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3 years ago

Use the law of cosines to find the balue of cos 0 . Round to answer to two decimal places

Mathematics

1 answer:

chubhunter [2.5K]3 years ago

6 0

Answer:

Step-by-step explanation:

Using the law of cosines then cosΘ is the following quotient

cosΘ = $\frac{a^2+b^2-c^2}{2ab}$

where a = 5.8, b = 10.5 and c = 10.9

cosΘ = $\frac{5.8^2+10.5^2-10.9^2}{2(5.8)(10.5)}$

= $\frac{33.64+110.25-118.81}{121.8}$

= $\frac{25.08}{121.8}$ = 0.21 → C

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A merchant bought some shirts for $120. The next day the price charged for each shirt was reduced by $1. The merchant calculated

Goshia [24]

Answer:

The merchant buys 30 shirts originally.

Step-by-step explanation:

Let us assume that the merchant bought x numbers of shirts in $120.

So, the cost for each shirt is $ $\frac{120}{x}$ .

Now, if the cost for each shirt is reduced by 1$, then he would have bought 10 shirts more i.e. (x + 10) shirts in $120.

So, we can write the following equation as

$(\frac{120}{x} - 1)(x + 10) = 120$

⇒(120 - x)(x + 10) = 120x

⇒ 120x - 10x + 1200 - x² = 120x

⇒ x² +10x - 1200 = 0

⇒ x² + 40x - 30x - 1200 = 0

⇒(x + 40)(x - 30) = 0

⇒ x = - 40 or x = 30

But x can not be negative.

Hence, the merchant buys 30 shirts originally. (Answer)

6 0

3 years ago

Amanda can dig a 10ft by 10ft hole in seven hours. Ming can dig the same hole in 10 hours. How long to dig the hole if they work

Klio2033 [76]

Answer:

The answer should be 4.12 hours

Step-by-step explanation:

Sorry if I am wrong.

5 0

3 years ago

In a certain region, 6% of a city’s population moves to the surrounding suburbs each year, and 4% of the suburban population mov

Charra [1.4K]

Answer:

Follows are the solution to this question:

Step-by-step explanation:

Following are the differential equation:

$\to P(C,S)t+1 = P(C,S)t+(- 0.06Ct +0.04St, 0.06Ct - 0.04St ) \ \ \ \\\\or \ \ \ \ \ \ \ \\\\ \to (0.94Ct + 0.04St, 0.96St + 0.06Ct)$

In equation:

$\to t = 0, \ as \ 2019\\\\\to Ct = 10,000,000 \\\\\to St = 800,000,000\\$

$\to P(C, S)1 = (0.94Ct + 0.04St, 0.96St + 0.06Ct) \\\\$

$= (0.94(10000000) + 0.04(800000), 0.96(800000) + 0.06(10000000))\\\\ = (9,400,000 + 32,000), (768,000 +6000000))\\\\ = (9432000, 1368000)$

$\to P(C, S)2 = (0.94(9432000) + 0.04(1368000), 0.96(1368000) + 0.06(9432000))$

$=(8,866,080 + 54,720), (1,313,280 + 565,920)\\\\=(8,920,800, 1,879,200)$

3 0

3 years ago

What is the perimeter of a square whose diagonal is 3 square root 2? Show all work on how you got your answer

Alika [10]

Answer:

Step-by-step explanation:

Given: Diagonal of square= $3\sqrt{2}$

To find the perimeter of square, we need to find the length of sides of square.

∴ Using the formula of diagonal to find side of square.

Formula; $Diagonal= s\sqrt{2}$

Where, s is side of square.

⇒ $3\sqrt{2} = s\sqrt{2}$

Dividing both side by √2

⇒ $s= \frac{3\sqrt{2} }{\sqrt{2} }$

∴ $s= 3$

Hence, Length of side of square is 3.

Now, finding the perimeter of square.

Formula; $Perimeter= 4s$

⇒ $Perimeter= 4\times 3$

∴ $Perimeter= 12$

Hence, Perimeter of square is 12.

6 0

3 years ago

A plane starts at the origin of the coordinate plane. The plane flies 0.5 units left and 3.5 units up to point X. What are the c

kondor19780726 [428]

Since the plane starts at (0,0), you don't have to factor in anything except for the translation. The plane would be at (-.5, 3.5)

8 0

3 years ago

Read 2 more answers