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Mathematics

2 answers:

Dima020 [189]3 years ago

6 0

the picture isn’t showing up

yaroslaw [1]3 years ago

3 0

Where’s the picture

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What is the density of a 60-gram pyramid with rectangular base 5 cm x 7 cm and height 9 cm?

JulijaS [17]

Answer:

0.571428571429 grams per cm³

Step-by-step explanation:

density = mass/volume

Let’s calculate the volume V of the pyramid :

V = (1/3)×base×height

= (1÷3)×(5×7)×9

= 105 cm³

Then

The density = mass/volume

= 60÷105

= 0.571428571429

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2 years ago

Evaluate the line integral using the fundamental theorem of line integrals. use a computer algebra system to verify your results

mario62 [17]

$\dfrac{\partial f}{\partial x}=\cos x\sin y\implies f(x,y)=\sin x\sin y+g(y)$

$\dfrac{\partial f}{\partial y}=\sin x\cos y=\sin x\cos y+\dfrac{\mathrm dg}{\mathrm dy}$
$\implies\dfrac{\mathrm dg}{\mathrm dy}=0\implies g(y)=C$

$f(x,y)=\sin x\sin y+C$

$\displaystyle\int_{\mathcal C}\cos x\sin y\,\mathrm dx+\sin x\cos y\,\mathrm dy=\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=f\left(\frac{3\pi}2,\frac\pi2\right)-f(0,-\pi)=-1$

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3 years ago

What is the length of AC?

Elan Coil [88]

well, the triangle is an isosceles, so it twin sides, and the twin sides make twin angles, as we see by the tickmarks on A and C, meaning AB = BC.

$\bf x+4=3x-8\implies 4=2x-8\implies 12=2x\implies \cfrac{12}{2}=x\implies 6=x \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ AC\implies x+4\implies 6+4\implies 10$