So, the rate at which the area of the circular surface of the cookie dough is increasing with respect to time is 80π mm^2/min and the rate at which the height is decreasing with respect to time is -2 mm/min.
Part A: The area of the circular surface of the cookie dough is given by A = πr^2, where r is the radius of the dough. The rate at which the area is changing with respect to time is given by dA/dt = 2πr*dr/dt. At time t, the radius is 20 mm and the rate at which it is increasing is 2 mm/min. Therefore, the rate at which the area of the circular surface of the cookie dough is increasing with respect to time is dA/dt = 2π(20 mm)(2 mm/min) = 80π mm^2/min.
Part B: The height of the dough is given by h, and the rate at which the height is decreasing with respect to time is given by dh/dt. Since the dough is retaining its cylindrical shape, the decrease in the height of the dough is exactly the opposite of the increase in the radius. At time t, the rate at which the radius is increasing is 2 mm/min, so the rate at which the height is decreasing with respect to time is dh/dt = -2 mm/min.
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Indicate the equation of the given line in standard form. The line containing the altitude to the hypotenuse of a right triangle whose vertices are P(-1, 1), Q(3, 5), and R(5, -5). Show calculations.
The linear function containing the altitude to the hypotenuse of a right triangle whose vertices are P(-1, 1), Q(3, 5), and R(5, -5) is given as follows:
y = -5x + 20.
How to define the linear functions?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.The hypotenuse is composed by segment QR, hence the points are:
Q(3,5) and R(5,-5).
The slope is given by the change in y divided by the change in x, hence:
m = (-5 - 5)/(5 - 3)
m = -5.
Hence:
y = -5x + b.
When x = 3, y = 5, hence the intercept b is obtained as follows:
5 = -15 + b
b = 20.
Hence the equation is:
y = -5x + 20.
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A plant is already 10.25 meters tall, and it will grow 5 centimeters every month. The plant's height, H (in meters), after x months is given by the following
function.
H(x)=0.05x+10.25
What is the plant's height after 30 months?
On solving the function H(x) = 0.05x + 10.25, the plant's height after a period of 30 months is obtained as 11.75 m.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The height of the plant is = 10.25 m
The rate at which plant grows is = 5 cm/month or 0.05m/month
The function for plant's height is given as - H(x) = 0.05x + 10.25
To find the plant's height after 30 months, substitute the value of x with 30 in the function -
H(30) = 0.05(30) + 10.25
Use the arithmetic operation of multiplication -
H(30) = 1.5 + 10.25
Use the arithmetic operation of addition -
H(30) = 11.75
Therefore, the plant's height after 30 months will be 11.75 m.
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MAKING FAIR DECISIONS
2. A group of 6 students are in the school chess club. Their teacher has 2 tickets to a chess tournament She wants to make sure she has a fair way of deciding which 2 students will win the tickets. She decides that every time a student wins a chess match, that student's name will be put in a hat for a chance to win the tickets. She will choose two names from the hat at the end of the week
Part A: Is the teacher's method fair? Explain. If it is not fair, explain how you would change her method to make it fair. (5 points: 1 point for correctly deciding whether the method is fair or unfair, 4 points for the explanation and, if it is unfair, for a correction to the method)
Part B: Two new students join the chess club. The teacher wants to include them in the chance to win the tickets. How can she set up a fair way to make the decision that includes everyone? Explain why this method is fair (5 points)
Part A: The teacher's method is partially fair.
Part B: She can set up a fair way to make the decision that includes everyone by making it an open tournament for all such that all can participate.
How can she make the decision to be fair?Part A: The teacher's method is fair in terms of giving all students an equal opportunity to win the tickets by playing chess matches and having their names put into the hat.
However, it does not take into account the skill level of the students, which could result in a less skilled student winning the tickets over a more skilled student. To make the method more fair, the teacher could use a combination of wins and chess ratings to determine which students have the best chance to win the tickets.
Part B: To include the new students in the chance to win the tickets, the teacher could have them play chess matches against the current club members and use a combination of wins and chess ratings to determine the two students who will win the tickets.
