Is every whole number a multiple of 1?

Mathematics

2 answers:

lora16 [44]3 years ago

8 0

Yes every whole number is a multiple of 1.

mr_godi [17]3 years ago

3 0

Yes except 0, as everything multiplied by 0 is 0

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Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!

lisabon 2012 [21]

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4 0

3 years ago

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Set up a triple integral in spherical coordinates to compute the volume of the region inside the sphere x² + y² + z² = 4 and abo

Mademuasel [1]

The plane meets the sphere in the cylinder

$z=1 \implies x^2+y^2+1^2 = 4 \implies x^2+y^2 = 3 = \left(\sqrt3\right)^2$

In spherical coordinates, the plane has equation

$z = \rho\cos(\phi) = 1 \implies \rho = \sec(\phi)$

and since

$\begin{cases}x = \rho\cos(\theta)\sin(\phi) \\ y=\rho\sin(\theta)\sin(\phi)\end{cases} \implies x^2+y^2 = \rho^2 \sin^2(\phi)$

the cylinder has equation

$\rho^2 \sin^2(\phi) = 3 \implies \rho = \sqrt3 \, \csc(\phi)$

The plane and cylinder thus meet when

$\sec(\phi) = \sqrt3\,\csc(\phi) \implies \tan(\phi) = \sqrt3 \implies \phi = \dfrac\pi3$

So, the volume of the region is given by

$\displaystyle \boxed{\int_0^{2\pi} \int_0^{\pi/3} \int_{\sec(\phi)}^2 \rho^2 \sin(\phi) \, d\rho \, d\phi \, d\theta}$

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2 years ago

Factor the trinomial 5x^2-x-4

LenaWriter [7]

Answer:

Step-by-step explanation:

$5x^2-x-4\\\\\mathrm{Break\:the\:expression\:into\:groups}\\=\left(5x^2+4x\right)+\left(-5x-4\right)\\\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}5x^2+4x\mathrm{:\quad }x\left(5x+4\right)\\\mathrm{Factor\:out\:}-1\mathrm{\:from\:}-5x-4\mathrm{:\quad }-\left(5x+4\right)\\\\=x\left(5x+4\right)-\left(5x+4\right)\\\\\mathrm{Factor\:out\:common\:term\:}5x+4\\=\left(5x+4\right)\left(x-1\right)$