Grandma Millie is shrinking! Her height decreases by \dfrac{1}{4} \text{ cm}
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cmstart fraction, 1, divided by, 4, end fraction, start text, space, c, m, end text each year.
What is her total change in height over 333 years?

The main idea is to exploit the trigonometric identity,

sin²(θ) + cos²(θ) = 1

2. For an integral containing 16 - 81x², you might substitute x = 4/9 sin(θ) (with differential dx = 4/9 cos(θ) dθ, but without an actual integral to work with this isn't really important). Then

16 - 81x² = 16 - 81 (4/9 sin(θ))²

… = 16 - 81 (16/81 sin²(θ))

… = 16 - 16 sin²(θ)

… = 16 (1 - sin²(θ))

… = 16 cos²(θ)

so that in the root expression, we would end up with

[tex]\left(16 - 81x^2\right)^{7/2} = \left(16\cos^2(\theta)\right)^{7/2} = 2^{14} |\cos(\theta)|^7[/tex]

since [tex](ab)^c=a^cb^c[/tex] for all real a, b, and c; [tex]16^{7/2}=\left(2^4\right)^{7/2}=2^{14}[/tex]; and [tex]\sqrt{x^2}=|x|[/tex] for all real x.

The goal is to replace x with some multiple of sin(θ) that makes the coefficients factor out like they did here, which then lets you reduce 1 - sin²(θ) to cos²(θ).

And don't be discouraged by the absolute values; in the context of a definite integral, there are things that can be done to remove them or otherwise simplify absolute value expressions.

3. Substitute z = 1/√8 sin(θ) (so that dz = 1/√8 cos(θ) dθ). Then

1 - 8z² = 1 - 8 (1/√8 sin(θ))²

… = 1 - 8 (1/8 sin²(θ))

… = 1 - sin²(θ)

… = cos²(θ)

so that

[tex]\left(1-8z^2\right)^{3/2} = \left(\cos^2(\theta)\right)^{3/2} = |\cos(\theta)|^3[/tex]

Answer:

Answer = 9

Step-by-step explanation:

Hope This Helps :) Have an awesome day

-2 and 4/5 ..............................

Simplifying, we get

-3 1/2 is -3.5

1 1/4 is 1.25

so, -3.5/1.25=

-2.8

Answer:

Your answer of coplanar is correct

Step-by-step explanation:

A skew line are 2 lines that aren't parallel and do not intersect.

Since there are arrows on either end of AC and RS , it mean those lines continue, and they will eventually intersect.

It is also not the other 2 clearly, since they do intersect and they don't make a 90° angle

So yes,

The answer is Coplanar

Hope this helps.

Answer:

it would take him to 7 hours drive 504 miles.

Step-by-step explanation:

360 miles → 5 hours

1 miles → (5/360) hours

504 miles → [(5/360)*504] hours

504 miles → 7 hours

Answer:

Step-by-step explanation:

This is a proportional relationship.

Use ratios:

Answer:

31 ft.

Step-by-step explanation:

so 52.5% leaves 47.5% left. and so you can take 21 * 1.475 (147.5%) and get 30.975. you round to the nearest tenth which goes up to 31 ft.

Answer:

40

Step-by-step explanation:

I got this by working through all the answer choices, this one is most logical :) I also submitted my assignment and got this correct !

stay happy :)

Step-by-step explanation:

Answer:

Therefore has one solution.

explanation:

Given equations:

6x + y = -7

-24x -7y = 25

Make y the subject:

6x + y = -7

y = -7 - 6x ..............equation 1

-24x -7y = 25

-7y = 25 + 24x

y = (25 + 24x)/-7 ..........equation 2

Solve them simultaneously:

(25 + 24x)/-7 = -7 - 6x

25 + 24x = -7 (-7 - 6x)

25 + 24x = 49 + 42x

42x - 24x = 25- 42

18x = -24

x = [tex]-\frac{4}{3}[/tex]

Then y is:

y = -7 - 6x

y = -7 - 6( [tex]-\frac{4}{3}[/tex])

y = 1

Has one separate value of x and y: (  [tex]-\frac{4}{3}[/tex] , 1 ); so it has one solution.

