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Hoochie [10]
3 years ago
5

Simplify 1-cot(x)/tan(x)-1

Mathematics
1 answer:
netineya [11]3 years ago
6 0
\bf  \cfrac{1-cot(x)}{tan(x)-1}\qquad 
\begin{cases}
cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}
\\\\ tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}
\end{cases}\qquad thus
\\\\\\
\cfrac{1-\frac{cos(x)}{sin(x)}}{\frac{sin(x)}{cos(x)}-1}\implies 
\cfrac{\frac{sin(x)-cos(x)}{sin(x)}}{\frac{sin(x)-cos(x)}{cos(x)}}\\\\
-----------------------------\\\\
recall\implies \cfrac{\frac{a}{b}}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c}\qquad thus\\\\
-----------------------------

\bf \cfrac{\frac{sin(x)-cos(x)}{sin(x)}}{\frac{sin(x)-cos(x)}{cos(x)}}\implies \cfrac{sin(x)-cos(x)}{sin(x)}\cdot \cfrac{cos(x)}{sin(x)-cos(x)}\implies \boxed{?}
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The volumes of two cylindrical cans of the same shape vary directly as the cubes of their radii. If a can with a six-inch radius
Cerrena [4.2K]

Answer:

The second similar can with a radius of 24-inch radius will hold 12 gallons

Step-by-step explanation:

The given parameters are;

The volumes of the cylindrical can ∝ (The radius of the cans)³

The volume of first can, V₁ = 1¹/₂ pints

The radius of the first can, r₁ = 6-inch

The radius of the second can, r₂ = 24-inch

Therefore, we have;

V ∝ r³

V = k × r³

∴ 1¹/₂ pints ∝ (6 in.)³

1¹/₂ pints = 43.3125 in³

∴ 43.3125 in³ = k × 216 in.³

The constant of proportionality, k = 43.3125/216 = 0.2005208333

Therefore, we have for the second can, we have;

V₂ = k × r₂³ = 43.3125/216 × (24 in.)³ = 2772 in.³

The volume of the second can = 2772 in.³

1 in.³ = 0.004329 gallons

∴ 2772 in.³ = 2772 × 0.004329 gallons = 12 gallons

Therefore, the volume the second similar can with a 24-inch radius will hold = 12 gallons.

8 0
3 years ago
Find the greatest common factor of the following monomials 26n5 12n2
Sidana [21]

The greatest common factor is 2n^{2}


We first have to look for the largest number that goes into both equations. The factors of 12 are 1, 2, 3, 4, 6 and 12. None of 3, 4, 6, or 12 go into 26 evenly. So 2 is the largest number you can take out.


With the variables, we take out as many as the lowest number will let us. Since the smallest number of n's is 2 in the second term, we take that many.

8 0
3 years ago
Write an equivalent expression by distributing the "-−" sign outside the parentheses:
charle [14.2K]

Answer:

6.6a+6b-7.1

Step-by-step explanation:

-(-6.6a-6b)-7.1\\\\=-(-6.6a)-(-6b)-7.1\\\\=6.6a+6b-7.1

7 0
3 years ago
Using the numbers 0-6 once, make 2 equivalent ratios
fenix001 [56]

Step-by-step explanation:

As we have to use the number 0-6 once to make 2 equivalent ratios.

so lets solve the problem.

Determining first equivalent ratio

as

  • 5 times 2 = 10

and

  • 32 times 2 = 64

so

  • Together will get 10/64

Therefore, first equivalent ratio

\:\frac{5}{32}=\frac{10}{64}

Determining second equivalent ratio

\frac{13}{65}=\frac{4}{20}

as

\frac{13}{65}=\frac{1}{5}

and

\frac{4}{20}=\frac{1}{5}

Therefore, second equivalent ratio

\frac{13}{65}=\frac{4}{20}

8 0
3 years ago
Nicole runs each lap in 4 minutes. She will run more than 24 minutes today. What are the possible numbers of laps she will run t
sdas [7]

7 or more laps. you can find this by multiplying 6 x 4 & anything above that would work too

7 0
3 years ago
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