The formula A=23.1 e^{0.0152t} models the population of a US state, A, in millions, t years after 2000.
a. What was the population of the state in 2000 ?
b. When will the population of the state reach 28.3 million?
a. In 2000 , the population of the state was ? million.
Answers
We want to study the population formula of a given US state according to exponential equation.
a) 23.1 millions.
b) in 2013 - 2014
What is exponential equation?
The exponential function may be a function denoted by f(x)=\exp or e^. Unless otherwise fixed, the term usually refers to the positive-valued operate of a true variable
Main body:
The population state is:
A = 23.1*e^(0.0153*t)
In millions.
Where t represents the number of years after 2000.
a) For the population at the year 2000, we need to evaluate the function at t = 0 (2000 is 0 years after 2000).
A(0) = 23.1*e^(0.0153*0) = 23.1
The population at year 2000 was 23.1 millions.
b) Now we want to solve:
A(t) = 28.3 = 23.1*e^(0.0153*t)
28.3/23.1 = e^(0.0153*t)
1.23 = e^(0.0153*t)
Now we can apply the natural logarithm to both sides:
ln(1.23) = ln( e^(0.0153*t) )
ln(1.23) = 0.0153*t
ln(1.23)/0.0153 = t = 13.5
Hence, 13.5 years after 2000 the population will be 28.3 million.
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Related Questions
Please help me <3 What is A, B, C
(If correct i will give you brainlist also u get lots of points)
Answers
A= -10140000 B= 3485800 C= 13414200
Step-by-step explanation: hope this helped!!!
B = 1.058*10^5 + 3.38 * 10^6 = 3485800
C= 1.352 * 10 ^ 7 - 1.058 * 10 ^ 5 = 13414200
a. What is the equation of the line that is perpendicular to the graph and intercepts the y-axis at (0,-6)
b. What is the equation of the line that is perpendicular to the graph and intercepts the y-axis at (2,-2)
Answers
a. The equation of the line that is perpendicular to the graph and intercepts the y-axis at (0,-6) is y = -1/m * x - 6
b. The equation of the line that is perpendicular to the graph and intercepts the y-axis at (2,-2) is y = -1/m * x - 2
what is intercepts?
The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
a. The equation of the line that is perpendicular to the graph and intercepts the y-axis at (0, -6) can be written as:
y = mx + b
where m is the slope and b is the y-intercept.
Since the line is perpendicular to the graph, the slope of the line is the negative reciprocal of the slope of the graph. The y-intercept is (-6).
Therefore, the equation of the line is y = -1/m * x - 6
b. The equation of the line that is perpendicular to the graph and intercepts the y-axis at (2, -2) can be written as:
y = mx + b
where m is the slope and b is the y-intercept.
Since the line is perpendicular to the graph, the slope of the line is the negative reciprocal of the slope of the graph. The y-intercept is (-2).
Therefore, the equation of the line is y = -1/m * x - 2
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What is the inverse of 12/(x-1)
100 points please I really want to figure this out
Answers
The inverse of the expression represented as 12/(x-1) is (12/x) + 1
How to determine the inverse of the expression?From the question, we have the following parameters that can be used in our computation:
12/(x - 1)
The given parameter is an expression
Also, we can see that the above expression is a quotient expression
So, we start by expressing it as an equation
This is represented as
y = 12/(x - 1)
Swap/Switch the positions of the variables x and y
So, we have the following representation
x = 12(y - 1)
This gives
y - 1 = 12/x
Make y the subject
y = (12/x) + 1
Hence, the inverse is (12/x) + 1
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57% of all the town's residents own a dog and 61% own a cat. Of the dog owners 42% also own a cat. If a town resident is chosen at random find: (round to 4 decimal places where possible) a. P(Own a Dog)b. P(Own a Cat)- c. P(Own a Cat and a Dog) d. P(Own a Dog GIVEN Own a Cat)
Answers
Among dog owners, 40% also keep cats.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Tw dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured
According to our question-
27% of households only own dogs.
12 percent own a cat but no dog.
