The diagram shows a frustum which is constructed from a pyramid.
(a) The surface area of the frustum.
(b) Find the volume of the frustum.
(c) Find the surface area of the original pyramid.
Answers
The surface area of the frustum is 1744 square units
The volume of the pyramid is 2031.33 cube units.
What is a frustum of a pyramid?
By cutting the top of a typical pyramid, the frustum is created, which is a pyramid. Because of this, it is known as a truncated pyramid. The frustum of the pyramid is that portion of a pyramid that is cut through by a plane parallel to its base and lies between the vertex and the base.
a) First, we calculate the height of the frustum.
Let height be H
The base length be L1=24
Base width be W1=12
Top length is L2=14
To width be W2=13
Side height be C=13
Using the formula, H
[tex]H=\sqrt{ C^{2} - \frac{(L1-L2)^{2}}{2}}\\H=\sqrt{ 13^{2} - \frac{(24-14)^{2}}{2}}\\H=\sqrt{ 169 -50}\\H=\sqrt{119} \\H=11[/tex]
Now, the surface area of the frustum is LSA+area of bases of a frustum
Here, P1= perimeter of the base1 of the frustum
P2 is the perimeter of the base 2 of the frustum
[tex]L.S.A=\frac{1}{2} .(P1+P2).L \\=\frac{1}{2} .(72+42).24 \\=\frac{1}{2} .(114).24 \\=1368[/tex]
Now, S1 =area of base1 of frustum =288
S2= area of base 2 of frustum=98
TSA is given by LSA+area of bases of a frustum
=1368+288+98
=1724.
Therefore the surface area is 1724 square units.
b) Volume is given by
[tex]V=\frac{1}{3}.H.(S1+S2+\sqrt{S1S2} )\\ V=\frac{1}{3} . 11.(386+168)\\V=2031.33[/tex]
Therefore the volume is 2031.33 cube units.
To learn more about the frustum of pyramids, visit the link below:
https://brainly.com/question/22430173
#SPJ4
Related Questions
15) How many terminal zeros does the integer equal to
80 power to the 16 times 75 power 8 have?
Answers
75=(5)2*3 so you have 16 (5) so 16 zero
At December 31, the records of Nortech Corporation provided the following selected and incomplete data:
Common stock (par $1; no changes during the current year).
Shares authorized, 500,000.
Shares issued, 2; issue price $12 per share.
Common Stock account, $100,000.
Shares held as treasury stock, 2,000 shares, cost $10 per share.
Net income for the current year, $24,500.
Dividends declared and paid during the current year, $14,700.
Retained Earnings balance, beginning of the year, $145,000.
Required:
Complete the following: TIP: To determine the number of shares issued, divide the balance in the Common Stock account by the par
value per share. (Round "per share" answers to 2 decimal places.)
1-a. Shares authorized
1-b. Shares issued
1-c. Shares outstanding
2. The balance in Additional Paid-in Capital would be
3. Earnings per share is
4. Dividends paid per share of common stock is
5. Treasury stock should be reported in the stockholders' equity section of the balance
sheet in the amount of
6. Assume that the board of directors approved a 2-for-1 stock split. After the stock split,
the par value per share will be
500,000
290,000
Answers
The solutions for the given questions are given below:
What is meant by income?Earnings from employment, investments, or company operations. Sam, for instance, had a weekly income of $770 after receiving $30 in bank interest, $700 from his employment, and an additional $40 from buying and selling veggies.
Wages is the amount of money obtained through employment; income is the entire amount of money obtained, which includes earnings, benefits, pensions, and other types of payments.
1.a 500000 shares have been authorized.
1/(210000) = 210000 shares issued Number of shares issued [Common stock account balance / par value of each share]
1-c) The number of shares outstanding is 210000 - 3100, or 206900 shares.
2) The APC Account Balance is $4620000, which is calculated as 210000 * (23 - 1).
3) Net income divided by the number of outstanding shares equals 165520 divided by 206900, or 0.8 per share.
4) The dividend per common share was paid at 53794/206900, or 0.26 per share.
