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lakkis [162]
2 years ago
5

If 0 < f ≤ 90 and cos(22f − 1) = sin(7f + 4), what is the value of f?

Mathematics
1 answer:
77julia77 [94]2 years ago
3 0

Answer:

f= 5

Step-by-step explanation:

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Calculations that allow a researcher to draw conclusions about how meaningful a result is are collectively called ______________
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Step-by-step explanation:

Inferential statistics, has to do with taking data from the samples that the researcher has and then making generalizations about the population through the sample gotten.

Through Inferential statistics, one can draw conclusion about a particular phenomenon. Therefore, the answer to the above question is Inferential statistics

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Use spherical coordinates to find the volume of the region that lies outside the cone z = p x 2 + y 2 but inside the sphere x 2
Harman [31]

I assume the cone has equation z=\sqrt{x^2+y^2} (i.e. the upper half of the infinite cone given by z^2=x^2+y^2). Take

\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\varphi\end{cases}\implies\mathrm dx\,\mathrm dy\,\mathrm dz=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi

The volume of the described region (call it R) is

\displaystyle\iiint_R\mathrm dx\,\mathrm dy\,\mathrm dz=\int_0^{2\pi}\int_0^{\sqrt2}\int_{\pi/4}^\pi\rho^2\sin\varphi\,\mathrm d\varphi\,\mathrm d\rho\,\mathrm d\theta

The limits on \theta and \rho should be obvious. The lower limit on \varphi is obtained by first determining the intersection of the cone and sphere lies in the cylinder x^2+y^2=1. The distance between the central axis of the cone and this intersection is 1. The sphere has radius \sqrt2. Then \varphi satisfies

\sin\varphi=\dfrac1{\sqrt2}\implies\varphi=\dfrac\pi4

(I've added a picture to better demonstrate this)

Computing the integral is trivial. We have

\displaystyle2\pi\left(\int_0^{\sqrt2}\rho^2\,\mathrm d\rho\right)\left(\int_{\pi/4}^\pi\sin\varphi\,\mathrm d\varphi\right)=\boxed{\frac43(1+\sqrt2)\pi}

4 0
2 years ago
-2x + y =0 <br> 5x + 3y = -11
Ivahew [28]

Answer:

(-1, -2)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

<u>Algebra I</u>

  • Solving systems of equations using substitution/elimination
  • Solving systems of equations by graphing

Step-by-step explanation:

<u>Step 1: Define Systems</u>

-2x + y = 0

5x + 3y = -11

<u>Step 2: Rewrite Systems</u>

-2x + y = 0

  1. Add 2x on both sides:                    y = 2x

<u>Step 3: Redefine Systems</u>

y = 2x

5x + 3y = -11

<u>Step 4: Solve for </u><em><u>x</u></em>

<em>Substitution</em>

  1. Substitute in <em>y</em>:                         5x + 3(2x) = -11
  2. Multiply:                                    5x + 6x = -11
  3. Combine like terms:                11x = -11
  4. Isolate <em>x</em>:                                   x = -1

<u>Step 5: Solve for </u><em><u>y</u></em>

  1. Define equation:                    y = 2x
  2. Substitute in <em>x</em>:                       y = 2(-1)
  3. Multiply:                                  y = -2

<u>Step 6: Graph Systems</u>

<em>Check the solution set.</em>

3 0
2 years ago
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