This method is fair because it gives all students, including the new ones, the opportunity to compete and be recognized for their chess skills, rather than simply giving the tickets to the two students who have been in the club the longest. Additionally, using a combination of wins and ratings ensures that the most skilled players have a better chance of winning the tickets.
Therefore, the correct answer is as given above
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A projectile is launched from ground level with an initial velocity of feet per second. Neglecting air resistance, its height in feet t seconds after launch is given by . Find the time(s) that the projectile will (a) reach a height of 192 ft and (b) return to the ground when 112 feet per second.
The time(s) that the projectile will (a) reach a height of 192 ft is 4 seconds and (b) return to the ground when is 8 seconds
What is time?Time is the continued sequence of existence and event that can occur in an apparently inevitable succession from the past through the present
The set height, s=192
(a) 192=-16t²+112t
-16t^2+112t-192=0
-t^2+8t-16=0
t^2-8t+16=0
(t-4)(t-4)=0
t=4 twice
The projectile will reach a height of 192ft after 4 sec on the way up and after 4 sec again on the way down
..
Also, set height, s=0
(b) -16t^2+128t=0
-t^2+8t=0
-t(t-8)=0
t=0 (reject)
or
t=8
The projectile will return to the ground after 8 sec
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Correct question:
A projectile is launched from the ground with an initial velocity of V0 feet per second. Neglecting air resistance, its height in feet per seconds after launch is given by s = -16t^2 +V0t. Find the time(s) that the projectile will
(a) reach a height of 192ft and
(b) return to the ground when V0= 112 feet per second.
7 - (3 + 41) + 6i
-10 + (6 - 5i) - 9i
Solve with explanation pls
The simplified form of the first expression is -37 + 6i and the second expression is -16 - 14i.
What is the arithmetic operations?
Arithmetic operations are basic mathematical operations that can be performed on numbers, such as addition, subtraction, multiplication, and division.
The first expression is 7 - (3 + 41) + 6i. To simplify this expression, we need to first simplify the parentheses. Inside the parentheses, we have 3 + 41 = 44. So the expression becomes:
7 - 44 + 6i
Next, we can simplify the arithmetic operations by combining like terms:
7 - 44 + 6i = -37 + 6i
The second expression is -10 + (6 - 5i) - 9i. Similar to the first expression, we need to simplify the parentheses first. Inside the parentheses, we have 6 - 5i = 6 - 5i. So the expression becomes:
-10 + 6 - 5i - 9i
Next, we can simplify the arithmetic operations by combining like terms:
-10 + 6 - 5i - 9i = -16 - 14i
Hence, the simplified form of the first expression is -37 + 6i and the second expression is -16 - 14i.
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volumes (cm)^3 of 20 brains have a mean of 1120.6cm^3 and a standard deviation of 124.5cm^3. use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. would a brain volume of 1389.6^3 be significantly high ? is 1389.6^3 significantly high? what are the significantly low values or lower and what are the significantly higher values.
The significantly low values are:
Lower than 871.6 cm³.
The significantly high values are:
Higher than 1369.6 cm³.
Hence a volume of 1389.6 cm³ is significantly high, as it is more than 2 standard deviations from the mean.
What is the range rule of thumb?The range rule of thumb states that measures that are more than two standard deviations from the mean in a data-set are considered unusual.
Considering the mean and the standard deviation for this problem, the bounds are given as follows:
Significantly low: Lower than 1120.6 - 2 x 124.5 = 871.6 cm³.Significantly high: Higher than 1120.6 + 2 x 124.5 = 1369.6 cm³.More can be learned about the range rule of thumb at brainly.com/question/15825971
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50 POINTS REWARD + BRAINLEST!! NEEDED ASAP!! PLEASE!!
15. The algebraic expression 25x - 1,500 can be used to describe the daily profit of a company that makes waffle irons.
A. What does the first term of the expression represent? What does the second term of the expression represent?
B. Explain what the algebraic expression represents if the company sells 350 waffle irons per day.
C. What is the company's profit for a 5-day week? Explain.
A). The first term represents the total cost of the waffle irons and the second term represents the expenses.