5) 3100 * 21 = $65,100 should be stated for Treasury Stock in the Stockholders' Equity part of the Balance Sheet.
6) Following the stock split, the par value of each share is equal to 1 / 2 ($0.50 per share).
To know more about income, visit:
https://brainly.com/question/28970926
#SPJ1
Identify all of the terms in the expression: 4x³ + x² + 3x + 6.
OA 6
OB 4, 3, 6
OC x³, x², x
OD 4x³, x², 3x, 6
Please help me
Answers
Answer:
OD 4x³, x², 3x, 6
Step-by-step explanation:
Find sin2x,cos2x, and tan2x if sin x=-3/√13 and x terminates in quadrant IV.
sin2x=
cos2x=
tan2x=
Answers
Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
sin x= -3/√13
So, B = √13 - 9 = √4 =2
cos x= 2/ √13
So, sin 2x= 2 sin x cos x =2 (-3/√13 )(2/√13 ) = -12/√13
and, cos 2x= 1- 2 sin²x
= 1- 2( -3/ √13 )²
= -5/ √13
and, tan 2x = sin 2x/ cos 2x = 5/12
Learn more about trigonometry here:
https://brainly.com/question/26719838
#SPJ1
"Use the formula A=P(1+r/n)ⁿt to solve the compound interest problem
Find how long it takes a $ 1700 investment to earn $ 500 interest if it is invested at 2 % interest compounded quarterly.
$ 500 interest will be earned in approximately years. (Round to the nearest tenth.)"
Answers
The compound interest is 61.342 years
What is compound interest ?
The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You will wind up with $110.25 at the conclusion of the second year.
Formulas for Compound Interest
Formula for Monthly Compound Interest.
Compounded Quarterly Formula: Interest compounded monthly is calculated 12 times a year. Four times a year are used to calculate interest that is compounded quarterly.
Formulas for compound interest are available on a daily, annual, and other basis.
A = 1700
P = 500
r = 2%
n = 4
r = R/100
r = 2/100
r = 0.02 per year,
Then, solve the equation for t
t = ln(A/P) / n[ln(1 + r/n)]
t = ln(1,700.00/500.00) / ( 4 × [ln(1 + 0.02/4)] )
t = ln(1,700.00/500.00) / ( 4 × [ln(1 + 0.005)] )
t = 61.342 years
To learn more about compound interest from the given link
https://brainly.com/question/24274034
#SPJ4
McKenna was asked to write the following expression in standard form.
When writing the expression in standard form, McKenna made a mistake.
a. McKenna made her first mistake in .
b. The correct expression in standard form is .
3 − 5(3a + 6)
3 − 5(3a + 6)
3 + (−5)(3a + 6)
−2(3a + 6)
−6a + (−12)
−6a − 12
Step 1
Step 2
Step 3
Step 4
Answers
a) The step in which McKenna made her first mistake is given as follows: Step 4.
b) The correct simplified expression in standard form is given as follows: -15a - 15.
How to simplify the expression?The expression in this problem is defined as follows:
3 − 5(3a + 6)
On the third step, the expression is given as follows:
3 + (−5)(3a + 6)
And on the fourth step, the expression is given as follows:
−2(3a + 6).
This is where the mistake happened, as the multiplication takes precedence over the subtraction.
Then to obtain the correct expression the first step is applying the distributive property, as follows:
3 − 5(3a + 6) = 3 - 15a - 18.
Then the like terms 3 and -18 are combined to obtain the correct simplified expression, as follows:
3 - 15a - 18 = -15a - 15.
More can be learned about the simplification of expressions at https://brainly.com/question/723406
#SPJ1
Determine whether each statement implies correlation or causation between two variables. Drag the items on the left to the correct location on the right.
Watching more TV increases the bill for electricity.
Drinking water helps flush out toxins.
Students with high scores in physics also got high scores in chemistry.
A survey shows that people who own a TV also own an automobile.
Vaccination reduces the chance of getting infected by the disease.
