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3 years ago

Find the area of the shaded region

Mathematics

1 answer:

Novay_Z [31]3 years ago

8 0

3.14159(pi) times radius squared
pi times 24 squared equals 1809.56
now find the area of the smaller circle
pi times 6 squared equals 113.1
now subtract the smaller circle from the bigger circle
1809.56 minus 113.1
answer is 1696.46

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7. By using binomial expansion show that the value of (1.01)^12 exceed the value of (1.02)^6 by 0.0007 correct to four decimal p

BlackZzzverrR [31]

Binomial expansion is used to factor expressions that can be expressed as the power of the sum of two numbers.

The proof that (1.01)^12 exceeds (1.02)^6 by 0.0007 is $\mathbf{(1.01)^{12} - (1.02)^6 \approx 0.0007 }$

The expressions are given as:

$\mathbf{(1.01)^{12}\ and\ (1.02)^6}$

A binomial expression is represented as:

$\mathbf{(a + b)^n = \sum\limits^n_{k=0}^nC_k a^{n - k}b^k}$

Express 1.01 as 1 + 0.01

So, we have:

$\mathbf{(1.01)^{12} = (1 + 0.01)^{12}}$

Apply the above formula

$\mathbf{(1.01)^{12} = ^{12}C_0 \times 1^{12 - 0} \times 0.01^0 + ......... .......... + ^{12}C_{12} \times 1^{12 - 12} \times 0.01^{12} }}$

$\mathbf{(1.01)^{12} = 1 \times 1 \times 1 + ......... .......... + 1 \times 1 \times 10^{-24} }}$

$\mathbf{(1.01)^{12} = 1 + ......... .......... + 10^{-24} }}$

This gives

$\mathbf{(1.01)^{12} = 1.1268\ (approximated)}$

Similarly,

Express 1.02 as 1 + 0.02

So, we have:

$\mathbf{(1.02)^6 = (1 + 0.02)^6}$

Apply $\mathbf{(a + b)^n = \sum\limits^n_{k=0}^nC_k a^{n - k}b^k}$

$\mathbf{(1.02)^6 = ^6C_0 \times 1^{6 - 0} \times 0.02^0 + ^6C_1 \times 1^{6 - 1} \times 0.02^1 +.............. + ^6C_6 \times 1^{6 - 6} \times 0.02^6 }$ $\mathbf{(1.02)^6 = 1 \times 1 \times 1 + 6 \times 1 \times 0.02 +.............. + 1 \times 1 \times 6.4 \times 10^{-11} }$

$\mathbf{(1.02)^6 = 1 + 0.12 +.............. + 6.4 \times 10^{-11} }$

This gives

$\mathbf{(1.02)^6 = 1.1261\ (approximated) }$

Calculate the difference as follows:

$\mathbf{(1.01)^{12} - (1.02)^6 \approx 1.1268 - 1.1261 }$

$\mathbf{(1.01)^{12} - (1.02)^6 \approx 0.0007 }$

The above equation means that:

(1.01)^12 exceed the value of (1.02)^6 by 0.0007

Read more about binomial expansions at:

brainly.com/question/9554282

7 0

3 years ago

The equation f(x)= 2/3 x + 1 is giving me some hard times can anyone help?

hjlf

F(x) = 2/3x + 1

This is in the slope-intercept form of an equation for a line.
Which is written as this: (Note f(x)= is the same as saying y= in this case)

y = mx + b

M is our slope. Slope is the RISE over the RUN

In other words it is y/x
For this graph y represents distance, and x represents time. (Life Tip: TIME is almost ALWAYS the X value)

In this case M = 2/3

So her speed is:
2 units/3 units

B is the y-intercept. The y-intercept is where the X-value equals 0. So, (0,y). Because the y-intercept is distance she should have a y-intercept of 0. (The origin) because that would mean at the start of the race she had no distance (aka she was at the starting line).

Because her y-intercept (b) = 1 she did have a head start.

Here are both the answers at once to make it easier for you:
Speed (Replace Units with whatever units you were given. Distance Units go on top. Time units on bottom. Example: Meters/Second))
2 units/3 units

Did she have a head start? (Unit being whatever distance unit you were given)
Yes, 1 unit.

7 0

4 years ago

What is the discriminant of the quadratic equation 0 = –x2 + 4x – 2?

Elis [28]

The formula to find the discriminant equals D = b^2-4ac.
(Quadratic equations have the formula ax^2+bx+c. A = -1, B = +4, C = -2.)

D = 4^2-4(-1)(-2). 8-8 = 0.

0 = 1 solution
-D = 0 solutions
+D = 2 solutions

The discriminant equals 0, also establishing that if you were asked to find the solutions, there would only be one.

6 0

4 years ago

Help pls<br> What is the solution to this system of equations?<br> x = 12 − y<br> 2x + 3y = 29

Oxana [17]

Answer:

Step-by-step explanation:

3 0

3 years ago

Graph the Inequality y>2x-5 on set of axis

vova2212 [387]

Https://www.quickmath.com/webMathematica3/quickmath/graphs/inequalities/basic.jsp#

8 0

3 years ago

Read 2 more answers