model aeroplane is made to a scale of 1 by two of the size of the real plane the area of the wings of the real plane are 40 m square find the area of the wings of the model in centimetre square

For finding the given literal equation is necessary to apply the power 2 on both sides of the given equation and after that you should rewrite the equation as a function of the variable m .

There are different power rules, see some them:

1. Multiplication with the same base: you should repeat the base and  add the exponents.

2. Division with the same base: you should repeat the base and  subctract the exponents.

3.Power. For this rule, you should repeat the base and multiply the exponents.

4. Zero Exponent. When you have an exponent equals to zero, the result must be 1.

The question gives: [tex]t=2\pi *\sqrt{\frac{m}{k}}[/tex] and from the previous equation, you should find [tex]m=\frac{kt^2}{4\pi ^2}[/tex].

STEP 1 - Applying the power 2 on both sides of the equation [tex]t=2\pi *\sqrt{\frac{m}{k}}[/tex].

[tex]t=2\pi *\sqrt{\frac{m}{k}}\\ \\ t^2=(2\pi *\sqrt{\frac{m}{k}})^2\\ \\ t^2=4\pi ^2*\frac{m}{k}[/tex]

STEP 2 - Rewriting the equation  [tex]t^2=4\pi ^2*\frac{m}{k}[/tex]  as a function of the variable m .

[tex]t^2=4\pi ^2*\frac{m}{k}\\ \\ t^2k=4\pi ^2m\\ \\ m=\frac{kt^2}{4\pi ^2}[/tex]

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Answer:

1. divide both sides of the equation by 2pi

2. square both sides of the equation

3. use the rule to simplify a fraction to a power

4. multiply both sides of the equation by k

Step-by-step explanation:

edg '22

Answer:240.5

Step-by-step explanation:

Angle C = 87°(calculated)

AB=C

AC=220=b

Sine laws c\sin87=220\66

c=240.5

Answer

16/9

Step-by-step explanation:

I don't know if this is right or not and I'm sry if its wrong

but 16/9 divided by 4 = 9/4 

Solving a system of equations we can see:

First, let's define the variables:

We can write the system of equations:

S = (3/4)*M

M = K - $18

S + M + K = $286.40

First, we can rewrite the second equation to get:

K = M + $18

Now we can replace the first and second equations into the third one:

(3/4)*M + M + (M + $18) = $286.40

Now we can solve this for M:

M*(1 + 1 + 3/4) = $286.40 - $18

M = $268.40*(4/11) = $97.60

Now we can find the other two values:

K = M + $18 =  $97.60 + $18 = $115.60

S =  (3/4)*M =  (3/4)*$97.60 = $73.20

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Answer:

b

Step-by-step explanation:

b shows direct variation because we can clearly tell that the slope of the graph is 1/2. The graph is also linear, and it crosses the origin (0,0).

a: This graph can be represented as y=2, and that is not a direct variation.

b: Above explanation. This graph is a direct variation.

c: This graph can be represented as x=-8, and that is not a direct variation.

d: This graph has the slope, but it does not cross the origin, so it is not a direct variation.

Answer:

Graph b

Step-by-step explanation:

Direct variation means "y varies directly as x”:

Direct variation equation:

[tex]y=kx[/tex]

where k is the (non-zero) constant of variation.

Note, therefore, that a direct variation equation passes through the origin,  as when x = 0:  

[tex]\implies y=k(0) \implies y=0[/tex]

Graph a

y does not change as x varies.

Therefore this graph does not model a direct variation.

Graph b

As x gets bigger, so does y.  As x gets smaller, so does y.  

The line passes through the origin (0, 0).

Therefore this graph models a direct variation.

Graph c

x does not change as y varies.

Therefore this graph does not model a direct variation.

Graph d

As x gets bigger, so does y.  As x gets smaller, so does y.  

However, the line does not pass through the origin (0, 0).

Therefore this graph does not model a direct variation.

The exponential equation that models this situation is:

[tex]V(t) = 18000(0.85)^t, 0 \leq t \leq 5[/tex].

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

For this problem, the parameters are:

A(0) = 18000, r = 0.15.

Hence the equation for the value of the car over the next 5 years is:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]A(t) = 18000(1 - 0.15)^t[/tex]

[tex]V(t) = 18000(0.85)^t, 0 \leq t \leq 5[/tex].

