Answers
Answer:
a. decay; b. growth; c. decay; d. neitherr = 4; a = 1; y = 1·4^xa. an = 3(5^(n-1)); b. f(x) = (3/5)(5^x); c. exponential growth; d. y-intercept: 3/5; first term: 3.Step-by-step explanation:
There are two kinds of exponential problems here.
exponential functions of the form f(x) = a·b^xexponential sequences of the explicit form an = a1·r^(n-1)The second problem gives you a table that suggests the sequence form, but it asks for the exponential function form. The third problem does something similar.
__
1.In an exponential function of the form f(x) = a·b^x, the function grows if b>1 and decays if b<1. Using this check, we can easily answer ...
a. 0.4 < 1 . . . decay
b. 1.3 > 1 . . . growth
c. 1/2 < 1 . . . decay
d. 1 = 1 . . . neither growth nor decay; the function is constant: j(x) = 1.
__
2.The value of x is given starting at 1, so we can consider this a geometric sequence. The common ratio is r = 16/4 = 4. The first term is a1 = 4, so the explicit formula for the sequence is ...
an = 4·4^(n-1)
When this is expanded to get rid of the constant in the exponent, we have ...
an = 4·(4^n)·(4^-1) = 1·4^n
We recognize this form as matching the functional form f(x) = a·r^x. The multiplier of the exponential factor is a=1. In summary, ...
r = 4; a = 1; f(x) = 1·4^x
__
3.The first term of this geometric sequence is a1 = 3. The common ratio is r = 15/3 = 5. Using the explicit formula, we have ...
a. explicit form: an = 3·5^(n-1)
Using the method of question 2 to write the functional form, we find ...
an = 3(5^n)(5^-1) = (3/5)(5^n)
b. functional form: f(x) = (3/5)(5^x)
c. function family: exponential growth functions
d. y-intercept: (3/5) . . . . read this from the f(x) form
1st term: the first term listed in the given sequence is 3
_____
Additional comment
The "y-intercept" of a sequence is irrelevant (undefined), as the sequence term numbering starts with 1, not 0. The domain of the explicit formula is natural numbers, which does not include 0.
Similarly, the "first term" of a function f(x) needs further definition. Here, we've answered the question by saying the first term is f(1). There is no conventional definition of a "first term" for a continuous function.
Related Questions
Help! The options are: proportional , not proportional
Answers
Answer: Not proportional
=======================================================
Explanation:
Let's assume the two fractions are equal.
If so, then,
[tex]\frac{0.2}{2.6} = \frac{0.3}{3.6}\\\\0.2*3.6 = 2.6*0.3\\\\0.72 = 0.78[/tex]
The last equation is false, so the first equation is false.
Therefore, the two ratios are not proportional.
-------------
Another approach:
Calculate the decimal value of each fraction
[tex]\frac{0.2}{2.6} \approx 0.07692\\\\\frac{0.3}{3.6} \approx 0.08333\\\\[/tex]
The two ratios result in different decimal values, so the two ratios are not equal, aka not proportional.
Please helpppppppppppppp
Answers
Answer:
Sides: a = 46 b = 46 c = 49
Step-by-step explanation:
i think
How do i solve that question?
Answers
a) The solution of this ordinary differential equation is [tex]y =\sqrt[3]{-\frac{2}{\frac{3\cdot t}{8}-\frac{\sin 2t}{4}+\frac{\sin 4t}{32}-2 } }[/tex].
b) The integrating factor for the ordinary differential equation is [tex]-\frac{1}{x}[/tex].
The particular solution of the ordinary differential equation is [tex]y = \frac{x^{3}}{2}+x^{2}-\frac{5}{2}[/tex].
How to solve ordinary differential equations
a) In this case we need to separate each variable ([tex]y, t[/tex]) in each side of the identity:
[tex]6\cdot \frac{dy}{dt} = y^{4}\cdot \sin^{4} t[/tex] (1)
[tex]6\int {\frac{dy}{y^{4}} } = \int {\sin^{4}t} \, dt + C[/tex]
Where [tex]C[/tex] is the integration constant.
