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Alex
3 years ago
8

your planning to build a boat. you have a sample board of wood that you want to use . the board has an area of 1/3 ft squared an

d weighs 1/5 lbs.what is the weight of the wood in pounds per square root?
Mathematics
1 answer:
frosja888 [35]3 years ago
8 0
Given:
Area of sample board: 1/3 square ft.
Weight of sample board: 1/5 lbs

We need to get the weight of the whole square foot.

1/3 square foot is only a part of the whole square foot. Its corresponding weight is 1/5 pounds. We need to divide the area by its corresponding weight to get the total weight per square foot.

1/3 ÷ 1/5 

Rules of dividing fractions:
1st fraction: 1/3 ; 2nd fraction: 1/5

1) Get the reciprocal of the 2nd fraction. 1/5 ⇒ 5/1

2) Multiply 1st fraction to the reciprocal of the 2nd fraction
1/3 * 5/1 = 5/3

3) Simplify fraction.
5/3 is an improper fraction. To simplify it, it needs to become a mixed fraction.

5/3 = 1 2/3 pounds.



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dimaraw [331]

Answer:

Part 4) sin(\theta)=\frac{12}{13}

Part 10) The angle of elevation is 40.36\°

Part 11) The angle of depression is 78.61\°

Part 12) arcsin(0.5)=30\°  or arcsin(0.5)=150\°

Part 13) -45\°  or 225\°

Step-by-step explanation:

Part 4) we have that

cos(\theta)=-\frac{5}{13}

The angle theta lies in Quadrant II

so

The sine of angle theta is positive

Remember that

sin^{2}(\theta)+ cos^{2}(\theta)=1

substitute the given value

sin^{2}(\theta)+(-\frac{5}{13})^{2}=1

sin^{2}(\theta)+(\frac{25}{169})=1

sin^{2}(\theta)=1-(\frac{25}{169})  

sin^{2}(\theta)=(\frac{144}{169})

sin(\theta)=\frac{12}{13}

Part 10)

Let

\theta ----> angle of elevation

we know that

tan(\theta)=\frac{85}{100} ----> opposite side angle theta divided by adjacent side angle theta

\theta=arctan(\frac{85}{100})=40.36\°

Part 11)

Let

\theta ----> angle of depression

we know that

sin(\theta)=\frac{5,389-2,405}{3,044} ----> opposite side angle theta divided by hypotenuse

sin(\theta)=\frac{2,984}{3,044}

\theta=arcsin(\frac{2,984}{3,044})=78.61\°

Part 12) What is the exact value of arcsin(0.5)?

Remember that

sin(30\°)=0.5

therefore

arcsin(0.5) -----> has two solutions

arcsin(0.5)=30\° ----> I Quadrant

or

arcsin(0.5)=180\°-30\°=150\° ----> II Quadrant

Part 13) What is the exact value of arcsin(-\frac{\sqrt{2}}{2})

The sine is negative

so

The angle lies in Quadrant III or Quadrant IV

Remember that

sin(45\°)=\frac{\sqrt{2}}{2}

therefore

arcsin(-\frac{\sqrt{2}}{2}) ----> has two solutions

arcsin(-\frac{\sqrt{2}}{2})=-45\° ----> IV Quadrant

or

arcsin(-\frac{\sqrt{2}}{2})=180\°+45\°=225\° ----> III Quadrant

5 0
3 years ago
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Aneli [31]

Answer:

-1 5/9

Step-by-step explanation:

so first, simplify the signs so they don’t confuse you,

-5/6 - 17/18 + 2/9 (Since there are two negatives near the end, and their tecxhnically being mulitplied, -2/9*-1 (I added 1 for place holder) and when you multiply a negatives by a negative, you get a positive.

So find the lcm of the denominators which is 18 in this case

-15/18 - 17/18 + 4/18

Now solve the problem from left to right

you’ll get -1 5/9 if you simplified

4 0
2 years ago
Read 2 more answers
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Arte-miy333 [17]
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2 years ago
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Rudiy27

Answer:

<u>Answer</u><u>:</u><u> </u><u>D</u>

Step-by-step explanation:

2(x - 3) \geqslant  - 3( - 3 + x)

open the brackets [ distributive property ]

2x - 6 \geqslant 9 - 3x

collect like terms:

2x + 3x \geqslant 9 + 6 \\ 5x  \geqslant 15

divide either sides by 5:

\frac{5x}{5}  \geqslant  \frac{15}{5}  \\  \\ { \underline{ \bf{ \:  \: x \geqslant 3 \:  \: }}}

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