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3 years ago

Samuel is preventing a boulder from rolling down a hill with a slope of 35°. If the boulder

Mathematics

1 answer:

Rashid [163]3 years ago

3 0

Answer:

1,809.98 lb*m/s^2

Step-by-step explanation:

First, we want to know how much weight of the boulder is projected along the path in which the boulder can move.

The weight of the boulder is:

W = 322lb*9.8 m/s^2 = (3,155.6 lb*m/s^2)

This weight has a direction that is vertical, pointing downwards.

Now, we know that the angle of the hill is 35°

The angle that makes the direction of the weight and this angle, is:

(90° - 35°)

(A rough sketch of this situation can be seen in the image below)

Then we need to project the weight over this direction, and that will be given by:

P = W*cos(90° - 35°) = (3,155.6 lb*m/s^2)*cos(55°) = 1,809.98 lb*m/s^2

This is the force that Samuel needs to exert on the boulder if he wants the boulder to not roll down.

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If bd is both the altitude and median of abc then abs is

AVprozaik [17]

Answer:

isosceles

Step-by-step explanation:

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3 years ago

What is the height, in yards, of a cylindrical water tank that holds 1,884 cubic yards of water and has a diameter of 120 feet?

mafiozo [28]

Answer:

The height of the tank is 0.5 yards.

Step-by-step explanation:

To determine what is the height, in yards, of a cylindrical water tank that holds 1,884 cubic yards of water and has a diameter of 120 feet, knowing that the volume of a cylinder is equal to pi multiplied by the radius squared, multiplied by the height, the following calculation must be done:

1 foot = 0.3333 yards

R = Diameter / 2

R = 120/2 = 60

3.14 x 60 ^ 2 x H = 1,884

3.14 x 3,600 x H = 1,884

3.14 x 1,200 x H = 1,884

3.768 x H = 1.884

H = 1,884 / 3,768

H = 0.5

Therefore, the height of the tank is 0.5 yards.

7 0

3 years ago

Angles and transversals thank you

faltersainse [42]

Answer:

#11-13: 118 , 97 , 62

#7-10: 92 , 125 , 56 , 130

Step-by-step explanation:

#11. Supplementary angles (A + B = 180)

(n + 7) + (3n - 47) = 180
n = 55
<ABC = 3(55) - 47 = 118 degrees

#12. Supplementary angles

83 + x = 180
x = 97
<ABC = 97 degrees

#13. Congruent angles (A = B)

(8x - 34) = (5x +2)
x = 12
<DEF = 5 (12) + 2 = 62 degrees

#7. Congruent angles

(3x +23) = 4x
x = 23
<ABC = 4(23) = 92 degrees

#8. Congruent angles

5x = (3x + 50)
x = 25
<MPQ = 3(25) + 50 = 125 degrees

#9. Congruent angles

(a + 28) = 2a
a = 28
<MNP = (28) + 28 = 56 degrees

#10. Congruent angles

5y = (2y + 78)
y = 26
<WXZ = 5(26) = 130 degrees

I hope this helps!

7 0

2 years ago

Billy has $3.00. Bubble gum costs $.30. He bought four pieces.

xenn [34]

Answer:

$0.30 x 4= $1.20

$3.00 divided by $1.20= $1.80

Step-by-step explanation:

I hope this is what you were looking for

7 0

3 years ago

Read 2 more answers

Comparing the two ratios 2/4 and 1/2 2/4 is larger

kumpel [21]

Answer:

3.5 : 7 > 1.2 : 2.5.

Step-by-step explanation:

1. Compare the ratios 4 : 5 and 2 : 3.

Solution:

Express the given ratios as fraction

4 : 5 = 4/5 and 2 : 3 =2/3

Now find the L.C.M (least common multiple) of 5 and 3

The L.C.M (least common multiple) of 5 and 3 is 15.

Making the denominator of each fraction equal to 15, we have

4/5 = (4 ×3)/(5 ×3) = 12/15 and 2/3 = (2 ×5)/(3 ×5) = 10/15

Clearly, 12 > 10

Now, 12/15 > 10/15

Therefore, 4 : 5 > 2 : 3.

2. Compare the ratios 5 : 6 and 7 : 9.

Solution:

Express the given ratios as fraction

5 : 6 = 5/6 and 7 : 9 =7/9

Now find the L.C.M (least common multiple) of 6 and 9

The L.C.M (least common multiple) of 6 and 9 is 18.

Making the denominator of each fraction equal to 18, we have

5/6 = (5 ×3)/(6 ×3) = 15/18 and 7/9 = (7 ×2)/(9 ×2) = 14/18

Clearly, 15 > 14

Now, 15/18 > 14/18

Therefore, 5 : 6 > 7 : 9.

3. Compare the ratios 1.2 : 2.5 and 3.5 : 7.

Solution:

1.2 : 2.5 = 1.2/2.5 and 3.5 : 7 =3.5/7

1.2/2.5 = (1.2 ×10)/(2.5 ×10 ) = 12/25 and 3.5/7 = (3.5 ×10)/(7 ×10) = 35/70 = 1/2

[We removed the decimal point from the ratios now, we will compare the ratio]

Now find the L.C.M (least common multiple) of 25 and 2

The L.C.M (least common multiple) of 25 and 2 is 50.

Making the denominator of each fraction equal to 50, we have

= 12/25 = (12 ×2)/(25 ×2) = 24/50 and 1/2 = (1 ×25)/(2 ×25) = 25/50

Now, 25/50 > 24/50

Therefore, 3.5 : 7 > 1.2 : 2.5.

4 0

2 years ago