The following structure is composed of three right rectangular prisms: two that each measure 12 inches by 10 inches by 5 inches and one right rectangular prism that measures 10 inches by 8 inches by 36 inches. What is the total volume of the structure? Show your work and/or explain your reasoning..

Answer:

[tex]\displaystyle y' = - \frac{e^{x^2 + 7} \sqrt{\csc 5x} \Bigg[ \bigg[ 5 \cot (5x) - 4x \bigg] \sin (3x + 4) - 6 \cos (3x + 4) \Bigg] }{2}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:
[tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:
[tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Derivative Rule [Basic Power Rule]:

Derivative Rule [Product Rule]:
[tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Derivative Rule [Chain Rule]:
[tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle y = e^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)}[/tex]

Step 2: Differentiate

∴ we have found the derivative of the function.

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

To find the derivative of the function [tex]\displaystyle\sf\:y=e^{x^{2}+7}\sin(3x+4)\sqrt{\csc(5x)}}[/tex] with respect to [tex]\displaystyle\sf x[/tex], we'll use the chain rule and product rule.

Let's break down the function into its individual parts:

[tex]\displaystyle\sf u= e^{x^{2}+7}[/tex]

[tex]\displaystyle\sf v= \sin(3x+4)[/tex]

[tex]\displaystyle\sf w= \sqrt{\csc(5x)}}[/tex]

Now, let's differentiate each part separately:

Using the chain rule, the derivative of [tex]\displaystyle\sf u= e^{x^{2}+7}[/tex] is:

[tex]\displaystyle\sf \dfrac{du}{dx}= (2x)e^{x^{2}+7}[/tex]

Using the chain rule, the derivative of [tex]\displaystyle\sf v= \sin(3x+4)[/tex] is:

[tex]\displaystyle\sf \dfrac{dv}{dx}= 3\cos(3x+4)[/tex]

To differentiate [tex]\displaystyle\sf w= \sqrt{\csc(5x)}}[/tex], we can rewrite it as [tex]\displaystyle\sf w= (\csc(5x))^{1/2}[/tex]. Using the chain rule, the derivative of [tex]\displaystyle\sf w[/tex] is:

[tex]\displaystyle\sf \dfrac{dw}{dx}= \dfrac{1}{2}(\csc(5x))^{-1/2}(-\cot(5x))(5)[/tex]

Simplifying the derivative [tex]\displaystyle\sf \dfrac{dw}{dx}[/tex]:

[tex]\displaystyle\sf \dfrac{dw}{dx}= -\dfrac{5\cot(5x)}{2\sqrt{\csc(5x)}}[/tex]

Now, using the product rule, the derivative of [tex]\displaystyle\sf y[/tex] with respect to [tex]\displaystyle\sf x[/tex] can be calculated as follows:

[tex]\displaystyle\sf \dfrac{dy}{dx}= \dfrac{du}{dx} \cdot v \cdot w + u \cdot \dfrac{dv}{dx} \cdot w + u \cdot v \cdot \dfrac{dw}{dx}[/tex]

Substituting the values of [tex]\displaystyle\sf \dfrac{du}{dx}[/tex], [tex]\displaystyle\sf \dfrac{dv}{dx}[/tex], and [tex]\displaystyle\sf \dfrac{dw}{dx}[/tex]:

[tex]\displaystyle\sf \dfrac{dy}{dx}= \left((2x)e^{x^{2}+7}\right) \cdot \sin(3x+4) \cdot \sqrt{\csc(5x)} + e^{x^{2}+7} \cdot \left(3\cos(3x+4)\right) \cdot \sqrt{\csc(5x)} - e^{x^{2}+7} \cdot \sin(3x+4) \cdot \dfrac{5\cot(5x)}{2\sqrt{\csc(5x)}}[/tex]

Simplifying further:

[tex]\displaystyle\sf \dfrac{dy}{dx}= \left(2xe^{x^{2}+7}\right) \sin(3x+4) \sqrt{\csc(5x)} + 3e^{x^{2}+7}\cos(3x+4) \sqrt{\csc(5x)} - \dfrac{5e^{x^{2}+7} \sin(3x+4) \cot(5x)}{2\sqrt{\csc(5x)}}[/tex]

Therefore, the derivative of [tex]\displaystyle\sf y[/tex] with respect to [tex]\displaystyle\sf x[/tex] is:

[tex]\displaystyle\sf y' = -2e^{x^{2}+7}\csc(5x)[5\cot(5x)-4x]\sin(3x+4) - 3e^{x^{2}+7}\sqrt{\csc(5x)}\cos(3x+4) - \dfrac{5e^{x^{2}+7}\sin(3x+4)\cot(5x)}{2\sqrt{\csc(5x)}}[/tex]

