What is the volume of the rectangular prism?
5 cm
8 cm
1 cm
cm3

The question is incomplete. The complete question is :

The volume of a right circular cone with radius r and height h is V = pir^2h/3. a. Approximate the change in the volume of the cone when the radius changes from r = 5.9 to r = 6.8 and the height changes from h = 4.00 to h = 3.96.

b. Approximate the change in the volume of the cone when the radius changes from r = 6.47 to r = 6.45 and the height changes from h = 10.0 to h = 9.92.

a. The approximate change in volume is dV = _______. (Type an integer or decimal rounded to two decimal places as needed.)

b. The approximate change in volume is dV = ___________ (Type an integer or decimal rounded to two decimal places as needed.)

Solution :

Given :

The volume of the right circular cone with a radius r and height h is

[tex]$V=\frac{1}{3} \pi r^2 h$[/tex]

[tex]$dV = d\left(\frac{1}{3} \pi r^2 h\right)$[/tex]

[tex]$dV = \frac{1}{3} \pi h \times d(r^2)+\frac{1}{3} \pi r^2 dh$[/tex]

[tex]$dV = \frac{2}{3} \pi r h (dr)+\frac{1}{3} \pi r^2 dh$[/tex]

a). The radius is changed from r = 5.9 to r = 6.8 and the height is changed from h = 4 to h = 3.96

So, r = 5.9  and dr = 6.8 - 5.9 = 0.9

     h = 4  and dh = 3.96 - 4 = -0.04

Now, [tex]$dV = \frac{2}{3} \pi r h (dr)+\frac{1}{3} \pi r^2 dh$[/tex]

[tex]$dV = \frac{2}{3} \pi (5.9)(4)(0.9)+\frac{1}{3} \pi (5.9)^2 (-0.04)$[/tex]

[tex]$dV=44.484951 - 1.458117$[/tex]

[tex]$dV=43.03$[/tex]

Therefore, the approximate change in volume is dV = 43.03 cubic units.

b).  The radius is changed from r = 6.47 to r = 6.45 and the height is changed from h = 10 to h = 9.92

So, r = 6.47  and dr = 6.45 - 6.47 = -0.02

     h = 10  and dh = 9.92 - 10 = -0.08

Now, [tex]$dV = \frac{2}{3} \pi r h (dr)+\frac{1}{3} \pi r^2 dh$[/tex]

[tex]$dV = \frac{2}{3} \pi (6.47)(10)(-0.02)+\frac{1}{3} \pi (6.47)^2 (-0.08)$[/tex]

[tex]$dV=-2.710147-3.506930$[/tex]

[tex]$dV= -6.22$[/tex]

Hence, the approximate change in volume is dV = -6.22 cubic units

Answer:

answer a

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

Answer:

32 yd²

Step-by-step explanation:

because 8 • 4 is 32 so it's 32 yd²

Answer:

A = 32 yds^2

Step-by-step explanation:

We know the formula for the area of a rectangle is

A = lw  where l is the length and w is the width

A = 4 yds * 8 yds

A = 32 yds^2

Answer:

50°

Step-by-step explanation:

By intersecting secants theorem:

[tex]m \angle \: 1 = \frac{1}{2} (140 - 40) \degree \\ \\ m \angle \: 1 = \frac{1}{2} \times 100 \degree \\ \\ m \angle \: 1 = 50 \degree [/tex]

Answer:

the answer is 50 on od

Step-by-step explanation:

Answer:

10^20

Step-by-step explanation:

So in this word problem, we have to multiply 10^13 bacteria cells on a single person by the 10^7 of people.

Always remember this, when you have exponenets with the same bases, and the question asks for multiplying and dividing exponents, you just need to add and subtract the exponent.

So in this case, we will just add since it calls for multipactation.

So we need to solve:

10^13+7

This will just equal:

10^20 power

Hope this helps ;)

Answer:

(2,067 + 49) x 21

Step-by-step explanation:

I did the math for each answer

Answer:

The answer is B-452.4

Step-by-step explanation:

The formula for volume of a cylinder is V= πr^2h

so you would do 3.14 times 6 squared times 4

6 squared is 36 times 4 equals 144. Then you multiply that by pi, or 3.14 and you get 452.16 round to the nearest tenth and get 452.2

Hope this helps!

Answer:

48

Step-by-step explanation:

Answer:

140 cm²

Step-by-step explanation:

The height of the parallelogram is 10cm . And its base is 14cm .We know that the area of parallelogram is product of base and height .

⇒ Area = base × Height

⇒ Area = 14cm × 10cm

⇒ Area = 140 cm² .

Answer:

30

Step-by-step explanation:

A=wl

1080=36w

divided by 36

equals 30

Answer:

5π/12

Step-by-step explanation:

5 pie / 12

(hope this helps can i plz have brainlist :D hehe)

Answer:

y = 3x + 5        

Step-by-step explanation:

1) First, find the slope between the pair of points. Use the slope formula [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. Substitute the x and y values of points A and B into the formula and simplify:

[tex]m = \frac{(-10)-(5)}{(-5)-(0)} \\m = \frac{-10-5}{-5-0} \\m = \frac{-15}{-5} \\m = 3[/tex]

So, the slope is 3.