B). The algebraic expression represents if the company sells 350 waffle irons per day will be 350x - 1500
C). The company's profit for a 5-day week is $250.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the algebraic expression 25x - 1,500 can be used to describe the daily profit of a company that makes waffle irons.
A). The first term represents the total cost of the waffle irons and the second term represents the expenses. Here 25 is the number of the waffle iron and the x is the number of days.
B). The algebraic expression represents if the company sells 350 waffle irons per day will be written as:-
350x - 1500
C). The company's profit for a 5-day week will be;-
Profit = 350x - 1500
Profit = ( 350 x 5 ) + 1500
Profit = 1750 - 1500
Profit = 250
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1.02 quiz what is the minimum of the sinusoidal?
Answer:
The function's minimal value is m = A |B|. When either sin x or cos x is equal to 1, this minimum is reached. Create a graph for the first example, y = 1 + 2 sin x.
Step-by-step explanation:
x^5-5x^3+4x=0 solve the equation
Answer:
x
=
0
,
x
=
1
,
x
=
2
,
x
=
−
1
, and
x
=
−
2
Explanation:
Start off by factoring out an
x
as follows
x
(
x
4
−
5
x
2
+
4
)
=
0
We can factor
x
4
−
5
x
2
+
4
Doing so we have
x
(
x
2
−
4
)
(
x
2
−
1
)
=
0
So in order for this to be equal to zero
x
=
0
OR
x
2
−
4
=
0
OR
x
2
−
1
=
0
Well
x
=
0
x
2
=
4
x
=
±
√
4
=
±
2
x
2
=
1
x
=
±
√
1
=
±
1
Enter deg after any value that is in degrees.
The concept of linear pairs from the given diagram shows that; GKH = 90°
How to identify linear pairs?A linear pair is formed when two straight lines intersect to form two angles that are adjacent to each other and are on a straight line.
Now, what this means is that ∠F KG and ∠GKH will sum up to 180 degrees because they are linear pairs from the question.
Due to the fact that ∠F KG = 90°, then we can say that;
∠F KG + ∠GKH = 180°
90° + ∠GKH = 180°
∠GKH = 180° - 90°
∠GKH = 90°
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Cathy saves 4/5 of the money she earns from her part-time job. How much does she save when she makes $140?
Step-by-step explanation:
Money she makes=$140
since she saves 4/5 of the money she earns that means that: 4/5×140 = $32
This means that she saves $32 out of $140 she makes or earn
The average car sold from dealership a is $25,700.if the salesperson receives 1.5%commission on the price of the car ,how much commission is made on the average car sold
Answer: $385.50
Step-by-step explanation: 25,700x1.5% = 385.50
What is the domain of f(x) = 5x – 7?
{x | x > –7}
{x | x < –7}
{x | x > 0}
{x | x is a real number}
Answer:
{x | x is a real number}
Step-by-step explanation:
x can have any real number value.
functions that aren't invertible can be made invertible by restricting their domains. for example, the function $x^2$ is invertible if we restrict $x$ to the interval $[0,\infty)$, or to any subset of that interval. in that case, the inverse function is $\sqrt x$. (we could also restrict $x^2$ to the domain $(-\infty,0]$, in which case the inverse function would be $-\sqrt{x}$.) similarly, by restricting the domain of the function $f(x).
When the domain of x is restricted, the function x2 becomes one-to-one, and the inverse function is x.
It is true that limiting a function's domain might cause it to become invertible. Because it is not one-to-one in the example, the function x2 is not invertible across its complete domain of real numbers (i.e., it assigns multiple outputs to some inputs). However, x2 becomes one-to-one and invertible when the domain of x is constrained to or any subset of that interval. The range of x2, which is, is used to define the inverse function in this situation, which is
The function x2 becomes one-to-one when the domain of x is constrained, and the inverse function is
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evaluate the limit by first interpreting the sum as a riemann sum for a function defined on [0, 16].