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Answer:

[tex]\huge\boxed{\sf 7x + 10\ cm}[/tex]

Step-by-step explanation:

= 5 + 2x + 2x + 5 + 3x

Combine like terms

= 2x + 2x + 3x + 5 + 5

= 7x + 10 cm

[tex]\rule[225]{225}{2}[/tex]

Answer:

7x + 10

Step-by-step explanation:

Perimeter is the sum of all the sides together, the distance around a shape.

3x + 5 + 2x + 2x + 5

Organize so the variables are on one side

3x + 2x + 2x + 5 + 5

Combine like terms:

7x + 10

Your answer would be: 7x + 10

I hope it helps! Have a great day!

bren~

Answer:

1083 seats

Step-by-step explanation:

this is an arithmetic sequence :

an = an-1 + c

in our case

a1 = 10 (10 seats in the first row)

a2 = a1 + 1 = 10 + 1 = 11

a3 = a2 + 1 = a1 + 1 + 1 = 10 + 1 + 1 = 12

an = an-1 + 1 = a1 + (n-1)×1 = a1 + n - 1 = 10 + n - 1 = 9 + n

a38 = a1 + 37 = 10 + 37 = 47 seats.

altogether this means the sum of the arithmetic sequence of a1 to a38.

the general sum of an arithmetic sequence from a1 to an is

n×(a1 + an)/2

in our case

38×(10 + 47)/2 = 19×57 = 1083 seats

Answer:

f(4) = 5

Step-by-step explanation:

Think about it this way

a point with an x value of 4,

this x value is put into the function,

then the function outputted a y value (or value) of 5.

So, we can name this function f(x)

Then,  we let x = 4,

then the output for f(4) = 5

Answer: f(4) = 5

Step-by-step explanation:

      If the point (4, 5) is on the graph of a function, this means that when you input 4 you get an output of 5.

      Inputs are usually shown with the x-coordinate, and outputs are usually shown with the y-coordinate.

      This means that (4, 5) is an input of 4 for an output of 5.

3) [tex]\angle ADB[/tex] and [tex]\angle BDE[/tex] are supplementary (if two angles form a linear pair, they are supplementary)

4) [tex]\angle ADC[/tex] and [tex]\angle CDE[/tex] are supplementary (if two angles form a linear pair, they are supplementary)

5) [tex]\angle ADB \cong \angle ADC[/tex] (supplements of congruent angles are congruent)

6) [tex]\triangle ADB \cong \triangle ADC[/tex] (SAS)

7) [tex]\angle ABD \cong \angle ACD[/tex] (CPCTC)

The missing length in the right triangle as given in the task content is; 156.

It follows from the complete question that the triangle given is a right triangle and the missing length (longest side) can be evaluated by means of the Pythagoras theorem as follows;

x² = 144² + 60²

x² = 20736 + 3600

x² = 24,336

x = √24336

x = 156.

Remarks: The complete question involves a right triangle and the missing length is the longest side.

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The area of the square is 100 inches square

The perimeter of a square is calculated using the formula;

Perimeter = 4 a

Where

a is the side

It is also important to know that the area of a square is calculated using the formula;

Area = a²

Where a represents the side of the square

Let's find the side by substituting the value of the perimeter in the formula, we have

40 = 4a

a = 40/4

a = 10 inches

Then , let's find the area by substituting the value of the side

Area = 10 ²

Area = 10 × 10

Area = 100 inches square

Thus, the area of the square is 100 inches square

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Answer:

Domain: All real numbers ; Range: y> -3

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

Here ,

4x + 9 =7x

--> 4x - 7x = -9

--> -3x = -9

--> ≠ x = -9/3

--> x = 3

The statement which is true is the slopes are all positive in quadrant I.

Given the differential equation is dy/dx=2x-2y

A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.

Given dy/dx=2x-2y

now slope=2x-2y

Along x-axis, y=0.

So, slope=2x≠0.

Since it depends upon x hence the slope along the y-axis are not horizontal.

Along y-axis, x=0.

So, slope=-2y≠0.

Since the slope along the x-axis are also not horizontal.

In quadrant I

x,y≥0

So, dy/dx≥0

Hence the slopes are all positive in quadrant I.

In quadrant IV,

x≥0,y≤0

so, dy/dx is  not always positive.

This, the slope are not all positive in quadrant IV.

Hence, the slope are all positive in quadrant I for the differential equation dy/dx=2x-2y.

