Identities and properties of logarithms ​

By using the formula of acceleration, it can be calculated that

Time taken by an earthworm  to accelerate from a speed of 0.01 m/s to 0.02 m/s over a distance of 0.9 m is 59.88 s

What is acceleration?

At first, it is important to know about velocity

Distance travelled by a body per unit interval of time in a particular direction is called Velocity

The rate of change of velocity is called acceleration.

Acceleration is a vector quantity as the direction is taken into account.

Initial velocity of earthworm (u)= 0.01 m/s

Final velocity of earthworm (v) = 0.02 m/s

Distance (s) = 0.9 m

We know,

[tex]v^2 = u^2 + 2as\\0.02^2 = 0.01^2 + 2 \times a \times 0.9\\0.02^2 - 0.01^2 = 1.8a\\(0.02 + 0.01)(0.02 - 0.01) = 1.8a\\a = \frac{0.03 \times 0.01}{1.8}\\a = 0.000167 \ ms^{-2}[/tex]

Again,

v = u + at

0.02 = 0.01 + 0.000167[tex]\times[/tex] t

t = [tex]\frac{0.02 - 0.01}{0.000167}[/tex]

t = 59.88 s

Time taken by an earthworm  to accelerate from a speed of 0.01 m/s to 0.02 m/s over a distance of 0.9 m is 59.88 s

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Answer: Let us assume speed of jet in still air =x

speed of wind =y

Jet flying against the wind

Relative speed of the jet = speed of jet in still air -speed of the wind=x-y

distance covered =3426

time =6 hours

distance = speed * time

3426=(x-y)*6

x-y =3426/6

x-y=571——(1)

Jet flying with the wind

Relative speed of the jet = speed of jet in still air +speed of the wind=x+y

distance covered =4026

time =6 hours

distance = speed * time

4026=(x+y)*6

x+y =4026/6

x+y=671———-(2)

solving 1 and 2 we get

x+y=671

x-y=571

x=621

y=50

speed of jet in the still air =x= 621 miles per hour

Step-by-step explanation:

The required percentage of height of 34 and 54 inches are 85% and 135%.

Given that,
The percentage of the height of 34 inches and 54 inches against the height of 40 inches is to be determined.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,

a,
percentage = 34/40 × 100%
Percentage = 85%

b,
percentage = 54/40 × 100%
Percentage = 135%

Thus, the required percentages of height of 34 and 54 inches are 85% and 135%.

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The linear equation in the slope-intercept is:

y = (-1/5)*x  - 26/5

And it can be written as:

y = (-1/5)*(x + 1) - 5

We can write the equation for line L as:

y = a*x +b

Where a is the slope and b is the y-intercept.

Two lines are perpendicular if the product between the slopes is equal to -1.

So if we want our line to be perpendicular to y= 5x, then we must have:

a*5 = -1

a = -1/5

So our line is something like:

y = (-1/5)*x + b

And the line passes through (-1, -5), replacing these values:

-5 = (-1/5)*-1 + b

-5 = 1/5 + b

-5 - 1/5 = b

-26/5 = b

The linear equation is:

y = (-1/5)*x  - 26/5

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Answer:

Step-by-step explanation:

Answer:

I think the answer is 33?

-4 2/3 ,-3 2/3, -1 2/3 2/3

The range of the function is y ≤ 3.

The set of a function's potential output values is known as its range.

Given, the graph of the function.

The range of a function is the set of values of y the function can take.

The maximum y value of the function is 3, and the graph is going down both sides infinitely.

Therefore, the range of the function is y ≤ 3.

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Using polar coordinates, volume of the given solid is, 32√3π.

What is volume of solid?

An object's space requirement is expressed in terms of its volume. The amount of unit cubes required to completely fill the solid is how much it weighs. We have a total of 30 unit cubes in the solid, so the volume is as follows: 2 units 3 units 1 unit Equals 30 cubic units

We have to find the volume of the solid Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4 using polar coordinates.