18% of people own both dogs and cats.
43% don't own either a dog or a cat.
18/45 dog owners also have cats.
*100% = 40%
Among dog owners, 40% also keep cats.
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Using the following year-end information for Calvin's Clothing, calculate the current ratio and acid-test ratio for the business:
Cash$52,000
Short-term investments 12,000
Accounts receivable 54,000
Inventory 325,000
Prepaid expenses 17,500
Accounts payable 106,500
Other current payables 25,000
Answers
The current ratio and acid-test ratio for the business is 3.50 and 0.90.
What is Working Capital?
Working capital is a gauge of a company's liquidity. This is crucial because it aids the business in making decisions about its current assets and liabilities.
Current ratio = Current Assets / Current Liabilities
Current ratio = 460,500 / 131,500
Current ratio = 3.5 times
Quick ratio
Quick ratio = Quick Assets \ Current Liabilities
Quick ratio = 118,000 / 131,500
Quick ratio = 0.90
Cash 52,000
Short-term investments 12,000
Accounts receivable 54,000
Inventory 325,000
Prepaid expenses 17,500
Total Current Assets 460,500
Total Quick assets 118,000
Accounts payable 106,500
Other current payables 25,000
Total Current Liabilities 131,500
Quick assets include Cash, Short term investments and accounts receivables
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Which box-and-whisker plot represents this data: ?
A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from 18 to between 24 and 26 with no median value.
A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from between 12 and 14 and between 26 and 28 with a median of 22.
A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from between 8 and 10 to 28 with a median between 20 and 22.
A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from between 12 and 14 to between 26 and 28 with a median between 20 and 22.
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A box-and-whisker plot which represents the given data is: B. A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from between 12 and 14 and between 26 and 28 with a median of 22.
What is a box-and-whisker plot?In Mathematics, a boxplot is also referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
By using an online box-and-whisker plot calculator, the five-number summary for the given data set include the following:
Minimum = 6.First quartile = 13.Median = 22.Third quartile = 27.5.Maximum = 30.By critically observing the box-and-whisker plots (see attachment), we can logically deduce that boxplot A correctly represents the given data set.
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Complete Question:
Which box-and-whisker plot represents this data: 6,9, 13, 13, 18, 20, 24, 25, 26, 28, 30, 30?
A train travels for 3.75 hours at 80 miles an hour. Use the formula d = r. t, where
d = distance, r = rate, and t = time, to find the distance the train traveled.
The distance traveled is
miles.
The solution is
Answers
The distance traveled by train would be 300 miles.
What is the relation between speed, distance, and time?
You can use the equivalent formula d = rt which means distance equals rate times time. To solve for speed or rate use the formula for speed, s = d/t which means speed equals distance divided by time. To solve for time use the formula for time, t = d/s which means time equals distance divided by speed.
A train travels for 3.75 hours at 80 miles per hour.
The distance traveled = speed * time
= 3.75 * 80
= 300 miles.
Hence, the distance traveled by train would be 300 miles.
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sam ran 63756 feet in 70 minutes whats samns rate in mph
Answers
Answer:
10.35 miles/hour
Step-by-step explanation:
Hence, Sam ran at the rate of 10.35 miles/hour .
A linear function h models a relashinship in which the dependent variable decreases 2 units for every 5 units the independent variable increase. Graph h when h(0)=4
Answers
By using slope intercept form of equation of line, the graph of
h(x) = [tex]-\frac{2}{5}x + 4[/tex] has been shown
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Let the independent variable be x and dependent variable be h(x)
The dependent variable decreases 2 units for every 5 units the independent variable increase.
Slope = [tex]-\frac{2}{5}[/tex]
So,
h(x) = [tex]-\frac{2}{5}x + c[/tex]
Now,
h(0) = 4
So, c = 4
h(x) = [tex]-\frac{2}{5}x + 4[/tex]
The graph has been attached here-
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Please help me with this problem
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a) The null hypothesis is: [tex]H_0: p \leq 0[/tex]
b) The alternative hypothesis is: [tex]H_1: p > 0[/tex]
c) The test statistic is: z = 9.71.
d) The correct option is of: A. Yes.
e) The confidence interval is of: 0.0819 < p < 0.1336.
