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geniusboy [140]
3 years ago
11

Can someone solve these?

Mathematics
1 answer:
Kaylis [27]3 years ago
4 0

Answer:

Step-by-step explanation:

You need to find out what x and y is first then you can solve it

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Let f(x)=x^3-x-1
alexira [117]
f(x) = x^3 - x - 1

To find the gradient of the tangent, we must first differentiate the function.

f'(x) = \frac{d}{dx}(x^3 - x - 1) = 3x^2 - 1

The gradient at x = 0 is given by evaluating f'(0).

f'(0) = 3(0)^2 - 1 = -1

The derivative of the function at this point is negative, which tells us <em>the function is decreasing at that point</em>.

The tangent to the line is a straight line, so we will have a linear equation of the form y = mx + c. We know the gradient, m, is equal to -1, so

y = -x + c

Now we need to substitute a point on the tangent into this equation to find c. We know a point when x = 0 lies on here. To find the y-coordinate of this point we need to evaluate f(0).

f(0) = (0)^3 - (0) - 1 = -1

So the point (0, -1) lies on the tangent. Substituting into the tangent equation:

y = -x + c \\\\ -1 = -(0) + c \\\\ -1 = c \\\\ \text{Equation of tangent is } \boxed{y = -x - 1}
6 0
3 years ago
Im a little stuck on this​ (please show how you did it)
nikklg [1K]

Answer:

all work is shown / pictured

5 0
3 years ago
Divide 2x2+7x-3 by 2x+5. Which expression represents the quotient and remainder
Fiesta28 [93]

Answer:

0

Step-by-step explanation:

7 0
3 years ago
Help me please!!!!!!!!!!
BlackZzzverrR [31]

Answer:

Option (4)

Step-by-step explanation:

In the picture attached,

m∠NLM = m∠LKN = 90°

In two similar triangles ΔLKN and ΔMKL,

By the property of similar triangles,

"Ratio of the corresponding sides of the similar triangles are proportional".

\frac{\text{LK}}{\text{KN}}=\frac{\text{KM}}{\text{LK}}

By substituting the values given,

\frac{h}{3}=\frac{2}{h}

\frac{2}{h}=\frac{h}{3}

Therefore, Option (4) will be the answer.

8 0
3 years ago
Solve the system.<br> x+3y= 22<br> 2x -y=2<br> (7,5)<br> (2,2)<br> (4,6)<br> no solution
kirill115 [55]

Answer:

x = 4 , y = 6

Step-by-step explanation:

Solve the following system:

{x + 3 y = 22 | (equation 1)

2 x - y = 2 | (equation 2)

Swap equation 1 with equation 2:

{2 x - y = 2 | (equation 1)

x + 3 y = 22 | (equation 2)

Subtract 1/2 × (equation 1) from equation 2:

{2 x - y = 2 | (equation 1)

0 x+(7 y)/2 = 21 | (equation 2)

Multiply equation 2 by 2/7:

{2 x - y = 2 | (equation 1)

0 x+y = 6 | (equation 2)

Add equation 2 to equation 1:

{2 x+0 y = 8 | (equation 1)

0 x+y = 6 | (equation 2)

Divide equation 1 by 2:

{x+0 y = 4 | (equation 1)

0 x+y = 6 | (equation 2)

Collect results:

Answer: {x = 4 , y = 6

7 0
3 years ago
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