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4 days ago

7

A jewellery shop sells 240 necklaces in a month. 180 were sold via the shops website, the rest were sold in a high street shop.

work out the ratio for online sales to shop sales

1 answer:

babunello [8.4K]4 days ago

4 0

3:4
180 / 6 = 30 / 10 = 3
240 / 6 = 40 / 10 = 4
3 = online sales
4 = physical store sales
online: store
=
3: 4

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An element with mass 570 grams decays by 26.9% per minute. How much of the element is remaining after 14 minutes, to the nearest

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Respuesta:

la cantidad de elemento restante después de 14 minutos = 7.091 g =~ 10 g

Explicación paso a paso:

Después de cada minuto, la cantidad que queda será

(100 - 26.9) % es decir, 73.1 %

lo que equivale a 0.731 veces la cantidad inicial.

Si el tiempo transcurrido se representa como t, la función f(t) indica la masa del elemento restante, nuestra ecuación será

f(t) = 570(0.731) ^ t

t= 14 minutos

f(14) = 570 (0.731) ^ 14

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Answer:

Step-by-step explanation:

The equation representing the sphere, which has its center at the origin, can be written as $x^2+y^2+z^2 = 64$ . For z equal to 4, we find

$x^2+y^2= 64-16 = 48$ .

This results in a circle with a radius of $4\sqrt[]{3}$ in the x-y plane.

c) We will build on the analysis from earlier to set limits in both Cartesian and polar coordinates. Initially, we recognize that x spans from $-4\sqrt[]{3}$ to $4\sqrt[]{3}$ . This determination is made by fixing y = 0 and identifying the extreme x values that fall on the circle. For y, we observe that it ranges between $-\sqrt[]{48-x^2}$ and $\sqrt[]{48-x^2}$ , which holds because y must reside within the interior of the identified circle. Lastly, z will extend from 4 up to the sphere; hence, it varies from 4 to $\sqrt[]{64-x^2-y^2}$ .

The respective triple integral representing the volume of D in Cartesian coordinates is

$\int_{-4\sqrt[]{3}}^{4\sqrt[]{3}}\int_{-\sqrt[]{48-x^2}}^{\sqrt[]{48-x^2}} \int_{4}^{\sqrt[]{64-x^2-y^2}} dz dy dx$ .

b) Remember that the cylindrical coordinates are expressed as $x=r\cos \theta, y = r\sin \theta,z = z$ , where r denotes the radial distance from the origin projected onto the x-y plane. Also note that $x^2+y^2 = r^2$ . We will derive new limits for each of the transformed coordinates. Recall that due to the prior circular constraint, $\theta[\tex] is the angle between the projection to the x-y plane and the x axis, in order for us to cover the whole circle, we need that [tex]\theta$ varies between 0 and $2\pi$ . Furthermore, r starts from the origin and extends to the edge of the circle, with r reaching a maximum of 4\sqrt[]{3}. Lastly, Z increases from the plane z=4 up to the sphere, where it is constrained by \sqrt[]{64-r^2}. Thus, the integral that computes the desired volume is as follows:

$\int_{0}^{2\pi}\int_{0}^{4\sqrt[]{3}} \int_{4}^{\sqrt[]{64-r^2}} rdz dr d\theta$ . It’s important to note that the r factor arises from the Jacobian associated with the transition from Cartesian to polar coordinates, ensuring the integral maintains its value. (Explaining how to calculate the Jacobian exceeds the scope of this response).

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