Answers
Determining whether each statement implies correlation or causation between two variables is as follows:
Correlation:Students with high scores in physics also got high scores in chemistry.A survey shows that people who own a TV also own an automobile.Causation:Watching more TV increases the bill for electricity.Drinking water helps flush out toxins.Vaccination reduces the chance of getting infected by the disease.How is correlation different from causation?Correlation indicates that one independent variable causes another dependent variable to change.
Causation indicates that one dependent variable or event is the direct result of the occurrence of the other event or independent variable.
Causation shows cause and effect - unlike correlation which points out two events simultaneously occur or two variables change at the same time.
Thus, correlation is a test of association in relationship, while causation focuses on cause and effect.
Learn more about correlation and causation at ttps://brainly.com/question/12479370
#SPJ1
Evaluate
16 ÷ (2 + 1/2 ) ²
A) 2 14/25
B) 4 1/4
C) 6 2/5
D) 8 1/4
Answers
Answer:
A) 2 14/25
Step-by-step explanation:
This is a question of order of operations, which PEMDAS helps describe.
P- parentheses
E - exponents
M, D - multiplication, division
A, S - addition, subtraction
In your problem, you'd start with P, what's in the parentheses.
16 ÷ (2 1/2)²
Then do the exponent, E. It might help to convert 2 1/2 to 5/2.
16 ÷ 25/4
Then divide, D. When dividing fractions, you can flip the numerator and denominator and multiply.
16 x 4/25
= 64/25
Then simplify. 25 goes into 64 two times, and there is 14 left over.
= 2 14/25
Answer:
A
Step-by-step explanation:
Evaluate the sum in the brackets first to give 2.5 and square that to give 6.25
Divide 16 by 6.25 to get A
HELP ME ASAP!!!!
I NEED THIS ANSWERED RIGHT NOW!!!!!!
Answers
Answer: The bisector of [tex]\angle BAC[/tex]
Step-by-step explanation:
This is a standard construction.
If you draw a random card from a standard deck of 52 cards, what are the odds of drawing the jack, queen, king, or ace of clubs? Write your answer in the form a:b as a fully reduced ratio. Note: In a standard deck of cards, each of the four suites has three face cards.
Answers
Answer:
12:52
Step-by-step explanation:
almost every card game has 52 cards, you have a 23% chance to draw a face card of any kind.
There are a king, queen, and jack for each of the four different suits: hearts, spades, clubs, and diamonds. The four suits have 13 cards each, for a total of 52 cards. Therefore, your chance of drawing a face card out of a deck of cards upon choosing the card at random is 12 out of 52, or about 23%.
help meeeeeeeeeee pleaseee
Answers
Answer: 51.85
Step-by-step explanation: you use the formula given and plug is 25 for t because it is the number of years. So you get 200*e^(-0.054*25) = 51.85
The following data represent the monthly cell phone bill for a person's phone for six randomly selected months.
$35.34, $42.09, $39.43, $38.87, $43.39, $49.26
Compute the mean, median, and mode phone bill. (Round to the nearest cent as needed)
Answers
The mean of the data is x(bar) = 41.396
The Median of the data is $40.76
The mode of all the values are appearing once and therefore there is no mode for the phone bill.
Now, According to the question:
Given the data:
$35.34, $42.09, $39.43, $38.87, $43.39, $49.26
Mean is the average of the data computed as x(bar) = Σ[tex]x_i[/tex] /n where [tex]x_i[/tex]
are the data points and n is the number of data points
x(bar) = 35.34 + 42.09 + 39.43 +38.87 +43.39 + 49.26 / 6
x(bar) = 248.38 /6
x(bar) = 41.396
The median is the data point that lies in the middle of the data set when the data is arranged in ascending or descending order.
Thus,
Ascending order:
$35.34, $38.87, $39.43, $42.09, $43.39, $49.26
The median lies between $39.43 and $42.09 and to get it, we find the average of the two numbers
Median = (39.43 + 42.09)/ 2
Median = $40.76
→ Mode is the value in a data set that is repeated most frequently. In the given data, all the values are appearing once and therefore there is no mode for the phone bill.
