How many cubes are needed to fill in the rectangular prism?

The average value of f(x) = 3x sin(x) on the interval [tex]\( 1 \leq x \leq 7 \) is approximately \( -1.6204 \).[/tex]

To find the average value of a function f(x) on a closed interval [a, b], we use the formula:

[tex]\[ \text{Average value} = \frac{1}{b - a} \int_{a}^{b} f(x) \, dx \]In this case, the function \( f(x) = 3x \sin(x) \) and the closed interval is \( 1 \leq x \leq 7 \).So, the average value of \( f(x) \) on the interval \( 1 \leq x \leq 7 \) is:\[ \text{Average value} = \frac{1}{7 - 1} \int_{1}^{7} 3x \sin(x) \, dx \][/tex]

[tex]\[ \text{Average value} = \frac{1}{6} \int_{1}^{7} 3x \sin(x) \, dx \][/tex]

Now, we need to compute the integral. We can do this using integration by parts:

[tex]Let \( u = 3x \) and \( dv = \sin(x) \, dx \).Then, \( du = 3 \, dx \) and \( v = -\cos(x) \).Using the integration by parts formula:\[ \int u \, dv = uv - \int v \, du \]\[ \int_{1}^{7} 3x \sin(x) \, dx = \left[ -3x \cos(x) \right]_{1}^{7} - \int_{1}^{7} (-\cos(x)) \cdot 3 \, dx \][/tex]

[tex]\[ = \left[ -3x \cos(x) \right]_{1}^{7} + 3 \int_{1}^{7} \cos(x) \, dx \]\[ = \left[ -3x \cos(x) \right]_{1}^{7} + 3 \left[ \sin(x) \right]_{1}^{7} \]\[ = \left[ -21 \cos(7) + 3 \sin(7) \right] - \left[ -3 \cos(1) + 3 \sin(1) \right] \][/tex]

Now, let's compute these values:

[tex]\[ \text{Average value} = \frac{1}{6} \left[ \left( -21 \cos(7) + 3 \sin(7) \right) - \left( -3 \cos(1) + 3 \sin(1) \right) \right] \]\[ \text{Average value} = \frac{1}{6} \left[ (-21 \times 0.7539 + 3 \times 0.6560) - (-3 \times 0.5403 + 3 \times 0.8415) \right] \]\[ \text{Average value} = \frac{1}{6} \left[ (-15.8359 + 1.9680) - (-1.6209 + 2.5245) \right] \][/tex]

[tex]\[ \text{Average value} = \frac{1}{6} \left[ -13.8679 + 4.1454 \right] \]\[ \text{Average value} = \frac{1}{6} \times (-9.7225) \]\[ \text{Average value} \approx -1.6204 \][/tex]

So, the average value of f(x) = 3x sin(x) on the interval [tex]\( 1 \leq x \leq 7 \) is approximately \( -1.6204 \).[/tex]

The average value of [tex]\(f(x) = 3x \sin(x)\)[/tex] on the interval [tex]\(1 \leq x \leq 7\)[/tex] is approximately 1.879.

To find the average value of [tex]\( f(x) = 3x \sin(x) \)[/tex]on the closed interval [tex]\( 1 \leq x \leq 7 \)[/tex], we can use the formula for the average value of a function on a closed interval [a, b] :

[tex]\[ \text{Average value} = \frac{1}{b - a} \int_a^b f(x) \, dx \][/tex]

In this case, a = 1 and b = 7, so:

[tex]\[ \text{Average value} = \frac{1}{7 - 1} \int_1^7 3x \sin(x) \, dx \][/tex]

Now, we need to evaluate the integral:

[tex]\[ \int_1^7 3x \sin(x) \, dx \][/tex]

This integral can be evaluated using integration by parts or by using a software tool. After evaluation, we find that the average value is approximately 1.879.

So, the correct answer is 1.879.

Complete Question:

Let f be the function given by f(x)=3xsinx. What is the average value of f on the closed interval 1≤x≤7 ?

−14.764

−2.461

1.879

8.161

In math, a loss of $20 is represented by the negative integer -20. The negative in front of the 20 represents the loss or decrement.

In mathematics, integers are whole numbers that can be either positive, negative, or zero. When we talk about a loss or decrement of something, it's universally symbolized with a negative integer.

In case of a loss of $20, it is represented as -20, where the negative sign indicates the loss or subtraction of money.

https://brainly.com/question/35879110

#SPJ3

Answer:

D. 2 1/4

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

9 pies/4 friends =

9/4 = 2 1/4

D

Answer:

the correct one is the quadrilateral with the parallelogram in it the one in the bottom corner under w

Step-by-step explanation:

hope this helps have a great day

Answer:

[tex]\frac{-19}{2}[/tex]

Step-by-step explanation:

[tex]\frac{5}{4}[/tex] + [tex]\frac{-43}{4}[/tex] = [tex]\frac{-19}{2}[/tex]

Answer:

14n+5

Step-by-step explanation:

Five more is +5

Product of 14 and a number would be 14n

So combined would be 14n+5

Answer:

(4,3)