By table of integrals we find the solution for each integral:
[tex]-\frac{2}{y^{3}} = \frac{3\cdot t}{8}-\frac{\sin 2t}{4}+\frac{\sin 4t}{32} + C[/tex]
If we know that [tex]x = 0[/tex] and [tex]y = 1[/tex], then the integration constant is [tex]C = -2[/tex].
The solution of this ordinary differential equation is [tex]y =\sqrt[3]{-\frac{2}{\frac{3\cdot t}{8}-\frac{\sin 2t}{4}+\frac{\sin 4t}{32}-2 } }[/tex]. [tex]\blacksquare[/tex]
b) In this case we need to solve a first order ordinary differential equation of the following form:
[tex]\frac{dy}{dx} + p(x) \cdot y = q(x)[/tex] (2)
Where:
[tex]p(x)[/tex] - Integrating factor[tex]q(x)[/tex] - Particular functionHence, the ordinary differential equation is equivalent to this form:
[tex]\frac{dy}{dx} -\frac{1}{x}\cdot y = x^{2}+\frac{1}{x}[/tex] (3)
The integrating factor for the ordinary differential equation is [tex]-\frac{1}{x}[/tex]. [tex]\blacksquare[/tex]
The solution for (2) is presented below:
[tex]y = e^{-\int {p(x)} \, dx }\cdot \int {e^{\int {p(x)} \, dx }}\cdot q(x) \, dx + C[/tex] (4)
Where [tex]C[/tex] is the integration constant.
If we know that [tex]p(x) = -\frac{1}{x}[/tex] and [tex]q(x) = x^{2} + \frac{1}{x}[/tex], then the solution of the ordinary differential equation is:
[tex]y = x \int {x^{-1}\cdot \left(x^{2}+\frac{1}{x} \right)} \, dx + C[/tex]
[tex]y = x\int {x} \, dx + x\int\, dx + C[/tex]
[tex]y = \frac{x^{3}}{2}+x^{2}+C[/tex]
If we know that [tex]x = 1[/tex] and [tex]y = -1[/tex], then the particular solution is:
[tex]y = \frac{x^{3}}{2}+x^{2}-\frac{5}{2}[/tex]
The particular solution of the ordinary differential equation is [tex]y = \frac{x^{3}}{2}+x^{2}-\frac{5}{2}[/tex]. [tex]\blacksquare[/tex]
To learn more on ordinary differential equations, we kindly invite to check this verified question: https://brainly.com/question/25731911
Find the value of each expression.
Answers
Answer:
I don't know if you still need an answer but- here ya go :)
a. -22 + 5 = -17
b. -22 - (-5) = -22 + 5 = -17
c. (-22)(-5) = 110
d. (-22) / 5 = -4.4
607
ery pc
Unit test
Students were surveyed about their preference between dogs and cats. The following two-way table
displays data for the sample of students who responded to the survey.
Sum
Preference
Male
Female
TOTAL
ing ar
Prefers dogs
36
20
56
Prefers cats
10
26
36
No preference
2
6
8
:59
Ze wil
the
TOTAL
48
52
100
Of students in the sample, what fraction were male?
ting
Choose 1 answer:
36
100
59
ew
®
56
100
st
lay
it to
in
52
Answers
Using proportions, it is found that the fraction of students in the sample that were male is:
[tex]\frac{56}{100}[/tex]
What is a proportion?A proportion is a fraction of total amount.
From the two-way table, we have that:
There is a total of 100 students in the sample.Of those, 56 are male.Thus, the fraction of students in the sample that were male is:
[tex]\frac{56}{100}[/tex]
You can learn more about proportions at https://brainly.com/question/24372153
Find the distance between the points (-2,-2) and (3,-3)
Distance =
Answers
Answer:
≈5.099
Step-by-step explanation:
1) the rule is:
[tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2};[/tex]
2) according to the rule above, the required distance is:
[tex]d=\sqrt{(-2-3)^2+(-2+3)^2}=\sqrt{26}[/tex]
d≈5.099
Add the following polynomials, then place the answer in the proper location on the grid. Write answer in descending powers of x. -4x2+3xy-y2 -7x2-xy+6y2 x2+4xy-2y2
Answers
Polynomials are algebraic expressions that have variables and constants
The result of adding the polynomials is [tex]-10x^2+6xy+3y^2[/tex]
How to determine the polynomialThe sum of the polynomials is given as:
[tex]-4x^2+3xy-y^2 -7x^2-xy+6y^2 + x^2+4xy-2y^2[/tex]
Collect like terms
[tex]-7x^2-4x^2+ x^2+3xy -xy +4xy-2y^2-y^2+6y^2[/tex]
Evaluate the like terms
[tex]-10x^2+6xy+3y^2[/tex]
Hence, the result of adding the polynomials is [tex]-10x^2+6xy+3y^2[/tex]
Read more about polynomials at:
https://brainly.com/question/4142886
A pair of boots originally cost $124. Now they are on sale for 75% of the original price. What is the sale price of the boots?
