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1 year ago

The law of cosines is a^2+b^2-2abcosC=c^2. Find the value of 2abcosC.

Mathematics

2 answers:

Ghella [55]1 year ago

5 0

Answer:

(D) $7=2abcosC$

Step-by-step explanation:

It is given from figure that c=1, a=2 and b=2, thus using the law of cosines, we get

$c^2=a^2+b^2-2abcosC$

Substituting the given values, we get

$(1)^2=(2)^2+(2)^2-2abcosC$

$1=4+4-2abcosC$

$1=8-2abcosC$

$1-8=-2abcosC$

$-7=-2abcosc$

$7=2abcosC$

Thus, the value of $2abcosC$ is $7$ .

Hence, option (D) is correct.

polet [3.4K]1 year ago

4 0

2ab x cos (C) = 7 because

a^2 + b^2 - 2ab x cos(C) = c^2
2ab x cos(C) = a^2 + b^2 - c^2
2ab x cos(C) = 2^2 + 2^2 - 1^2
2ab x cos (C) = 7

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Manny is making 12 quarts of orange juice from concentrate and water. The number of quarts of water is 3 times the number of qua

trasher [3.6K]

Answer: There are 3 quarts of concentrate and 9 quarts of water.

Step-by-step explanation:

Since we have given that

Ratio of number of quarts of water to number of quarts of concentrate is

3:1

Number of quarts of orange juice from concentrate and water = 12 quarts

So, the number of quarts of concentrate would be

$\dfrac{1}{4}\times 12\\\\=\dfrac{12}{4}\\\\=3\ quarts$

the number of quarts of water would be

$\dfrac{3}{4}\times 12\\\\=3\times 3\\\\=9\ quarts$

Hence, there are 3 quarts of concentrate and 9 quarts of water.

8 0

2 years ago

Chuck has a gross pay of $815.70. By how much will Chuck’s gross pay be reduced if he has the following items withheld? federal

tangare [24]

Chuck has a gross pay of $815.70. His gross pay will be reduced by:

Federal tax of $56;
Social Security tax that is 6.2% of his gross pay;
Medicare tax that is 1.45% of his gross pay;
State tax that is 19% of his federal tax.

Let's count:

1. gross pay of $815.70 - 100%,

Social Security tax of $x - 6.2%.

Then

$\dfrac{815.70}{x}=\dfrac{100}{6.2} ,\\ \\815.70\cdot 6.2=x\cdot 100,\\ \\x=\dfrac{815.70\cdot 6.2}{100} =50.5734.$

2. gross pay of $815.70 - 100%,

Medicare tax of $y - 1.45%.

Then

$\dfrac{815.70}{y}=\dfrac{100}{1.45} ,\\ \\815.70\cdot 1.45=y\cdot 100,\\ \\y=\dfrac{815.70\cdot 1.45}{100} =11.82765.$

3. Federal tax of $56 - 100%,

State tax $z - 19%.

Then

$\dfrac{56}{z}=\dfrac{100}{19} ,\\ \\56\cdot 19=z\cdot 100,\\ \\z=\dfrac{56\cdot 19}{100} =10.64.$

4. Chuck’s gross pay will be reduced by

$\$56+\$50.5734+\$11.82765+\$10.64=\$129.04105\approx \$129.04.$

3 0

2 years ago

Read 2 more answers

$1.12 for 8.2 ounces? Unit Rate

Reil [10]

That is around 13 or 14 cents. The specific answer is 13.65853659 cents, but you can either round up to 14 or round down to 13 (rounding up to 14 is the correct way to do it.)

First you divide 1.12 by 8.2 to get the unit rate because It takes $1.12 to buy 8.2 ounces. 1.12/8.2=13.65853659

4 0

1 year ago

For the upcoming holiday season, Dorothy wants to mold 20 bars of chocolate into tiny pyramids. Each bar of chocolate contains 6

lorasvet [3.4K]

Answer:

A. 180

Step-by-step explanation:

$20*6=120\ in^{3}\ of\ chocolate \\\\\frac{1*1*2}{3} =\frac{2}{3}\ in^{3}\ per\ pyramid\\\\\frac{120}{\frac{2}{3} }\ cubes\\\\\frac{120*3}{2}\ cubes\\\\\frac{360}{2}\ cubes\\\\180\ cubes$