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2 years ago

Convert 28.7251° to degrees, minutes, and seconds. Round to the nearest second.

Mathematics

1 answer:

Leni [432]2 years ago

8 0

28.7251 =

28 degrees

then take the decimal and multiply by 60 to get the minutes

so 0.7251 *60 = 43.506, use the whole number (43)

so now you have 28 degrees, 43 minutes

now take the remaining decimal ( 0.506) and multiply by 60

0.506*60= 30.36

when you have a decimal left over for the seconds, keep that as is.

so you now have 28 degrees, 43 minutes and 30.36 seconds

use ' for minutes and " for seconds

28 degrees 43' 30.36"

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Darcie wants to crochet a minimum of 3 blankets blankets to donate to a homeless shelter. Darcie crochets at a rate of 1/15 of a

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Answer:

The inequality to determine the number of days, $s$ , Darcie can skip crocheting and still meet her goal is:

$s\leq 15$

Thus, Darcie can skip a maximum of 15 days.

Step-by-step explanation:

Question

Darcie wants to crochet a minimum of 3 blankets to donate to a homeless shelter. Darcie crochets at a rate of 1/15 of a blanket per day. She has 60 days until when she wants to donate the blankets, but she also wants to skip crocheting some days so she can volunteer in other ways. Write an inequality to determine the number of days, s, Darcie can skip crocheting and still meet her goal.

Given:

Darcie has a target to crochet a minimum of 3 blankets.

Rate at which Darcie crochets = $\frac{1}{15}$ of a blanket per day.

Darcie has 60 days to crochet the blankets

To write an inequality to determine the number of days, $s$ , Darcie can skip crocheting and still meet her goal.

Solution:

The number of days Darcie can skip crocheting is represented by $s$

So, number of days left for Darcie to crochet = $60-s$

In 1 day Darcie crochets $\frac{1}{15}$ of a blanket.

So, in $(60-s)$ days she will crochet = $\frac{1}{15}(60-s)$ blankets.

Her aim is to crochet at least 3 blankets.

Thus, the inequality can be given as:

$\frac{1}{15}(60-s)\geq 3$

Solving for $s$

Multiplying both sides by 15 to remove fractions.

$15\times\frac{1}{15}(60-s)\geq 3\times 15$

$60-s\geq 45$

Subtracting both sides by 60.

$60-60-s\geq 45-60$

$-s\geq -15$

Dividing both sides by -1.

$\frac{-s}{-1}\leq \frac{-15}{-1}$ [ On dividing by negative number the sign of the inequality is reversed]

∴ $s\leq 15$

Thus, Darcie can skip a maximum of 15 days.

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1 year ago

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Find the distance from (4, −7, 6) to each of the following.

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Answer:

(a) 6 units

(b) 4 units

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Step-by-step explanation:

The distance d from one point (x₁, y₁, z₁) to another point (x₂, y₂, z₂) is given by;

d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Now from the question;

(a) The distance from (4, -7, 6) to the xy-plane

The xy-plane is the point where z is 0. i.e

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d = √[(4 - 4)² + (-7 - (-7))² + (0 - 6)²]

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d = √(-6)²

d = √36

d = 6

Hence, the distance to the xy plane is 6 units

(b) The distance from (4, -7, 6) to the yz-plane

The yz-plane is the point where x is 0. i.e

yz-plane = (0, -7, 6).

Therefore, the distance d is from (4, -7, 6) to (0, -7, 6)

d = √[(4 - 0)² + (-7 - (-7))² + (6 - 6)²]

d = √[(4)² + (0)² + (0)²]

d = √(4)²

d = √16

d = 4

Hence, the distance to the yz plane is 4 units

(c) The distance from (4, -7, 6) to the xz-plane

The xz-plane is the point where y is 0. i.e

xz-plane = (4, 0, 6).

Therefore, the distance d is from (4, -7, 6) to (4, 0, 6)

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(d) The distance from (4, -7, 6) to the x axis

The x axis is the point where y and z are 0. i.e

x-axis = (4, 0, 0).

Therefore, the distance d is from (4, -7, 6) to (4, 0, 0)

d = √[(4 - 4)² + (-7 - 0)² + (6 - 0)²]

d = √[(0)² + (-7)² + (6)²]

d = √[(-7)² + (6)²]

d = √[(49 + 36)]

d = √(85)

d = 9.22

Hence, the distance to the x axis is 9.22 units

(e) The distance from (4, -7, 6) to the y axis

The x axis is the point where x and z are 0. i.e

y-axis = (0, -7, 0).

Therefore, the distance d is from (4, -7, 6) to (0, -7, 0)

d = √[(4 - 0)² + (-7 - (-7))² + (6 - 0)²]

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d = √[(16 + 36)]

d = √(52)

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Hence, the distance to the y axis is 7.21 units

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The z axis is the point where x and y are 0. i.e

z-axis = (0, 0, 6).

Therefore, the distance d is from (4, -7, 6) to (0, 0 6)

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