Answers
Answer:
Sale Price = 31$
Step-by-step explanation:
Sale price= originally price × (1- sale percentage /100)
=124× (1- 75/100)
=124× 0.25
=31 $
What is an equation of the line that is parallel to y = 3x-8 and passes
through the point (4,-5)?
Answers
Parallel lines have equal slopes, so the slope of the line we want to find is 3.
Substituting into point-slope form,
[tex]y+5=3(x-4)\\\\y+5=3x-12\\\\\boxed{y=3x-17}[/tex]
Use the table in the following problem.
Which industry had the greatest percentage increase in profits as a percentage of sales between 1966 and 1974?
-Chemicals
-Petroleum
-Drugs
What was the percentage increase (to the nearest tenth)?
-13.4%
-11.8%
Answers
Answer:Petroleum = 15.32%
Drugs = 12.9%
Chemicals = 2.5%
Motor Vehicles = -56.5% (Negative)
Electrical = -18.8% (Negative)
Food = 3.7%
Step-by-step explanation:
100!! points
A jar contains only pennies, nickels, dimes, and quarters. There are 16 pennies, 11 dimes, and 20 quarters. The rest of the coins are nickels. There are 74 coins in all. How many of the coins are not nickels? If n represents the number of nickels in the jar, what equation could you use to find n?
Answers
Answer: 23n (nickels)
16p + 11d + 20q = 47x
x = number of coins that aren't nickels
y = number of coins in all
n = nickels
so there are 74 coins in all
70y - 47x = 23n
there are 23 nickels
lets check: 23n + 16p + 11d + 20q = 70y
Cobalt-60 is subject to radioactive decay, and each year the amount present is reduced by 12.3%. (a) The amount of cobalt-60 present is an exponential function of time in years. What is the base of this exponential function? . (b) What is the half-life of cobalt-60? Round your answer to one decimal place. yr
Answers
Using an exponential function, it is found that:
a) The base is of 0.877.
b) The half-life of cobalt-60 is of 5.3 years.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal, and 1 - r is the base.Item a:
Each year the amount present is reduced by 12.3%, hence [tex]r = 0.123[/tex], and the base is:
[tex]1 - r = 1 - 0.123 = 0.877[/tex]
Item b:
This is t for which A(t) = 0.5A(0), hence:
[tex]A(t) = A(0)(0.877)^t[/tex]
[tex]0.5A(0) = A(0)(0.877)^t[/tex]
[tex](0.877)^t = 0.5[/tex]
[tex]\log{(0.877)^t} = \log{0.5}[/tex]
[tex]t\log{0.877} = \log{0.5}[/tex]
[tex]t = \frac{\log{0.5}}{\log{0.877}}[/tex]
[tex]t = 5.3[/tex]
The half-life of cobalt-60 is of 5.3 years.
You can learn more about exponential functions at https://brainly.com/question/25537936
HELPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
765
Step-by-step explanation:
ad both side of the polygon which you will get 17 and 45 times those two and you'll [tex]765ft^2\\[/tex]
Are the ratios 2:1 and 8:4 equivalent?
Answers
Answer:
Yes
Step-by-step explanation:
Just like with fractions, 8:4 can be reduced to 2:1
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\large\text{2 : 1}\\\\\large\text{= 2}\times\large\text{4 : }\large\text{1}\times\large\text{4}\\\\\large\text{= 8 : 4}[/tex]
[tex]\large\textsf{8 : 4}\\\\\large\textsf{= 8}\div\large\textsf{4 : 4}\div\large\textsf{4}\\\\\large\textsf{= 2 : 1}[/tex]
[tex]\large\textbf{Thus, 2:1 \& 8:4 ARE equivalent.}[/tex]
[tex]\huge\textbf{Therefore, your answer is: \boxed{\mathsf{YES!}}}\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
How do you factor 125-x^3?
