Answer:
8.4 cm
Step-by-step explanation:
The longest side of an acute isosceles triangle is 12 centimeters.
Let x be the length of the smallest side
Isosceles triangle has one longest side and two smallest sides
so its acute triangle
[tex]c^2<a^2 +b^2[/tex]
where c is the longest side
a and b are two shortest sides 'x'
[tex]c^2<x^2 +x^2[/tex]
[tex]12^2<x^2 +x^2[/tex]
[tex]144<2x^2[/tex]
divide both sides by 2
[tex]72<x^2[/tex]take square root on both sides
[tex]8.4<x[/tex]
So 8.4 cm
Which expressions are equivalent to -6(b+2)+8−6(b+2)+8minus, 6, left parenthesis, b, plus, 2, right parenthesis, plus, 8 ? Choose all answers that apply: Choose all answers that apply: (Choice A) A -6b+2+8−6b+2+8minus, 6, b, plus, 2, plus, 8 (Choice B) B -6b-4−6b−4minus, 6, b, minus, 4 (Choice C) C None of the above
Answer:
B. [tex]-6b-4[/tex]
Step-by-step explanation:
Given expression is [tex]-6(b+2)+8[/tex]
Simplifying the expression now
Lets use distributive property of multiplication to solve it.
As given, [tex]-6(b+2)+8[/tex]
Distributing -6 with b and 2.
= [tex](-6b-12)+8[/tex]
Opening the parenthesis
= [tex]-6b-12+8[/tex]
= [tex]-6b-4[/tex]
∴ As from the given options, [tex]-6b-4[/tex] is the correct choice.
Answer:
B
Step-by-step explanation:
Its right got it from khan
John is a new college graduate working at his first job. After years of living in an apartment he has decided to purchase a home. He has found a great neighborhood from which he can walk to work. Before buying a home in the area he has decided to collect some data on the homes in this neighborhood. A data set has been compiled that represents a sample of 100 homes in the neighborhood he is considering. The variables included in this data set include:* Value: the current value of the home as determined by the county tax assessor. * Size: the size of the home in square feet. * Year: the year the homes were built. * Basement: does the home have a basement
When analyzing data on homes in a neighborhood, focus on variables like value, size, year built, and basement presence. The sample data set of lawn areas is quantitative and continuous.
Data Analysis Process:
When collecting data on homes in a neighborhood, you can analyze it by looking at variables like value, size, year built, and basement presence. To make sense of the data, you can calculate statistics like the median home value and the variation in values to get a clearer picture of the housing market.
Data Types:
The areas of lawns in square feet sampled from five houses represent quantitative data, specifically continuous data, as they can take on any value within a range without restrictions.
If x2 + y2 = 25, what is the value of
at the point (4,3)?
O A. -25/27
OB.-7/27
OC. 7/27
D. 3/4
OE. 25/27
Answer:
A. -25/27
Step-by-step explanation:
Given:
The equation is given as:
[tex]x^2+y^2=25[/tex]
To find: [tex]\frac{d^2 y}{dx^2}[/tex] at (4, 3)
Differentiating the above equation with respect to 'x', we get:
[tex]\frac{d}{dx}(x^2+y^2)=\frac{d}{dx}(25)\\\\2x+2yy'=0\\\\x+yy'=0\\\\yy'=-x\\\\y'=\frac{-x}{y}------- (1)[/tex]
Value of [tex]y'[/tex] at (4,3) is given as:
[tex]y'_{(4,3)}=-\dfrac{4}{3}-------- (2)[/tex]
Now, differentiating equation (1) with respect to 'x' again, we get:
[tex]y''=\frac{d}{dx}(\frac{-x}{y})\\\\y''=\frac{y(-1)-(-x)y'}{y^2}\\\\y''=\frac{-y+xy'}{y^2}[/tex]
Now, value of [tex]y''[/tex] at (4,3) is given as by plugging 4 for 'x', 3 for 'y' and [tex]\frac{-4}{3}[/tex] for [tex]y'[/tex]
[tex]y''_{(4,3)}=\frac{-3+(4)(-\frac{4}{3})}{3^2}\\\\y''_{(4,3)}=\frac{-3-\frac{16}{3}}{9}\\\\y''_{(4,3)}=\frac{-9-16}{3}\div 9\\\\y''_{(4,3)}=\frac{-25}{3}\div 9\\\\y''_{(4,3)}=\frac{-25}{3}\times \frac{1}{9}\\\\y''_{(4,3)}=-\frac{25}{27}[/tex]
Therefore, the value of the second derivative at (4, 3) is option (A) which is equal to -25/27.
does anyone know the answer??