Step-by-step explanation:

3x + 2y = 18

5x – 2y = 14

Add the two equations together to eliminate y

3x + 2y = 18

5x – 2y = 14

------------------------

8x    =   32

Divide each side by 8

8x/8 = 32/8

x = 4

Now determine the value for y

3(4) +2y = 18

12 +2y =18

Subtract 12 from each side

12-12+2y = 18-12

2y = 6

Divide by 2

2y/2 =6/2

y=3

Answer:

x=4 and y=3

Step-by-step explanation:

x+2y=18

5x−2y=14

Add these equations to eliminate y:

8x=32

Then solve8x=32for x:

8x=32

8x

8

=

32

8

(Divide both sides by 8)

x=4

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

3x+2y=18

Substitute4forxin3x+2y=18:

(3)(4)+2y=18

2y+12=18(Simplify both sides of the equation)

2y+12+−12=18+−12(Add -12 to both sides)

2y=6

2y

2

=

6

2

(Divide both sides by 2)

y=3

Answer:

x=4 and y=3

Answer:

1hr=60minutes

ATQ,20 minutes/60 minutes=1/n

1/3=1/n

so the value of n is 3...

Step-by-step explanation: Hope i helped please give brainliest!

Answer:

C,D,E,H 2020 edge

Step-by-step explanation:

I did the assignment

Answer:C D E H

Step-by-step explanation:

Answer:

RS = 15 and RT = 18, then ST = 3!   :D

Step-by-step explanation:r = 1 --> s=15 & t=18 so st = 270

r = 3 --> s = 5 & t = 6 so st = 30

r = 5 --> s = 3 & t = 3.6 so st = 10.8

etc

==============

In literal terms:

s = 15/r

t = 18/r

Step-by-step explanation:

Answer:

$36

Step-by-step explanation:

The amount spent on cloths is 1/3

The amount earned from washing the car is $5

Amount at the end of the week is $29

Let the amount earned that week be x

Then amount spent on cloths = 1/3x

so the equation is

x- 1/3 x+$5=$29

2/3 x=29-5

2/3 x= 24

x=(24*3)/2= $36

Answer:

8 weeks

Step-by-step explanation:

because you multiply the two books to get the total price then divide by 5 to get how many weeks he has to save 5 dollars

The volume of the given rectangular prism is option C. [tex]24 un^{3}[/tex].

Step-by-step explanation:

Step 1:

The dimensions of the given rectangular prism are 4 units × 3 units × 2 units.

So we take the length equals 4 units, the width is equal to 3 units and the height is 2 units.

Step 2:

The volume of this rectangular prism is calculated by multiplying the given prism's length, its width, and its height.

The Volume of the given rectangular prism = [tex]( Length) (Width) (Height) = (4units) (3units) (2 units) = 24 unit^{3} .[/tex]

So the given right rectangular prism's volume is [tex]24 unit^{3}[/tex] which is option C.

By using the formula (Area = Length x Width) we can rearrange the equation to find the height of the rectangular poster. It comes out to be 4 feet.

To answer your question, we must use the formula for the area of a rectangle, which is Area = Length x Width. Here, the area of the poster is given as 38 square feet and the width is 9.5 feet. The length is what we're trying to find. We can set this up as an equation 38 = Length x 9.5. To find the Length, we divide both sides of the equation by 9.5 resulting in Length = 38 ÷ 9.5. Solving the equation gives us a length of approximately 4 feet. So, the 'height' of the poster would be 4 feet.

https://brainly.com/question/33599290

#SPJ3

Answer:

See explanation

Step-by-step explanation:

Let the given equation be:

[tex]5 {x}^{2} - 400 = 0[/tex]

This implies that:

[tex]5 {x}^{2} = 400[/tex]

Divide through by 5 to get;

[tex] {x}^{2} = 80[/tex]

Take square root to obtain:

[tex]x = \pm \sqrt{80} [/tex]

This implies that

[tex]x = \pm4 \sqrt{5} [/tex]

[tex]x = - 4 \sqrt{5} \: or \: x = 4 \sqrt{5} [/tex]

Answer:

14

Step-by-step explanation:

In this case LCM is needed and the LCM of 2and 7 is 14. I hope this helps.

Answer:

47 degrees

Step-by-step explanation:

The interior angles of a triangle always equal 180 degrees, so add the other angles together and subtract that from 180

31+102= 133

180-133=47

Answer:

47

Step-by-step explanation:

Answer:

29.33π cm³  or 92.10 cm³

Step-by-step explanation:

To find the volume of a cone with height 5.5 and radius 4, we will simply use the formula;

volume of a cone = [tex]\frac{1}{3}[/tex] π r² h

h = 5.5  and r= 4, we will simply plug in these values into our formula

volume of a cone  =  [tex]\frac{1}{3}[/tex]   ×  π   × (4)² (5.5)

                               = [tex]\frac{1}{3}[/tex]  ×π × 16 × 5.5

                                =88π   /  3

                                 =29.33π

volume of cone = 29.33π

But π= 3.14

plugging in π=3.14, we have;

volume of cone = 29.33(3.14)=29.10

Answer:

