What is the area of the shaded region?​

We are given the function to differentiate:

[tex]{\quad \qquad \sf \rightarrow y=x^{e^x}}[/tex]

Do take natural log on both sides, then we will be having

[tex]{:\implies \quad \sf ln(y)=ln(x^{e^{x}})}[/tex]

[tex]{:\implies \quad \sf ln(y)=e^{x}ln(x)\quad \qquad \{\because ln(a^b)=bln(a)\}}[/tex]

Now, differentiate both sides by using so called chain rule and the product rule

[tex]{:\implies \quad \sf \dfrac{1}{y}\dfrac{dy}{dx}=e^{x}ln(x)+\dfrac{e^x}{x}}[/tex]

[tex]{:\implies \quad \boxed{\bf{\dfrac{dy}{dx}=x^{e^x}\bigg\{\dfrac{e^x}{x}+ln(x)e^{x}\bigg\}}}}[/tex]

Hence, Option B) is correct

Product rule of differentiation:

Where, u and v are functions of x

The expressions are equivalent.

[tex] \sqrt{ \frac{2x}{9} } = \frac{ \sqrt{2x} }{ \sqrt{9} } = \frac{ \sqrt{2x} }{3} = \frac{1}{3} \sqrt{2x} \\ [/tex]

Answer:

Around 295m

Step-by-step explanation:

Answer:

295.44 m to the neaest hundredth

Step-by-step explanation:

A line drawn from the kite  perpendicular to the ground forms 2 right triangles. Let this  line be x m.

Also let y be the distance from Allison to the bottom of the line.

Consider 'Alison' triangle

cos 70 = y/150

y = 51.303 m

sin 70 = x/150

x = 150 sin 70 = 140.954 m

Consider 'Marcs' triangle

tan 30 = x / (AM - y)

tan 30 = 140.954 / (AM - 51.303)

AM - 51.303 =  140.954/tan 30

AM =  140.954/tan 30 + 51.303

AM = 295.442  m

Answer:

$1.95 for 5kg

Step-by-step explanation:

0.96 x2 is 1.92 and not even 5kg so if you get 5kg worth of the 0.96$ per kg then it will be more expensive.

So $1.95 for 5kg is the better deal.

Answer:

c. 4,250.00

Step-by-step explanation:

The initial deposit amount is $4,250.00.

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

Given that,

The worth of an investment is $6774.50

The time period is 22 years.

The rate of interest is 2.7%.

Now, Based on the above information, the calculation is as follows:

We know that;

SI = P x r x t

SI = P x 2.7% x 22

SI = 0.594P

Now,

Investment worth = P  + SI

= P + 0.594P

= 1.594P  

So, we get;

1.594P  = 6774.50

P  = $4,250  

Therefore, we can conclude that the initial deposit amount is,

⇒ $4,250.00

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Volume of cylinder,=πr²h

(22÷7)×5²×3

3.14×25×3

235.5

Answer :

235.5 units³

Answer:

x < 16

Step-by-step explanation:

∣x−7∣ < 9

x < 9 + 7

x < 16

Answer:

7x < 9

Step-by-step explanation:

because the absolute value of -7 is 7 and 7 + x = 7x.

The coordinate point of a point is the location (i.e. the x and y location) on the coordinate plane

From the complete question (see attachment), the coordinate of point A is:

A = (-4,1)

This means that the x-coordinate of point A is -4

In (a), we have the coordinate of point A to be

A = (-4,1)

This means that the y-coordinate of point A is 1

From the complete question, the coordinate of point B is:

B = (3,-2)

This means that the x-coordinate of point B is 3

In (c), we have the coordinate of point B to be

B = (3,-2)

This means that the y-coordinate of point B is -2

From the complete question, the x-coordinate of point C is the same as the x-coordinate of point A

Given that the x-coordinate of point A is -4

This means that the x-coordinate of point C is -4

From the complete question, the y-coordinate of point C is the same as the y-coordinate of point B

Given that the y-coordinate of point B is -2

This means that the y-coordinate of point C is -2

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Answer:

Question 16: 44 inches

Question 18: 10, 24, 26

Step-by-step explanation:

Question 16:

Pythagoras Theorem: c^2 = a^2 + b^2, where c is the hypotenuse and the longest side.