Simplifying further, we have:

[tex]\displaystyle\sf y' = -2e^{x^{2}+7}\csc(5x)[5\cot(5x)-4x \sin(3x+4) - 6e^{x^{2}+7}\cos(3x+4)\sqrt{\csc(5x)}[/tex]

Therefore, the derivative of [tex]\displaystyle\sf y[/tex] with respect to [tex]\displaystyle\sf x[/tex] is:

[tex]\displaystyle\sf y' = -2e^{x^{2}+7}\csc(5x)[5\cot(5x)-4x]\sin(3x+4) - 6e^{x^{2}+7}\cos(3x+4)\sqrt{\csc(5x)}[/tex]

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Answer:

Ax+By=C

Step-by-step explanation:

:)

keeping in mind that the vertex will be half-way between the directrix and the focus point, in this case the directrix is below the focus point, meaning is a vertical parabola, Check the picture below.

Answer:

C. parallelogram

D. rectangle

E. kite

Step-by-step explanation:

Cannot be the square because all sides are the same. A trapezoid can have two sides the same, but not two pairs of equal sides. The remaining shapes can have two pairs of equal length sides. see image.

Answer:

25.45584...

Step-by-step explanation:

The length of the hypotenuse can be found using the pythagorean theorem: [tex]a^{2} +b^{2} =c^{2}[/tex] So in this situation, the solution can be found by solving [tex]\sqrt{2(18)^{2} }[/tex]

The sum-product pattern

If the polynomial is of the form x 2 + b x + c x^2+bx+c x2+bx+cx, squared, plus, b, x, plus, c and there are factors of c that add up to b.

I am not sure what you meant but hopefully you meant this

Answer:

If the polynomial is of the form x2 + bx + cx²+bx+cx2+bx+cx, squared, plus, b, x, plus, c and there are factors of c that add up to b.

Step-by-step explanation:

Do mark BRAINLIEST

Area = length x width

Half the perimeter = length + width

half the perimeter = 14 inches.

Find 2 numbers when added together = 14 and when multiplied together = 48

6 + 8 = 14

6 x 8 = 48

the dimensions are 6 inches by 8 inches

Answer:

This can lead to cyclical patterns of predator and prey abundance, where prey increase in number and then, with abundant food, predator number increases ...

Step-by-step explanation:

Answer:

q=50

d=22

Step-by-step explanation:

Answer:

I believe the answer is C

Step-by-step explanation:

Answer:

9.42 cube.yd

Step-by-step explanation:

Volume of cylinder= πr^2h

Answer:

You mowed 112.5 square meters of your grass.

Step-by-step explanation:

First, convert the percentage to a fraction.

75% = 3/4

Then to find 75% of 150, multiply 3/4 and 150.

(3/4) * 150

(3*150)/4

450/4

112.5

We can now say that 75% of 150 is 112.5, meaning you mowed 112.5 square meters of your grass.

Answer:

[tex]\huge\boxed{\sf 112.5 \ m^2\\}[/tex]

Step-by-step explanation:

Grass mowed:

= 75% of 150 m²

[Key: "of" means "to multiply" and "%" means "out of 100"]

[tex]\displaystyle = \frac{75}{100 } \times 150\\\\= \frac{75 \times 15}{10} \\\\= \frac{1125}{10} \\\\= 112.5 \ m^2\\\\\rule[225]{225}{2}[/tex]

Answer:

7 inches

Step-by-step explanation:

The area of a rectangle A is equal to its length times its width (or base times height if you want to put it that way.)

Since A = b*h, h = A/b. Plugging in values gives you 91.7/ 13.1 = 7 inches.

So the answer is 7 inches.

Answer:

D

Step-by-step explanation:

-3(4x - 2) - 2x

-12x + 6 -2x

-14x + 6

Answer:
since its a triangle then angles have to be 90 (the right angle) and 50 (which is given)
180-90-50 = 40
Answer = 40

Step-by-step explanation:

Answer:

x = - 9

y = 5

Step-by-step explanation:

EQ1 + EQ2

Substitute the value of X in either EQ1 or EQ2

Answer:

Step-by-step explanation:

No choice is given but here is the general interpretation.

Y-intercept is where the plot crosses the y-axia at x=0. In this case, x is T which represents number of TVs owned by the family. T=0 meaning there is no TV and B = 96.66 is the one month's electric bill in dollars for all other appliances in the home.

Given function

Now

Compare to slope intercept form y=mx+b

Here y intercept may be the fixed charge .