88/3

Step-by-step explanation:

i just did the assignment

Answer:

2,674.14 g

Step-by-step explanation:

Recall that the formula for radioactive decay is

N = N₀ e^(-λt)

where,

N is the amount left at time t

N₀ is the initial amount when t=0, (given as 42,784 g)

λ = coefficient of radioactive decay

  = 0.693 ÷ Half Life

  = 0.693 ÷ 18

  = 0.0385

t = time elapsed (given as 72 years)

e = exponential constant ( approx 2.7183)

If we substitute these into our equation:

N = N₀ e^(-λt)

= (42,787) (2.7183)^[(-0.0385)(72)]

= (42,787) (2.7183)^(-2.7726)

=  (42,787) (0.0625)

= 2,674.14 g

Final answer:

After 72 years, which corresponds to 4 half-lives of the curium with a half-life of 18 years, the remaining amount of a 42,784 gram sample would be 2,674 grams, as it halves every 18 years.

Explanation:

The question asks how much of a radioactive sample of curium, with an initial mass of 42,784 grams and a half-life of 18 years, will remain after 72 years. To answer this, we apply the concept of radioactive decay, which follows a geometric sequence where the quantity of a radioactive substance halves every half-life period.

In this scenario, 72 years consist of 4 half-lives (since 72 ÷ 18 = 4). Therefore, after each half-life, the mass of the curium would be reduced by half. Following the sequence:

After 18 years, half of the 42,784 grams would remain, which is 21,392 grams.

After 36 years, half of that would remain, becoming 10,696 grams.

After 54 years, again half of that would remain, so 5,348 grams.

Finally, after 72 years, halving once more, we would be left with 2,674 grams.

The amount of curium remaining after 72 years is 2,674 grams.

Answer:15/8

Step-by-step explanation:

Answer:

15/8

Step-by-step explanation:

Cross multiply, 8x=15. Divide by 15 on both sides, 15/8 is your answer.

Answer:

9.57 inch

Step-by-step explanation:

(4/3)×pi×8³ = 14×16×h

h = (4/3)×pi×8³ ÷ (14×16)

h = 64pi/21 inch

Or, 9.57 inch (3 sf)

Steps to solve:

5a - 2(-3a + b)

~Distribute

5a + (-2 * -3a) + (-2 * b)

~Simplify

5a + 6a - 2b

~Simplify

11a - 2b

Best of Luck!

Answer:

[tex]2.25\ in^{2}[/tex]

Step-by-step explanation:

Area of a square is given by

[tex]A=b*b=b^{2}[/tex]

Where A is area and b is the length of any side. This question has only one thing that is square in shape, the mat hence the question directly requires its area.

Given that the mat has square shape and has dimensions of 1.5 in each then the area will be

A=1.5*1.5=2.25 square inches

Therefore, the area is 2.25 square inches.

Answer:

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

We can solve simultaneous equations using substitution method, elimination method or graphical method. But for this purpose, we will be using the elimination method.

3x+4y=8 Equation 1

2x+y=42 Equation 2

Multiply Equation 1 by 2 and equation 2 by 3, so as to get the same coefficient for x

2(3x+4y=8)= 6x+8y=16 Equation 3

3(2x+y=42)= 6x+3y=126 Equation 4

Subtract equation 4 from 3, to eliminate x

6x-6x=0

8y-3y= 5y

16-126= -110

We now have 5y=-110

Divide both sides by 5,

y= -110/5

= -22

Substituting for y in equation 2

2x+(-22)= 42

2x= 42+22

2x=64

x= 64/2

= 32

(x, y)

(32, -22)

Well, there can be three different steps.

Rearrange the equation so "y" is on the left and everything else on the right.

Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)

Shade above the line for a "greater than" (y> or y≥) or below the line for a "less than" (y< or y≤).

Answer:

The Answer is A. 252π ft3

Step-by-step explanation:

Hence volume of shaded sphere is  [tex]113.09734ft^{2}[/tex]

What is Volume?

Volume refers to part inside 3 d figure which tell how much space it occupies.

How to solve?

Given two concentric spheres  one with D=12 ⇒ R= 6 feet other with r=3feet.

volume of shaded part[tex]=\frac{4}{3} \pi R^{3}-\frac{4}{3} \pi r^{3}[/tex]

[tex]=\frac{4}{3} \pi (R-r)^{3}[/tex]

[tex]=\frac{4}{3} \pi 3^{3}[/tex]=[tex]113.09734[/tex][tex]ft^{2}[/tex]

Hence volume of shaded sphere is  [tex]113.09734ft^{2}[/tex]

Learn more about volume

https://brainly.com/question/26402559

#SPJ2

Answer:

3 3/7 hours

Step-by-step explanation:

(8×6)/(8+6) = 48/14 = 3 3/7 hours

Answer:

-2/3

[tex]\sqrt50[/tex]

-1

-2.3145

Step-by-step explanation:

Answer:

-2/3

\sqrt50

-1

-2.3145

Step-by-step explanation:

please brainlist!