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3 years ago

What is the density of the rectangular prism 3cm 4cm 6cm that weighs 36 grams?

Mathematics

1 answer:

ANEK [815]3 years ago

8 0

Answer:

a. 0.5 g/cc

Step-by-step Explanation:

Given:

Measurement of rectangular prism = 3 cm × 4 cm × 6 cm

Mass of rectangular prism = 36 grams

Required:

Density of rectangular prism

SOLUTION:

$Density = \frac{Mass}{Volume}$

Mass = 36 g

Volume = 3*4*6 = 72 cm³

$Density = \frac{36}{72}$

Density = 0.5 g/cc

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Write an inequality to represent the graph.

lakkis [162]

Answer:

$y \leq -\frac{3}{4}x+2$

y is less than or equal to negative three fourths times x plus 2

Step-by-step explanation:

step 1

Find the slope of the solid line

we have the ordered pairs

(0,2) and (4,-1)

Find the slope m

$m=(-1-2)/(4-0)$

$m=-\frac{3}{4}$

step 2

Find the linear equation of the solid line in slope intercept form 

$y=mx+b$

we have

$m=-\frac{3}{4}$

$b=2$ ---> the y-intercept is given

substitute

$y=-\frac{3}{4}x+2$

step 3

Find the inequality

Remember that the solution is the shaded area below the solid line

therefore

The inequality is

$y \leq -\frac{3}{4}x+2$

y is less than or equal to negative three fourths times x plus 2

3 0

3 years ago

(a) Use the reduction formula to show that integral from 0 to pi/2 of sin(x)^ndx is (n-1)/n * integral from 0 to pi/2 of sin(x)^

Sedbober [7]

Hello,

a)
$I= \int\limits^{ \frac{\pi}{2} }_0 {sin^n(x)} \, dx = \int\limits^{ \frac{\pi}{2} }_0 {sin(x)*sin^{n-1}(x)} \, dx \\

= [-cos(x)*sin^{n-1}(x)]_0^ \frac{\pi}{2}+(n-1)*\int\limits^{ \frac{\pi}{2} }_0 {cos(x)*sin^{n-2}(x)*cos(x)} \, dx \\

=0 + (n-1)*\int\limits^{ \frac{\pi}{2} }_0 {cos^2(x)*sin^{n-2}(x)} \, dx \\

= (n-1)*\int\limits^{ \frac{\pi}{2} }_0 {(1-sin^2(x))*sin^{n-2}(x)} \, dx \\
= (n-1)*\int\limits^{ \frac{\pi}{2} }_0 {sin^{n-2}(x)} \, dx - (n-1)*\int\limits^{ \frac{\pi}{2} }_0 {sin^n(x) \, dx\\

$
$I(1+n-1)= (n-1)*\int\limits^{ \frac{\pi}{2} }_0 {sin^{n-2}(x)} \, dx \\
I= \dfrac{n-1}{n} *\int\limits^{ \frac{\pi}{2} }_0 {sin^{n-2}(x)} \, dx \\
$

b)
$\int\limits^{ \frac{\pi}{2} }_0 {sin^{3}(x)} \, dx \\
= \frac{2}{3} \int\limits^{ \frac{\pi}{2} }_0 {sin(x)} \, dx \\
= \dfrac{2}{3}\ [-cos(x)]_0^{\frac{\pi}{2}}=\dfrac{2}{3} \\




$

$\int\limits^{ \frac{\pi}{2} }_0 {sin^{5}(x)} \, dx \\
= \dfrac{4}{5}*\dfrac{2}{3} \int\limits^{ \frac{\pi}{2} }_0 {sin(x)} \, dx = \dfrac{8}{15}\\





$

c)

$I_n= \dfrac{n-1}{n} * I_{n-2} \\

I_{2n+1}= \dfrac{2n+1-1}{2n+1} * I_{2n+1-2} \\
= \dfrac{2n}{2n+1} * I_{2n-1} \\
= \dfrac{(2n)*(2n-2)}{(2n+1)(2n-1)} * I_{2n-3} \\
= \dfrac{(2n)*(2n-2)*...*2}{(2n+1)(2n-1)*...*3} * I_{1} \\\\

I_1=1\\

$

3 0

3 years ago

What value of x is in the solution set of 3(x-4)greater than or equal to 5x+2

Gnesinka [82]

3(x-4)>= 5x+2

Distributing 3 on x-4

3(x)-3(4)>=5x+2

3x-12>=5x+2

Now we need to move x terms together and the numbers together and for that we subtract 5x to both sides and add 12 to both sides

-2x >=14

Now we need to get rid of -2, and for that we divide both sides by -2 and on dividing by negative number, the sign of inequality change , that is

x<=-7

5 0

3 years ago

20000000000000x 3065

Verizon [17]

Answer:

61300000000000000

Step-by-step explanation:

7 0

3 years ago

A snowmobile traveled 32 miles in 2 1/3 hours.

sergey [27]

Answer:

13.7 mph

Step-by-step explanation:

d = st

Given:

d = 32 miles
t = 2 1/3 hr = 7/3 hr

Find the rate s:

s = d/t
s = 32÷7/3 = 32 × 3/7 = 96/7 ≈ 13.7 mph (rounded)

4 0

2 years ago