The limit in question is
[tex]$$\lim_{n\to \infty} \frac{1^3 + 2^3 + 3^3 + \dots + n^3}{n^4}$$[/tex]
This limit can be interpreted as the Riemann sum of a function defined on the interval [0, 16]. To calculate the sum, we need to first find the function that is being approximated. To do this, we can use the fact that the numerator of the limit can be rewritten as a single summation:
[tex]$$\sum_{k=1}^n k^3 = \frac{n^2 (n+1)^2}{4}$$[/tex]
This means that the function we are approximating is [tex]$f(x) = \frac{x^2 (x+1)^2}{4}$[/tex]
Now, to calculate the Riemann sum, we need to divide the interval [0, 16] into $n$ equal subintervals. The width of each subinterval is given by [tex]$\Delta x = \frac{16}{n}$\\The Riemann sum is given by $$\sum_{i=1}^n f\left(x_i\right) \Delta x = \sum_{i=1}^n \frac{\left(x_i\right)^2 \left(x_i+1\right)^2}{4} \cdot \frac{16}{n}$$[/tex]
where [tex]$x_i = \frac{16i}{n}$[/tex]
Plugging this into the limit, we get
[tex]$$\lim_{n\to \infty} \frac{1^3 + 2^3 + 3^3 + \dots + n^3}{n^4}\\ = \lim_{n\to \infty} \frac{\sum_{i=1}^n \frac{\left(x_i\right)^2 \left(x_i+1\right)^2}{4} \cdot \frac{16}{n}}{n^4} = \\frac{16}{4} \lim_{n\to \infty} \frac{\sum_{i=1}^n \frac{\left(x_i\right)^2 \left(x_i+1\right)^2}{n}}{n^3}$$[/tex]
Finally, we can take the limit of the above expression to get
[tex]$$\lim_{n\to \infty} \frac{1^3 + 2^3 + 3^3 + \dots + n^3}{n^4} = \frac{16}{4} \cdot \frac{f(16)}{16^3} = \frac{1}{4}$$[/tex]
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Answer the following
i could really use some help please
Answer:
B 6
Step-by-step explanation:
Answer:
B. 6
Step-by-step explanation:
6 x -14 = 3x + 4
3x = 18
X = [tex]\frac{18}{3}[/tex] Which equals =
6
Function Tables
Thank you!
The complete function tables are written above.
What is a function? What is a quadratic function?A function describes a relationship between a dependent and independent variable. Example -
y = f(x) = 5x + 9
A quadratic function is of the form -
f(x) = ax² + bx + c
Given are the function tables as shown in the image attached.
{ 4 } -
Rule : h = 8c
{c} 2 3 4 5 6 7
{h} 16 24 32 45 48 56
{5} -
Rule : k = 2r
{r} 6 7 8 9 12 11 14
{k} 12 14 16 18 24 22 28
{6} -
Rule : k = 2r
{r} 6 7 8 9 12 11 14
{k} 12 14 16 18 24 22 28
Therefore, the complete function tables are written above.
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which of the following is most likely to contribute to a statistically significant but clinically meaningless value
When an occurrence is so common that it shouldn't be the result of chance or external influences on the study, it is said to be "statistically significant."
Different clinical significance exists. It alludes to tangible results. It frequently refers to the actual impact of a medical problem (or medical treatment) on a patient's health. The effects of a medicine are clinically meaningful if they provide alleviation. A medical problem is also considered clinically significant if it affects a patient's quality of life or expected lifespan.
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An airplane travels 4466 kilometers against the wind in 7 hours and 5866 kilometers with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind? Note that the ALEKS graphing calculator can be used to make computations easier. Rate of the plane in still air: Rate of the wind: km h km h 010 S
The Rate of plane in still air and rate of wind is 738 , 100 respectively .
What is Linear equation ?
Linear equation can be defined as the equation in which the highest degree is one
Given ,
An airplane travels 4466 kilometers against the wind in 7 hours and 5866 kilometers with the wind in the same amount of time.