What are the hypothesis tested?
At the null hypothesis, it is tested if there is not enough evidence that the proportion for men is greater, that is, the subtraction is not greater than 0:
[tex]H_0: p \leq 0[/tex]
At the alternative hypothesis, it is tested if there is evidence that the proportion for men is greater, that is, if the subtraction is greater than 0, hence:
[tex]H_1: p > 0[/tex]
We have a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.01, hence the critical value is of:
z = 2.327.
Thus the decision rule regarding the test statistic is given as follows:
z < 2.327 -> not enough evidence of difference -> do not reject the null hypothesis.z > 2.327 -> enough evidence of difference -> reject the null hypothesis.What are the mean and the standard error of the distribution of differences?For each sample, the mean and the standard error are given as follows:
Men: [tex]p_m = \frac{88}{800} = 0.11, s_m = \sqrt{\frac{0.11(0.89)}{800}} = 0.0111[/tex]Women: [tex]p_w = \frac{6}{2750} = 0.0022, s_w = \sqrt{\frac{0.0022(0.9978)}{2750}} = 0.0009[/tex]Hence, for the distribution of differences, the mean and the standard error are given as follows:
Mean: p = 0.11 - 0.0022 = 0.1078.Standard error: s = sqrt(0.0111² + 0.0009²) = 0.0111.What are the test statistic and the conclusion:The test statistic is given by the division of the mean by the standard error of the sampling distribution of the difference of sample proportions, hence:
z = 0.1078/0.0111 = 9.71.
z > 2.327 -> enough evidence that the proportion is greater.
What is the confidence interval?The confidence interval is obtained as the mean plus/minus the multiplication of the standard error and of the critical value.
Then the bounds of the interval are:
Lower bound: 0.1078 - 2.327 x 0.0111 = 0.0819.Upper bound: 0.1078 + 2.327 x 0.0111 = 0.1336.More can be learned about the test of an hypothesis at https://brainly.com/question/13873630
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You are given the figure below as well as the following information: m <9 = 110⁰ m<8 = 70° p parallel q. Use the figure and the given information to answer Question
what is m < 15
A. 70
B. 110
C. 80
D. 100
Answers
Answer:
B. 110°
Step-by-step explanation:
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Linear Pair
Two adjacent angles that sum to 180° (two angles which when combined together form a straight line).
Corresponding Angles Postulate
When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.
Given:
m∠9 = 110°m∠8 = 70°p || qApply the Vertical Angle Theorem to find the measure of angle 8:
⇒ m∠3 = m∠8 = 70°
As angles 7 and 8 form a linear pair:
⇒ m∠7 + m∠8 = 180°
⇒ m∠7 + 70° = 180°
⇒ m∠7 = 110°
As line p is parallel to line q, apply the Corresponding Angles Postulate to find the measure of angle 15:
⇒ m∠15 = m∠7 = 110°
Therefore, the measure of angle 15 is 110°.
35/17 as rounded decimal tenths place
Answers
A box is filled with 5yellow cards, 8blue cards, and 7green cards. A card is chosen at random from the box. What is the probability that the card is not blue?
Answers
Probability that a card is chosen is not blue is 3/5
What is Probability?Probability means possibility.
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty.topic. One is the probability of every event in a sample space.
According to the probability formula, the likelihood that an event will occur is equal to the proportion of favorable outcomes to all outcomes.
probability that an event will occur P(E) = Number of favorable outcomes/Total Number of outcomes
Total number of cards in the box is 5+8+7=20 cards
Number of cards that are not not blue = 5 + 7 = 12 cards
Probability that a card is chosen is not blue = Number of favorable outcomes/Total Number of outcomes = 12/20 = 3/5
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Probability that a card is chosen is not blue is 3/5
What is Probability?
Probability means possibility. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. topic. One is the probability of every event in a sample space.
