The surface area of a snowball melting decreases at a rate of 6cm/min. how is the volume changing when the radius is 3

For a given number X, its cube is written as X^3.

Here we want to see if we can find a number that is exactly 3 more than its cube, this means that:

[tex]X = X^3 + 3[/tex]

We will see that yes, there exists a number with this property.

Then we can try to solve this to find the number with that given property.

We can rewrite it as:

[tex]-X^3 + X - 3 = 0[/tex]

Now we can solve this for X, as the question asks about existence and not for the exact number, we can graph this the above function:

[tex]f(X) = -X^3 + X - 3[/tex]

And if it crosses the x-axis, then at some point we have:

[tex]f(X) = 0[/tex]

This would imply that there exists a real number that is 3 more than its cube.

The graph can be seen below, and we can see that it intersects the X-axis, then yes, there is a number that is exactly 3 more than its cube.

And by watching the graph, we can see that the number is:

[tex]X = -1.672[/tex]

If you want to learn more, you can read:

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Answer:

its -2

please brainleist

Answer:

<SRU and <VUW

Step-by-step explanation:

Corresponding angles occur when two lines are cut by a third line (transverse line).

In the problem you can see two lines (QRS) and (TUV) cutting by (PRUW).

Two angles are corresponding if one is on the outside (outside the two lines) and the other is on the inside (between the two lines).

In this graphic some of the corresponding angles are <SRP and <VUP, <PRQ and <RUT, <WUV and <URS.

Answer:

1200

Step-by-step explanation:

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Kiersten’s will earn 1200 dollars from his online business  this month.

Given,

Subscription fees received by Kiersten for a month by each subscriber is $10.

Since the number of members is 100 last month, so total earning of Kiersten will be,

[tex]100\times 10=1000[/tex] dollars.

According to the question, this month, 30 new members joined the website, and 10 members cancelled their subscription.

So the number of members increased will be 20.

Hence the kiersten have total 120 members this month, so the total earning of kiersten this month will be,

[tex]120\times 10=1200[/tex] dollars.

Thus kiersten earn 1200 dollars from his online business.

For more details on Unitary method follow the link:

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8/3 is the greatest value among 8/3, 2.28, 10/12, and 0.199.

The greatest value to be determined among 8/3, 2.28, 10/12, and 0.199.

Fraction is defined as the number of compositions that constitute the Whole.

Here,
= 8/3, 2.28, 10/12, and 0.199.
= 2.66, 2.28 , 0.62 and 0.199
The greatest among the 2.66, 2.28, 0.62, and 0.199 is 2.66

Thus, 8/3 is the greatest value among 8/3, 2.28, 10/12, and 0.199.

Learn more about fractions here:
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The measure of base angle is [tex]$$\boxed{{{70}^ \circ }} if the vertex angle is {40^ \circ }$$[/tex] .

Further explanation:

Given:

Vertex angle of the isosceles triangle is [tex]{40^ \circ }[/tex] .

Explanation:

The triangle three sided close Figure.

There are three type of triangles.

1. Equilateral triangle

2. Isosceles triangle

3. Scalene triangle

Equilateral triangle has all sides equal and all the angles are equal.

Isosceles triangle has 2 sides equal to each other and the two base angles are equal to each other.

Scalene triangle has all sides unequal and the angles are also not equal to each other.

The sum of all the angles of the triangle is [tex]{180^ \circ }[/tex].

Consider the base angle as y.

The value of y can be obtained as follows,

[tex]\begin{aligned}y+y+40&=180\\2y+40&=180\\2y&=180-40\\2y&=140\\y&=\frac{{140}}{2}\\y&={70^ \circ }\\\end{aligned}[/tex]

The measure of base angle is [tex]$$\boxed{{{70}^ \circ}} if the vertex angle is {40^ \circ}$$[/tex].

Learn more:

1. Learn more about inverse of the function https://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Triangles

Keywords: vertex angle, isosceles triangle, base angle, perpendicular, altitudes, point, triangle, circumcenter, bisectors, perpendicular bisectors, angles, angle bisectors, median, intersection, incenter, right angle triangle, equilateral triangle, obtuse, acute.

Answer:

Hence the number in decimal is:

0.125

Step-by-step explanation:

We are given that:

The top 1/8 of the runners advance to the finals for the track and field competition.

We are asked to find the decimal value of the number i.e. we have to represent 1/8 in the decimal value.

on dividing the number 1 ( which is in numerator) by 8 ( which is in denominator) we obtain:

[tex]\dfrac{1}{8}=0.125[/tex]

Hence the number in decimal is:

0.125

A quotient is a quantity produced by the division of two numbers. Hence, the quotient number is [tex]2[/tex].

What is quotient ?