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Answer:

a = 2m - b , a = 15

Step-by-step explanation:

(a)

m = [tex]\frac{1}{2}[/tex] (a + b) ← multiply both sides by 2 to clear the fraction

2m = a + b ( subtract b from both sides )

2m - b = a

(b)

when m = 19 and b = 23 , then

a = 2(19) - 23 = 38 - 23 = 15

a. 'a' in terms of m and b is given by: a = 2m - b.
b. when m = 19 and b = 23, the value of 'a' is 15.

a. To express a in terms of m and b, we can rearrange the mean formula:

m = (1/2)(a + b)

Now, we'll solve for 'a':

Multiply both sides by 2 to eliminate the fraction:

2m = a + b

Subtract 'b' from both sides:

2m - b = a

So, 'a' in terms of m and b is given by: a = 2m - b.

b. Now that we have the expression for 'a', we can find its value when m = 19 and b = 23:

a = 2m - b

a = 2(19) - 23

a = 38 - 23

a = 15

So, when m = 19 and b = 23, the value of 'a' is 15.

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The probability of it landing heads up at least three times is 1/4.

According to the statement

We have a given that the coin is tossed 4 times And we have to find the probability of it landing heads up at least three times.

So, we know that the

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.

So, According to the statement

Coin is tossed 4 times and we have to probability of find heads three times it means n = 3.

To get 3 heads, means that one gets only one tail. This tail can be either the 1st coin, the 2nd coin, the 3rd, or the 4th coin.

Thus there are only 4 outcomes which have three heads.

The probability is 4/16 = 1/4.

So, The probability of it landing heads up at least three times is 1/4.

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Answer:

2:7

Step-by-step explanation:

If 2 of the puppies are brindle that leaves 7 that are not out of the nine making the ratio 2:7.

x<3

Step-by-step explanation:

–2(5 – 4x) < 6x – 4

(–10 + 8x) < 6x – 4

8x –6x < –4 + 10

2x < 6

x < 3

The width of the freezer is 2.25ft

The formula for calculating the volume of rectangular prism is expressed as:

V = lwh

Given the following

length l = 8feet

w is the width

height h = 3feet

Substitute

54 = 8*3w

54 = 24w

w = 54/24

w = 2.25ft

Hence the width of the freezer is 2.25ft

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Tangent of a circle is a line which touches the circle at a point from outside the circle.

Given a tangent to a circle through a point outside the circle.

We have to draw a tangent to a circle from point outside the circle.

Tangent of a circle is a line which touches the circle at a point from outside the circle.. The point at which tangent touches the circle is known as point of contact.The radius of the circle and tangent are perprndicukar to each other at the point of contact. There cannot be any tangent  to the circle through a point inside the circle. There can be one tangent to a point on the circle. The steps of drawing a tangent to a circle are as under:

1) Draw a circle with the radius neede with center O.

2) Join center of the circle O and any point P on the circle OP is the radius of the circle.

3) Draw a line perpendicular to radius OP through point P which is the intersection point of tangent and circle.

This line is the tangent to the circle at P.

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Answer:

igu

you could crop out question n use pic :)

Answer:

the only one digit number that is cube and square would be 1

Step-by-step explanation:

because 1 x1 = 1 and 1×1×1= 1

no other one digit number is both a square number and cubic number :)

hope it helps please let me know if you need more help :)

x = 4 would be the solution of the given problem.

I can't speak to the first part of this question, as I don't totally have context for what they're asking, but we can solve for x using one of the laws of logarithms, namely:

log.m + log.n = log.mn

Using this law, we can combine and rewrite our initial equation as

log(x^2- x) = 3

Remember that logarithms are simply another way of writing exponents. The logarithm  is just another way of writing the fact . Keeping that in mind, we can express our logarithm in terms of exponents as

log(x^2- x) = 3 --> x^2- 2x = 8

2³ = 8, so we can replace the left side of our equation with 8 to get

x^2 - 2x - 8 =0

(x-4)(x+2) = 0

Hence x = 4 0r -2. As x cannot be negative so it would be 4.

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The first table is filled correctly and can be used to determine how long it takes for Elias and Niko to polish the silver.

The first table is filled correctly and can be used to determine how long it takes for Elias and Niko to polish the silver.

The rate is the unit rate.

