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3 years ago

What is true about the number 3.872? Check all that apply.

Mathematics

2 answers:

gavmur [86]3 years ago

8 0

Answer: The 7 is in the hundredths place.

The 3 is in the ones place.

3.872 is equivalent to (3 × 1) + (8 × 0.1) + (7 × 0.01) + (2 × 0.001).

Step-by-step explanation:

In the question, 3 is in the ones place. The first number after the decimal point is the tenths. In the question, the place value of 8 is 8 tenths; 7 is in the hundredths place.

3.872 = (3 × 1) + (8 × 0.1) + (7 × 0.01) + (2 × 0.001)

= 3 + 0.8 + 0.07 + 0.002

= 3.872

The number is pronounced as three and eight hundred seventy-two thousandths

Korvikt [17]3 years ago

7 0

Answer:

The 7 is in the hundredths place.

The 3 is in the ones place.

3.872 is equivalent to (3 × 1) + (8 × 0.1) + (7 × 0.01) + (2 × 0.001).

Step-by-step explanation:

Given the number 3.872, to check all the given options that are true apply to the number, let's take a look at each position occupied by each digit. In order words, let's consider their place value.

Thus,

The 3 is in the ones place and as such has a value of 3.

8 is in the tenths place having a place value of 0.8 (⁸/10)

7 is in the hundredths place having a place value of 0.07 (⁷/100)

2 is in the thousandths place having a place value of 0.002 (²/1000)

Going by these, the following statements are true :

"The 7 is in the hundredths place."

"The 3 is in the ones place."

"3.872 is equivalent to (3 × 1) + (8 × 0.1) + (7 × 0.01) + (2 × 0.001)."

The number is pronounced as three and eight hundred seventy-two thousandths rather than the option given.

Therefore, only 3 if the options are correct

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Find an equation for the line that passes through the points (5.-5) and (-4,-2)

ANEK [815]

Answer:

$\large\boxed{y=-\dfrac{1}{3}x-\dfrac{10}{3}\to x+3y=-10}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (5, -5) and (-4, -2).

Substiute:

$m=\dfrac{-2-(-5)}{-4-5}=\dfrac{-2+5}{-9}=\dfrac{3}{-9}=-\dfrac{1}{3}$

Put the value of the slope and the coordinates of the point (5, -5) to the equation of a line:

$-5=-\dfrac{1}{3}(5)+b$

$-5=-\dfrac{5}{3}+b$ add 5/3 to both sides

$-\dfrac{15}{3}+\dfrac{5}{3}=b\\\\-\dfrac{10}{3}=b\to b=-\dfrac{10}{3}$

Finally we have the equation of a line in the slope-intercept form:

$y=-\dfrac{1}{3}x-\dfrac{10}{3}$

Convert to the standard form (Ax + By = C):

$y=-\dfrac{1}{3}x-\dfrac{10}{3}$ multiply both sides by 3

$3y=-x-10$ add x to both sides

$x+3y=-10$

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3 years ago

Jose earns a weekly salary of $322. How much does he make in 44 weeks?

ioda

Answer:

14168

Step-by-step explanation:

322 x 44 = 14168

hope this helps!

3 0

3 years ago

A sphere of radius r is cut by a plane h units above the equator, where

Anika [276]

Consider the top half of a sphere centered at the origin with radius $r$ , which can be described by the equation

$z=\sqrt{r^2-x^2-y^2}$

and consider a plane

$z=h$

with $0$ . Call the region between the two surfaces $R$ . The volume of $R$ is given by the triple integral

$\displaystyle\iiint_R\mathrm dV=\int_{-\sqrt{r^2-h^2}}^{\sqrt{r^2-h^2}}\int_{-\sqrt{r^2-h^2-x^2}}^{\sqrt{r^2-h^2-x^2}}\int_h^{\sqrt{r^2-x^2-y^2}}\mathrm dz\,\mathrm dy\,\mathrm dx$

Converting to polar coordinates will help make this computation easier. Set

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

Now, the volume can be computed with the integral

$\displaystyle\iiint_R\mathrm dV=\int_0^{2\pi}\int_0^{\arctan\frac{\sqrt{r^2-h^2}}h}\int_{h\sec\varphi}^r\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta$

You should get

$\dfrac{2\pi}3\left(r^3\arctan\dfrac{\sqrt{r^2-h^2}}h-\dfrac{h^3}2\left(\dfrac{r\sqrt{r^2-h^2}}{h^2}+\ln\dfrac{r+\sqrt{r^2-h^2}}h\right)\right)$