Hence, The mean of the data is x(bar) = 41.396
The Median of the data is $40.76
The mode of all the values are appearing once and therefore there is no mode for the phone bill.
Learn more about Mean , Median , Mode at:
https://brainly.com/question/15323584
#SPJ4
Pam bought different drinks for a party she was throwing. After the party, she had the following drink amounts left over.
\dfrac1{2}
2
1
start fraction, 1, divided by, 2, end fraction liter of soda
\dfrac15
5
1
start fraction, 1, divided by, 5, end fraction liter of water
\dfrac8{10}
10
8
start fraction, 8, divided by, 10, end fraction liter of apple juice
Which statement correctly compares the amounts of 2 left over drinks?
Choose 1 answer:
(Choice A)
A
Pam had less water left over than apple juice.
(Choice B)
B
Pam had more soda left over than apple juice.
(Choice C)
C
Pam had less soda left over than water.
Answers
Answer:
A) Pam had less water left over than apple juice.
Step-by-step explanation:
Given amounts of drinks left over:
[tex]\dfrac{1}{2}\; \sf liter \;of \;soda[/tex][tex]\dfrac{1}{5}\; \sf liter \;of \;water[/tex][tex]\dfrac{8}{10}\; \sf liter \;of \;apple\;juice[/tex]To compare the amounts of drinks left over, convert the fractions into equivalent fractions that have the same denominator.
The denominators of the three fractions are 2, 5 and 10.
The lowest common multiple of the denominators is 10.
Therefore, rewrite the first two fractions so that their denominators are also 10.
[tex]\textsf{Soda}: \quad \dfrac{1}{2}=\dfrac{1 \cdot 5}{2 \cdot 5}=\dfrac{5}{10}[/tex]
[tex]\textsf{Water}: \quad \dfrac{1}{5}=\dfrac{1 \cdot 2}{5 \cdot 2}=\dfrac{2}{10}[/tex]
Therefore, as:
[tex]\dfrac{2}{10} < \dfrac{5}{10} < \dfrac{8}{10}[/tex]then:
water < soda < apple juiceTherefore, Pam had less water left over than apple juice.
Answer:
a) Pam had less water than apple juice.
★ Water < Soda < Apple juice
Step-by-step explanation:
Converting the fraction into decimals,
→ Soda left = 1/2 = 0.5 litres
→ Water left = 1/5 = 0.2 litres
→ Apple juice left = 8/10 = 0.8 litres
Let's order them in ascending order,
→ 0.2 < 0.5 < 0.8
→ 1/5 < 1/2 < 8/10
→ Water left < Soda left < Apple juice left
Now the applicable options is,
→ Pam had less water than apple juice.
Hence, option (a) is correct answer.
Please help - if could throw this out the window I would
Answers
The speed of the car will be 25.41 m/h
What is speed and velocity ?Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, velocity is a vector quantity, whereas speed is a scalar quantity
According to the given information
d = [tex]\frac{s^{2} }{10}[/tex] + s
We are given that
distance is 90 feet
So, the expression becomes
90 = [tex]\frac{s^{2} }{10}[/tex] + s
[tex]s^{2}[/tex] + 10s - 900 = 0
which is quadratic in s
So applying the discriminant formula
[tex]$$[/tex]s [tex]=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}[/tex]
[tex]$$[/tex]and then we input the values:
s [tex]=\frac{-10 \pm \sqrt{(10)^2-4(1)(900)}}{2(1)}$$[/tex]
and solve:
s [tex]=\frac{-10 \pm \sqrt{3700}}{2}$$[/tex]
It will have two answers
s = -35.41 m/h
s = 25.41m/h
Speed cannot be negative
So
The speed of the car will be 25.41 m/h
To know more about Speed
https://brainly.com/question/18220407
#SPJ1
Last month, Lucy and Britney each read three books. The tables show the number of pages in each book and the time it took Lucy and Britney to read each book. Which of the tables, if any, represent a proportional relationship? Responses
Answers
The table that represents a proportional relationship is Table A.
What is a proportional relationship?A proportional relationship exists between two variables when their ratios are equal or equivalent.