Let speed of plane be Vp and Va
Now,
Vp - Va = 4466 / 7
Vp+Va = 5866 / 7
So, Evaluating the equations,
we get,
2Vp = (4466+5866) / 7
Vp = 1476 / 2
Vp = 738
So substitute Vp =738 in Vp-Va = 4466/7
738 - Va = 638
Va = 738 - 638
Va = 100.
Hence, The Rate of plane in still air and rate of wind is 738 , 100 respectively .
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Solve the system of linear equations by elimination.
5x+6y=50
x-6y=-26
Answer:x=4, y=5
Step-by-step explanation:
please please please help
Answer:
[tex]\underline{x\quad \:\:\:\:\:\:-8\quad\quad\;\;-6\quad\quad0\quad\quad\quad\;\; \;\;2}\\y\quad\quad\;\;\;\boxed{\dfrac{1}{3}}\quad\quad\quad \boxed{0} \quad\;\boxed{-1} \quad\quad \boxed{\dfrac{4}{3}}[/tex]
Step-by-step explanation:
The strategy is to substitute the value of each of the given x values into the equation
[tex]y = -\dfrac{x}{6} - 1[/tex]
and find the corresponding value for [tex]y[/tex]
[tex]x\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{x}{6} - 1\\\line(1,0){180}\\\\[/tex]
[tex]-8\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{-8}{6} - 1 = \bf{{\dfrac{1}{3}[/tex]
[tex]-6\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{-6}{6}-1 = \bf{0}[/tex]
[tex]0\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{0}{6}-1 = \bf{-1}[/tex]
[tex]2\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{2}{6} -1 =\bf{-}\dfrac{4}{3}[/tex]
[tex]\line(1,0){180}\\\\[/tex][tex]\line(1,0){180}\\\\[/tex]
if the pattern below contiunues which equation(s) is a recursive formula that reprsents the number of sequences in this sequence
The recursive formula that represents the number of sequences in this sequence is n(n-1)(n-2)/6, where n is the number of terms in the sequence.
This recursive formula is based on the pattern of the sequence. The sequence has three terms, a, b and c, and then three combinations of two terms, ab, ac and bc, and then one combination of all three terms, abc. This pattern of three terms, then three combinations of two terms, then one combination of all three terms continues as the sequence increases.
The recursive formula represents this pattern in a mathematical equation. The formula is n(n-1)(n-2)/6, where n is the number of terms in the sequence. This formula is derived from the fact that for each term there are two other terms that can combine with it to form a two-term combination, and one combination of all three terms. Therefore, for n terms, there are n(n-1)/2 two-term combinations and one combination of all three terms, for a total of n(n-1)(n-2)/6 sequences.
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The complete question is
if the pattern below contiunues which equation(s) is a recursive formula that reprsents the number of sequences in this sequence 5, 10, 20, 40.
Given the geometric sequence where a1 = 7 and the common ratio is 3, what is the domain for n?
All integers where n ≥ 1
All integers where n ≥ 0
All integers where n > 7
All integers
The domain for 'n' will be all integers where n ≥ 1. Then the correct option is A.
What is a geometric sequence?A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.
Let a₁ be the first term and r be the common ratio. Then the nth term of the geometric sequence is given as,
aₙ = a₁ · (r)ⁿ⁻¹
The geometric sequence where a₁ = 7 and the common ratio is 3. Then the formula is given as,
aₙ = 7 · (3)ⁿ⁻¹
In the geometric sequence, the value of the exponent should be greater than or equal to zero. Then we have
n - 1 ≥ 0
n ≥ 1
The domain for 'n' will be all integers where n ≥ 1. Then the correct option is A.
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Points D, B, and E are collinear. Find the value of a so that points A, B, and C are
collinear.
Because x is 6, points A, B, and C are collinear.