Answers
Step-by-step explanation:
We have
[tex]125 - x {}^{3} [/tex]
First, 125 is a perfect cube because
[tex]5 \times 5 \times 5 = 125[/tex]
and
x^3 is a perfect cube because
[tex]x \times x \times x = x {}^{3} [/tex]
so we can use the difference of cubes identity
[tex]( {x}^{3} - {y}^{3} ) = (x - y)( {x}^{2} + xy + {y}^{2} )[/tex]
Let say we have two perfect cubes:
64 because 8×8×8=64
and 27 because 3×3×3=27 and let subtract
[tex]64 - 27[/tex]
we know that
[tex]64 - 27 = 37[/tex]
but using the difference of cubes identity we should get the same thing.
Remeber cube root of 64 is 4 and cube root of 27 is 3 so we have
[tex](4 - 3)( {4}^{2} + 4(3) + 3 {}^{2} )[/tex]
[tex]1(16 + 12 + 9) = 1(37) = 37[/tex]
So the difference of cubes works for real numbers. This is a good way to help remeber the identity using real numbers.
Back on to the topic,
we know that 5 is cube root of 125 and x is the cube root of x^3 so we have
[tex](5 - x)( {5}^{2} + 5x + {x}^{2} ) = [/tex]
[tex](5 - x)(25 + 5x + {x}^{2} )[/tex]
First Image is the answer the second is the steps
Best of Luck
Pleas help I’ll make most Brainly
Answers
Answer:
70%
Step-by-step explanation:
divide 21 by 30 to get .70 multiply by 100 to make percent
70% (or just move decimal two places to the right)
Answer:
70%
Step-by-step explanation:
100 ÷ 30 = 3.3333333333333
21 x 3.3333333333333/30 x 3.3333333333333 = 70/100
21/30 = 0.7
0.7 x 100 = 70%
Kaycee made 8 identical bags using 7 yards of fabric. How much fabric did Kaycee use for each bag?
Answers
Answer:
0.43 yards is the answer
Step-by-step explanation:
Which is true about the solution to the system of inequalities shown? y > 3x + 1 y < 3x – 3 On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.
Answers
Answer:Option B.Step-by-step explanation:The given inequalities are The related equations of given inequalities areThe tables of values areFor line 1 For line 2x y x y0 -1 0 -33 0 9 0Plot these ordered pairs on a coordinate plane and connect them by straight lines.The sign of both inequalities is "<" it means both lines are dotted and everything below the lines is shaded.From the below graph it is clear that all values that satisfy are solutions. Therefore, the correct option is B.
Which linear function represents the line given by the point-slope equation y-8=1/2(x – 4)?
O f(x) = 1/2x+4
o Ax) = 1/2x + 6
o f(x) = 1/2x – 10
o f(x) = 1/2x= 12
Answers
Answer:
y = -3x + 14.
it's my answer
Answer:
B) f(x) = 1/2x + 6Step-by-step explanation:
Convert the given equation into slope - intercept form:
y - 8 = 1/2(x - 4)y - 8 = 1/2x - 2y = 1/2x + 8 - 2y = 1/2x + 6The matching choice is B
i need help please i’m struggling
Answers
Answer:
(A) 46 seconds
Step-by-step explanation:
You can arrive at an answer to this question at least two ways:
1)Read the time from the graph.
Locate 144 on the vertical scale, just below halfway from 140 to 150. Locate the point on the graph that is at this vertical height. It is a little more than halfway between 40 and 50 on the horizontal scale.
The only answer choice in that neighborhood is t = 46 seconds.