With a proportional relationship, there is a constant rate of change between the comparable variables.
Proportions refer to ratios of equality between two or more variables.
Where there is a proportional relationship, we can determine the constant rate of change as the same quotient.
For instance, when the number of pages per book is divided by the reading time, a constant rate of change is established if the reading speed is the same for all three books.
Table A:Pages Lucas Read 208 156 234
Time (hours) 8 6 9
Reading speed 26 26 26 (234/9)
Table B:Pages Britney Read 168 120 348
Time (hours) 6 4 12
Reading speed 28 30 29 (348/12)
Thus, the constant rate of change or proportional relationship can be found in Table A and not in Table B.
Learn more about proportional relationships at https://brainly.com/question/2143065
#SPJ1
Question Completion:Table A:Pages Lucas Read 208 156 234
Time (hours) 8 6 9
Table B:Pages Britney Read 168 120 348
Time (hours) 6 4 12
what are the solutions of 2x^2 + 3x = -5
Answers
Answer:
No solution
Step-by-step explanation:
The square root of a negative number is not a real number
8 An electricity company charges the same fixed amount for each unit of electricity used. David uses this graph to work out the total cost of the electricity he has used.
(a) Work out the gradient of the straight line.
(b) What does the gradient of this line represent?
Answers
The gradient of the line is 4/30 and it means that the amount for each unit of electricity used is 4/30
(a) How to determine the gradient of the straight line.From the question, we have the graph that can be used in our computation:
From the graph, we have the following ordered pairs
(0, 0) and (30, 4)
Rewrite the above points properly
So, we have the following ordered pairs
(x, y) = (0, 0) and (30, 4)
The gradient of the line is then calculated using the following slope equation
gradient = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (0, 0) and (30, 4)
Substitute the known values in the above equation
So, we have the following equation
gradient = (4 - 0)/(30 - 0)
Evaluate
gradient = 4/30
Hence, the gradient of the line is 4/30
(b) What does the gradient of this line represent?Generally, slope or gradient means rate
This means that the gradient of this line represent the rate
i.e. the amount for each unit is 4/30
Read more about slope at
https://brainly.com/question/3493733
#SPJ1
there are 12 levels in Zoe new video game suppose she plays the same number of levels each day what are all the possibilities for the number of days Zoe could play the game show your work. Its about multiples and factors
Answers
Let no of level in one day is x. So, Zoe can play x= 12 level in a day.
What is probability?The likelihood might be between 0 and 1, with 0 denoting impossibility and 1 denoting certainty. In a sample space, each occurrence has a probability of one overall. the possibility that two or more events will follow one another. Since there are two or more of them, the events are either dependent or independent events. A dependent event—also referred to as a conditional event—is one in which the occurrence of the first event affects the occurrences that follow. The total number of outcomes will differ.
Write formula for the probability.Probability = Possible outcomes/total outcomes
Factors of 12 can be written as:
1 * 12 = 12
2 * 6 = 12
3 * 4 = 12
For this question look for factors of 12-These would be
1 and 12 (1 x 12 = 12)
2 and 6 (2 x 6 = 12)
3 and 4 (3 x 4 = 12)
Hence Zoe could either play
1 level each day for 12 days
2 levels each day for 6 days
3 levels each day for 4 days
4 levels each day for 3 days
Or...
12 levels in one day
To learn more about probability visit the link:
https://brainly.com/question/16722133
#SPJ1
Look at photo for problem
Just need chart filled out
4. y=-2(x+2)²-3
Answers
Following values can be filled in the table:
(0,-3), (-1,0), (1,-8), (-2,1), (2,-15)
It can be solved using the concept of graph plotting and function.
What is graph?
When a set of points are connected together to form a strcture then the structure is known as graph. The set of ponts is known as ordered pair.
Consider the eqution.
[tex]y=-2(x+2)^2-3[/tex]
Substitute the simplest value x = 0 and find the value of y.
[tex]y=-2(0+2)^2-3\\=-11\\[/tex]
Now, substitute x = -1 and find the value of y.
