Hello everyone! Please help me with this! I don't undertsand how to solve it :(​

Answer:

the third option

Step-by-step explanation:

Answer:

[tex] \displaystyle d)\frac{d ^{2} y}{d{x}^{2} } = 2 + \frac{ 42}{ {x}^{4} }[/tex]

Step-by-step explanation:

we would like to figure out the second derivative of the following:

[tex] \displaystyle y = \frac{ {x}^{4} + 7}{ {x}^{2} } [/tex]

we can rewrite it thus rewrite:

[tex] \displaystyle y = {x}^{2} + 7 {x}^{ - 2} [/tex]

take derivative in both sides:

[tex] \displaystyle \frac{dy}{dx} = \frac{d}{dx}( {x}^{2} + 7 {x}^{ - 2} )[/tex]

by sum derivation we obtain:

[tex] \displaystyle \frac{dy}{dx} = \frac{d}{dx}{x}^{2} + \frac{d}{dx} 7 {x}^{ - 2}[/tex]

by exponent derivation we acquire:

[tex] \displaystyle \frac{dy}{dx} = 2{x}^{} - 14 {x}^{ - 3}[/tex]

take derivative In both sides once again:

[tex] \displaystyle \frac{d ^{2} y}{d{x}^{2} } = \frac{d}{d x } (2{x}^{} - 14 {x}^{ - 3})[/tex]

use difference rule which yields:

[tex] \displaystyle \frac{d ^{2} y}{d{x}^{2} } = \frac{d}{d x } 2{x}^{} - \frac{d}{dx} 14{x}^{ - 3}[/tex]

use exponent derivation which yields:

[tex] \displaystyle \frac{d ^{2} y}{d{x}^{2} } = 2 + 42{x}^{ - 4}[/tex]

by law of exponent we get:

[tex] \displaystyle \frac{d ^{2} y}{d{x}^{2} } = 2 + \frac{ 42}{ {x}^{4} }[/tex]

hence, our answer is d)

Answer:

2&3

Step-by-step explanation:

Answer:

During the early days of mathematical expressions the Greeks needed a shorthand form of representing the summation of several terms hence the choice of ∑ as a sigma Notation.

Step-by-step explanation:

The summation symbol ∑ is the upper case equivalent of capital S in Greek and S represents sum in English.

During the early days of mathematical expressions the Greeks needed a shorthand form of representing the summation of several terms hence the choice of ∑ as a sigma Notation.

Answer:

During the early days of mathematical expressions the Greeks needed a shorthand form of representing the summation of several terms hence the choice of ∑ as a sigma Notation.

The summation symbol ∑ is the upper case equivalent of capital S in Greek and S represents sum in English.

During the early days of mathematical expressions the Greeks needed a shorthand form of representing the summation of several terms hence the choice of ∑ as a sigma Notation.

Step-by-step explanation:

its correct on EDGE2021

Answer:

1733.28 Square inches

Step-by-step explanation:

2(3.14)(6^2)+2(3.14)(6)(40)= 1733.28

r = radius (which is 6 in. Because radius is half of circumference and the circumference is 12 in.)

h = height of cylinder (which is 40 in. Shown in the diagram)

Answer:

1733.28 square inches

Step-by-step explanation:

Hi there!

What we know:

1) Determine the radius of the base (r)

The radius is equal to half the diameter. Given the diameter 12 in., we know that the radius would be 6 in.

Radius = 6

2) Plug all values into the SA equation and solve

[tex]SA=2\pi r^2+2\pi rh\\SA=2\pi (6)^2+2\pi (6)(40)\\SA=2\pi (36)+2\pi (240)\\SA=72\pi+480\pi\\SA=552\pi\\SA=552(3.14)\\SA=552(3.14)\\SA=1733.28[/tex]

Therefore, the surface area of the cylinder is 1733.28 square inches.

I hope this helps!

Answer:

48

Hope this helps!

Step-by-step explanation:

The Triangle Sum Theorem states that the interior angles of a triangle add up to 180 degrees. A square for an angle symbolizes that the angle is 90 °, as is the case with angle ∠ACB.