According to the probability formula, the likelihood that an event will occur is equal to the proportion of favourable outcomes to all outcomes.
probability that an event will occur P(E) = Number of favorable outcomes/Total Number of outcomes
Total number of cards in the box is 5+8+7=20 cards
Number of cards that are not not blue = 5 + 7 = 12 cards
Probability that a card is chosen is not blue = Number of favorable outcomes/Total Number of outcomes = 12/20 = 3/5
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A store owner sells a mix that is 45% cashew nuts. How many pounds of cashews should he add to 36lb of this mix to get a mix that is 60% cashews
SHOW STEPS PLease
Answers
To make this mixture 60% cashews, 240 pounds of cashews must be added to 36 pounds of this mixture.
Explain the term proportion?Comparing two integers that each stand for a component of a whole results in a proportion. In essence, a percentage declares that two fractions are equal, regardless of the difference in amount. For instance, the ratio of half of 10 marbles to half of 50 marbles is 10.For the stated question-
Let the total amount of mix be 'x'.
45% of the mix is cashew nuts: 0.45x.
Now, 60% cashews is made by making 36 lb; 0.60x.
Then, 0.45x + 36 = 0.6x
x = 36/0.15
x = 240
Thus, 240 pounds of the cashews should be added to 36lb of this mix to get a mix that is 60% cashews.
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write down in trems of n an expression for the nth term in the following sequences 1 8 15 22 29
Answers
The expression which defines the nth term of the given sequence, in terms of n as required in the task content is; T (n) = 1 + 7(n - 1).
Which expression represents the nth term of the expression in terms of n?It follows from the task content that the expression which represents the nth term of the given sequence be determined.
By observation, the first term, a of the sequence is; 1.
Also, since; 8 - 1 = 15 - 8 = 22 - 15 = 29 - 22 = Common difference, d = 7.
It follows that the expression is a arithmetic sequence which can be modelled by;
T (n) = a + d (n - 1)
Since the constant common difference of consecutive terms in the sequence is; 7,
The required expression for the nth term of the expression is;
nth = 1 + 7(n -1)
On this note, the nth term is given by the expression; T (n) = 1 + 7 (n -1).
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Write this set of rational numbers from lest to greatest -11 3/4, 7, -7, 13, -13
Answers
Write this set of rational numbers from least to greatest -11 3/4, 7, -7, 13, -13:
Answer:
-13 , -11 , -7 , 3/4 , 7 , 13
Δ PQR, P=(4 x+11)°, m∠Q=(2 x+1)°, and m∠R=(7 x-14)°. Find m∠P.
Answers
Answer:
67°
Step-by-step explanation:
Th sum of the interior angles of a triangle is 180. Set the measurements of the three sides to 180 and solve for x. Then substitute in the value for x in 4x +11
4x + 11 + 2x + 1 + 7x -14 = 180 Combine like terms
13x - 2 = 180 Add 2 to both sides
13x = 182 Divide both sides by 13
x = 14
Plug this in for x
4x + 11
4(14) + 11
56 + 11
67
a dining hall had a total of 20 tables— some long rectangular tables and some round ones. Long tables can seat 10 people. Round tables can seat 8 people. on a busy evening, all 182 seats at the tables are occupied. a write a system of equations to represent this scenario
Answers
The solution of linear equations in two variables gives the following results.
The number of long tables = 11The number of round tables = 9 What are linear equations in two variables?A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero.
Given:
Total number of tables in dining hall = 20 people
The number of people who can seat at long table = 10 people
The number of people who can seat at the round table = 10 people
According to the question, let’s assume a linear equation in two variables
number of long tables = x
number of round tables = y
⇒ x +y=20 ………… (1)
⇒10 x + 8 y=182 ………...(2)
Multiply equation (1) by 8 and subtract it from equation 2.
⇒ 10x+8y=182 ………… (2)
⇒ 8x+8 y=160 ………....(1)
⇒2x=22
⇒x=11
now put the value of x in equation (1) we get,
⇒11+y=20
⇒y=20-11
⇒y=9
Therefore, the number of long tables = 11
The number of round tables = 9
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which of the following is the best approximation of the volume of this cylinder
Radius=8
Height=3
Answers
Answer:
..........................