[tex]y=-2(-1+2)^2-3\\=-5\\[/tex]
Now, substitute x = 1 and find the value of y.
[tex]y=-2(1+2)^2-3\\=-21\\[/tex]
Now, substitute x = -2 and find the value of y.
[tex]y=-2(-2+2)^2-3\\=-3\\[/tex]
Now, substitute x = 2 and find the value of y.
[tex]y=-2(2+2)^2-3\\=-35\\[/tex]
Hence, following values can be filled in the table:
(0,-11), (-1,-5), (1,-21), (-2,-3), (2,-35)
It can be solved using the concept of graph plotting.
Learn more about the graph plotting form the following link:
https://brainly.com/question/25020119
#SPJ4
Figure HEFG below is a parallelogram. If UH=19 and FH= 5x-7, find X
Answers
A parallelogram is a quadrilateral that has two pairs of parallel sides.
In a parallelogram, opposite sides and angles are equal.
The adjacent angles add up to 180 degrees.
The value of x is 5.2.
What is a parallelogram?
A parallelogram is a quadrilateral that has two pairs of parallel sides.
In a parallelogram, opposite sides and angles are equal.
The adjacent angles add up to 180 degrees.
We have,
UH and FH are the two sides of the diagonal.
UH and FH are equal.
UH = FH
19 = 5x - 7
19 + 7 = 5x
5x = 26
x = 5.2
Thus,
The value of x is 5.2.
Learn more about parallelograms here:
https://brainly.com/question/1563728
#SPJ1
car is traveling at a steady speed It travels 1 1/2 miles in 2 1/4 minutes How far will it travel in 23 minutes? In ?
Answers
Answer:
15 1/3 miles in 23 minutes
(2/3)x in x minutes
Step-by-step explanation:
1 1/2=1.5
2 1/4=2.25
Convert to unit ratio
[tex]1.5/2.25=(2/3)/1[/tex]
2/3*23=46/3
Simplify
15 1/3 miles in 23 minutes
(2/3)x in x minutes
Factor the expression completely
54a⁶b²+ 9ab²
Answers
To factor the expression 54a⁶b²+ 9ab², you can use the fact that a common factor of 54a⁶b² and 9ab² is ab².
Thus, you can rewrite the expression as:
ab²(54a⁶ + 9)
You can then factor the expression inside the parentheses using the fact that 3 is a common factor of both 54 and 9:
ab²(3 * 18a⁶ + 3 * 3)
This can be simplified as:
ab²(6a⁶ + 9)
This expression is completely factored and cannot be further simplified. Therefore, the completely factored form of the expression is:
ab²(6a⁶ + 9)
Please help me I just look at the photo I am so confused
Answers
Answer:
Step-by-step explanation:
1:Pl 2:Th 3:Th 4:P 5:P 6:Pl 7:Pl 8:Th 9:Th 10:Th 11:Pl 12:P
There you go, the numbers go down. So Iowa is 1 and so on, I don't know if they are all right but I did my best.
Solve the systems of equations
5x - 4y = -10
-4x + 5y = 8
x =
y =
Answers
The solution of the system of equation are;
⇒ x = - 2
⇒ y = 0
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The system of equation are,
⇒ 5x - 4y = - 10
⇒ - 4x + 5y = 8
Now,
Find the solution as;
The system of equation are,
⇒ 5x - 4y = - 10 ..(i)
⇒ - 4x + 5y = 8 ..(ii)
Multiply by 4 in equation (i) + Multiply by 5 in equation (ii);
⇒ 20x - 16y + (- 20x + 25y) = - 40 + 40
⇒ 9y = 0
⇒ y = 0
And, - 4x + 5y = 8
⇒ - 4x + 0 = 8
⇒ x = - 2
Thus, The solution of the system of equation are;
⇒ x = - 2
⇒ y = 0
Learn more about the system of equation visit:
https://brainly.com/question/12933204
#SPJ1
NO LINKS!! Please help me with these problems. Exponential.
Answers
Answer:
f(x) = 10400·(1/4)^x; table values: x = -1, f(x) = 162.5g(x) = 1.8·2.4^xIncorrect for b < 1.Step-by-step explanation:
You want to write exponential functions through the given points.