Therefore, as ∠CAB = 2x and ∠ABC = 3x, and angles ∠ACB, ∠CAB, and ∠ABC make up the interior angles of the triangle, we can say that ∠ACB + ∠CAB + ∠ABC = 180, so 90 + 2x + 3x = 180

90 + 2x + 3x = 180

90 + 5x = 180

subtract 90 from both sides to separate the x and its coefficient

5x = 90

divide both sides by 5 to separate the x

x = 18

(a) ∠CAB = 2x = 18(2) = 36

(b) ∠ABC = 3x = 18(3) = 54

(c) Any triangle with a 90° angle is called a right triangle. This has a 90° triangle, and is therefore a right triangle. Similarly, a 90° angle in a triangle is called a right angle.

Answer:

Sleeping - 30.2%

School - 17.6%

Homework - 0%

EC - 6.73%

Computer - 13.45%

Phone - 0%

Television - 1.68%

Excercise - 6.73%

Family time - 20.18%

Other - 3.36%

Step-by-step explanation:

hope this helps :)

Answer:

35square meters

Step-by-step explanation:

5×7=35

Answer:

c

Step-by-step explanation:

to much working out but just as a summary section of working out

3*15=45

300+45=$345(1st year)

345+300=645

6.45*15=96.75

645+96.75=$741.75(2nd year)

keep on doing that until you beat 2 in list and use common sense to realise that (d) is too big, and (b, a) is too small so (c) is the correct amount. (this is quicker than actually doing all 20 years)

The total money with Lin after 20 years will be $4910.   

The formula for compound interest -

[tex]$A = P(1 + \frac{r}{n}) ^{nt}[/tex]

Given is that Lin is saving $300 per year in an account that pays 15% interest per year, compounded annually.

We can write the total money with Lin after 20 years as -

[tex]$A = P(1 + \frac{r}{n}) ^{nt}[/tex]

A = 300(1 + 0.15/1)²⁰

A = 300(1 + 0.15)²⁰

A = 300 x (1.15)²⁰

A = 300 x 16.37

A = 4910

Therefore, the total money with Lin after 20 years will be $4910.   

To solve more questions on compound interest, visit the link below -

https://brainly.com/question/29134153

#SPJ2

Answer: 4) The center is located at (1, 3), and the radius is 6

Step-by-step explanation:

Solve the general equation of the circle.

x^2 -2x +1+ y^2-6y+9= 26+1+9 (x-1)^2+(y-3)^2=36=6^2

Hence, the coordinates of the center (1,3) And the radius will be 6

The center is located at (1,3) and the radius is 6.

"The center is the point from which all of the points on the circle are the same distance."

"The radius is the exact distance from the center to any point on the circle."

We have

[tex]x^{2} -2x+y^{2}-6y = 26\\[/tex]

Add 1 and 9 on both sides of equation

⇒[tex]x^{2} -2x+1+y^{2}-6y+9 = 26+1+9[/tex]

⇒[tex](x-1)^{2} +(y-3)^{2}= 36[/tex]

⇒[tex](x-1)^{2}+(y-3)^{2}=6^{2}[/tex].......(1)

We know the Standard form of equation of the circle

[tex](x-h)^{2}+(y-k)^{2} =r^{2}[/tex]

By comparing the standard form and equation (1)

Center (h, k) = (1, 3) and radius is 6

Hence, The center is located at (1,3) and the radius is 6.

Learn more about circle here

https://brainly.com/question/13658927

#SPJ2

Answer:

[tex]AB = 21.3[/tex]

Step-by-step explanation:

Given

[tex]\sin(25) = \frac{9}{c}[/tex]

See attachment

Required

Find AB

We have:

[tex]\sin(25) = \frac{9}{c}[/tex]

Make c the subject

[tex]c = \frac{9}{\sin(25)}[/tex]

[tex]c = 21.3[/tex]

From the attached triangle;

[tex]AB = c = 21.3[/tex]

Hence:

[tex]AB = 21.3[/tex]

Answer:

A two-column proof uses a table to present a logical argument and assigns each column to do one job, and then the two columns work in lock-step to take a reader from premise to conclusion.

