What is 16,640 in word form

The measurenicnt of the circumference of a circle is found to be 56 centimeters. The possible error in measuring the circumferen

BartSMP [9]

Answer:

(a) Approximate the percent error in computing the area of the circle: 4.5%

(b) Estimate the maximum allowable percent error in measuring the circumference if the error in computing the area cannot exceed 3%: 0.6 cm

Step-by-step explanation:

(a)

First we need to calculate the radius from the circumference:

$c=2\pi r\\r=\frac{c}{2\pi } \\c=8.9 cm$

I leave only one decimal as we need to keep significative figures

Now we proceed to calculate the error for the radius:

$\Delta r=\frac{dt}{dc} \Delta c\\\\\frac{dt}{dc} = \frac{1}{2 \pi } \\\\\Delta r=\frac{1}{2 \pi } (1.2)\\\\\Delta r= 0.2 cm$

$r = 8.9 \pm 0.2 cm$

Again only one decimal because the significative figures

Now that we have the radius, we can calculate the area and the error:

$A=\pi r^{2}\\A=249 cm^{2}$

Then we calculate the error:

$\Delta A= (\frac{dA}{dr} ) \Delta r\\\\\Delta A= 2\pi r \Delta r\\\\\Delta A= 11.2 cm^{2}$

$A=249 \pm 11.2 cm^{2}$

Now we proceed to calculate the percent error:

$\%e =\frac{\Delta A}{A} *100\\\\\%e =\frac{11.2}{249} *100\\\\\%e =4.5\%$

(b)

With the previous values and equations, now we set our error in 3%, so we just go back changing the values:

$\%e =\frac{\Delta A}{A} *100\\\\3\%=\frac{\Delta A}{249} *100\\\\\Delta A =7.5 cm^{2}$

Now we calculate the error for the radius:

$\Delta r= \frac{\Delta A}{2 \pi r}\\\\\Delta r= \frac{7.5}{2 \pi 8.9}\\\\\Delta r= 0.1 cm$

Now we proceed with the error for the circumference:

$\Delta c= \frac{\Delta r}{\frac{1}{2\pi }} = 2\pi \Delta r\\\\\Delta c= 2\pi 0.1\\\\\Delta c= 0.6 cm$

5 0

4 years ago

(Brainliest) PLEASE HELPP MEEE

zloy xaker [14]

Answer:

1. According to the angle bisector theorem, DAC = BAC

2. Same kind of goes for BC

3. X must be equal in both equations. x= 3

9(3) -7 = 20

4(3) +8 = 20

Hope this helped!

8 0

3 years ago

This is what I am supposed to do, I’m confused on what to do on 3,4, and 5. PLEASE HELP ASAP!!!!!! 30 POINTS!!!!!

max2010maxim [7]

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

To calculate m use the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

3

Using (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 3, 6)

m = $\frac{6-0}{-3-0}$ = $\frac{6}{-3}$ = - 2

Since the line passes through the origin (0, 0) then y- intercept is 0

y = - 2x ← equation of line

4

let (x₁, y₁ ) = (6, 0) and (x₂, y₂ ) = (0, 3)

m = $\frac{3-0}{0-6}$ = $\frac{3}{-6}$ = - $\frac{1}{2}$

note the line crosses the y- axis at (0, 3) ⇒ c = 3

y = - $\frac{1}{2}$ x + 3 ← equation of line

5

let (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (-2, - 3)

m = $\frac{-3-3}{-2-0}$ = $\frac{-6}{-2}$ = 3

note the line crosses the y- axis at (0, 3) ⇒ c = 3

y = 3x + 3 ← equation of line

7 0

4 years ago

let a = (a1, a2) and b = (b1, b2) and c = (c1,c2) be three non zero vectors. if a1b2 - a2b1 is not equal to 0. then show three a

Ksenya-84 [330]

Consider the contrapositive of the statement you want to prove.

The contrapositive of the logical statement

p ⇒ q

is

¬q ⇒ ¬p

In this case, the contrapositive claims that

"If there are no scalars α and β such that c = αa + βb, then a₁b₂ - a₂b₁ = 0."

The first equation is captured by a system of linear equations,

$\begin{cases}c_1 = \alpha a_1 + \beta b_1\\ c_2 = \alpha a_2 + \beta b_2\end{cases}$

or in matrix form,

$\begin{pmatrix}c_1\\c_2\end{pmatrix} = \begin{pmatrix}a_1&b_1\\a_2&b_2\end{pmatrix}\begin{pmatrix}\alpha\\\beta\end{pmatrix}$

If this system has no solution, then the coefficient matrix on the right side must be singular and its determinant would be

$\begin{vmatrix}a_1&b_1\\a_2&b_2\end{vmatrix} = a_1b_2-a_2b_1 = 0$

and this is what we wanted to prove. QED

3 0

3 years ago

GIVING BRAINLIEST!!!!!! 32+4X(16 x 1/2)-2 show your work

belka [17]

The answer should be 62

7 0

3 years ago

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