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2 years ago

Calculus The following curve passes through (3,1) Using linear lineralization

Mathematics

1 answer:

Novay_Z [31]2 years ago

6 0

Answer:

Option 1.1

Step-by-step explanation:

The linearization of a curve implies the use of calculus to find the local value for the derivative and approximating the function by the use of the formula

$F(x) \approx F(x_0) + F'(x_0)(x-x_0)$

The function is given in such way that it's much easier to find the derivative by implicit differentiation than isolating any of the variables

$2x^2y+y=2x+13$

Differentiating with respect to x, we have

$4xy+2x^2y'+y'=2$

Computing y' in the given point (3,1) we have

4(3)(1)+2(9)y'+y'=2

$y'=\frac{2-12}{19}$

$y'=-\frac{10}{19}$

The function will be approximated with the expression

$F(x) = 1 -\frac{10}{19}(x-3)$

To find the approximate value for x=2.8

$F(2.8) = 1-\frac{10}{19}(-0.2)=1.1$

The correct value is the option 1.1

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-13x=90-2y <br> -6x=48-2y

Kisachek [45]

While it's pretty obvious to most of us that

-13x=90-2y

-6x=48-2y

is a system of linear equations, it'd be well to include that info plus the instructions "solve this system of linear equations."

Subtract the 2nd equation from the first:

-13x=90-2y

+6x=-48+2y

-----------------------

-7x = 42. Then x = -42/7, or x = 6.

Now subst. 6 for x in either one of the given equations. Suppose we use the 2nd equation:

-6x=48-2y

Then -6(6)=48-2y, or -36 = 48 - 2y, or 2y = 48+ 36 = 84. Then y = 42.

The solution is (6, 42).

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2 years ago

Try to sketch by hand the curve of intersection of the parabolic cylinder y = x2 and the top half of the ellipsoid x2 + 7y2 + 7z

vovikov84 [41]

Plug $y=x^2$ into the equation of the ellipsoid:

$x^2+7(x^2)^2+7z^2=49$

Complete the square:

$7x^4+x^2=7\left(x^4+\dfrac{x^2}7+\dfrac1{14^2}-\dfrac1{14^2}\right)=7\left(x^2+\dfrac1{14}\right)^2+\dfrac1{28}$

Then the intersection is such that

$7\left(x^2+\dfrac1{14}\right)^2+7z^2=\dfrac{1371}{28}$

$\left(x^2+\dfrac1{14}\right)^2+z^2=\dfrac{1371}{196}$

which resembles the equation of a circle, and suggests a parameterization is polar-like coordinates. Let

$x(t)^2+\dfrac1{14}=\sqrt{\dfrac{1371}{196}}\cos t\implies x(t)=\pm\sqrt{\sqrt{\dfrac{1371}{196}}\cos t-\dfrac1{14}}$

$y(t)=x(t)^2=\sqrt{\dfrac{1371}{196}}\cos t-\dfrac1{14}$

$z=\sqrt{\dfrac{1371}{196}}\sin t$

(Attached is a plot of the two surfaces and the intersection; red for the positive root $x(t)$ , blue for the negative)

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3 years ago

16.A company sells calculators for $35 each. Businesses

Olenka [21]

Answer: $3550 or letter: I

Step-by-step explanation: 35*100= $3,500 + $50 (tax)= $3,550 or in your case it is closest to letter i

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2 years ago

Is the sqaure root of 32 rational or irrational

DanielleElmas [232]

The square root of 32 is irrational = 5.6568424949

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3 years ago

Read 2 more answers

Help me solve this ASAP. Will mark brainlest Give the equation of the line with the following slope and.y-intercept m=0 b=7/2

svetlana [45]

Answer:

y = $\frac{7}{2}$

Step-by-step explanation:

A line with a slope of zero is a horizontal line parallel to the x- axis.

The equation of a horizontal line is

y = c

where c is the value of the y- coordinates the line passes through.

Here the line passes through (0, $\frac{7}{2}$ ) with y- coordinate $\frac{7}{2}$ , thus

y = $\frac{7}{2}$ ← equation of line

6 0

2 years ago