Find 910−238 . Express your answer as a mixed number in simplest form.
Answers
By converting the given improper fraction 910/238 as a mixed number we get the result as 3[tex]\frac{14}{17}[/tex].
What is a mixed number?A mixed number is one that includes both a whole number and a legal fraction. A number with both an integer (whole number) and a correct fraction is referred to as a mixed number or mixed fraction (a fraction whose numerator is less than its denominator).
Pretzels, peanuts, Cheerios, and of course rice and corn Chex make up this mixture, which is dubbed a "mix." Numerals with both an integer and a fraction included are known as mixed numerals. The term "mixed number" refers to the combination of these two types of numbers.
Given,
910/238 is an improper fraction.
Now by dividing both the numerator and denominator by 14, we get
(910/14)/(238/14)
=65/17
Now, 65/17 can be written as a mixed number as 3[tex]\frac{14}{17}[/tex].
Therefore, By converting the given improper fraction 910/238 as a mixed number we get the result as 3[tex]\frac{14}{17}[/tex].
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The complete question is:
"Find 910/238. Express your answer as a mixed number in simplest form."
-8x-8 = -49.44
+ 8x+12y=58.20
Answers
Step-by-step explanation:
-8x-8 = -49.44+ 8x+12y=58.20
I need help thank you
Answers
It follows that someone who watches TV for 11 hours can complete 19 situps.
How to find the calculation?This information was provided to us by the question.
A linear equation in slope-intercept form is one with the formula y = ax + b.
Claim: A line with slope a contains the point (0,b) on the y-axis and the solutions of the equation y = ax + b (where a and b are numbers) form a line with slope a.
a=−1.077
b=30.98
r2=0.744769
r=−0.863
Where
X is the amount of situps.
Y is the quantity of television viewing hours.
X equals 11, so
Including this in the existing formula
Y = (-1.077)(11) + 30.98
Y = −11.847 + 30.98
Y = 19.133
which equals around 19
So, it follows that someone who watches TV for 11 hours can complete 19 situps.
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The plane is perpendicular to the axis but does not go through the vertex.
The plane intersects the double cone at only the vertex.
The plane is not intersecting the vertex, not parallel to the axis, not perpendicular to the axis, not parallel to the side of the cone, and it intersects only one cone.
The plane is tangent to both of the cones.
answers:
line
point
circle
elipse
match these
Answers
The plane is perpendicular to the axis but does not go through the vertex. The plane intersects the double cone at only the vertex is ellipse.
How to identify the properties of an ellipse?A planar curve that has two focal points is normally called an ellipse on the condition that at every point on the curve, it will be seen that the sum of the two distances from the focal points is constant. This generalizes the shape of a circle, which is a unique variety of an ellipse whereby the two focus points coincide.
The plane is said to not be intersecting with the vertex, not parallel to the axis nor perpendicular to the axis, then not parallel to the side of the cone, but it intersects only one cone is called a circle.
A circle is defined as a closed, two-dimensional object whereby every point in the plane is seen to be equally spaced from a central point. The line of reflection symmetry is seen to be formed by all lines that transverse the circle. Additionally, every angle has rotational symmetry around the center.
Thus, the conclusion is that the first two options are properties of an ellipse.
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Help!
Use the given conditions to write an equation for the line in point-slope form and slope-intercept form.
Slope = -8, passing through (-4,-9)
Answers
Answer:
-12,-17
Step-by-step explanation:
If a sample of a certain solution is determined to have a [H3O+] concentration of 8.25×10−3 moles/liter, what is its pH?
Answers
where log is the base-10 logarithm and [H+] stands for the hydrogen ion concentration in units of moles per liter solution.
