Plot the points A(3, 10), B(-3,5) and C(-1,-6) on the graph paper. Join them in pairs and identify the figure so formed.​

[tex] \frac{dx}{dt} = 28.2 \: \frac{m}{hr}[/tex]

Step-by-step explanation:

Let y = height of the pole = 35 m (constant)

x = length of the shadow

They are related as

[tex] \tan \theta = \frac{y}{x} [/tex]

or

[tex]x = \frac{y}{ \tan\theta } = y \cot \theta[/tex]

Taking the time derivative of the above expression and keeping in mind that y is constant, we get

[tex] \frac{dx}{dt} = y( - \csc^{2} \theta) \frac{d \theta}{dt} [/tex]

Before we plug in the numbers, let's convert the degree unit into radians:

[tex]40° \times ( \frac{\pi \: rad}{180°}) = \frac{2\pi}{9} \: radians[/tex]

Since the angle is decreasing, then d(theta)/dt is negative. Therefore, the rate at which the shadow is lengthening is

[tex] \frac{dx}{dt} = (35 \: m)( - \csc^{2} \frac{2\pi}{9} )( - \frac{1}{3} \frac{rad}{hr} )[/tex]

or

[tex] \frac{dx}{dt} = 28.2 \: \frac{m}{hr} [/tex]

Answer:

Option A

Step-by-step explanation:

From the graph attached,

Distance of point A of rectangle ABCD = 5 units

Distance of point E of rectangle EFGH = 5 units

Similarly, all the vertices of the rectangles ABCD and EFGH are equidistant from the y-axis.

Therefore, rectangle ABCD and rectangle EFGH may overlap each other by reflecting each other across y-axis.

Let's check by the rule of reflection,

Rule for the reflection of a point (x, y) across y-axis is given by,

(x, y) → (-x, y)

Following this rule,

A(-5, 5) → E(5, 5)

B(-3, 4) → F(3, 4)

C(-4, 1) → G(4, 1)

D(-6, 2) → H(6, 2)

Therefore, rule for the reflection is applicable in this question.

Option A will be the answer.

Answer:

x - y = 25

Step-by-step explanation:

3x - 4y = 15

-2x + 3y = 10

Add the two equations together

 3x - 4y = 15

-2x + 3y = 10

----------------------

x - y = 25

Answer:

[tex]{\Huge{\underline{\underline{\textbf{\textsf{Answer}}}}}}[/tex]

>> 3x - 4y = 15

>> -2x + 3y = 10

Add the two equations together

>> 3x - 4y = 15

>> -2x + 3y = 10

----------------------

Hence, x - y = 25

Answer:

B maybe

Step-by-step explanation:

Answer:

[tex]n=1.3\times 10^{12}[/tex]

Step-by-step explanation:

Given that,

The radius of a cell, r = 10⁻³ cm

The density of the cell, d = 1.1 g/cm³

The weight of the Koala, m = 6 kg = 6000 grams

The density of an object is given by:

[tex]d=\dfrac{m}{V}[/tex]

For n cells,

[tex]nd=\dfrac{m}{V}\\\\n=\dfrac{m}{dV}[/tex]

Put all the values,

[tex]n=\frac{6000}{\frac{4}{3}\cdot\pi\cdot\left(10^{-3}\right)^{3}\cdot1.1}\\\\n=1.3\times 10^{12}[/tex]

So, there are [tex]1.3\times 10^{12}[/tex]cells in the average koala.

Answer:

9000 Pounds (lbs) = 4.017859 Tons (t)

1 lbs = 0.000446 t

1 t = 2,240 lbs

Step-by-step explanation:

Answer:

root 324=18

root 441=21

root 529=23

Step-by-step explanation:

root 324 = 18

root 441 = 21

root 524 = 23

5 belong to whole number. b I don't know

Answer:

true. true. false.

Step-by-step explanation: i’m in love with the shape of u. we push and pull like magnet whatever

Answer:

A, c, d

Step-by-step explanation:

Answer:

C & D

Step-by-step explanation:

In order to find the perimeter, we would need to add all the sides. w+L+w+L would be adding the lengths and the widths. Simplifying this, we would get 2w, because there are 2 sides that are the same width, and 2 sides that are 2 lengths.

w+L+w+L or w+w+L+L or 2w+2L

Hope this helps!

--Applepi101

Answer:

The fourth (last) function is the correct one.

Step-by-step explanation:

Look at the parent function y = √x,  Its graph goes through (0, 0).  On the other hand, if y = √(x - h), the graph goes through (h, 0) if h is positive, and the graph is translated h units to the right from the graph of y = √x.  If h is negative, the graph is translated h units to the left.

In the four possible answers given, the values of h are {-4, 9, 5, -9}, in that order.  h = -9 results in the graph that is positioned 9 units to the left of the graph of y = √x.  This graph is furthest to the left.  Thus the fourth choice is the correct one.