__
2)Use the given formula, and solve it for the time.
d = 1.5t +75
144 = 1.5t +75 . . . the distance of interest is 144
69 = 1.5t . . . . . . . .subtract 75
69/1.5 = t = 46 . . . seconds
Determine the open intervals on which the function is increasing, decreasing, or constant. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
f(x) = x^3 − 9x^2 + 1
Answers
Answer:
Inc:(-∞,0) and (6,∞) Dec: (0,6)
Step-by-step explanation:
You could also use derivatives or look at the graph:
f'(x)=3x^2-18x
3x^2-18x=0
x=0,6
These are your critical points.
To check if they are really critical points or if they are increasing or decreasing and to see if they aren't inflection points, plug the points back on the equation.
Find the value of each variable.
Answers
Answer:
x=7 y=12.124
Step-by-step explanation:
hope this helps
-3x-4y<8 graph the inequality
please help!!
Answers
Answer:
y > [tex]\frac{3}{4}[/tex] x - 2
Step-by-step explanation:
thats the answer rearranged your graph should look like this
The graph shows Dan's earnings for different hours worked. Select the terms that can be used to describe Dan's earnings
Answers
The graph is an illustration of a linear function
The term that can be used to describe Dan's earning is that he earns $10.25 per hour
How to determine the hourly rateFrom the graph, we have the following ordered pairs
(x,y) = {(4,41) (7,71.75)}
The slope (m) is then calculated as:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{71.75 - 41}{7 -4}[/tex]
Simplify
[tex]m = \frac{30.75}{3}[/tex]
Evaluate the quotient
[tex]m = 10.25[/tex]
Hence, Dan's hourly earning is $10.25 per hour
Read more about linear functions at:
https://brainly.com/question/15602982
find the area of KLMN
Answers
Answer:
Step-by-step explanation:
Step-by-step explanation:
the first thing we notice : the quadrilateral has 2 pairs of equally long sides with 2 angles being openly 90°.
so, we are dealing with a rectangle here.
we know that one pair of the sides (NK = LM) are 24 cm long.
and we know that KL:LM = 3:4.
that means that the pair KL = MN are the shorter sides of the rectangle. and their length is according to the ratio 3/4 of NK=LM.
3/4 × 24 = 18 cm
the area of that rectangle is therefore
18 × 24 = 432 cm²
There are 25 newspapers in a stack. The stack weighs 15.5kg. What is the weight of each newspaper?
Answers
Answer:
0.62kg or 620g.
Step-by-step explanation:
If there are 25 newspapers in a stack that weighs 15.5kg, 15.5 divided by 25 would give you the weight of one newspaper, which is 0.62kg.
To convert kilograms to grams:
0.62kg x 1000 = 620g
Answer:
0.62 kg
Step-by-step explanation:
25 newspaper = 15.5kg
1 newspaper = ? Y
cress cross
25 newspaper Y = 15.5 kg × 1 newspaper
25 newspaper 25 newspaper
Y = 15.5 kg
25
Y = 0.62 kg
15. Macy doesn't have any money in her bank account,
but begins saving $ 15 each week. Robby has $20 in
his bank account and saves $ 10 each week. After
how many weeks will Macy and Robby have the same
amount in their accounts? Use the graph to solve.
Answers
Answer:
4 weeks
Step-by-step explanation:
because 15x4=60
and 10x4=40+ 20 =60
Emma's class has a jar of earthworms. The class measures the length of each earthworm and records the data in a line plot. What is the difference between the lengths of the shortest and the longest earthworms?
The lowest length is 4 3/4
The highest length is 6 3/4
How would I set this up to solve???
Answers
Step-by-step explanation:
refer the above attachment
1/7 f = 6
Solve equation
Answers
Answer:
42
Step-by-step explanation:
Round each fraction to help you estimate the solution for the following equation: 7/8 + 6/8
Answers:
1/2
1
1 1/2
2
Answers
Answer:
13/8 or 1 1/2
Step-by-step explanation:
Step 1
Since our denominators match, we can add the numerators.
7 + 6 = 13
So what's the answer so far?
13/8
Step 2
Can this fraction be reduced?
First, we attempt to divide it by 2...
No good. So next you try the next prime number, which is 3...
No good. So next you try the next prime number, which is 5...
No good. So next you try the next prime number, which is 7...
No good. So next you try the next prime number, which is 11...
No good. 11 is larger than 8. So we're done reducing.
And we're done! Here's the final answer to 7/8 + 6/8