1. TableThe exponential function ...
f(x) = a·b^x
will have the values ...
f(0) = af(1) = ab ⇒ b = f(1)/f(0)Using these relations we can write the function from the table values:
f(x) = 10400·(2600/10400)^x
f(x) = 10400·(1/4)^x
Then your table is ...
[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7}\vphantom{\dfrac{b}{g}}x&-1&0&1&3&4&6\\\cline{1-7}\vphantom{\dfrac{b}{g}}f(x)&41600&10400&2600&162.5&40.625&2.5390625\\\cline{1-7}\end{array}[/tex]
2. PointsUsing the given points in the exponential function form, we have ...
4.32 = a·b^1
59.71968 = a·b^4
Dividing the second equation by the first, we find ...
59.71968/4.32 = b^3 ⇒ b = 2.4
Using this in the first equation, we get ...
4.32 = a·2.4 ⇒ a = 1.8
The equation of the function is ...
g(x) = 1.8·2.4^x
3. IncreasingThe exponential function ...
y = a·b^x . . . . . . a > 0, b > 0
will be increasing when the growth factor (b) is greater than 1. When 'b' is less than 1, the function will be decreasing.
Sarah's belief is incorrect.
Answer:
[tex]\textsf{1.} \quad f(x)=10400(0.25)^x[/tex]
(-1, 41600) and (3, 162.5)
[tex]\textsf{2.} \quad g(x)=1.8(2.4)^x[/tex]
3. Sarah is incorrect.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$f(x)=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Question 1The y-intercept is when x = 0.
Therefore, from inspection of the given table, the y-intercept is 10400:
[tex]\implies a=10400[/tex]
Substitute point (1, 2600) and a = 10400 into the exponential function and solve for b:
[tex]\implies 2600=10400b^1[/tex]
[tex]\implies 2600=10400b[/tex]
[tex]\implies b=\dfrac{2600}{10400}[/tex]
[tex]\implies b=0.25[/tex]
Therefore, the equation of the function is:
[tex]\boxed{f(x)=10400(0.25)^x}[/tex]
Find the value of x when f(x) = 41600:
[tex]\begin{aligned} f(x)&=41600\\\implies 10400(0.25)^x&=41600\\(0.25)^x &=\dfrac{41600}{10400}\\(0.25)^x &=4\\\ln (0.25)^x &=\ln 4\\x \ln (0.25)&=\ln 4\\x&=\dfrac{\ln 4}{\ln (0.25)}\\x&=-1\end{aligned}[/tex]
Find the value of f(x) when x = 3:
[tex]\begin{aligned}x=3 \implies f(3) & =10400(0.25)^3\\& =10400(0.015625)\\& = 162.5\end{aligned}[/tex]
Therefore, the completed table is:
[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} \vphantom{\dfrac12}x & -1 & 0 & 1 & 3 & 4 & 6\\\cline{1-7} \vphantom{\dfrac12}f(x) &41600 &10400 &2600 &162.5 &40.625 & 2.5390625\\\cline{1-7} \end{array}[/tex]
Question 2Given points:
(1, 4.32)(4, 59.71968)Substitute the given points into the exponential formula g(x) = abˣ
[tex]\implies ab=4.32[/tex]
[tex]\implies ab^4=59.71968[/tex]
To find b, divide the equations:
[tex]\implies \dfrac{ab^4}{ab}=\dfrac{59.71968}{4.32}[/tex]
[tex]\implies b^3=13.824[/tex]
[tex]\implies b=\sqrt[3]{13.824}[/tex]
[tex]\implies b=2.4[/tex]
Substitute one of the points and the found value of b into the equation and solve for a:
[tex]\implies 2.4a=4.32[/tex]
[tex]\implies a=\dfrac{4.32}{2.4}[/tex]
[tex]\implies a=1.8[/tex]
Therefore, the equation of the function is:
[tex]\boxed{g(x)=1.8(2.4)^x}[/tex]
Question 3Sarah is incorrect. For an exponential function in the form a · bˣ:
If a > 0 and b > 1 then it is an increasing function.If a > 0 and 0 < b < 1 then it is a decreasing function.A light is on the top of a 12 ft tall pole and a 5’6’’ tall person is walking away from the pole at a rate of 2 ft/sec At what rate is the tip of the shadow moving away from the pole when the person is 25 ft from the pole? At what rate is the tip of the shadow moving away from the person when the person is 25 ft from the pole? please give all solutions
Answers
Part a: the rate at which the shadow's tip moves away from the pole while the subject is 25 feet distant is 48/13 ft/sec.
