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3 years ago

Find cot 0 if cos 0=3/13

2 answers:

6 0

3/4 root 10
you make a right triangle. use Pythagorean theorem. and find the opposite side. then reduce the radical of 160. and do tan and then flip them around to make cot.

nekit [7.7K]3 years ago

6 0

<h2>Answer:</h2>

The value of:

$\cot \theta=\dfrac{3}{4\sqrt{10}}$

<h2>Step-by-step explanation:</h2>

We are given,

$\cos \theta=\dfrac{3}{13}$

We know that cos θ is the ratio of base and hypotenuse of a right angled triangle corresponding to θ.

On applying Pythagorean Theorem in ΔABC we get:

$13^2=3^2+a^2\\\\\\i.e.\\\\\\169=9+a^2\\\\\\a^2=160\\\\\\i.e.\\\\\\a=4\sqrt{10}$

Hence, the value of $\cot \theta$ is defined as the ratio of base to perpendicular length of the triangle.

Hence,

$\cot \theta=\dfrac{3}{4\sqrt{10}}$

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Using the graph as your guide, complete the following statement.

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The answer is
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The vertex of this parabola is at (-2,-3). When the y-value is -2, the x-value is -5. What is the coefficient of the squared ter

ra1l [238]

Answer:

The coefficient of the squared term of the equation is 1/9.

Step-by-step explanation:

We are given that the vertex of the parabola is at (-2, -3). We also know that when the <em>y-</em>value is -2, the <em>x-</em>value is -5. Using this information we want to find the cofficient of the squared term in the parabola's equation.

Since we are given the vertex, we can use the vertex form:

$\displaystyle y=a(x-h)^2+k$

Where <em>a</em> is the leading coefficient and (<em>h, k</em>) is the vertex.

Since the vertex is (-2, -3), <em>h</em> = -2 and <em>k</em> = -3:

$\displaystyle y=a(x-(-2))^2+(-3)$

Simplify:

$y=a(x+2)^2-3$

We are also given that <em>y</em> = -2 when <em>x</em> = -5. Substitute:

$(-2)=a(-5+2)^2-3$

Solve for <em>a</em>. Simplify:

$\displaystyle \begin{aligned} -2&=a(-3)^2-3\\ 1&=9a \\a&=\frac{1}{9}\end{aligned}$

Therefore, our full vertex equation is:

$\displaystyle y=\frac{1}{9}(x+2)^2-3$

We can expand:

$\displaystyle y=\frac{1}{9}(x^2+4x+4)-3$

Simplify:

$\displaystyle y=\frac{1}{9}x^2+\frac{4}{9}x-\frac{23}{9}$

The coefficient of the squared term of the equation is 1/9.

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3 years ago

A day pass at a theme park cost $16 for children and $24.50 for adults. How much would it cost to get passes for 1 adult and 2 c

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Answer:

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Step-by-step explanation:

2 children is $32.

1 adult is just $24.50

Add these up: $32 + $24.50 = $56.50.

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Which is a true statement about an isosceles right triangle?

AnnyKZ [126]

Let $l$ be the length of a leg. Using the pythagorean theorem, the hypotenuse is

$h = \sqrt{l^2+l^2}=\sqrt{2l^2}=l\sqrt{2}$

So, the hypotenuse is $\sqrt{2}$ times as long as either leg.

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3 years ago

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 449 gram setting. It is

stealth61 [152]

Answer:

We accetp H₀

Step-by-step explanation:

Information:

Normal distribution

Population mean = μ₀ = 449

Population standard deviation σ unknown

Sample size n = 23 n < 30 we use t-student test

so n = 23 degree of fredom df = n - 1 df = 23- 1 df = 22

Sample mean μ = 448

Sample standard deviation s = 20

Significance level α = 0,05

1.-Hypothesis Test

Null hypothesis H₀ μ₀ = 449

Alternative hypothesis Hₐ μ₀ ≠ 449

Problem statement ask for determine decision rule for rejecting the null hypothesis. For rejecting the null hypothesis we have to get an statistic parameter wich implies that μ is bigger or smaller than μ₀

2.-Significance level α = 0,05 ; as we have a two tail test

α/2 = 0,025

Then from t - student table for df = 22 and 0,025 (two tail-test)

t(c) = ± 2.074

3.- Compute t(s)

t(s) = ( μ - μ₀ ) / s /√n

plugging in values

t(s) = (448 - 449) / 20 /√23 ⇒ t(s) = - 1*√23 /20

t(s) = - 0.2398

4.-Compare t(c) and t(s)

t(s) < t(c) - 0.2398 < - 2.074

Therefore t(s) in inside acceptance region. We accept H₀

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4 years ago