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iren [92.7K]
3 years ago
8

If I drop a book from the same height as a feather which will land first?

Mathematics
2 answers:
g100num [7]3 years ago
4 0
The book will land first
liberstina [14]3 years ago
4 0
The book will drop first because it is heavier, but the feather is lighter.
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The area of the sector formed by the 110 degree central angle is 50 units squared. What is the circumference of the circle
Mama L [17]

Answer:

The circumference of the circle is C=45.346 \:units.

Step-by-step explanation:

A sector is the part of a circle enclosed by two radii of a circle and their intercepted arc. A pie-shaped part of a circle.

The area of a circle is given by A_{circle}=\pi r^2

The formula used to calculate the area of a sector of a circle is:

A_{sector}=\frac{central \:angle}{360} \cdot {Area \:of \:whole \:circle}\\\\A_{sector}=\frac{\theta}{360} \cdot \pi r^2

The circumference of a circle is the distance around the outside of the circle and its given by

C=2\pi r

We know the central angle \theta = 110º and the area of the sector 50 units squared.

First, we use the formula to calculate the area of a sector to find the radius.

50=\frac{110}{360} \cdot \pi r^2\\\\\frac{110}{360}\pi r^2=50\\\\\frac{11\pi }{36}r^2=50\\\\11\pi r^2=1800\\\\r^2=\frac{1800}{11\pi }\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\r=\sqrt{\frac{1800}{11\pi }},\:r=-\sqrt{\frac{1800}{11\pi }}

The radius can't be negative. Therefore,

r=\sqrt{\frac{1800}{11\pi }}\approx 7.217 \:units

Next, we apply the formula for the circumference of a circle.

C=2\pi (7.217)=45.346 \:units

7 0
3 years ago
Solve Systems of Equations Algebracallyy=x+2 y=-3x
Sphinxa [80]

y = x + 2

y = -3x

Do y = -3x in y = x + 2

y = x + 2

-3x = x + 2

-3x - x = 2

-4x = 2

x = -2/4

x = -1/2

Now put x = -1/2 in y = -3x

y = -3x

y = -3.(-1/2)

y = 3/2

5 0
3 years ago
Divide 4x2 − 19x − 30 by x − 6.
padilas [110]

Answer: 4x+5

Step-by-step explanation:

6 0
3 years ago
A spherical balloon has a 34-in. diameter when it is fully inflated. Half of the air is let out of the balloon. Assume that the
jeka57 [31]

Answer:

a. 20,579.52 cubic inches

b.10,289.76  cubic inches.

c. 13.49 inches

Step-by-step explanation:

Hi, to answer this question we have to calculate the volume of a sphere:

Volume of a sphere: 4/3 π r³

Since diameter (d) = 2 radius (r)

Replacing with the value given:

34 =2r

34/2=r

r= 17 in

Back with the volume formula:

V = 4/3 π r³

V =4/3 π (17)³

V = 20,579.52 cubic inches

The volume of the half-inflated balloon is equal to the volume of the sphere divided by 2.

20,579.52/2 = 10,289.76  cubic inches.

To find the radius of the half-inflated balloon we have to apply again the volume formula and substitute v=10,289.76

10,289.76= 4/3 π r³

Solving for r

10,289.76/ (4/3 π)= r³

2,456.5 = r³

∛2,456.5 = r

r = 13.49 inches

7 0
3 years ago
An item is priced at $80. It is on sale for 20% off the regular price. What is the sale price?
Masja [62]
Regular Pirce = $80.

Discount = 20%

Discount = 20% x $80 = 0.2 x 80 = $16

Sale Price = 80 - 16 = $64

----------------------------------------------------
Answer: The Sale Price is $64.
----------------------------------------------------
4 0
3 years ago
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