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3 years ago

How to find (a) and (b)?

Mathematics

1 answer:

rodikova [14]3 years ago

3 0

Answer:

A) Gradient = -3

B) 3y - x = 7

Step-by-step explanation:

The curve has the equation;

y = x³ - 6x² + 9x + 1

We are given the pints it passes through as;

A(2,3) and P(3, 1)

A) to find the gradient, we will find the derivative of the given equation.

Thus;

Gradient = y' = 3x² - 12x + 9

At point A, x = 2. Thus;

Gradient = 3(2²) - 12(2) + 9

Gradient = 12 - 24 + 9

Gradient = -3

B) since the gradient of the tangent = -3, it means the gradient of the normal will be; -1/-3 = 1/3

Thus, equation of the normal to the curve at point A will be;

(y - 3) = ⅓(x - 2)

Multiply both sides by 3 to get;

3y - 9 = x - 2

3y - x = 9 - 2

3y - x = 7

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Bob flipped a coin and got "heads" 9 times in a row! What is the probability that the next flip will be a "head?"

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Answer:

50/50 chance

Step-by-step explanation:

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2 years ago

Write a polynomial expression, in simplified form, that represents the AREA of the blanket and use the expression to evaluate th

pochemuha

Answer:

Polynomial expression that represents the area of blanket:

$A(x)=(6x^2+5x-21)cm^2$

If $x=2$ : $A(2)=13cm^2$

Step-by-step explanation:

The area of the rectangle can be calculated with the formula:

$A=lw$

Being l the lenght of the rectangle and w the width of the rectangle.

In this case, the lenght and the width are represented with:

$l=(3x+7)cm$

$w=(2x-3)cm$

Substitute them into $A=lw$ :

$A(x)=(3x+7)(2x-3)$

Then:

Use Distributive property (Remember the Product of powers property: $b^a*b^c=b^{(a+c)}$ ):

$A(x)=(3x+7)(2x-3)\\A(x)=6x^2-9x+14x-21$

Add like terms:

$A(x)=(6x^2+5x-21)cm^2$ (Simplied form)

Evaluate $x=2$ :

$A(2)=(6(2)^2+5(2)-21)cm^2\\A(2)=(6(4)+10-21)cm^2\\A(2)=(24-11)cm^2\\A(2)=13cm^2$

6 0

3 years ago

Can someone please help me with this math question

lora16 [44]

Answer:

C'(4,4)

Step-by-step explanation:

The dilation of quadrilateral ABCD over the origin by a scale factor of 2 has the rule

(x,y)→(2x,2y)

So,

A(-3,-1)→A'(-6,-2)
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C(2,2)→C'(4,4)
D(3,-2)→D'(6,-4)

Hence, the coordinates of the image point C' are (4,4) (see attached diagram for details)

8 0

3 years ago

Read 2 more answers

Complete the following statement of congruence

OLga [1]

Answer:

B. angle STR

Step-by-step explanation:

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3 years ago

How can i show my work for 414 divided by 9

alexandr402 [8]

You could:

414/9
=1/46
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There's not much more work to show sorry

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3 years ago

How to find (a) and (b)?​

How to find (a) and (b)?