So, the volume is

[tex]2\int\limits\int\limits_D {\sqrt{16-x^2-y^2} } \, dA[/tex]

[tex]2\int\limits^2^\pi _0 {\int\limits^4_2 {\sqrt{16-r^2} } rdrdtheta[/tex]

[tex]2\int\limits^2^\pi _0 {(-\frac{1}{3})(16-r^2)_2^4 } \, dtheta[/tex]

[tex]2\int\limits^2^\pi _0 {(-\frac{1}{3})(-2\sqrt{3}) } \, dtheta[/tex]

[tex]\int\limits^2^\pi _0 {16\sqrt{3} } \, dtheta[/tex]

[tex]32\sqrt{3}\pi[/tex]

Hence, the volume of the given solid using polar coordinates is, [tex]32\sqrt{3}\pi[/tex].

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If lliot and Jack share some money in the ratio . 8:5 Elliot got £21 more than Jack. The amount that Elliot received is £56.

Given data;

Sharing ratio 8:5

Amount Elliot got = 21

In order to determine  the amount that Elliot received we need to formulate and equation and then use the formulated equation to find the amount received.

Equation

21 × 8 ÷ (8-5)

Hence,

£21 × 8 ÷ (8-5)

£168 ÷ 3

=  £56

Therefore Elliot received £56.

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The expression used to find the width using division is:

W = A/L

We know that for a rectangle of width W and length L, we know that the area is given by the product between these two dimensions, then:

A = L*W

We want a expression using division that can be used to find the width, so, suppose we know the values of the area and the length, the we can divide both sides by L to get:

A/L = W

This expression gives the width.

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Answer: 3.28 inches

Step-by-step explanation:

Fabric used for players and coaches is 776.32 inches.

Number of players is 29 and coaches is 3

So fabric used for each player and coach for the headbands is

776.32/29+3 = 24.26 inches

So, for the players 24.26 of fabric will be used for the headbands.

Total fabric used for the wristbands is 247.66 inches

Fabric used for the wristband is

247.66/29 = 8.54 inches

So, total amount of fabric used by Shelia for the wristband and headband is 24.26 + 8.54 = 32.8 inches.

To make a square using the method of completing the square.

[ (a + b)² = a² + 2ab + b² ]

[ (a - b)² = a² - 2ab + b² ]

x² - 13x + 31 = 0

(x - 13/2)² + (293/4) = 0

The number added to complete the square is 293/4.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

x² - 13x + 31 = 0

To make a square using the method of completing the square.

[ (a + b)² = a² + 2ab + b² ]

[ (a - b)² = a² - 2ab + b² ]

x² - 2 x (13/2)x + (13/2)² - (13/2)² + 31 = 0

(x - 13/2)² + 169/4 + 31 = 0

(x - 13/2)² + (293/4) = 0

Thus

The number added to complete the square is 293/4.

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Answer: 8

Step-by-step explanation:

(Sum of first 5 quizzes) / 5 quizzes = 8

Sum of 1st 5 quizzes = 8 x 5 = 40

let x = score on the 8th quiz

(40 + 7 + 5 + x) / 8 = 7.5

52 + x = (7.5)(8) = 60

x = 60 - 52 = 8

Answer:

B is never true

Step-by-step explanation:

you can't get a negative number when you have a even power

The standard score (z-score) of the given sample mean is equal to 7.11

A standard score is also referred to as a z-value or z-score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

Mathematically, the standard score of a given sample mean can be calculated by using this formula:

[tex]Z=\frac{\bar{x}\;-\;\mu}{ \frac{\delta}{n} }[/tex]

Where:

Where:

Substituting the given parameters into the formula, we have;

Standard score, z = (30 - 31)/(9/64)

Standard score, z = -1/0.140625

Standard score, z = 7.11

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Answer: A

Step-by-step explanation :

HE ASKED YOU ABOUT AN EQUALTULAR ( TO EQUALED AND OPPSITE ANGLE )

The maximum number of guests that can fill all the standard rooms is twice the number of the standard rooms

Information from the question

each standard room can fill 2 guests

the maximum number of guests that all standard rooms can accommodate = ?

The problem is solved by multiplication

each standard room (1) = 2 guests

all standard rooms = ?

cross multiplying

? * 1 = 2 * all standard rooms

? = all standard rooms times two

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Answer:

Here,

Let the age of Adam be x

and ,Brian be y

so,x=y+20.........eqn 1

and ,2(y+2)=x

or,2y+4=x......eqn 2

Now ,

subtracting eqn1 and eqn 2

so, x=y+20

x=2y+4

- - -

______________

0 = -y+16

so,y=16 and x=y+20 =16+20=36 .

so Adam is 36 years old and brian is 16.