Yes it does include the test point (0, 0)

switch sides

Multiply both sides by -1 reverses the inequality

Thus, the following (0, 0) comes under the following x > -5/3 and y > -5

Answer:

64

Step-by-step explanation:

(-2(-4))^2

8^2

64

hope that helps

Answer:

Same spent $281.85 or approximately $282

That part is total cookies as per algebraic formula x^2-(a+b)x+ab=0

Hence

The inequality is

[tex]\\ \rm\rightarrowtail x^2-30x+224>=0[/tex]

[tex]\\ \rm\rightarrowtail (x-14)(x-16)>=0[/tex]

[tex]\\ \rm\rightarrowtail 14\leqslant x\leqslant 16[/tex]

Solution range

Atleast means the range

Atleast 2 more than Martha

The widths of Kyle's and Myla's boxes for the considered case are obtained as: width of Kyle's box = 2 ft, width of Myle's box = 2 ft

Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:

[tex]V = a\times b \times c \: \: unit^3[/tex]

A storage box oftenly has the shape of a right rectangular prism.

We're specified that:

For Kyle's box:

For Myla's box:

Using the formula for volume of right rectangular prism to find the missing widths:

[tex]12 = 2 \times 3 \times x\\12 = 6 \times x\\\text{Dividing both the sides by 6}\\2= x\\x = 2 \: \rm ft[/tex]

[tex]16 = 4 \times 2 \times y\\16 = 8 \times x\\\text{Dividing both the sides by 8}\\2= y\\y = 2 \: \rm ft[/tex]

Thus, the widths of Kyle's and Myla's boxes for the considered case are obtained as: width of Kyle's box = 2 ft, width of Myle's box = 2 ft

Learn more about volume of a right rectangular prism here:

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Answer:

£122

Step-by-step explanation:

Total no. of pens :- 60× 14= 840

Cost of all pens :- £270

Total no. of pens sold :- 560

Cost of those pens :- £392

Charles made a profit of  £122, By selling (2/3)rd of his pens.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Charles buys 60 packs of pens and there are 14 pens in each pack.

If each pack costs £4.50.

So, The Total cost is,

=  £(60×4.50).

=  £270.

The total number of pens is,

= (14×60).

= 840, And he manages to sell (2/3) of it which is,

= (2/3)×840.

= 560.

Now, The total money made by him is,

= 540×0.7.

=  £392.

Therefore, The profit he made is  £(392 - 270) =  £122.

learn more about numerical expressions here :

https://brainly.com/question/29199574

#SPJ7

Hello!

First, "the difference" of 2 numbers means you subtract these numbers.

Then, 4 cubed is written as follows:

4³

Subtract:

4³-25

[If necessary] Evaluate:

64-25

39

Hope everything is clear.

Let me know if you have any questions!

Always remember: Knowledge is power!

The statement that is true about trend lines is: A. A trend line should be as close as possible to the points.

A trend line, which can also be called the line of best fit, is a straight line that represents the pattern of a data, which can be positive or negative.

A trend line does not necessarily need to connects all the points, but goes through some points to show the pattern. It may not even be necessary to go through any of the points, what's improtant is for the trend line to be close to as many points as possible.

Therefore, the statement that is true about trend lines is: A. A trend line should be as close as possible to the points.

Learn more about trend lines on:

https://brainly.com/question/2589459

Step-by-step explanation:

volume = 176 cm³

height = 7.8

radius = ?

pi = 3.14

volume of cylinder = πr²h

176 = 3.14 × r² × 7.8

176 = 24.492 × r²

176/24.4 = r²

7.21 = r²

√7.21 = r². ( Using long division )

r = 2.69 ( approx. )

Answer:

1.25 x 10^3

Step-by-step explanation:

i took the test

The percentage of the runners having times less than 14.4 sec is 0.15%. Then the correct option is A.

It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.

The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.

The times of all 15 years old who run a certain race are approximately normally distributed with a given mean μ = 18 sec and standard deviation σ = 1.2 sec.

The percentage of the runners has times less than 14.4 sec.

Then the z-score will be given as

[tex]\rm z = \dfrac{X - \mu}{\sigma }\\\\\\z = \dfrac{14.4 - 18}{1.2}\\\\\\z = -3[/tex]

Then the percentage will be

[tex]\rm P(z < -3)=0.00135 = 0.135 \% \approx 0.15 \%[/tex]

More about the normal distribution link is given below.

https://brainly.com/question/12421652

Answer:

A.  0.15%

Step-by-step explanation:

edge 2022

Answer:

I think the answers is 27, just add all of those squares.