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1 year ago

Solve the following equation for x: 6x-16=14

Mathematics

1 answer:

Ivenika [448]1 year ago

8 0

To solve the equation for x, first, we add 16 from both sides of the equation:

$\begin{gathered} 6x-16+16=14+16, \\ 6x=30. \end{gathered}$

Now, we divide by 6:

$\frac{6x}{6}=\frac{30}{6}.$

Finally, we get that:

$x=5.$

Answer:

$x=5.$

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What are the exact values of sin(2π3radians) and cos(2π3radians)

deff fn [24]

We know that
2π/3 radians-------> convert to degrees-----> 2*180/3---> 120°
120°=90°+30°

Part a) Find <span>sin(2π/3)
</span>sin(2π/3)=sin (90°+30°)
we know that
sin (A+B)=sin A*cos B+cos A*sin B
so
sin (90°+30°)=sin 90*cos 30+cos 90*sin 30
sin 90=1
cos 30=√3/2
cos 90=0
sin 30=1/2
sin (90°+30°)=1*√3/2+0*1/2-----> √3/2

the answer part a) is
sin(2π/3)=√3/2

Part b) Find cos (2π/3)
cos (2π/3)=cos (90°+30°)
we know that
cos (A+B)=cos A*cos B-sin A*sin B
so
cos (90°+30°)=cos 90*cos 30-sin 90*sin 30
sin 90=1
cos 30=√3/2
cos 90=0
sin 30=1/2
cos (90°+30°)=0*√3/2-1*1/2----> -1/2

the answer part b) is
cos (2π/3)=-1/2

8 0

3 years ago

An option to buy a stock is priced at $150. If the stock closes above 30 next Thursday, the option will be worth $1000. If it cl

valentina_108 [34]

Answer:

Step-by-step explanation:

An option to buy a stock is priced at $150. If the stock closes above 30 next Thursday, the option will be worth $1000. If it closes below 20, the option will be worth nothing, and if it closes between 20 and 30, the option will be worth $200. A trader thinks there is a 50% chance that the stock will close in the 20-30 range, a 20% chance that it will close above 30, and a 30% chance that it will fall below 20.

a) Let X represent the price of the option

$1000 20/100 = 0.2

$200 50/100 = 0.5

$0 30/100 = 0.3

b) Expected option price

$= \sum x.P(X=x)\\\\ = 1000 * 0.2 + 200 * 0.5 + 0 = \$ 300$

Therefore expected gain = $300 - $150 = $150

c) The trader should buy the stock. Since there is an positive expected gain($150) in trading that stock option.

7 0

4 years ago

!!!!!! URGENT PLS HELP ME ANSWER !!!!

laila [671]

Answer:

1) A = 547.1136, C = 82.896

2) A = 678.5226, C = 92.316

3) A = 844.5344, C = 102.992

4) A = 1554.49625, C = 139.73

5) A = 1561.4906, C = 140.044

6) A = 994.8776, C = 111.784

Step-by-step explanation:

$A = \Pi (\frac{D}{2})^2 = 3.14 * (\frac{26.4}{2})^2 = 3.14 * 13.2^2 = 547.1136$

$C = \Pi D = 3.14 * 26.4 = 82.896$

$A = \Pi r^2 = 3.14*(14.7)^2 = 678.5226$

$C = 2\Pi r = 14.7*2 * 3.14 = 92.316$

$A = \Pi (\frac{D}{2})^2 = 3.14 * (\frac{32.8}{2})^2 = 3.14 * 16.4^2 = 844.5344$

$C = \Pi D = 3.14 * 32.8 = 102.992$

$A = \Pi (\frac{D}{2})^2 = 3.14 * (\frac{44.5}{2})^2 = 3.14 * 22.25^2 = 1554.49625$

$C = \Pi D = 44.5*3.14 = 139.73$

$A = \Pi r^2 = 3.14*22.3^2 = 1561.4906$

$C = 2\Pi r = 2 * 3.14 * 22.3 = 140.044$

$A = \Pi r^2 = 3.14 * 17.8^2 = 994.8776$

$C = 2\Pi r = 2 * 3.14 * 17.8 = 111.784$

8 0

3 years ago

What is the degree of v7

nikklg [1K]

2.645 lalalalalalalalalala

3 0

3 years ago

Elena needs to ship a 61 cm concert flute to a customer. She has two rectangular boxes. One is 25 cm by 25 cm by 50 cm. The othe

spin [16.1K]

A) V= lwh ,so, V= 25cm*25cm*50cm= 31250 cm^3 shape

b) V=lwh,so, V=10cm*12cm*58cm= 6960 cm^3 shape
c) It is a) because the volume is much bigger.

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4 years ago