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butalik [34]
3 years ago
15

Find the exact value of the expression. Do not use a calculator. If tan θ = 9, find the exact value of cot θ

Mathematics
1 answer:
adelina 88 [10]3 years ago
3 0

\bf tan(\theta )=9\implies tan(\theta )=\cfrac{\stackrel{opposite}{9}}{\stackrel{adjacent}{1}}\impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}


\bf c=\sqrt{1^2+9^2}\implies c=\sqrt{82} \\\\[-0.35em] ~\dotfill\\\\ cos(\theta )=\cfrac{\stackrel{adjacent}{1}}{\stackrel{hypotenuse}{\sqrt{82}}}\implies \stackrel{\textit{rationalizing the denominator}}{cos(\theta )=\cfrac{1}{\sqrt{82}}\cdot \cfrac{\sqrt{82}}{\sqrt{82}}}\implies cos(\theta )=\cfrac{\sqrt{82}}{82}

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An artist combines copper and other metals to make bronze. A bronze sculpture
natka813 [3]

Answer:

The dolphin statue is 86% copper, while the bird statue is 83% copper, making the dolphin sculpture more coppery.

Step-by-step explanation:

Since an artist combines copper and other metals to make bronze, and a bronze sculpture of a dolphin contains 43 g of copper for every 7 g of other metals, while a bronze sculpture of a bird contains 83 g of copper for every 17 g of other metals, to determine which sculpture is more coppery the following calculation must be performed:

Dolphin:

43 + 7 = 50

50 = 100

43 = X

43 x 100/50 = X

86 = X

Bird:

83 + 17 = 100

100 = 100

83 = X

83 x 100/100 = X

83 = X

Therefore, the dolphin statue is 86% copper, while the bird statue is 83% copper, making the dolphin sculpture more coppery.

3 0
3 years ago
PLEASE HELP!! I"LL MARK YOU AS A BRAINLEIST
Anon25 [30]

Answer:

3 units to the right

Reasoning:

The x-3 will cause it to shift 3 units right, as x=3 would be the equivalence as x=0 then

I hope this helps and good luck!

7 0
3 years ago
What on a number line are the fractions before 1
AVprozaik [17]
The most used fractions on a number line used before 1 are 1/4, 1/2, 1/3, 2/4, 2/3, and 3/4.

4 0
4 years ago
Replace ? with a whole number to make the statements true.
Makovka662 [10]

Answer:

  a.  5

  b.  545

  c.  0

Step-by-step explanation:

These are straightforward division problems, easily solved using your own memorized multiplication facts, or using a calculator.

a.  20 ÷ 4 = 5 means 5 × 4 = 20

b.  2725 ÷ 5 = 545 means 545 × 5 = 2725

c.  0 ÷ 5 = 0 means 0 × 5 = 0

_____

When using the Google calculator and standard keyboard symbols, you can use the slash (/) for "divided by" and the asterisk (*) for "times."

8 0
4 years ago
Evaluate 6j+23+kl−3, when j=3, k=7, and l=33.<br><br> Enter your answer in the box.
Umnica [9.8K]

Answer:

269

Step-by-step explanation:

1) Substitute in the given values for each variable:

6(3)+23+(7)(33)-3

2) Simplify:

18+23+231-3

3) Simplify again:

269

8 0
3 years ago
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