Now, since Elias polishes all of the silver himself in 40 minutes, his rate is 1/40.

Similarly, Niko’s rate would be 1/50.

Their time is the same because they are working at the same time, and as such we can write that as t. Then, the part of the silver polished would be the rate * time, or:

Thus;

Part polished by Elias: ¹/₄₀ * t

Part Polished by Niko: ¹/₅₀ * t

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A survey of 969 adult investors asked how often they tracked their portfolio. The probability that an adult investor tracks his or her portfolio daily is 0.238.

From the table it is clear that the number of responses daily by the adult investors is 231.

Probability is the ration of the number of possible value to the total value.

Here the number of daily response by the adult investors = 231

The total adult investors = 969

Hence, the The probability that an adult investor tracks his or her portfolio daily = 231/969 = 0.238.

Therefore, in the total number of 969 adult investors, the probability that the investors response daily is 0.238.

Disclaimer: The question is incomplete. The following is the correct question.

Question: Recently, the stock market took big swings up and down. A survey of 969 adult investors asked how often they tracked their portfolio. The table shows the investor responses. What is the probability that an adult investor tracks his or her portfolio daily

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The largest possible area of one of the circles would be 314. 2 cm²

It is important to note that the formula for finding the area of a circle is given as;

Area = [tex]\pi r^2[/tex]

From the information given, we have the sides of the square to have a value of 20cm

Also note that the measure of the sides of the square is the size of the diameter of the circle

But we need to find the radius

radius = diameter/2

radius = 20/ 2 = 10cm

Substitute value of radius into the formula for area

Area = 3. 142 × 10^2

Area = 3. 142 × 10 × 10

Area = 314. 2 cm²

The area of the circle is 314. 2cm^2

Thus, the largest possible area of one of the circles would be 314. 2 cm²

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Surface area = 400 unit square

Surface area = 1100 unit square

Surface area = 1100 unit square

Surface area = 2400 unit square

The first figure is a cuboid;

Surface area of a cuboid = 2lw+2lh+2hw

L = 9

W = 11

h = 4

Surface area = 2( 9 × 11) + 2(9 × 4) + 2( 4× 11)

Surface area = 2(99) + 2(36) + 2(44)

Surface area = 198 + 72 + 88

Surface area = 400 unit square

Surface area of a triangular prism = Area of top + area of base

Area of the top = 1/ 2 b × h

Area = 1/2 × 4 × 8

Area = 16 unit square

Area of base = length × width

Area = 4× 4

Area = 16 unit square

Surface area = 16 + 16

Surface area = 1100 unit square

Surface area of a cylinder = 2πrh + 2πr² = 2 ( 3. 412 × 7. 5 × 15) + 2 ( 3. 141× 7. 5 × 7.5)

Surface area = 706. 95 + 353. 48

Surface area = 1100 unit square

Surface area of a cone =πr(r+ √h² + r2)

Surface area = [tex]3. 142 * 15 ( 15 + \sqrt{10^2 +34^2 }[/tex]

Surface area = [tex]47. 13 * 50. 44[/tex]

Surface area = 2400 unit square

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Answer:

The possible length of the third side is greater that 4ft and less that 20 ft

4<x<20

Answer:

v =L× b×h

=5× 4×3

=60 cubic centimeter

Answer:

Step-by-step explanation:

Trigonometry is a branch of mathematics that relates the measures of sides and angles in a triangle. The various trig functions of an angle are defined in terms of the sides of a right triangle containing that angle. Consequently, the Pythagorean theorem can be used to relate certain trig functions to each other, and to obtain formulas for the sum and difference of angles.

The Pythagorean theorem relates side measures in right triangles. For relating side measures to each other or to angles in non-right triangles, one or both of the Law of Sines and the Law of Cosines must be used.

  both b) and c)

The Law of Sines relates side lengths and the sines of angles. Knowing three side lengths tells you nothing about the angles except the ratio of their sines.

The Law of Cosines relates three side lengths and one angle. Knowing the three side lengths, the angle measure can be found.

There is no Tangent Law.

Trigonometry is a calculation tool, not a measuring tool. As such, it allows calculation of angles and sides (of a triangle) that cannot be physically measured.

Paintings benefit greatly from rules of proportion and perspective. In general, trigonometry is not directly involved. (Computer-generated art may implement these rules of perspective using trigonometry. Paintings, in general, make no direct use of trigonometry.)