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Brrunno [24]
2 years ago
7

PLEASE HELP!!

Mathematics
1 answer:
Elena-2011 [213]2 years ago
5 0
For this case we have the following equation:
 S = 0.159 + 0.118logD
 Substituting S = 0.2 we have:
 0.2 = 0.159 + 0.118logD
 From here, we clear the value of D.
 We have then:
 0.2 - 0.159 = 0.118logD
 logD = (0.2 - 0.159) / (0.118)
 logD = 0.347457627
 10 ^ (logD) = 10 ^ 0.347457627
 D = 10 ^ (0.347457627)
 D = 2.23 mm
 Answer:
 
The average diameter, D, of the sand particles for a beach is:
 
D = 2.23 mm
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In circle D, angle ADC measures (7x + 2)°. Arc AC
Akimi4 [234]

Answer:

The measure of angle ABC is 36° ⇒ 1st answer

Step-by-step explanation:

Let us revise some important facts in the circle

The measure of the center angle is equal to the measure of its subtended arc

The measure of the inscribed angle is equal to half the measure of the central angle subtended by the same arc

The vertex of a central angle is the center of the circle and its sides are radii in the circle

The vertex of an inscribed angle is a point on the circle, and its sides are chords in the circle

In circle D

∵ D is the center of the circle

∵ A and C lie on the circle

- DA and DC are radii

∴ ∠ADC is a central angle subtended by arc AC

∴ m∠ADC = m of arc AC

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∵ m of arc AC = (8x - 8)°

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- subtract 7x from both sides

∴ x - 8 = 2

- Add 8 to both sides

∴ x = 10

Substitute the value of x in the measure of ∠ADC

∵ m∠ADC = 7(10) + 2 = 70 + 2

∴ m∠ADC = 72°

∵ AB and BC are two chords in circle D

∴ ∠ABC is an inscribed angle subtended by arc AC

∵ ∠ADC is a central angle subtended by arc AC

- By using the 2nd fact above

∴ m∠ABC =  m∠ADC

∴ m∠ABC =  × 72

∴ m∠ABC = 36°

7 0
2 years ago
Amal Worked a total of 30 hours last week. On Saturday And Sunday He Worked 5 times as many hours than he worked the rest of the
Lilit [14]
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If x is how much he worked on the weekdays and he worked 5 times as much on Sat and Sun, then hopefully you agree that on Sat and Sun he worked 5x hours.
So we have 5x hours on the weekends and x hours on the weekdays, so in total for the whole week we have 5x + x = 6x hours in total.
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