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3 years ago

A circle is placed in a square with a side length of 8 mm, as shown below. Find the area of the shaded region.

Mathematics

1 answer:

zalisa [80]3 years ago

3 0

Answer:

9.76 mm^2

Step-by-step explanation:

area of square minus area of circle = answer

area of square is 64

area of circle is pi * r squared

r is 8 ÷2 = 4

r squared is 4 * 4

area of circle is pi * 4 * 4 = pi * 16 = 50.24

64 - 50.24 = 9.76

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A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 30 ft/s. Its height

Crank

Answer:

a) h = 0.1: $\bar v = -11\,\frac{ft}{s}$ , h = 0.01: $\bar v = -10.1\,\frac{ft}{s}$ , h = 0.001: $\bar v = -10\,\frac{ft}{s}$ , b) The instantaneous velocity of the ball when $t = 2\,s$ is $-10$ feet per second.

Step-by-step explanation:

a) We know that $y = 30\cdot t -10\cdot t^{2}$ describes the position of the ball, measured in feet, in time, measured in seconds, and the average velocity ( $\bar v$ ), measured in feet per second, can be done by means of the following definition:

$\bar v = \frac{y(2+h)-y(2)}{h}$

Where:

$y(2)$ - Position of the ball evaluated at $t = 2\,s$ , measured in feet.

$y(2+h)$ - Position of the ball evaluated at $t =(2+h)\,s$ , measured in feet.

$h$ - Change interval, measured in seconds.

Now, we obtained different average velocities by means of different change intervals:

$h = 0.1\,s$

$y(2) = 30\cdot (2) - 10\cdot (2)^{2}$

$y (2) = 20\,ft$

$y(2.1) = 30\cdot (2.1)-10\cdot (2.1)^{2}$

$y(2.1) = 18.9\,ft$

$\bar v = \frac{18.9\,ft-20\,ft}{0.1\,s}$

$\bar v = -11\,\frac{ft}{s}$

$h = 0.01\,s$

$y(2) = 30\cdot (2) - 10\cdot (2)^{2}$

$y (2) = 20\,ft$

$y(2.01) = 30\cdot (2.01)-10\cdot (2.01)^{2}$

$y(2.01) = 19.899\,ft$

$\bar v = \frac{19.899\,ft-20\,ft}{0.01\,s}$

$\bar v = -10.1\,\frac{ft}{s}$

$h = 0.001\,s$

$y(2) = 30\cdot (2) - 10\cdot (2)^{2}$

$y (2) = 20\,ft$

$y(2.001) = 30\cdot (2.001)-10\cdot (2.001)^{2}$

$y(2.001) = 19.99\,ft$

$\bar v = \frac{19.99\,ft-20\,ft}{0.001\,s}$

$\bar v = -10\,\frac{ft}{s}$

b) The instantaneous velocity when $t = 2\,s$ can be obtained by using the following limit:

$v(t) = \lim_{h \to 0} \frac{x(t+h)-x(t)}{h}$

$v(t) = \lim_{h \to 0} \frac{30\cdot (t+h)-10\cdot (t+h)^{2}-30\cdot t +10\cdot t^{2}}{h}$

$v(t) = \lim_{h \to 0} \frac{30\cdot t +30\cdot h -10\cdot (t^{2}+2\cdot t\cdot h +h^{2})-30\cdot t +10\cdot t^{2}}{h}$

$v(t) = \lim_{h \to 0} \frac{30\cdot t +30\cdot h-10\cdot t^{2}-20\cdot t \cdot h-10\cdot h^{2}-30\cdot t +10\cdot t^{2}}{h}$

$v(t) = \lim_{h \to 0} \frac{30\cdot h-20\cdot t\cdot h-10\cdot h^{2}}{h}$

$v(t) = \lim_{h \to 0} 30-20\cdot t-10\cdot h$

$v(t) = 30\cdot \lim_{h \to 0} 1 - 20\cdot t \cdot \lim_{h \to 0} 1 - 10\cdot \lim_{h \to 0} h$

$v(t) = 30-20\cdot t$

And we finally evaluate the instantaneous velocity at $t = 2\,s$ :

$v(2) = 30-20\cdot (2)$

$v(2) = -10\,\frac{ft}{s}$

The instantaneous velocity of the ball when $t = 2\,s$ is $-10$ feet per second.

8 0

3 years ago

Tom buys a shirt for $22.00 plus 7% sales tax. His cousin buys a shirt for $18.00 plus 4% sales tax. a. How much do Tom and his

likoan [24]

Tom is spending more on tax totaling 23.54
while his cousin is only spending 18.72

How to get tax with percent take base price ex:22+ 7%

transform percent into a decimal : .07

now multiply the decimal times base price : 22x0.07

tax is a $1.54 now add that to your base price 22

and you get your total $23.54

4 0

3 years ago

What is the area of this triangle in the coordinate plane?

SpyIntel [72]

Answer:2. Given the points A, B, C, D, calculate:

(a) the angle B of the triangle ABC

(b) the area of the triangle ABC

(c) the median BE of the triangle ABC

(d) the height AH of the triangle ABC

(e) the volume of tetrahedron ABCD

(f) the point E so that ABCE is a parallelogram.

A(-1, 2, -3), B(4, -1, 0), C(2, 1, -2), D( 3,4,5)

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

A worker is paid $18.50 per hour for the first 40 hours of work and time and a half for any overtime exceeding 40 hours per week

Lisa [10]

Answer:

The worker's pay is $795.50.

Step-by-step explanation:

The worker gets paid $18.50 for the first 40 hours of work. The worker works 46 hours. 18.50 • 40 = 740. He worked 6 hours overtime. $18.50 ÷ 2 = $9.25. $9.25 • 6 = $55.50.

$740 + $55.50= $795.50

5 0

3 years ago

A bag contains 39 coins consisting of quarters and nickels the total value of the coins is $6.35 which system of equation can be

MA_775_DIABLO [31]

Answer:

The system of equation to determine the quantity of nickels and quarters is simultaneous equation.

Nickels = 17

Quarters = 22

Step-by-step explanation:

Given

Let n represent number of nickels

Let q represent number of quarters

From line 1 of the question, we understand that

Total coins = 39

So, n + q = 39 because the made up of the nickels and the quarters

It's also stated that the total value of these 39 coins is $6.35.

First, it should be noted that

1 nickel is worth 0.05 and 1 quarter is worth 0.25, we can represent the total value of the coins with the following equation

0.05n + 0.25q = 6.35

At this point, we have two equation such can be solved simultaneously

n + q = 39 ------- (1)

0.05n + 0.25q = 6.35 ------- (2)

So, the system of equation to determine the quantity of nickels and quarters is simultaneous equation.

Solving further.....

Make q the subject of formula in equation (1)

q = 39 - n

Substitute 39 - n for q in equation 2

0.05n + 0.25q = 6.35 becomes

0.05n + 0.25(39 - n) = 6.35

0.05n + 9.75 - 0.25n = 6.35

Collect like terms

0.05n - 0.25n = 6.35 - 9.75

-0.2n = -3.4

Divide through by -0.2

-0.2n/-0.2 = -3.4/-0.2

n = 17

Recall that q = 39 - n

Substituton 17 for n in this equation

q = 39 - 17

q = 22

Hence, there are 17 nickels and 22 coins

7 0

3 years ago