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Ivahew [28]
3 years ago
7

The curve with equation y2 = 5x4 − x2 is called a kampyle of eudoxus. find an equation of the tangent line to this curve at the

point (−1, 2).
Mathematics
1 answer:
Vesnalui [34]3 years ago
3 0
To find the tangent line we will need the slope of the tangent at x=-1 (the x-coordinate of the point given). We find the slope by using the derivative of the curve.

Th curve given is y^{2} =5 x^{4} - x^{2} which can be solved for y by taking the root of both sides. We obtain y=(5 x^{4}- x^{2} ) ^{1/2}

We find the derivative using the chain rule. Bring down the exponent, keep the expression in the parenthesis, raise it to 1/2 - 1 and then take the derivative of what is inside.

y’=(1/2)(5 x^{4} - x^{2} )^{-1/2}(20 x^{3} -2x)

Next we evaluate this expression for x=-1 and obtain:
\frac{20(-1)^{3} -(2)(-1)}{2 \sqrt{5(-1 ^{4}-(-1 ^{2})  } }= \frac{-20+2}{2 \sqrt{5-1} }=-18/4=-9/2

So we are looking for a line through (-1,2) with slope equal to -9/2. We use y=mx+b with m=-9/2, x=-1 and y=2 to find b.

2=(-9/2)(-1)+b
2-(9/2)=b
b=-5/2

So the tangent line is given by y=(-9/2)x+(-5/2)

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Choose the equations that are not linear equations. - x - y = 2, x^2 + y = 4, x/2 - y^3 = 1, x = 5
tekilochka [14]

Answer:

  • x^2 + y = 4
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Step-by-step explanation:

Any equation with a product of variables, or with a variable in an exponent or denominator, is <em>not a linear equation</em>. Here, "product of variables" includes powers and roots—any expression with an exponent other than 1, or a total of exponents other than 1.

7 0
3 years ago
Write the word as an equation. The product of a number m and 2 is 8. An equation that represent this word sentences is?
ollegr [7]

Answer:

2(xm) = 8

Step-by-step explanation:

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3 0
2 years ago
2. The table shows the mass of fibres in 100 grams of each food item below. Food Mass of fibre (grams per 100 grams) Beans Bread
Andre45 [30]

Given that the amount of fiber in 100 grams of beans is 3.6 grams the amount of fiber consumed from  \mathbf{\frac{2}{3}} of the small tin is <u>4.8 grams</u>.

<h3>How can the amount of fiber consumed be calculated?</h3>

From the given table, we have;

Mass of fiber in 100 g of beans = 3.6 grams

Mass of beans in the small tin = 200 grams

The quantity of the beans eaten = \frac{2}{3} of the small tin

Required:

The amount of fiber to consumed from eating  \frac{2}{3} of the small tin

Solution;

Amount  \ of \ fiber \ consumed = 200 \, g \times \dfrac{3.6 \, g}{100 \, g}  \times \dfrac{2}{3}  = \mathbf{4.8 \, g}

Therefore;

The amount of fiber consumed by eating \frac{2}{3} of the small tin = <u>4.8 grams</u>

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The smallest natural number divisible by 2,3,4,5,6,8 and 9 is____.
SVETLANKA909090 [29]

Answer:

360

Step-by-step explanation:

You will need 2 * 2 * 2 for the smallest number to be divisible by 8 with all the others.

You will need 3 * 3  for the smallest number to be divisible by 9 with all the others.

Finally you will need 1 five

The smallest number divisible by all of these is 2*2*2*3*3*5 = 360

  • 360/2 = 180 works
  • 360/3 = 120 works
  • 360/5 = 72   works
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  • 360/8 = 45 works
  • 360/9 = 40 works.

There is no smaller number below 360 which will work.

7 0
3 years ago
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