When a circular plate of metal is heated in an​ oven, its radius increases at a rate of 0.02 cm divided by min0.02 cm/min. at what rate is the​ plate's area increasing when the radius is 4040 ​cm?

To solve this problem, we assume that velocity is a linear function of time:
v(t) = m t + b
where
v = velocity

t = time

m = slope of line

b = y-intercept of line equation

When t = 2 hours, v = 18 km/h, therefore:
2 m + b = 18         (1)

When t = 4 hours,  v = 4 km/h, therefore
4 m + b = 4          (2)

Subtract (1) from (2) to obtain
4 m – 2 m = 4 - 18
2 m = -14
m = -7

From (1), calculate for b:
b = 18 – 2(-7) = 32

Part A. The equation in standard form is therefore:
v = -7 t + 32

Part B. To graph the equation for the first 8 hours, we create a table as shown below. Assign values of t from 0 to 8 hours then calculate the corresponding velocity.

To prove this Pythagorean Identity, we have to know that:

cot = 1 / tan

and we also know that:

tan = sin / cos

Therefore,

cot = 1 / tan = cos / sin

So we can write the given equation in the form of:

1 + (cos^2 θ / sin^2 θ) = csc^2 θ

Expanding the left hand side of the equation:

(sin^2 θ / sin^2 θ) + (cos^2 θ / sin^2 θ) = csc^2 θ

(sin^2 θ + cos^2 θ) / sin^2 θ = csc^2 θ

We know that given a unit circle, sin^2 θ + cos^2 θ = 1. So:

1 / sin^2 θ = csc^2 θ

The equation above is already true basing on the trigonometric identities. Therefore:

csc^2 θ = csc^2 θ

Three interior angles of the given triangle are 60°, 30°, and 90°.

A triangle is a two-dimensional geometrical figure that has three sides, three vertices, and three interior angles.

Given,  two exterior angles of a triangle are 120° and 150°.

Therefore, the first interior angle is

[tex]= (180 - 120)[/tex] degrees

[tex]= 60[/tex] degrees

The second interior angle is

[tex]= (180 - 150)[/tex] degrees

[tex]= 30[/tex] degrees

The third interior angle is

[tex]= [180 - (60+30)][/tex] degrees

= 90 degrees

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Answer:

The vertex J' is at (-8,1).

Step-by-step explanation:

If is given that the triangle JKL reflected once to map onto triangle J'K'L'.

The vertices of the triangle JKL are J(8,1), K(5,7) and L(3,4). The vertex L'(-3,4).

[tex]L(3,4)\rightarrow L'(-3,4)[/tex]

It is in the form of

[tex](x,y)\rightarrow (-x,y)[/tex]

Since the y-coordinate remains same and the sign of x coordinate is changed. It shows the reflection across the y axis.

The vertices of image are,

[tex]K(5,7)\rightarrow K'(-5,7)[/tex]

[tex]J(8,1)\rightarrow J'(-8,1)[/tex]

Therefore the vertex J' is at (-8,1).

Answer:

The absolute value of a number is the distance the number is from 0 on a number line. Since distance is never negative, absolute value is never negative.Step-by-step explanation:

To solve this problem, let us first define what probability means in this case. It would be:

Probability = (number of colors to choose from) / (total number of colors)

There are a total of 5 colors on the spinner. The number of colors to choose from spins 1 to 8 would be 5 out of 5, while for the last spin 9 the number of colors to choose from would only be brown so that would be 1 out of 5. The total probability would be the product of the probability of each spins, therefore:

Probability = 1st spin * 2nd spin * 3rd spin * 4th spin * 5th spin * 6th spin * 7th spin * 8th spin * 9th spin

Probability = (5/5) *(5/5) *(5/5) *(5/5) *(5/5) *(5/5) *(5/5) *(5/5) * (1/5)

Probability = 0.2

There is a 20% chance to get brown on the last spin.

Answer:

1/5

Step-by-step explanation:

Think of it like this. If there is five spots it can potentially land on, and only 1 brown spot, the answer would be 20 %, or as a fraction, 1/5.

The answer is 222

All you do is multiply 500 by 0.15, which gives you 75. Then subtract that from 500 to give you 425. Now multiply this 425 by 0.15 then subtract the product form 425. Continue this process until it is done 5 times. Your answer on the fifth time will be your answer.

There are 4,356,000 different passwords are possible.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A phone banking password consists of 2 letters followed by 4 digits.

And, The letters B, I, S, and O are not used, and the last digit cannot be 0.

Hence, We can formulate;

Number of different passwords are possible are,

⇒ 22 × 22 × 10× 10 × 10 × 9.

⇒ 4,356,000

Thus, There are 4,356,000 different passwords are possible.

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The name of the shape graphed by the function r ^ 2 = 9 cos (2 theta) is called the “lemniscate”. A lemniscate is a plane curve with a feature shape which consists of two loops that meet at a central point. The curve is also sometimes called as the lemniscate of Bernoulli.

Explanation:

The period of coskθ is 2π/k. In this case, k = 2 therefore the period is π.

r ^ 2 = 9 cos 2θ ≥0 → cos 2θ ≥0. So easily one period can be chosen as θ ∈ [0, π] wherein cos 2θ ≥0.

As cos(2(−θ)) = cos2θ, the graph is symmetrical about the initial line.

Also, as cos (2(pi-theta) = cos 2theta, the graph is symmetrical about the vertical θ = π/2

A Table for half period [0,π4/] is adequate for the shape in Quarter1

Use symmetry for the other three quarters:

(r, θ) : (0,3)(3/√√2,π/8)(3√2/2,π/6)(0,π/4)

Answer:

lemniscate

Step-by-step explanation:

a p e x

Hence, the area of shaded region is:

72 square inches.