125^2 = 117^2 + b^2

15,625 = 13,689 + b^2

15,625 - 13689 = b^2

1936 = b^2

√1936 = b

44 = b

Question 18:

Pythagoras Theorem: c^2 = a^2 + b^2, where c is the hypotenuse and the longest side. You have to try all the possibilities. The ones that match are the lengths.

The answers are 10, 24, 26

c^2 = a^2 + b^2

26^2 = 10^2 + 24^2

676 = 100 + 576

676 = 676

Answer:

336 feet

Step-by-step explanation:

We can multiply to solve this :)

56 x 6 = 336

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

Volume of prism = Area of base× height

= l×b×h

=4.8×23×0.9

= 99.36 m³

All options are incorrect : )

Answer:

The answer is B

Step-by-step explanation:

Im 3 weeks late lol sorry. I took the quiz.

Answer:

32.24

Step-by-step explanation:

To get the height, use Pythagoras theorem on the smaller triangle

8^2=2^2+x^2

x^2=64-4

x=√60=2√15.

then for the base use P.T for the bigger triangle

10^2=y^2+√60^2

y^2=100-60

y=√40=2√10

1/2×(2√10+2)×2√15

=32.24

Answer:

B

Step-by-step explanation:

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The volume of the post = volume of rectangular prism - volume of cylindrical hole = 3,223.0 cm³.

Volume = (l)(w)(h)

Volume = πr²h

Volume of the post = volume of rectangular prism - volume of cylindrical hole

= (l)(w)(h) - πr²h

= (10)(12)(30) - π(2²)(30)

Volume of the post = 3,223.0 cm³

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Answer:

X.

10, 20, 30, 40, 50, 60

Add them:

10 + 20 + 30 + 40 + 50 + 60

= 210

Then divide that sum by the many numbers there are, and there are 6 numbers in which we added.

210 ÷ 6

= 35, the mean for this is 35.

F.

4, 5, 6, 2, 3, 5

Add them:

4 + 5 + 6 + 2 + 3 + 5

= 25

Then divide that sum by the many numbers there are, and there are 6 numbers in which we added.

25 ÷ 6

= 4.1666..., the mean for this is 4.17.

Answer:

4 sets

Step-by-step explanation:

16 + 17 + 18 = 51

17 + 18 + 19 = 54

18 + 19 + 20 = 57

19 + 20 +21 = 60

Answer:

- 43

Step-by-step explanation:

f ( x ) = - 2x² + 2x - 3

To find : f ( 5 )

f ( 5 ) = f ( x )

Here,

x = 5

f ( 5 ) = - 2x² + 2x - 3

        = - 2 ( 5 )² + 2 ( 5 ) - 3

        = - 2 ( 25 ) + 10 - 3

        = - 50 + 7

f ( 5 ) = - 43

Answer:

-43

Step-by-step explanation:

oon edge

mark me brain

Answer:

9/13

Step-by-step explanation:

Total = 9 + 4

= 13

Probability: 9/13

Answer:

256 fluid ounces

Step-by-step explanation:

2 gallons = 8 quarts

8 quarts = 18 pints

18 pints = 32 cups

32 cups = 256 fluid ounces

1 gallon = 4 quarts x 2 that's 2 gallons = 8 quarts

1 quarts = 2 pints x 8 that's 8 quarts = 16 pints

1 pints = 2 cups x 16 that's 16 pints = 32 cups

1 cup = 8 fluid ounces x 32 that's 32 cups = 256 fluid ounces

Answer:

Lateral surface area=perimeter×Height

Total surface area=Perimeter (p)×Height(h)+2×Area of cross section

[tex]\\ \rm\Rrightarrow (-3\dfrac{1}{3})^2[/tex]

[tex]\\ \rm\Rrightarrow (\dfrac{-10}{3})^2[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{(-10)^2}{3^2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{100}{9}[/tex]

[tex]\\ \rm\Rrightarrow 11\dfrac{1}{9}[/tex]

Answer:

100/9 (or) 11 1/9

Step-by-step explanation:

Q) (-3 1/3)² = ?

→ (-3 1/3)²

→ (-10/3)²

→ 100/9

→ [ 11 1/9 ]

Hence, the solution is 11 1/9.

Answer:

The answer is (A.)

Step-by-step explanation:

Answer: A on edge 22

Step-by-step explanation:

Answer: the lenght is 30 feet

Step-by-step explanation:

if this is hight times lenght then yea it should be 30 feet

Interest be I

Total:-

Answer:

x = 16

Step-by-step explanation:

3√x = x - 4

Raise the equation to the second power.