Answer:

121

Step-by-step explanation:

(4 - 3+2·5)²

Multiply

(4-3+10)²

Now add and subtract

(1+10)²

11²

121

Step-by-step explanation:

i. 3x-1=20

or, 3x= 21

x= 7

ii. 3x+1= 22

3x= 21

x= 7

iii. 2x-5=99

2x= 104

x=52

iv. g(3)= 3+5/2= 11/2

g(0)= 0+ 5/2=5/2

g(-3)= -3+5/2 = -1/2

x+5/2= 0

so, x= -5/2

Answer:

second option is correct (for question no 20)

Step-by-step explanation:

coordinate points are:

(3,1) = (x1,y1)

(5,9) = (x2,y2)

slope (m) = y2-y1/x2-x1

=9-1/5-3

=8/2

=4

Now using slope intercept form

y=mx + b

y=4x + b

since the line passes through the point (3,1) it satisfies the equation

y=4x + b

1=4*3 + b

1-12 = b

-11 = b

substituting the value of b in equation

y=4x + b

y=4x +(-11)

y=4x - 11

Step-by-step explanation:

the answer is in the above image

but I do not get the meaning of Dy

Answer:

Step-by-step explanation:

Lucy=65

Eva= X points

Total:

Points =  65 + 65 = 130

Answer:

(a) [tex]y = 350,000 \times (1 + 0.07132)^t[/tex]

(b) (i) The population after 8 hours is 607,325

(ii) The population after 24 hours is 1,828,643

(c) The rate of increase of the population as a percentage per hour is 7.132%

(d) The doubling time of the population is approximately, 10.06 hours

Step-by-step explanation:

(a) The initial population of the bacteria, y₁ = a = 350,000

The time the colony grows, t = 12 hours

The final population of bacteria in the colony, y₂ = 800,000

The exponential growth model, can be written as follows;

[tex]y = a \cdot (1 + r)^t[/tex]

Plugging in the values, we get;

[tex]800,000 = 350,000 \times (1 + r)^{12}[/tex]

Therefore;

(1 + r)¹² = 800,000/350,000 = 16/7

12·㏑(1 + r) = ㏑(16/7)

㏑(1 + r) = (㏑(16/7))/12

r = e^((㏑(16/7))/12) - 1 ≈ 0.07132

The  model is therefore;

[tex]y = 350,000 \times (1 + 0.07132)^t[/tex]

(b) (i) The population after 8 hours is given as follows;

y = 350,000 × (1 + 0.07132)⁸ ≈ 607,325.82

By rounding down, we have;

The population after 8 hours, y = 607,325

(ii) The population after 24 hours is given as follows;

y = 350,000 × (1 + 0.07132)²⁴ ≈ 1,828,643.92571

By rounding down, we have;

The population after 24 hours, y = 1,828,643

(c) The rate of increase of the population as a percentage per hour =  r × 100

∴   The rate of increase of the population as a percentage = 0.07132 × 100 = 7.132%

(d) The doubling time of the population is the time it takes the population to double, which is given as follows;

Initial population = y

Final population = 2·y

The doubling time of the population is therefore;

[tex]2 \cdot y = y \times (1 + 0.07132)^t[/tex]

Therefore, we have;

2·y/y =2 = [tex](1 + 0.07132)^t[/tex]

t = ln2/(ln(1 + 0.07132)) ≈ 10.06

The doubling time of the population is approximately, 10.06 hours.

Answer:

5

Step-by-step explanation:

As for estimation, you may round 39.76 to the whole number, resulting in 40.

7.94 to 8

40 / 8 = 5

5 is your answer for the result of estimation

Answer:

vertex = (- 4, - 75 )

Step-by-step explanation:

Given a quadratic in standard form

y = ax² + bx + c ( a ≠ 0 )

Then the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

y = 4x² + 32x - 11 ← is in standard form

with a = 4, b = 32 , then

x = - [tex]\frac{32}{8}[/tex] = - 4

Substitute x = - 4 into the equation for corresponding y- coordinate

y = 4(- 4)² + 32(- 4) - 11

  = 4(16) - 128 - 11

  = 64 - 139

   = - 75

vertex = (- 4, - 75 )

Answer:

2

Step-by-step explanation:

Answer:

2011: 567 2012: 567*(1-.015) 2013: 567*(1-.015)*(1-.015) 2014: 567*(1-.015)567*(1-.015)*(1-.015) you see the pattern; and, if so, you can build an little equation giving you the answer

Answer:

339

Step-by-step explanation:

a = 567 (.95)¹⁰

a = 339.4838445482

Rounded

339

Answer:

[tex]a^{12}[/tex]

Step-by-step explanation:

Identity Used :   [tex]a^x \times a^y = a^{x+ y}[/tex]

       [tex]a^5 \times a^7 = a^{5 + 7} = a^{12}[/tex]

The line the puck traveled is the hypotenuse of a right triangle.

Using the Pythagorean theorem:

Travel = sqrt( 4^2 + 30^2)

Travel = sqrt( 16 + 900)

Travel = sqrt(916)

Travel = 30.265 feet ( round the answer as needed)

Step-by-step explanation:   6  22  22  51

one orange box is 10  the other box looks like 15

the scale factor is 15/10  or 1.5

the smaller triangle blue box is a 4

multiply 4 by the scale factor  1.5

  4 × 1.5  = 6