a number is 42. What is the number?

What is 18/42 in the simplest form?

Answers

(18)/(42)=(18:2)/(42:2)=(9)/(21)=(9:3)/(21:3)=\boxed{(3)/(7)}
18 | 2 
9 | 3
3 | 3
1

42 | 2
21 | 3
7 | 7
1 

2,3
GCF (18,42) = 2*3 = 6
(18)/(42) = (18:6)/(42:6) = (3)/(7)

Can someone help me with this math question?

Answers

Answer:

y = x + 2

Step-by-step explanation:

the formula for this basic equation is

y = mx + b

m = 5/5   (slope)

b = 2   (y-intercept)

5/5 simplified is just 1

so if we put it in the equation you get y = 1x + 2

but 1x is the same as just saying x

so

y = x + 2

4 (2a+3b)(5x+y)
How many factors make up this product ?

Answers

Three factors: "4", "2a+3b" and "5x+y"

On a scale drawing with a scale of 1 cm = 0.9 m, the height of a tree is 1.2 cm. How tall is the actual tree in meters?

Answers

1cm=.9m
we can multiply this by 1.2 because it will help when solving the equation
1.2cm=1.08m 
this is your answer!

Edward walked 3/4 mile from his home to the park. Then he walked 2/4 mile from the park to the library. Which distance is shorter?

Answers

2/4. Because it is half but 3/4 is greater than half
2/4 because 2 is lower than 3

How many 1-inch cubes do you need to create a cube with an edge length of 5 inches?

Answers

You need 125 1-inch cubes to create a cube with annedge length of 5 inches
125 cubes to get to 5 inches 5 * 5*5=125
Other Questions
Please rewrite each fraction in at least two different waysa)11/2 b)3/8 c)10/7
John gets a new job and receives a $500 signing bonus. After that he makes 150 a day The slope is?
Whats 600 divided by 4
Please help!!!!!!!!!!!!