Answer:

No

Step-by-step explanation:

To find point (3, -1), begin at the origin. Move 3 units to the right, then 1 unit down.  

Neither of the lines go through the point (3, -1)

Answer:

No

Step-by-step explanation:

No, (3, -1) is not a solution to the system. Because, lines are not intersecting at this point.

Actually, both the lines are going parallel to each other. Hence, there will be no solution.

Percentage

0.4 x 0.4 = 0.16 =16% (d)

Answer:

[tex]\frac{3x}{(x-3)(x+1)}[/tex]

Step-by-step explanation:

[tex]\frac{2x-1}{x^2-2x-3}[/tex] + [tex]\frac{1}{x-3}[/tex]

= [tex]\frac{2x-1}{(x-3)(x+1)}[/tex] + [tex]\frac{1}{x-3}[/tex]

multiply the numerator/ denominator of 2nd fraction by (x + 1)

= [tex]\frac{2x-1}{(x-3)(x+1)}[/tex] + [tex]\frac{x+1}{(x-3)(x+1)}[/tex]

add the numerators , leaving the common denominator

= [tex]\frac{2x-1+x+1}{(x-3)(x+1)}[/tex]

= [tex]\frac{3x}{(x-3)(x+1)}[/tex]

Answer:

A) (x+1)(x-3)

B) 3x / x^2 - 2x - 3

or (3x ÷ x^2 - 2x - 3)

Hope this helps!

Answer:

d.  [tex]x = 10[/tex]

e. [tex]x=\sqrt[3]{\dfrac{15}{4}}[/tex]

Step-by-step explanation:

I've typed up my workings in MS Word and attached them (as it's very difficult to type this in the Brainly equation editor).

I've used the product, quotient and power log laws.

Product:     [tex]log_a(x)+log_a(y)=log_a(xy)[/tex]

Quotient:    [tex]log_a(x)-log_a(y)=log_a(\dfrac{x}{y})[/tex]

Power:    [tex]p\log_a(x)=log_a(x^p)[/tex]

Answer:

6(1+5)

Step-by-step explanation:

The greatest common factor is 6

(6 + 30) = 6(1+5)

6(1+5) is the answer

Hope this helps :)

Have a nice day!

Answer:

Frank served 32

Alan served 18

Linda served 24

Step-by-step explanation:

78-6=72

72 divided by 4 = 18

Next time if you need help on these kind of questions, try drawing a bar diagram, it really helps

Answer: x= how many short answer response questions on the test and y= how many multiple choice questions

hope this helps :)

Step-by-step explanation:

Answer:

1) 4x² + 4x

2) 2x² - 1

Explanation:

     in these type of questions, we go right to left serially in function

given:

1)

fg(x)

f(2x+1)

(2x+1)²-1

4x² + 4x + 1 -1

4x² + 4x

2)

gf(x)

g(x²-1)

2(x²-1) + 1

2x² - 2 + 1

2x² - 1

Answer:

Step-by-step explanation:

Surface area:

Answer:

149.5

Step-by-step explanation

Answer:

149.50

Step-by-step explanation:

i did 29.1+78.8 = 107.90+ 41.5 and that's how i got 41.5

Answer:

Solution

Given,

In right angle triangle

AB=28

AC=18

BC = ?

By using Pythagoras therom

H square =B square +P square

28 = 18 + P

28-18 = P

10 = P

therefore BC = 10

Answer:

  280.2 m²

Step-by-step explanation:

The height of the triangle is found using the Pythagorean theorem.

  a² +b² = c²

  13² +b² = 20²

  b² = 20² -13² = 400 -169 = 231

  b = √231 ≈ 15.199 . . . . meters

The area of the figure is 1/4 the area of a circle with radius √231 together with the area of the triangle with base 13 and height √231.

