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ddd [48]
3 years ago
8

A wooden plank is leaning against a wall. The bottom of the plank is 3 feet from the wall. Answer each of the following question

s, and show all your work.
(a) Find AC, the approximate length of the plank. Round to the nearest tenth of a foot.

(b) Find BC, the height off the ground where board touches as wall. Round to the nearest foot.

Mathematics
1 answer:
Nadusha1986 [10]3 years ago
3 0

AB = ==> distance between the bottom of the plank; and the wall ===> 3 ft.

C ====> 49 degrees

For letter a, to solve for AC:

AC ==> HYPOTENUSE. The angle C is the OPPOSITE side of AB.

use sine :

sin A ===> opposite/hypotenuse

Solve:

sin 49 ====> 3/AC

AC ====> 3 / sin 49

AC ====> 3.96 ft.

For letter b, to solve for BC:

We are now given with the base (3 ft.); and; the hypotenuse (3.96 ft.) so we can use the Pythagorean theorem:

a^2 + b^2 = c^2

Let:

a ===> AB

b ===> BC

c ===> AC

(AB)^2 + (BC)^2 ===> (AC)^2

3^2 + (BC)^2 ===> (3.96)^2

(BC)^2 ===> (3.96)^2 - 3^2

(BC)^2 ===> 6.6816

sqrt (BC)^2 ===> sqrt 6.6816

Answer: BC ===> 2.58 ft.

Hope that helps!!!! : )

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Jeanette is starting a business selling handmade necklaces. She has decided to invest an initial amount of $400 for advertising,
lana66690 [7]

Answer:

25 necklaces

Step-by-step explanation:

each necklace brings $16 profit (20-4=16)

400÷ 16= 25

so, at 25 necklaces, there will be enough profit to break even after paying for the advertising.

8 0
2 years ago
Solve the equation X³+2X²-5X -6​
Natali [406]

Answer: x = {-1, -3, 2}

<u>Step-by-step explanation:</u>

x³ + 2x² - 5x - 6 = 0

Use the rational root theorem to find the possible roots:  ±1, ±2, ±3, ±6

Use Long division, Synthetic division, or plug them into the equation to see which root(s) work <em>(result in a remainder of zero)</em>.

I will use Synthetic division.  Let's try x = 1

1 |  1    2    -5     -6

  |<u>  ↓    1      3     -2 </u>      

     1     3    -2    -8   ← remainder ≠ 0 so x = 1 is NOT a root

 Let's try x = -1

- 1 |  1     2    -5    -6

   |<u>  ↓    -1     -1     6 </u>      

      1     1     -6     0   ← remainder = 0 so x = -1 is a root!

The coefficients of the reduced polynomial are: 1, 1, -6  -->   x² + x - 6

Factor: x² + x - 6

          (x + 3)(x - 2)

Set those factors equal to zero to solve for x:

x + 3 = 0   --> x = -3

x - 2 = 0    --> x = 2

Using Synthetic Division and Factoring the reduced polynomial, we found

x = -1, -3, and 2

6 0
2 years ago
Find the distance travelled by Rubina if she takes 4 rounds of rectangular park whose length and breadth is 45m and 30m
ANTONII [103]
  • Length (l) = 45 m
  • Breadth (b) = 30 m
  • We know, perimeter of a rectangle = 2(length + breadth)
  • Therefore, perimeter of the rectangle
  • = 2(I + b)
  • = 2(45 + 30) m
  • = 2 × 75 m
  • = 150 m
  • So, the distance travelled by Rubina
  • = 4 × 150 m
  • = 600 m

<u>Answer:</u>

<em><u>The </u></em><em><u>distance </u></em><em><u>travelled</u></em><em><u> </u></em><em><u>by </u></em><em><u>Rubina </u></em><em><u>is </u></em><em><u>6</u></em><em><u>0</u></em><em><u>0</u></em><em><u> </u></em><em><u>m.</u></em>

Hope you could get an idea from here.

Doubt clarification - use comment section.

5 0
2 years ago
Ewkrfmwekosdfgseargfaerfgaerfmwoegm :
REY [17]

Answer:

Ok thats really cool thanks :)

5 0
3 years ago
Prove that the statement (ab)^n=a^n * b^n is true using mathematical induction.
mamaluj [8]

Answer:

see below

Step-by-step explanation:

      (ab)^n=a^n * b^n

We need to show that it is true for n=1

assuming that it is true for n = k;

(ab)^n=a^n * b^n

( ab) ^1 = a^1 * b^1

ab = a * b

ab = ab

Then we need to show that it is true for n = ( k+1)

or (ab)^(k+1)=a^( k+1) * b^( k+1)

Starting with

  (ab)^k=a^k * b^k    given

Multiply each side by ab

ab *  (ab)^k= ab *a^k * b^k

   ( ab) ^ ( k+1) = a^ ( k+1) b^ (k+1)

Therefore, the rule is true for every natural number n

5 0
3 years ago
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