What is this pH?The pH of water determines how acidic or basic it is. The scale runs from 0 to 14, with 7 being neutral. pHs less than 7 indicate acidity, while pHs greater than 7 indicate base. pH is a measure of the relative amount of free hydrogen and hydroxyl ions in water.Hawkes Learning says the answer is 0.0. I tried this problem and got it wrong at first, but they said the correct answer is 0.0.Before attempting to answer this question, it may be useful to review the properties of logarithms and the definition of pH.The pH of a solution is a measure of the concentration of hydrogen ions, as well as its acidity or alkalinity. The pH scale is normally between 0 and 14. Aqueous solutions with a pH less than 7 at 25 ° C are acidic, while basic or alkaline solutions have a pH greater than 7.pH=−log([H3O+])
=−log(8.25×10−3)
=−log(8.25)−log(10−3) loga(xy)=loga(x)+loga(y)
=−log(8.25)+1 log(10x)=x
=0.0 round off to one decimal place
pH is defined as the negative logarithm of hydrogen ion concentration present in a solution.To calculate the pH of the reaction, we use the equation:[tex]pH = -log[H^{+} ][/tex]where,
Putting values in above equation, we get:Hence, the pH of the solution is 1.022To learn more about pH refer to:
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Answer to this required:
Answers
120=(p*3*5)/100
120*100=p*15
12000/15=p
Principal amount is 800
Amount received at end=800+ 120
920
Explain special rights. Im confused how to find missing sides and angles
Answers
Answer:
all triangle sum must be 180 right angles are 90 degree like the top to left in the figuresum what you have and give it ad equals to 180 then solveWhat is the probability of getting a ten or a jack from a deck of pocker cards
Answers
The probability of getting a 10 or a jack from a deck of poker cards (52 cards) is 15.38%.
What is probability?Probability is concerning about numerical description
Is how likely is an event is occur or how likely it is true.
As per the given sequence -
there are four 10 cards and four jack cards respectively
4+4=8
If you want to get one from the 52 cards, so it's 8 out of 52. 8/52
To calculate the percentage, you must multiply 8 by 100, then divide by 52.
Thus,
8*100/52=15.38
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A solid object is made with the combination of a cylinder and a cone having same radii. The height of the cylinder and the slant height of the cone are 30 cm and 26 cm respectively. If the total cost of painting the total surface of the solid object at the rate of Rs 210 per 100 sq. cm is Rs 6336, find the height of the cone.
Answers
The total surface area of the solid object is the sum of the surface area of the cylinder and the surface area of the cone.
The surface area of the cylinder is 2πr(r+h), where r is the radius of the cylinder and h is its height.
The surface area of the cone is πr(l+r), where r is the radius of the cone and l is its slant height.
Since the cylinder and the cone have the same radius, we can call this radius r.
The total surface area of the solid object is therefore 2πr(r+h) + πr(l+r).
We are told that this total surface area is equal to 6336/210 = 30 sq. cm.
Thus, we can set up the equation: 2πr(r+h) + πr(l+r) = 30.
We are trying to find the value of l, which is the slant height of the cone. We are given the value of h, which is the height of the cylinder. We can substitute this value into the equation to get:
2πr(r+30) + πr(l+r) = 30.
This equation can be rearranged and solved for l to find the slant height of the cone.
l = sqrt(900 - 60r).
Since we are given that the slant height of the cone is 26 cm, we can substitute this value into the equation to solve for the radius of the cone:
26 = sqrt(900 - 60r)
Solving for r, we find that the radius of the cone is 15 cm.
Substituting this value back into the equation for the slant height of the cone, we find that the height of the cone is:
l = sqrt(900 - 60(15)) = sqrt(300) = 17.67 cm.
Thus, the height of the cone is approximately 17.67 cm.
A polynomial ppp is graphed. What could be the equation of ppp?
Choose 1 answer:
Answers
A function’s roots are determined when y=0 such that an equation for x input will generate y=0 output. In other words, the roots are where the function crosses the x-axis. Remember, when a function touches the x-axis, that root has multiplicity. When a function intercepts the x-axis at a point, there is multiplicity of 1. Therefore roots -3 and 2 touch the x-axis, so there is multiplicity of 2. The root -1 intercepts the x-axis, so it has multiplicity 1.