2) Now, identify the y-intercept of the line, or the point at which the line intersects the y-axis. All points on the y-axis have an x-value of 0. We're told that (0,5) is a point the line intersects, and since it has an x-value of 0, that must be the y-intercept.  

3) Using slope-intercept format, represented by the equation [tex]y = mx + b[/tex], write the equation of the line. Remember that the number in place of [tex]m[/tex], or the coefficient of the x-term, is the slope. So, substitute 3 for [tex]m[/tex]. Also, remember that [tex]b[/tex] represents the y-intercept of a line, so substitute 5 in its place, too. This gives the following answer:

[tex]y = 3x + 5[/tex]

Answer:

the no elephant or bear car precedes the first car with lions is 0.60

Step-by-step explanation:

The computation of the probability is shown below:

= 1 - (no depend or acrobat car precedes)

=  1 - (4 ÷ 20  + 4 ÷ 20)

= 1 - 8 ÷ 20

= 20 - 8 ÷ 20

= 12 ÷ 20

= 0.60

Hence, the no elephant or bear car precedes the first car with lions is 0.60

The same would be considered and relevant too

Answer:

x=2

Step-by-step explanation:

To solve this equation combine like terms and move all like terms to the same side. Then, isolate the variable.

First, combine like terms that are on the same side,

-10x+4=-2x-12

Next, move -10x to the other side by adding it to both sides,

4=8x-12

Then, add 12 to both sides as well,

16=8x

Finally, isolate x by dividing the whole equation by 8,

2=x

Answer:

x=2

Step-by-step explanation:

I know the answer is x=2.

First, I set up the equation.

-7x+4-3x=-2x-12

Next, I added like values on each side.

-10x+4=-2x-12

Then, I added 10x to both sides.

4=8x-12

Then, I added 12 to both sides.

16=8x

Next, I divided 8 on both sides.

2=x

To make sure 2 is the true value of x, I inserted 2 to all values of x in the equation. -7(2)+4-3(2)=-2(2)-12. Both sides of the equation are -16. So, 2 is the real value of x in this equation.

Answer:

10.3

Step-by-step explanation:

6²+b²=9²

36+b²=81

b²=81-36

b²=45

b=√45

b=6.7

So CE is 6.7.

6²+b²=7²

36+b²=49

b²=49-36

b²=13

b=√13

b=3.6

so EA is 3.6

AC = CE+EA = 6.7+3.6 = 10.3

Answer:

The solution to this question is 104.25cm²

Step-by-step explanation:

u

Answer:

hi

Step-by-step explanation:

i think so

A=

[tex] = \pi \times {r}^{2} [/tex]

=3,14×5,76²=104,177

hope it helps

have a nice day

Answer:

4

Step-by-step explanation:

the third side = x

Pythagorean theorem: a² + b² = c²

3² + x² = 5²

=> x² = 5² - 3²

=> x = √5² - 3²

=> x = √25 - 9

=> x = √16

=> x = 4

Answer:

3/4 h

Step-by-step explanation:

Please put how many pizzas there are and how much money he has (please put the full question)

Answer:

The answer is 40

Step-by-step explanation:

The cost of 50 pounds of beans is 40 dollars.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We can use a ratio to solve the problem;

5 pounds/ 4 dollars  = 50 pounds/ x dollars

Using cross products;

5x = 4 x 50

5x = 200

Divide by 5;

5x/5 = 200/5

x = 40

The cost of 50 pounds of beans is 40 dollars.

Learn more about the unitary method, please visit the link given below;

https://brainly.com/question/23423168

#SPJ2

Answer:

1. y = -2x+5

2. y = 3/4 - 3

3. intercept = -5 slope =  4/3

4. intercept = 1 slope = -1/2

Answer:

So 4 ÷ 1/5 = 4 × 5. So your answer is 5.

Answer:

an arithmetic sequence

Step-by-step explanation:

I think it's because it adds 5 each time and in arithmetic sequences there's a common difference, so it'd be an arithmetic sequence :)

Answer:

i think its =y7x-4

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

The slope is going to be associated with an “x” and we know that the slope equals -7 so it’s important to add the NEGATIVE sign.

Also, the x-intercept is POSITIVE. It won’t be A because their x-intercept is negative. It won’t be C because their slope is positive. It won’t be D. because they didn’t put -7 as a slope.

Answer:

Assuming that this data is used to conduct a hypothesis test to test the manufacturers' claim, the test statistic we an use is:

the paired sample t-test.

Step-by-step explanation:

a) Data and Analysis:

Subject   Before   After

1                 225      215

2                245     240

3                 188      188

4                210       212

5               282       175

6               275      260

7               230      225

8               195      200

9               190       185

b) The paired sample t-test is used to compare the means from the same dataset but at different times (say, one month apart).  It supports the comparison of sample data before and after the data subjects have taken the dietary supplement.  When the t-value is high, it is an evidence that the null hypothesis should be rejected.  The higher value of the t-test, therefore, indicates that there is a large difference between the two sample sets.  On the other hand, a small t-value shows similarity between the two sample sets.