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2 years ago

Students are making the scenery for a school play. They use a large piece of plywood

Mathematics

1 answer:

Kruka [31]2 years ago

8 0

Answer:

57.72 in^2

Step-by-step explanation:

Question 1. Shapes are triangle, semi-circle, and rectangle.

Question 2.Find area of rectangle first. Then area of triangle and circle. Subtract area of triangle and circle. Then add the difference with the rectangles area.

Question 3.

Rectangle's area:48 in^2

Triangles area:8*4/2= 16 in^2

Circle Area: pi*r^2/2(since its a semi-circle)

3.14*2^2=3.14*4=12.56/2=6.28 in^2

Question 4.

16-6.28=9.72

9.72+48=57.72 in^2

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Part A: Virginia earned $14 walking her neighbors' dogs on Saturday. She earned some extra money on Sunday doing the same thing.

shutvik [7]

Part A: 14 + 14 = y or 14•2 = y
Part B: (n•2) - 2 = a

Not 100% sure that this is correct but, hope this helps! :) If you have any questions than ask me.

7 0

3 years ago

Prove the formula for (d/dx)(cos−1(x)) by the same method as for (d/dx)(sin−1(x)). Let y = cos−1(x). Then cos(y) = and 0 ≤ y ≤ π

gtnhenbr [62]

Answer:

$\frac{d(cos^{-1}x )}{dx} = \frac{-1}{\sqrt{1-x^2} }$

Step-by-step explanation:

Given the differential (d/dx)(cos−1(x)), to find the equivalent formula we will differentiate the inverse function using chain rule as shown below;

let;

$y = cos^{-1} x \\\\taking \ cos\ of\ both\ sides\\\\cosy = cos(cos^{-1} x)\\\\cosy = x\\\\x = cosy\\\\\frac{dx}{dy} = -siny\\$

$\frac{dy}{dx} = \frac{-1}{sin y} \\\\from\ trigonometry\ identity,\ sin^{2} x+cos^{2}x = 1\\sinx = \sqrt{1-cos^{2} x}$

Therefore;

$\frac{dy}{dx} = \frac{-1}{\sqrt{1-cos^{2}y } }$

Since x = cos y from the above substitute;

$\frac{dy}{dx} = \frac{-1}{\sqrt{1-x^{2}} }$

Hence, $\frac{d(cos^{-1}x )}{dx} = \frac{-1}{\sqrt{1-x^2} }$ gives the required proof

5 0

4 years ago

Solve and Graph the System of Linear Equations 1) 3 X + 2 Y = 4 X + 2 Y = -4

nikklg [1K]

Answer:

y=-4

x=-12

Step-by-step explanation:

Set up the system

Then you have to cancel out a variable

Then you solve for the remaining variable

Then plug in to find other variable

I'm sorry if that's confusing:/

5 0

3 years ago

What is the slope of a line perpendicular to y =3/4 x+2

Irina18 [472]

Answer:

-3/4 slope

Step-by-step explanation:

y = 3/4 x +2 has a slope of 3/4

Perpendicular lines intersect.

So the slope of the perpendicular line must be opposite.

6 0

3 years ago

Find the number of 4-digit numbers that contain at least three even digits.

mylen [45]

Answer:

2625

Step-by-step explanation:

First let's see all the possible combinations.

(Even=E, Odd= O)

1) EEEO

2) EEOE

3) EOEE

4) OEEE

5) EEEE

Now let's see what E and O possibly could be

E = 0, 2, 4, 5, 6 and 8 (5)

O = 1, 3, 5, 7, 9 (5)

Now we are just simply gonna multiply

1) EEEO = 4*5*5*5

2) EEOE = 4*5*5*5

3) EOEE = 4*5*5*5

4) OEEE = 5*5*5*5

5) EEEE = 4*5*5*5

The even contains a 0, so you can't put 0 in, so (5-1=4), there are only 4 digits for the even.

500 times 4 = 2000

5⁴ = 625

2000+625= 2625

6 0

3 years ago