  Triangle Area = 1/2bh

  = 1/2(13)(15.199) ≈ 98.791 . . . . square meters

__

The area of the 1/4 circle is ...

  Sector Area = (1/4)πr² = 1/4π(√231)² = (231π)/4 ≈ 181.427 . . . . square meters

__

The figure area is the sum of the triangle and quarter circle areas:

  figure area = 98.791 m² +181.427 m² ≈ 280.2 m²

_____

Additional comment

If you use 3.14 for π, then the total will be 280.1 m².

Answer:

280.2 sq meters

Step-by-step explanation:

First you have to find the third side of the triangle because it is the height of the triangle and also the radius of the circle. Using Pythagorean theorem:

x^2 + 13^2 = 20^2

x^2 + 169 = 400

x^2 = 400 - 169

x^2 = 231

x = sqroot(231)

x = 15.2

Area of triangle:

A = 1/2 b•h

= 1/2•13•15.2

= 98.8

Area of a circle:

A = pi•r^2

Area of a 1/4 Circle:

A = 1/4•pi•r^2

=1/4(3.14)(15.2)^2

= 181.4

Area of Whole Shape:

98.8 + 181.4

= 280.2 sq meter

Answer:

Step-by-step explanation:

The apothem of the square is four time lower than the area squared. Thus, to do this, we must use the formula A = s^2

Using this, we do A = s^2, and replace s for 12. Doing exponents first following order of operations (PEMDAS), we get 144. Now, that's only one side of the square. Since the square is 4 sides, we must multiply by four. Thus, your answer is (144 * 4) = 576 cm^2.

Answer: 576 cm squared.

Answer:

(7, 3)

Step-by-step explanation:

We can solve this system using elimination. In this scenario, we can eliminate x by subtracting the two equations:

x-3y=-2

x+3y=16

-3y-3y=-2-16

-6y=-18

Divide both sides by -6

y=3

Plug 3 back in for y to solve for x:

x-3(3)=-2

x-9=-2

Add 9 to both sides

x=7

(x, y) = (7, 3)

Answer:

0.25

Step-by-step explanation:

the sqare root of 5 normally is 25, therefore in decimals its the same but in decimals..... so 0.25... is the correct option :)

Hope this helps!

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Answer:

25

Step-by-step explanation:

Multiply both factors (0.5) x (0.5) = 0.25

[tex]~~~~~~~~~~~~\underset{\textit{payments at the end of the period}}{\textit{Future Value of an ordinary annuity}}\\ \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right][/tex]

[tex]\begin{cases} A= \begin{array}{llll} \textit{accumulated amount}\\ \end{array}\\ pymnt=\textit{periodic payments}\dotfill &150\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &35 \end{cases}[/tex]

[tex]A=150\left[ \cfrac{\left( 1+\frac{0.04}{12} \right)^{12\cdot 35}-1} {\frac{0.04}{12}} \right]\implies A= 150\left[ \cfrac{\left( \frac{301}{300} \right)^{420}~~ - ~~1}{\frac{1}{300}} \right] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A\approx 137059.64~\hfill[/tex]

Answer:

49

Step-by-step explanation:

Answer:

x = 14

Step-by-step explanation:

Think:

What subtracts 10 can get you 4?

Or you can add 10 on both sides.

Answer:

1 less-than x less-than 2

b.

0 less-than x less-than 3

c.

1 greater-than x greater-than 2

d.

0 greater-than x greater-than 3

Answer:

The Answer is A.  1 < x < 2

Step-by-step explanation:

Answer:

Flight arrived in london on 5 : 35 pm Wednesday

Step-by-step explanation:

Time = 16 h 35 min

Time difference = 7 h

Flight time  =  8am

So

     According to perth time flight reached in london is

         8 am + 16 h 35 m =  8 am + ( 12 h + 4h + 35 m) =

         8pm + 4h +35 =  12am + 35m   = 12 : 35 am

The time difference is 7 h ,so minus this from  perth time

      12 : 35 am -  7h  =   5 : 35 pm

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