(3√x)² = (x - 4)²

9x = x² - 8x + 16

Rewrite the equation with the values on the left.

-x² + 17x - 16 = 0

x² - 17x + 16 = 0

Factor.

(x - 16)(x - 1) = 0

Set each part equal to 0.

x - 16 = 0

x = 16

x - 1 = 0

x = 1

Your solutions are 16 and 1, but it doesn't end there. Both of these may not satisfy the original equation, so plug them back in.

3√x = x - 4

3√16 = 16 - 4

3(4) = 12

12 = 2

16 is a solution.

3√x = x - 4

3√1 = 1 - 4

3(1) = -3

3 ≠ -3

1 is NOT a solution.

Answer:

D

Step-by-step explanation:

for 20 pounds of grass seed, we need 356 pounds of fertilizer

20 pounds of grass seed : 356 pounds of fertilizer

divide both sides by 20 to get 1 pound of grass seed on one side, as we want to figure out the corresponding amount of fertilizer for 1 pound of grass seed

20 pounds of grass seed/20 : 356 pounds of fertilizer/20

1 pound of grass seed: 17.8 pounds of fertilizer

So, before solving further, let's recall that, a deck of card have 52 cards, with 26 black cards, and 26 red cards, out of which, let's first consider red cards,so 13 of 26 are heart, and the other 13 out of 26 is diamond, now let's consider the black cards, so 13 of 26 black cards are spades and the other 13 out of 26 black cards are clubs, every type have an ace card, and 9 cards numbering from 2-10 and three face cards naming, queen, king and Jack. And the probability of any event is defined as the ratio of no. of favourable outcomes to Total no. of possible outcomes, so let's stary solving all the parts one by one :

7) [tex]{:\implies \quad \sf P(Red\:\:card)=\dfrac{26}{52}}[/tex]

[tex]{:\implies \quad \boxed{\bf{P(Red\:\:card)=\dfrac12}}}[/tex]

8) [tex]{:\implies \quad \sf P(Jack\:\:of\:\:diamonds)=\dfrac{1}{52}}[/tex]

[tex]{:\implies \quad \boxed{\bf{P(Jack\:\:of\:\:diamonds)=\dfrac{1}{52}}}}[/tex]

9) [tex]{:\implies \quad \sf P(Ace)=\dfrac{4}{52}}[/tex]

[tex]{:\implies \quad \boxed{\bf{P(Ace)=\dfrac{1}{13}}}}[/tex]

10) [tex]{:\implies \quad \sf P(A\:\:black\:\:10)=\dfrac{2}{52}}[/tex]

[tex]{:\implies \quad \boxed{\bf{P(A\:\:black\:\:10)=\dfrac{1}{26}}}}[/tex]

11) [tex]{:\implies \quad \sf P(A\:\:heart)=\dfrac{13}{52}}[/tex]

[tex]{:\implies \quad \boxed{\bf{P(A\:\:heart)=\dfrac14}}}[/tex]

12) [tex]{:\implies \quad \sf P(Not\:\:a\:\:club)=\dfrac{39}{52}}[/tex]

[tex]{:\implies \quad \boxed{\bf{P(Not\:\:a\:\:club)=\dfrac34}}}[/tex]

The expression that can be used to find the perimeter of the rectangle is 62 centimeters 2(5x−2)+2(3x+1).

The perimeter of the rectangle is equal to the 2 times sum of the length and width of the rectangle.

Zohar is using scissors to cut a rectangle with a length of 5x – 2 and a width of 3x + 1 out of a larger piece of paper.

The expression that can be used to find the perimeter of the rectangle is given by;

[tex]\rm Perimeter \ of \ rectangle = 2 (length +width)\\\\\rm Perimeter \ of \ rectangle = 2 (5x-2+3x+1)\\\\ \rm Perimeter \ of \ rectangle = 2 (7x-1)\\\\ \rm Perimeter \ of \ rectangle = 16x-2\\\\When , x\ =\ 4\\\\ \rm Perimeter \ of \ rectangle = 14x-2\ = 16(4)-2\ =\ 64-2\ =\ 62\\[/tex]

Hence, the expression that can be used to find the perimeter of the rectangle is 62 centimeters 2(5x−2)+2(3x+1).

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