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1 year ago

Use the Law of Cosines to find the specified missing value. Approximate your answer to the nearest tenth.

Mathematics

1 answer:

Charra [1.4K]1 year ago

4 0

<h3>Answer: 176.6</h3>

Work Shown:

$b^2 = a^2 + c^2 - 2*a*c*\cos(B)\\\\b^2 = 150^2 + 30^2 - 2*150*30*\cos(150)\\\\b^2 \approx 31194.22863406\\\\b \approx \sqrt{31194.22863406}\\\\b \approx 176.618879608211\\\\b \approx 176.6\\\\$

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Please help asap! I need this done tomorrow

d1i1m1o1n [39]

Answer:

2x + 3y = 4

Step-by-step explanation:

The standard form:

Ax + By = C

So from the given form, arrange it to the standard form.

First, simplify the form by distribution.

y + 6 = -2/3(x - 11)

y + 6 = -2/3x + 22/3

Next, you make the fractions into whole by multiplying both sides by 3(this would eliminate all fractions).

(3)y + 3(6) = 3(-2/3x) + 3(22/3)

3y + 18 = -2x + 22

Now, arrange the "Ax" and the "C's".

3y + 18 = -2x + 22

2x + 3y + 18 = 22

2x + 3y = 22 - 18

2x + 3y = 4

Cheers!

6 0

3 years ago

The half-life of a radioactive substance is the time it takes for a quantity of the substance to decay to half of the initial am

posledela

Step-by-step walkthrough:

Well a standard half-life equation looks like this.

$N = N_0 * (\frac{1}{2})^{t/p$

$N_0$ is the starting amount of parent element.

$N$ is the end amount of parent element

$t$ is the time elapsed

$p$ is a half-life decay period

We know that the starting amount is 74g, and the period for a half-life is 2.8 days.

Therefore you can create a function based off of the original equation, just sub in the values you already know.

$N(t) = 74g * (\frac{1}{2})^{t/2.8days$

This is easy now that we have already made the function. Here we just reuse it, but plug in 2.8 days.

$N(t) = 74g * (\frac{1}{2})^{t/2.8days} = N(2.8days) = 74g * (\frac{1}{2})^{2.8days/2.8days}\\= 74g * \frac{1}{2} = 37g$

Now we just gotta do some algebra. Use the original function but this time, replace $N(t)$ with 10g and solve algebraically.

$10g = 74g * (\frac{1}{2})^{t/2.8days}\\\\\frac{10g}{74g} = (\frac{1}{2})^{t/2.8days}$

Take the log of both sides.

$log(\frac{5}{37}) = log((\frac{1}{2})^{t/2.8days})$

Use the exponent rule for log laws that, $log(b^x) = x*log(b)$

$log(\frac{5}{37}) = \frac{t}{2.8days} * log(\frac{1}{2})$

$\frac{log(\frac{5}{37})}{log(\frac{1}{2})} = \frac{t}{2.8days}$

$2.8 * \frac{log(\frac{5}{37})}{log(\frac{1}{2})} = t$

slap that in your calculator and you get

$t = 8.1 days$

7 0

1 year ago

Sequence: 13, 11, 9, 7, ..<br> an = an-1 <br>a1 =

TiliK225 [7]

Answer:

−

Step-by-step explanation:

This is an arithmetic sequence since there is a common difference between each term. In this case, adding

−

to the previous term in the sequence gives the next term. In other words,

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Arithmetic Sequence:

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This is the formula of an arithmetic sequence.

(

−

)

Substitute in the values of

and

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(

−

)

(

−

)

Simplify each term.

Tap for more steps...

−

Add

and

−

4 0

2 years ago

PLEASE HELPPP

Y_Kistochka [10]

Answer:

Step-by-step explanation:

4 0

2 years ago

∠DEF and ∠FEG are supplementary. m∠DEF=(3x+5)°, and m∠FEG=(2x)°. What is the measure of ∠DEF?

Alex787 [66]

Answer:

DEF = 110

Step-by-step explanation:

Supplementary angles add to 180

3x+5 +2x = 180

Combine like terms

5x +5 = 180

Subtract 5 from each side

5x = 175

Divide each side by 5

5x/5 = 175/5

x =35

DEF = 3x+5

= 3*35 +5

= 105+5

= 110

6 0

2 years ago