Answer:

Figure A was translated right 4 units and up 2 units

The correlation coefficient that is most likely to match a line of best fit of the form y = mx + b for this situation is of:

0.9.

The correlation coefficient is an index that measures correlation between two variables, assuming numeric values between -1 and 1.

If the correlation coefficient is positive, the relation is positive, that is, they are direct proportional. If the correlation coefficient is negative, they are inverse proportional.

If the absolute value of the correlation coefficient is greater than 0.6, the relationship between the two variables is classified as strong.

In the context of this problem, the variables are listed as follows:

The total price increases with the number of bananas bought, and there is a strong positive relationship between these two variables, hence the coefficient should be greater than 0.6 and the correct option is:

0.9.

The problem is given by the image shown at the end of the answer.

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Answer:

1

2

[

x

2

2

−

x

3

3

]

2

0

=

1

2

[

(

4

2

−

8

3

)

−

(

0

)

]

=

1

2

(

−

2

3

)

=

−

1

3

Step-by-step explanation:

The fifth term of the geometric progression is -0.125 and the sum of the first 20 terms is  [tex]\frac{4}{3}(\frac{1-2^{20} }{2^{20} }) }[/tex]

A geometric progression or a geometric sequence is the sequence, in which each term is varied by another by a common ratio.

All terms of a geometric progression have a common multiple called the common ratio.

if a = -2, which is first term

r = -0.5 which is common ration,

Then fifth term = a[tex]r^{4}[/tex]

substitute a and r into the above equation, you have

fifth term = (-2)([tex](-0.5)^{4}[/tex] = - 0.125

sum of G.P when the common ratio is less than 1, we have

[tex]\frac{a(1 - r^{n} )}{1 - r}[/tex]

where n = number of terms = 20

sum = [tex]\frac{-2(1 - (-0.5)^{20}) }{1--0.5}[/tex] =  [tex]\frac{4}{3}(\frac{1-2^{20} }{2^{20} }) }[/tex]

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In the given equation [12.5x + 5y = C] the constant C is always 50 with different given values of x and y.

So, the values of C are:

Calculate as follows:

(A) When x = -2 and y = 15.

(B) When x = 0 and y = 10.

(C) When x = 2 and y = 5.

(D) When x = 4 and y = 0.

Therefore, in the given equation [12.5x + 5y = C] the constant C is always 50 with different given values of x and y.

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The future value of the annuity investment is expressed in option A

The future value formula is used to calculate the future value (FV) of an investment with given inputs of compounding periods (N), interest/yield rate (I/Y), starting amount, and periodic deposit/annuity payment per period (PMT).

The formula can be expressed as

FV = [MP(1 + r/n)^nt - 1] / [r/n]

We can substitute the values into the equation;

FV = 250[(1 + 0.062/12)^12 * 30] / 0.062 /12

The answer to this question is option A

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The exact arc length of f(x)=√2x+1 is 4.5.

The arc length is the separation between two points along a curve segment. The arc length of a function f(x) is given by the formula,

[tex]L=\int\limits^a_b {\sqrt{1+f'(x)^2}} \, dx[/tex]

Where f'(x) is derivative of function f(x). The arc length is, to put it simply, the distance that passes across the curved line of the circle that forms the arc. It should be noted that the arc's length is greater than the separation of its ends along a straight line.

Finding the arc length of f(x)=√2x+1 0≤x≤4, using the formula,

First finding the derivative of function,

[tex]f'(x)=\frac{d(\sqrt{2x+1})}{dx} \\\\=\frac{2}{2\sqrt{2x+1}} \\\\=\frac{1}{\sqrt{2x+1}}[/tex]

Now, putting the derivative of function f(x) in the formula of arc length L,

[tex]L=\int\limits^a_b {\sqrt{1+f'(x)^2}} \, dx\\\\L=\int\limits^4_0 {\sqrt{1+(\frac{1}{\sqrt{2x+1}})^2}} \, dx\\\\L=\int\limits^4_0 {\sqrt{1+\frac{1}{2x+1}}}\\\\L=\int\limits^4_0 {\sqrt{\frac{2x+1+1}{2x+1}}}\\L=\int\limits^4_0 {\sqrt{\frac{1}{2x+1}}}\\\approx4.5[/tex]

Therefore, the exact arc length of f(x)=√2x+1 is 4.5.

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