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1 year ago

What is the best approximation of the projection of (2,6) onto (5,-1)

Mathematics

1 answer:

Darya [45]1 year ago

5 0

Answer:

0.15(5,-1)

Step-by-step explanation:

$\frac{v_{1} * v_{2} }{|v_{2}|^{2} }*v_{2}$ ⇒ $\frac{(2)(5)+(6)(-1)}{\sqrt{5^2+(-1)^2} }(5,-1)$ ⇒ $\frac{4}{26} (5,-1)$ ⇒ $0.15(5,-1)$

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a) The curve with equation y2 = x3 + 3x2 is called the Tschirnhausen cubic. Find an equation of the tangent line to this curve a

Neporo4naja [7]

Answer:

Tangent at (1,2) has value $\frac{15}{4}$ . And (-2, 4) is the point of intersection of horizontal tangent.

Step-by-step explanation:

Given curve equation,

$y^2=x^3+3x^2\hfill (1)$

To find tangent at (x,y)=(1,2) and point of intersection of horizontal tangent, differentiate (1) withrespect to x we get,

$2y\frac{dy}{dx}=x^3+3x^2$

$\implies \frac{dy}{dx}=\frac{3(x^2+2x)}{2y}$

At (1, 2), tangent line is,

$\frac{dy}{dx}|_{(1,2)}}=\frac{15}{4}$

To find point of intersection of horizontal tangent we have to do,

$\frac{dy}{dx}=0$

$\implies x(x+2)=0\implies x=0 or -2$

Thus,

At x=0, y=0

but snce,

$\lim_{y\to 0}\frac{dy}{dx}\to \infty$

at (0,0) there exist a vertical tangent. And,

At x=-2, y=4.

Thus (-2, 4) is the point of intersection of horizontal tangent.

6 0

2 years ago

A function is expressed by the equation y=0.3x−6. For what value of the independent variable will the value of the function be e

Anna11 [10]

Answer:

0; 10; 20

Step-by-step explanation:

x is the independent variable

y is the dependent variable

y is dependent on x

a) For what value of the independent variable will the value of the function be equal to −6

y=0.3x−6

-6 = 0.3x-6

0=0.3x

x = 0

Therefore, if the independent variable is 0, the value of the function will be -6.

b) For what value of the independent variable will the value of the function be equal to −3

y=0.3x−6

-3 = 0.3x-6

0.3x = -3+6

0.3x = 3

x = 3/0.3

x = 10

Therefore, if the independent variable is 10, the value of the function will be -3.

c) For what value of the independent variable will the value of the function be equal to 0.

y=0.3x−6

0=0.3x-6

6 = 0.3x

x = 6/0.3

x = 20

Therefore, if the independent variable is 20, the value of the function will be 0.

7 0

1 year ago

A manageress earned £24,500 last year. This year she earns £25,235.

Korolek [52]

Answer:

Step-by-step explanation:

245000 last year

This year 25235

(y2 - y1) / y1)*100 = your percentage change

(where y1=start value and y2=end value)

(( £25.235 - £24.500) / £24.500) * 100 = 0 %

There ain't no percentage change as there needs to be a bigger difference between the two numbers plus u should use the formula

7 0

1 year ago

the diagonal of a tv is 26 inches long assuming that this diagonal forms a tv pair 30-60-90 right triangles what are the exact l

Alexxandr [17]

It is an application of Pythagorean Theorem

And it is clear that the lower angle is 30 and the apex angle is 60 (this is how always normal TVs look like) ... refer to the image I attached

So, to calculate the width and the length:

$\frac{length}{26} =cos(30)\\~\\length=26*cos(30)=13 \sqrt{3} ~~in$

$\frac{width}{26} =sin(30)\\~\\width=26*sin(60)=13~~in$

You can after that round the length to be 22.517 in

Hope you got the idea

3 0

2 years ago

Given AC ≅ FE and CB ≅ ED which statement is correct?

Kisachek [45]

Answer:

D is the correct answer.

Step-by-step explanation:

3 0

1 year ago

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