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2 years ago

Find the area of the blue shape below. Use 3.14 for π

Mathematics

1 answer:

Anika [276]2 years ago

7 0

Answer:

1413.86 ft^2.

Step-by-step explanation:

The diameter of the circle = 50 - 2(18)

= 50-36

= 14 ft.

So its radius is 7 ft.

The total area of the blue shape

= 2(35 * 18) + 3.14*7^2

= 1413.86 ft^2.

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A bucket that weighs 4lband a rope of negligible weight are used todraw water from a well that is 80ftdeep. The bucket is filled

liq [111]

Answer:

Workdone = 3200 lb.ft

Step-by-step explanation:

We are told that the bucket is filled with 40 lb of water but water leaks out of a hole in the bucket at a rate of 0.2lb/s

Thus,

Weight of water at any given time (t) would be;

w(t) = 40 - 0.2t - - - - (1)

We are told the bucket is pulled up at a rate of 2ft/s.

Thus, height at time (t); y = 0 + 2t = 2t

Since y = 2t,

Then,t = y/2

Put y/2 for t in eq 1

Thus; w(y) = 40 - 0.2(y/2)

w(y) = 40 - 0.1y

Now, at y = 80 ft, we have;

w(80) = 40 - 0.1(80)

w(80) = 40 - 8 = 32 lb

Since 32 lbs are left, it means there is always water in the bucket.

Thus, work done is;

W = 80,0[∫(Total weight).dy]

W = 80,0[∫[(weight of rope) + (weight of bucket) + (weight of water)]dy]

W = 80,0[∫[0 + 4 + 40 - 0.1y]dy]

Integrating, we have;

W = [44y - y²/20] at boundary of 80 and 0

So,

W = [44(80) - 80²/20] - [0 - 0²/20]

W = 3200 lb.ft

8 0

3 years ago

A new car is purchased for $47, 000 and over time its value depreciates by one half

andrey2020 [161]

Answer:

$1500

Step-by-step explanation:

you can figure it out by going in increments of 4.5 years because that is the info you have from the problem so

47000 4.5 years later is 23500

9 years = 11750

13.5y = 5875

18y = 2937.5

22.5 years later is 1468.75

22.5 years is about 23 years and to the nearest hundred dollars that is $1500 so that is the answer

Hope this helps! :)

5 0

3 years ago

Read 2 more answers

Look at these equations.

Ganezh [65]

Answer:

1.5

Step-by-step explanation:

a+8=b+5

a+3=b

b=1.5

5 0

3 years ago

Read 2 more answers

You know the measure of the exterior angle which forms a linear pair with the vertex angle. Describe two ways you can find measu

aev [14]

Answer:

Step-by-step explanation:

A linear pair are two given angles whose sum is equal to $180^{o}$ .

Let the exterior angle be represented by $x^{o}$ , and the three interior angles of the triangle be represented by $a^{o}$ , $b^{o}$ and $c^{o}$ .

Assume that the vertex angle $c^{o}$ is the linear pair to the exterior angle $x^{o}$ .

i.e $x^{o}$ + $c^{o}$ = $180^{o}$ (sum of angles on a straight line)

Thus,

i. $a^{o}$ + $b^{o}$ = $x^{o}$ (sum of two opposite interior angles is equal to an exterior angle)

⇒ $a^{o}$ = $x^{o}$ - $b^{o}$

Also,

$b^{o}$ = $x^{o}$ - $a^{o}$

But,

$a^{o}$ + $b^{o}$ + $c^{o}$ = $180^{o}$ (sum of angles in a triangle)

⇒ $c^{o}$ = $180^{o}$ - ( $a^{o}$ + $b^{o}$ )

and

$a^{o}$ + $b^{o}$ = $180^{o}$ - $c^{o}$

ii. $a^{o}$ + $b^{o}$ + $c^{o}$ = $180^{o}$ (sum of angles in a triangle)

$a^{o}$ = $180^{o}$ - ( $b^{o}$ + $c^{o}$ )

Also,

$a^{o}$ + $b^{o}$ = $x^{o}$

⇒ $b^{o}$ = $x^{o}$ - $a^{o}$

$c^{o}$ = $180^{o}$ - $x^{o}$

8 0

3 years ago

15 points!!! GEOMETRY help please!!<br> Questions attached!

dolphi86 [110]

3. Look at the picture.

We have the right angle triangle. We know the sum of measures of angles in triangle is equal 180°. Therefore:

$x^o+90^o+43^o=180^o\\\\x^o+133^o=180^o\ \ \ |-133^o\\\\x^o=47^o$

$Answer:\ \boxed{47^o}$

4.
Look at the picture.

Use Pythagorean theorem:

$x^2+14^2=(10+x)^2\\\\x^2+196=10^2+2\cdot10\cdot x+x^2\ \ \ \ |-x^2\\\\196=100+20x\ \ \ |-100\\\\20x=96\ \ \ |:20\\\\x=4.8$

$Used:\ (a+b)^2=a^2+2ab+b^2$

$Answer:\ \boxed{4.8\ units}$

5.
TRUE: 1; 2; 4

6.
We find a slope of the line OP:

$m=\dfrac{y_2-y_1}{x_2-x_1}\\\\O(2;\ 6)\to x_1=2;\ y_1=6\\\\P(4;\ 3)\to x_2=4;\ y_2=3\\\\m=\dfrac{3-6}{4-2}=\dfrac{-3}{2}$

We have: $OP:\ y=-\dfrac{3}{2}x+b$

Now, we must find the slope of the line perpendicular to the line OP.
We know:

$k:y=m_1x+b;\ l:y=m_2x+c\\\\k\ \perp\ l\iff m_1m_2=-1$

therefore

$-\dfrac{3}{2}m_2=-1\ \ \ |\cdot\left(-\dfrac{2}{3}\right)\\\\m_2=\dfrac{2}{3}$

So. We have the answer! :)

$Answer:\ \boxed{y=\dfrac{2}{3}x+\dfrac{1}{3}}$

6 0

3 years ago