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3 years ago

What is 1/3^5 whole form?

Mathematics

2 answers:

Kruka [31]3 years ago

8 0

1/3^5 = 1/243 because 3^5 = 243

Alisiya [41]3 years ago

6 0

1/3^5 = 1/27 or 0.037037.

Hoped I helped!

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Show that every triangle formed by the coordinate axes and a tangent line to y = 1/x ( for x > 0)

vfiekz [6]

Answer:

Step-by-step explanation:

given a point $(x_0,y_0)$ the equation of a line with slope m that passes through the given point is

$y-y_0 = m(x-x_0)$ or equivalently

$y = mx+(y_0-mx_0)$ .

Recall that a line of the form $y=mx+b$ , the y intercept is b and the x intercept is $\frac{-b}{m}$ .

So, in our case, the y intercept is $(y_0-mx_0)$ and the x intercept is $\frac{mx_0-y_0}{m}$ .

In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph $(x_0,\frac{1}{x_0})$ . Which means that $y_0=\frac{1}{x_0}$

The slope of the tangent line is given by the derivative of the function evaluated at $x_0$ . Using the properties of derivatives, we get

$y' = \frac{-1}{x^2}$ . So evaluated at $x_0$ we get $m = \frac{-1}{x_0^2}$

Replacing the values in our previous findings we get that the y intercept is

$(y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}$

The x intercept is

$\frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0$

The triangle in consideration has height $\frac{2}{x_0}$ and base $2x_0$ . So the area is

$\frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2$

So regardless of the point we take on the graph, the area of the triangle is always 2.

6 0

3 years ago

The student council is selling tickets to a school dance. One teacher decides to pay $10 for his class, and the students in the

Lostsunrise [7]

Hi,

x + y = 350 (equation 1)

3x + 2y = 950 (equation 2)

Use Substitution Method

Isolate variable x in equation 1

x = 350 – y (equation 3)

Substitute equation 3 into equation 2

3(350 – y) + 2y = 950

1050 – 3y + 2y = 950

3y – 2y = 1050 – 950

y = 100

Substitute y = 100 into equation 1

x + 100 = 350

x = 250

Answer: 250 $3 tickets and 100 $2 tickets were sold.

8 0

3 years ago

Please answer the question with words

dangina [55]

Words words words words words words words words words words words words words words words words words words

7 0

3 years ago

4 Solve the system of equations using the substitution method. y = 2 2x+y=8

Sindrei [870]

Answer: 2

Step-by-step explanation:

5 0

2 years ago

If 2 apple and 5 bananas cost 4.20 dollars and 3 apples and 4 bananas coke 4.So dollars what is the price of a apple and banana

e-lub [12.9K]

Answer:

An apple costs $0.45 and a banana costs $0.66.

Step-by-step explanation:

This question is solved by a system of equations.

I am going to say that:

An apple costs x.

A banana costs y.

2 apple and 5 bananas cost 4.20 dollars

This means that:

$2x + 5y = 4.2$

$2x = 4.2 - 5y$

$x = 2.1 - 2.5y$

3 apples and 4 bananas cost 4.

This means that:

$3x + 4y = 4$

Since $x = 2.1 - 2.5y$

$3(2.1 - 2.5y) + 4y = 4$

$6.3 - 7.5y + 4y = 4$

$3.5y = 2.3$

$y = \frac{2.3}{3.5}$

$y = 0.66$

Then:

$x = 2.1 - 2.5(0.66) = 0.45$

An apple costs $0.45 and a banana costs $0.66.

7 0

2 years ago