A quotient is a quantity produced by the division of two numbers.

Let us assume that the quotient is [tex]x[/tex]

So, by using the given information it is of the form

[tex]\frac{1}{4}=\frac{x}{8}\\x=\frac{8}{4}\\x=2[/tex]

Hence, the quotient number is [tex]2[/tex].

To know more about quotient

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The required expression is:

0.035 × [tex]10^2[/tex] = 3.5  where the product is 1 < [tex]10^x[/tex] <  100.

To ensure that the product is greater than 1 but less than 100 when multiplying 0.035 by a power of ten, we need to find the appropriate exponent that will give us a result within this range.

Let's express 0.035 as a product of a number between 1 and 10 and a power of ten:

0.035 = 3.5 × [tex]10^{-2}[/tex]

Multiplying by a power of ten increases the value. We want the product to be greater than 1 but less than 100. So, we need to increase the exponent of ten until we reach a value within this range.

0.035 × [tex]10^x[/tex]

To ensure that the product is greater than 1, we need to increase the exponent enough to make the coefficient (3.5) greater than 1:

3.5 × [tex]10^x[/tex] > 1

[tex]10^x[/tex] > [tex]\frac{1}{3.5}[/tex]

[tex]10^x[/tex] > 0.29

To ensure that the product is less than 100, we need to find an exponent that doesn't increase the coefficient (3.5) too much:

3.5 × [tex]10^x[/tex] < 100

[tex]10^x[/tex] <  [tex]\frac{100}{3.5}[/tex]

[tex]10^x[/tex] < 28.57

Now, we need to find the appropriate exponent x that satisfies both conditions. This exponent should make the product greater than 1 but less than 100.

To simplify, we can use the fact that [tex]10^1[/tex] = 10 and [tex]10^2[/tex] = 100:

[tex]\[ 10^0[/tex] < [tex]10^x[/tex] < [tex]10^2[/tex]

Now, we can choose any exponent between 0 and 2 that satisfies the inequality. For example, we can choose x = 1:

0.035 × [tex]10^1[/tex] = 0.035 × 10 = 0.35

The product of 0.035 multiplied by [tex]10^1[/tex]  is 0.35, which is not greater than 1 but less than 100.

Putting x = 2,

0.035 × [tex]10^2[/tex] = 0.035 × 100 = 3.5

Here, the product is greater than 1 but less than 100.

The question is:

Write an expression to multiply 0.035 times a power of ten so that the product is greater than 1, but less than 100.

The answer would be 60 km/h. :D

Answer:

The standard form equation is B.

The centre of the circle is B

The radius is B.

Step-by-step explanation:

Firstly, the equation can all be divided by 7:

(7x² + 7y²− 28x + 42y − 35)  ÷ 7 =

x² + y² - 4x + 6y - 5 = 0

x² - 4x + y² + 6y - 5 = 0

Now add [tex]\frac{1}{2}* b[/tex]

0.5 * 4 = 2, 2² = 4 so 4

0.5 * 6 = 3. 3² = 9 so 9

(x² - 4x + 4) + (y² + 6y + 9) - 4 - 9 - 5 = 0

As the standard form of a circle is (x - a)² + (y - b)²= r² , we need to change this to this. Simply find a number that multiplies to 4 and adds to -4 ( -2 ) and a number that multitplies to 9 and adds to 6 (3):

(x - 2)² + (y + 3)²

Also, we need to subtract the square of the number inside the brackets, as this is completing the square:

-2 * -2 = 4

3 * 3 = 9

So we need to subtract 4 and 9, and 5 as that was in the original:

(x - 2)² + (y + 3)² - 4 - 9 - 5 = 0

To find the radius, we need to move this numbers over to the other side making them positives:

(x - 2)² + (y + 3)² = 4 + 9 + 5

(x - 2)² + (y + 3)² = 18

The centre of the circle in (x - a)² + (y - b)² is [tex]a[/tex] and [tex]b[/tex]

The radius is the square root of whatever (x - a)² + (y - b)² equals, so the square root of 18 is the radius:

√18 = √9√2

= 3√2

= [tex]3 * (2x^{\frac{1}{2} } )[/tex]

Answer:  The correct option is (A)  F   T  →  T.

Step-by-step explanation:  We are given to select the correct illustration of the truth value of the following conditional statement :

"If ice is hot, then rain is wet".

Let p : Ice is hot. This is a false statement.

And

q : rain is wet. This statement is true.

We know that

The statement "if p then q" is written as p ⇒ q.

Since p is false and q is true, so p ⇒ q will be true.

That is,

p      q      p ⇒ q

F      T         T

Thus, the correct illustration is   F    T   →   T.

Option (A) is CORRECT.