We have to find the area of the shaded region i.e. we have to find the area of a triangle.

Clearly the shaded triangle is in the shape of a right triangle.

we will firstly find the dimension of the triangle in order to find it's area.

Clearly the base(b) of a triangle is 36/4= 9 inches.

( since the side of the rectangle of length 36 inches is divided into 4 equal parts)

similarly the height(h) of the right triangle is:

48/3=16 inches.

( since the side of rectangle of measure 48 inches is divided into 3 equal parts)

Hence, the area of triangle is calculated as:

[tex]Area=\dfrac{1}{2}\times b\times h\\\\\\Area=\dfrac{1}{2}\times 9\times 16\\\\Area=72\text{square\ inches}[/tex]

Hence, the area of shaded region is:

72 square inches.

Answer:

[tex]y= 470 - 50x[/tex]

Step-by-step explanation:

Wayne needs to drive 470 miles to reach Milwaukee. Suppose he drives at a constant speed of 50 miles per hour.

Let x represents the number of hours he drives and y represents the distance in miles.

constant speed is 50 miles per hour.

Distance =speed x time

speed is 50 miles per hour and time is x

So distance = [tex]50x[/tex]

Wayne needs to drive 470 miles to reach Milwaukee.

To find out y, we need to subtract 50x from 470

[tex]y= 470 - 50x[/tex]

Answer:

the last one

y = 470 - 50x

In given table of exponential function,

The interval between neighboring  x-values is of 1 unit.

The ratio is  4  between neighboring y-values

Observing given table.

To find  interval between neighboring  x-values . We have to take difference between consecutive x - values.

[tex]1-0=2-1=3-2=4-3=5-4=1[/tex]

Since, in every consecutive x- values , difference of 1 is present.

So, The interval between neighboring  x-values is of 1 unit.

To find ratio between neighboring y-values , we have to take ratio of consecutive y - values.

     [tex]\frac{4}{1}=\frac{16}{4}=\frac{64}{16}=\frac{256}{64}=4[/tex]

Thus, The ratio is  4  between neighboring y-values

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When a point in quadrant 2 is rotated 180 degrees counterclockwise, it will land in quadrant 4.

A point lies in quadrant 2. If it is rotated 180 degrees counterclockwise, which quadrant will the point come to rest?

Answer:

-8

Step-by-step explanation:

Given : [tex]y=-200-12(x)[/tex]

To Find:What is the y-value when x equals -16?

Solution:

We are given that You're studying different function tools and begin working with this function:

[tex]y=-200-12(x)[/tex]

Now we are supposed to find the value of y when x is -16

So, substitute x = -16 in the equation

[tex]y=-200-12(-16)[/tex]

[tex]y=-200+192[/tex]

[tex]y=-8[/tex]

So, Value of y is -8

Hence the y-value when x equals -16 is -8

Answer: 12 and 36

Step-by-step explanation: The best way to approach a word problem like this is to break it down sentence by sentence.

We know that the sum of two numbers is 48 so we can move on to the next sentence. Now, let's take a look at the second sentence. One number is 3 times as large as the other.

This sentence tells us what variables we are going to use to represent our numbers.

So if we use x to represent one of our numbers, and one number is 3 times as large as the other, we can use 3x to represent our other number. Also, make sure to always label your variables.

X ⇒ first number

3x ⇒ second number

Now let's look back at the first sentence. "The sum of two numbers is 48". This sentence tells us how we will set up our equation. "The sum" if our variables are X and 3x will be X + 3x = 48.

Keep in mind, the word "is" means equal.

Now we have the following equation and we can solve for X.

X + 3x = 48

We start by simplifying on the left side to get 4x.

Now we have the following equation.

4x = 48

÷4    ÷4   ← divide both sides of the equation by 4

 X = 12

So our first number, X, is 12 and our second number will be 3 × 12 or 36.

Therefore, our two numbers are 12 and 36.

there are 60 minutes per hour

24/60 = 0.4 miles per minute

0.4*5 = 2

they will ride 2 miles in 5 minutes

The explicit formula for this geometric sequence is: a_n = 3 (-2)^{n-1}. he common ratio is negative, so the domain is all odd positive integers.

Explicit formula:

The explicit formula for a geometric sequence is of the form: a_n = a_1 r^{n-1}

In this case, the first term is 3 and the common ratio is −2. Therefore, the explicit formula for this geometric sequence is:

a_n = 3 (-2)^{n-1}

Restrictions to the domain:

The domain of a geometric sequence is all positive integers, unless the common ratio is negative. In this case, the common ratio is negative, so the domain is all odd positive integers.

Example:

Using the explicit formula, we can find the fourth term of the sequence as follows:

a_4 = 3 (-2)^{4-1} = 3 (-2)^3 = -24

We can also verify that the domain of the sequence is all odd positive integers by checking the first few terms:

n | a_n

1 | 3

2 | -6

3 | 12

4 | -24

5 | 48

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One bottle has a height of 12 centimeters or 12 cm. Let us call this h1, so h1 = 12 cm

While the other bottle has a height of 15 centimeters or 15 cm. Let us call this h2, so h2 = 15 cm

The difference in height can be calculated by subtracting the smaller number from the bigger number, therefore:

difference in height = h2 – h1

difference in height = 15 cm – 12 cm

difference in height = 3 cm

We know that in 1 meter there is:

1 meter = 100 centimeters = 1000 millimeters

Therefore,

difference in height = 3 cm (1000 millimeters / 100 centimeters)

difference in height = 30 mm

Answer:

difference in height = 30 mm