You have to find x.
Answer:x = 9.01
Step-by-step explanation:
The given triangle is a right angle triangle.
From the given right angle triangle the hypotenuse of the right angle triangle is 17
With 35 degrees as the reference angle,
x represents the adjacent side of the right angle triangle.
The unlabelled side represents the opposite side of the right angle triangle.
θ = 35 degrees
To determine x, we would apply trigonometric ratio
Cos θ = adjacent side/hypotenuse side. Therefore,
Cos 35 = x/11
x = 11 Cos 35 = 11 × 0.8192
x = 9.01
Answer:
9.01
Step-by-step explanation:
The right angle triangle with a focused angle of degree is easily solved using Trig Ratio that can easily be recalled with this word :
SohCahToa.
What it means is:
If the Opposite side to the focused angle is given and also the hypotenuse is given, we use sine
Cosine if Adjacent and Hypotenuse is given.
Tangent if the opposite and Adjacent is given.
Now, to the question:
The Adjacent and the Hypotenuse is given. Therefore we'll use Cosine.
Therefore:
Cos 35 = x / 11
Cross multiplying:
11 cos 35 = x
11 * 0.8192 = x
Theresfore,
x = 9.01
Hope it helped?
A fast food restaurant sold 30 burgers with cheese if the ratio burger soup with cheese compared to without cheese was 5 : 1 one how many burgers did they sell total
Answer:36 burgers were sold.
Step-by-step explanation:
Let x represent the total number of burgers, with or without cheese that was sold.
The total number of burgers with cheese that the fast food sold is 30.
if the ratio burger sold with cheese compared to without cheese was
5 : 1 , the total ratio would be the sum of both proportions. It becomes
5 + 1 = 6
Therefore
5/6 × x = 30
5x/6 = 30
Cross multiplying by 6, it becomes
5x = 30 × 6 = 180
x = 180/5 = 36
Therefore, the number of burgers without cheese sold would be
36 - 30 = 6
A 400-room property that assigns 16 rooms to one section housekeeper and groups the section housekeepers in teams of 5 will need the following number of teams to service the guestrooms when the property is full:
Answer:
We conclude that we need 5 teams to service the guestrooms when the property is full.
Step-by-step explanation:
When the property of 400 rooms is full, and as we know that one housekeeper gets 16 rooms. We calculate to need 400/16=25 housekeeper.
We know that one team has 5 housekeepers, and that we have 25 housekeepers. We conclude that we need 25/5=5 teams to service the guestrooms when the property is full.
76.8 is 32% of what number
Answer: 240
Step-by-step explanation:
A gardener is mowing a 20 by 40 yard rectangular pasture using a diagonal pattern. He mows from one corner of the pasture to the corner diagonally opposite. What is the length of this pass with the mower? Give your answer in simplified form. Recall from the Pythagorean Theorem that, for a right triangle, the square of the length of the diagonal is equal to the sum of the squares of the lengths of the sides.
A. 10 times square root 20
B. 20 times square root 2
C. 400 times square root 5
D. 20 times square root 5
20 * (sqrt) 5 is the correct answer or “D”
recently took this trust me 100% i’m just here to help anybody :)
Answer:
d
Step-by-step explanation:
using Pythagorean theorem you would do a^2 + b^2 = c^2 so 20^2 + 40^2 = 2000 do the square root of 2000 and you get 20* square-root of 5
Need a little help with one please
Answer:
That would be the side-side-side (SSS) postulate, which states that if all the sides of a triangle are in a fixed ratio to all the corresponding sides of another triangle, then the two triangles are said to be congruent.