Part b: the speed of the shadow from the speed of the man is 22/13 ft/sec.
Explain the term rate of change?Rate of Change: How quickly a parameter changes over a predetermined amount of time. It is frequently used while discussing momentum and is typically expressed as a proportion of one variable's change to another's corresponding change.A 5 feet 6 inch tall individual is going away from a 12 foot tall pole with a light on top at a 2 foot per second pace.
A) the speed at which the shadow's tip moves away from the pole while the subject is 25 feet distant;
Similar triangles allow us to say:
12/L = 55/(L - x)
Simpllifying,
12(l - x) = 5.5l
12l - 12x = 5.5l
6.5l = 12x
x = (6.5/12)l
Differentiate with respect to time;
dx/dt = (6.5/12)dl/dt or
dl/dt = (12/6.5)(dx/dt)
As, dx/dt = 2
dl/dt = (12/6.5)(2)
dl/dt = 24/6.5
dl/dt = 48/13 ft/sec
B: When a person is 25 feet from a pole, the point of the shadow travelling away from them at:
Subtract the speed of the shadow from the speed of the man.
Therefore,
48/13 - 2 = 22/13 ft/sec.
Thus, the speed of shadow from the speed of the man is 22/13 ft/sec.
To know more about the rate of change, here
https://brainly.com/question/8728504
#SPJ4
Bill is in a hot air balloon that has just taken off and is floating above its launching point.
Lillian is standing on the ground, 9 meters away from the launching point. If Bill and Lillian
are 15 meters apart, how high up is Bill?
meters
Submit
Answers
Reasoning: 9+15=24
Marco uses 2 gallons of water while brushing his teeth. He uses 10 gallons of water to wash clothes. How many more cups of water does Marco use while washing his clothes than brushing his teeth? there’s are 16 cups in 1 gallon
Answers
Answer: 192 cups
Step-by-step explanation: there's 16 cups in 1 gallon so you would do 2×16=32 to get 32 cups. Then you would do 10×16=160 to get 160 cups. Now add 32+160=192 cups.
What is the name of the point located at
(
4
,
3
)
?
A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point M is plotted 3 units above the origin. Point T is plotted 5 units above the origin. Point Y is plotted 1 unit to the right of the origin. Point Z is plotted 1 unit to the right and 4 units above the origin. Point N is plotted 1 unit to the right and 5 units above the origin. Point L is plotted 2 units to the right and 2 units above the origin. Point W is plotted 3 units to the right and 2 units above the origin. Point P is plotted 4 units to the right of the origin. Point X is plotted 4 units to the right and 3 units above the origin. Point O is plotted 5 units to the right and 4 units above the origin. Point S is plotted 5 units to the right and 5 units above the origin.
A.
Point M
B.
Point P
C.
Point W
D.
Point X
Answers
The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
The name of the point located at (4, 3) is X.
Option D is the correct answer.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The coordinates of a point = (4, 3)
Point (4, 3) is located on the graph at point X.
(4, 3) means 4 is on the x-axis and 3 is on the y-axis.
The meeting point is point X.
Thus,
The name of the point located at (4, 3) is X.
Option D is the correct answer.
Learn more about coordinates here:
https://brainly.com/question/13118993
#SPJ1
Two-fifths of the students in the music class of twenty students were boys. How many boys are in the music class?
Answers
Answer:
8
Step-by-step explanation:
the answer is 8
Answer:
8
Step-by-step explanation:
total students=20
boys=2/5×20
=8