What is intersecting lines?The intersection of two lines in Euclidean geometry can be the empty set, a point, or another line. Distinguishing these cases and locating the intersection have applications in computer graphics, motion planning, and collision detection, among others. The intersecting lines are two lines that share exactly one common point. The intersecting lines have a point in common. The point of intersection is the common point that exists on all intersecting lines. When two or more lines intersect in a plane, they are referred to as intersecting lines. The intersecting lines share a common point, which exists on all of them and is known as the point of intersection.
Here,
Since the opposite angle are equal in intersecting lines,
42=7x
x=6
The value of x is 6 so that points A, B, and C are collinear.
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Show that the quadrilateral, formed by joining the mid-points of the sides of a square is also a square.
Since the mid-points of opposite sides of a square are equal, the quadrilateral formed will also be a square.
A four-sided polygon whose all sides are equal is a square. This means that the opposite sides of a square are equal in length and the opposite angles are also equal. Furthermore, the diagonals of a square bisect each other at their mid-points. Therefore, if the mid-points of opposite sides of a square are joined, a quadrilateral is formed. Since the opposite sides and angles are equal, the quadrilateral formed is also a square. To prove this, we can draw a line from the mid-point of one side of the square to the mid-point of the opposite side. We can then draw a line from the mid-point of the other side of the square to the mid-point of the opposite side. This will form a quadrilateral, and due to the equal sides and equal angles, it will be a square.
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Which expression is equivalent to 64x - 16?
O 16(4x + 1)
O-16 (4x - 1)
16(4x - 1)
- 16(4x + 1)
whoever answers first will be brainlyist
HELP WANTED TYY!!! Charlie has two different-sized vases for flowers. The dimensions of his small vase with a diameter of 6 cm are shown below.
A vase shaped like a cylinder is shown. A dashed line drawn across the bottom of the vase is labeled six centimeters. The height of the vase is labeled twenty-one centimeters.
His large vase has the same height as the small vase, but its diameter is 2 times greater. How do the volumes of Charlie’s two flower vases compare? Use 3.14 for π.
Select the answers from the drop-down lists to correctly complete each sentence.
The volume of his large vase is ________ = A) 2,373.84 B) 593.46 C) 791.28
D) 1582.56 cm^3.
This is _______ = A) 4 B) 2 C) 3
times the volume of his small vase.
The volume of his large vase is 2,373.84cm^3 (option A)
The is 4 times the volume of the small verse. (option A)
What is the volume of the large verse?A cylinder is a three-dimensional object. It is a prism with a circular base.
volume of a cylinder = nr^2h
Where:
π = 3.14r = radius = diameter / 2 h = heightRadius of the small verse = 6/2 = 3 cm
Volume of the small verse = 3.14 x 3² x 21 = 593.46 cm³
Radius of the large verse = (2 x 6) / 2 = 6cm
Volume of the large verse = 3.14 x 6² x 21 = 2,373.84 cm³
Difference in volumes = 2,373.84 cm³/ 593.46 cm³ = 4
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At a local pizza shop, the delivery person earns $2 for every pizza delivered, plus $70 per day. How many pizzas must the delivery person deliver to earn more than $100 in one day? Write an inequality to represent this situation.
70 + 2x > 100 is an inequality to represent this situation.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given, At a local pizza shop, the delivery person earns $2 for every pizza delivered, plus $70 per day.
Let "x" be the number of pizzas he delivers
Thus, the Total money he earns by delivering pizza = 70 + 2x
To earn more than 100$ inequality represents
70 + 2x > 100
So,
2x > 30
x > 15
Therefore, to earn more than 100$ every day he needs to deliver at least 15 pizzas.
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if log 5 a= 3, then log 5 (a^3) =
There a rule for logarithms:
[tex]\log_n(a^m) = m \cdot \log_n(a)[/tex]
So when you're working with [tex]\log_5(a^3)[/tex], we can use that rule to rewrite this as
[tex]\log_5(a^3) = 3 \cdot \log_5(a)[/tex]
And since the first part tells us (on paper) that [tex]\log_5(a) = 2[/tex], then we can say
[tex]\log_5(a^3) = 3 \cdot \log_5(a) = 3 \cdot 2 = 6[/tex]