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3 years ago

May I also have help with this question

Mathematics

2 answers:

KATRIN_1 [288]3 years ago

5 0

The independent variable (the one they want) is the # of hours worked, since that determines the price.

All the other answers contain information not included in the problem

Nana76 [90]3 years ago

3 0

(B) as you are finding the independent variable which is the number of hours so it would be B or C. But the plumber didn't travel so it is B

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Please dont ignore, Need help!!! Use the law of sines/cosines to find..

Ket [755]

Answer:

16. Angle C is approximately 13.0 degrees.

17. The length of segment BC is approximately 45.0.

18. Angle B is approximately 26.0 degrees.

15. The length of segment DF "e" is approximately 12.9.

Step-by-step explanation:

By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.

For triangle ABC:

$\sin{A} = \sin{103\textdegree{}}$ ,
The opposite side of angle A $a = BC = 26$ ,
The angle C is to be found, and
The length of the side opposite to angle C $c = AB = 6$ .

$\displaystyle \frac{\sin{C}}{\sin{A}} = \frac{c}{a}$ .

$\displaystyle \sin{C} = \frac{c}{a}\cdot \sin{A} = \frac{6}{26}\times \sin{103\textdegree}$ .

$\displaystyle C = \sin^{-1}{(\sin{C}}) = \sin^{-1}{\left(\frac{c}{a}\cdot \sin{A}\right)} = \sin^{-1}{\left(\frac{6}{26}\times \sin{103\textdegree}}\right)} = 13.0\textdegree{}$ .

Note that the inverse sine function here $\sin^{-1}()$ is also known as arcsin.

By the law of cosine,

$c^{2} = a^{2} + b^{2} - 2\;a\cdot b\cdot \cos{C}$ ,

where

$a$ , $b$ , and $c$ are the lengths of sides of triangle ABC, and
$\cos{C}$ is the cosine of angle C.

For triangle ABC:

$b = 21$ ,
$c = 30$ ,
The length of $a$ (segment BC) is to be found, and
The cosine of angle A is $\cos{123\textdegree}$ .

Therefore, replace C in the equation with A, and the law of cosine will become:

$a^{2} = b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}$ .

$\displaystyle \begin{aligned}a &= \sqrt{b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}}\\&=\sqrt{21^{2} + 30^{2} - 2\times 21\times 30 \times \cos{123\textdegree}}\\&=45.0 \end{aligned}$ .

For triangle ABC:

$a = 14$ ,
$b = 9$ ,
$c = 6$ , and
Angle B is to be found.

Start by finding the cosine of angle B. Apply the law of cosine.

$b^{2} = a^{2} + c^{2} - 2\;a\cdot c\cdot \cos{B}$ .

$\displaystyle \cos{B} = \frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}$ .

$\displaystyle B = \cos^{-1}{\left(\frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}\right)} = \cos^{-1}{\left(\frac{14^{2} + 6^{2} - 9^{2}}{2\times 14\times 6}\right)} = 26.0\textdegree$ .

For triangle DEF:

The length of segment DF is to be found,
The length of segment EF is 9,
The sine of angle E is $\sin{64\textdegree}}$ , and
The sine of angle D is $\sin{39\textdegree}$ .

Apply the law of sine:

$\displaystyle \frac{DF}{EF} = \frac{\sin{E}}{\sin{D}}$

$\displaystyle DF = \frac{\sin{E}}{\sin{D}}\cdot EF = \frac{\sin{64\textdegree}}{39\textdegree} \times 9 = 12.9$ .

7 0

3 years ago

I need help on 2 & 3

lora16 [44]

Answer:

NUMBER TWO IS ------ 22,29,37

I DONT KNOW NUMBER THREE

Step-by-step explanation:

I HOPE I HELPED U 229 999 0523

5 0

3 years ago

Write each fraction or mixed number as a decimal. 3 1/5=?

kompoz [17]

The answer is 15 or 3 I think but I'm not sure

5 0

3 years ago

The price of a particular stock is represented by the linear equation y=-0.91x+103.47

Mama L [17]

To find the price of the stock after 12 weeks, you would have to plug in 12 to x

That would make your equation: y = -0.91(12) + 103.47

Then, you solve:

-0.91(12) would be -10.12

Your equation will now look like this:

y = - 10.12 + 103.47

Then you add -10.12 to 103.47

-10.12 + 103.47 = 92.55

y = 92.55

After 12 weeks, the price of the stocks would be $92.55

4 0

3 years ago

Read 2 more answers

a recipe for one pumpkin pie calls for 1 1/4 cups of sugar Elena only has 1/2 cup of sugar and she needs to make for pumpkin pie

seraphim [82]

Answer: she would need four and a half cups more of sugar.

Step-by-step explanation:

You have to add together all of them sugar she would have needed so (1 1/4 times 4) and then subtract what she already had and that gives you 4 and 1/2 cups she would need. Hope this helps

7 0

3 years ago