Step-by-step explanation:

Basically in simple terms, one side is the statements, and the otherside is the reasoning

Answer: the 23rd term of the arithmetic sequence=91

Step-by-step explanation:

The nth term of an arithmetic sequence is given as

an=a+  (n-1) d

Given common difference , d=4 and

first term is a^1 = 3.

We have that

a₂₃=3+  (23-1) 4

a₂₃=3+  (22) 4

a₂₃=3+  88

a₂₃=91

the 23rd term of the arithmetic sequence=91

Answer:

mean = adding up all the numbers then divid by number of numbers

Step-by-step explanation:

I.e 2 5 7 9 7 add up = 30

30 ÷ 5 = 6 so 6 is the mode

[tex]\longrightarrow{\blue{ 2 \: ( \: 32 \: y + 3 \: x \: )}}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]64 \: y + 6 \: x[/tex]

[tex] = 2 \: ( \: 32 \: y + 3 \: x \: )[/tex]

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

Answer:

2 ( 32y + 3 x)

Step-by-step explanation:

64 y + 6x

factor out 2 from the equation

2 ( 32y + 3 x)

Answer:

I think 180

Step-by-step explanation:

I think 180 because it looks like M+n are supplimetary angles.

Sorry if this is wrong.

Answer:

Hi, there the answer is -1

Step-by-step explanation:

Answer:

ummmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm   and i Oop

Step-by-step explanation:

Step-by-step explanation:

[tex]8 log_{5}( {x}^{5} ) = 8 \times 5 log_{5}(x) \\ = 40 log_{5}(x) [/tex]

Answer:

the mean is 9.

Step-by-step explanation:

7

Answer:

Perimeter = 30

Area = 30

Step-by-step explanation:

[tex](x+8)^2 -x^2 = 12^2[/tex]

[tex]x^2 +16x +64 - x^2 = 144[/tex]

[tex]16x+64=144[/tex]

[tex]16x = 80[/tex]

[tex]x = 5[/tex]

Double check:

[tex]\sqrt{12^2 + 5^2} = (5+8)\\\sqrt{12^2 + 5^2} = 13\\13 = 13[/tex]

Perimeter:

[tex]12+5+13=30[/tex]

Area([tex]\frac{1}{2}bh[/tex]):

[tex]\frac{1}{2}[/tex] × 12 × 5 = 30

According to Pythagorean theorem,

Δ  (Hypotenuse)² = (1st Leg)² + (2nd Leg)²

⇒  (x + 8)² = x² + 12²

⇒  x² + 64 + 16x = x² + 144

⇒  16x = 80

⇒ x = 5

Hypotenuse = (x + 8) = (5 + 8) = 13

1st Leg = 5

2nd Leg = 12

We know that : Perimeter is the Sum of all sides of the Triangle

⇒  Perimeter = Hypotenuse + 1st Leg + 2nd Leg

⇒  Perimeter = 13 + 5 + 12

⇒  Perimeter = 30

We know that :

[tex]\bigstar \ \ \boxed{\sf{\textsf{Area of a Triangle is given by} : \dfrac{1}{2} \times Base \times Height}}[/tex]

Base = 1st Leg

Height = 2nd Leg

[tex]\implies \sf{\textsf{Area of the Triangle} = \dfrac{1}{2} \times 5 \times 12}[/tex]

[tex]\implies \sf{\textsf{Area of the Triangle} = 30}[/tex]

Answer:

A. 10,000

Step-by-step explanation:

A. is 10,000, so it is equivalent to 10,000

B. -10,000    No

C. 100   No.

D. 10   No.

Answer:

294(p)^7

Step-by-step explanation:

7(p)^2 x 3p x 14(p)^4

=> 7 x 3 x 14 x (p)^2 x (p) x (p)^4

=> 21 x 14 x (p)^(2+1+4)

=> 294(p)^7

Answer:

a =9  b=0 c=6

Step-by-step explanation:

6+9x^2

Rewrite

9x^2 +0x+6

This is in the form

ax^2+bx+c

a =9  b=0 c=6

Answer:

10

Step-by-step explanation:

d = √(x2  -x1)² + (y2 - y1)²

√(-6 - 0)² + [1 - (-7)]²

√(-6)² + (8)²

√(36) + (64)

√100

= 10