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bekas [8.4K]
1 year ago
11

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:

a.

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

b.

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

c.

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:

a

n

=

−

2

n

+

15

Step-by-step explanation:

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

−

2

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

a

n

=

a

1

+

d

(

n

−

1

)

.

Arithmetic Sequence:

d

=

−

2

This is the formula of an arithmetic sequence.

a

n

=

a

1

+

d

(

n

−

1

)

Substitute in the values of

a

1

=

13

and

d

=

−

2

.

a

n

=

13

+

(

−

2

)

(

n

−

1

)

Simplify each term.

Tap for more steps...

a

n

=

13

−

2

n

+

2

Add

13

and

2

.

a

n

=

−

2

n

+

15

4 0
2 years ago
PLEASE HELPPP
Y_Kistochka [10]

Answer:

A

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
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