Step-by-step explanation:
Looking at triangles ABC and DEF, we notice that:
[tex]\frac{AB}{DE} = \frac{AC}{DF}=\frac{BC}{EF}[/tex]
since
[tex]\frac{3}{18} = \frac{6}{36}=\frac{7}{42}=\frac{1}{6}[/tex]
Let me know if you have further questions.
Determine which of the following passages are arguments. For those that are, identify the conclusion. For those that are not, determine the kind of nonargument. Since the 1950s a malady called whirling disease has invaded U.S. fishing streams, frequently attacking rainbow trout. A parasite deforms young fish, which often chase their tails before dying, hence the name.
Answer:
Non Arguement passage.
Step-by-step explanation:
The passage given is a non arguement passage , the passage is more of a report especially the introductory part where the author said ''Since the 1950s a malady called whirling disease has invaded U.S. fishing streams, frequently attacking rainbow trout.'' this highlighted phrase is a report gathered or investigated by the author which was gotten as a result of his own personal findings or from history. For an argument passage, the introductory part will have portrayed what the author implied, there will be an indication of the authors stance or favoured opinion which of course will be backed by evidence from his or her findings. as such, there is nothing of such which may serve as a precursor to indicate or informed us if the passage is that of an arguement. Again, the passage is a report and not an argument. as nothing can be inferred from the paragraph to point to us if it is an argument passage.
However, there is a conclusion in the passage and conclusions has arrived by the author must have been from a detailed findings and research, if possible an experimental study before a conclusion can be reached as the last line of the paragraph says ''A parasite deforms young fish, which often chase their tails before dying, hence the name.'' The conclusion is that parasite are known to cause deformation in young fish.
Diego measured the length of a pain to be 22 cm the actual length of the pen is 23 cm which of these is the closest to the percent error For Diego measurement
The percent error For Diego measurement is 4.3 % decrease
Solution:
Given that, Diego measured the length of a pain to be 22 cm
The actual length of the pen is 23 cm
To find: percent error
Percent error is the difference between a measured and actual value, divided by the actual value, multiplied by 100%
The formula for percent error is given as:
[tex]\text{Percent error } = \frac{\text{Measured value - actual value}}{\text{Actual value}} \times 100[/tex]
Here given that,
Measured value = 22 cm
Actual value = 23 cm
Substituting the values in formula,
[tex]Percent\ Error = \frac{22-23}{23} \times 100\\\\Percent\ Error = \frac{-1}{23} \times 100\\\\Percent\ Error = -0.043 \times 100\\\\Percent\ Error = -4.3[/tex]
Here, negative sign denotes percent decrease
Thus percent error For Diego measurement is 4.3 % decrease
Johnathan ran 5 days this week. The most he ran in one day was 3.5 miles. Write an inequality that shows the distance johnathan could of ran any day this week
An inequality that shows the distance Johnathan could of ran any day this week is:
[tex]x\leq 3.5[/tex]
Solution:
Let "x" be the distance Johnathan can run any day of this week
Given that,
Johnathan ran 5 days this week. The most he ran in one day was 3.5 miles
Therefore,
Number of days ran = 5
The most he ran in 1 day = 3.5 miles
Thus, the maximum distance he ran in a week is given as:
[tex]distance = 5 \times 3.5 = 17.5[/tex]
The maximum distance he ran in a week is 17.5 miles
If we let x be the distance he can run any day of this week then, we get a inequality as:
[tex]x\leq 3.5[/tex]
If we let y be the total distance he can travel in a week then, we may express it as,
[tex]y\leq 17.5[/tex]
Suppose you add two vectors A and B . What relative direction between them produces the resultant with the greatest magnitude? What is the maximum magnitude?
Answer: The resultant would be the sum and the difference between the vectors.
Step by step explanation: 1. The possible resultant is between the sum of the 2 vectors and the difference between the two vectors.
2. The greatest magnitude is when the vectors lie in the same direction and the sum would be the scalar sum of the two vectors. The angle between the two would be zero degree.
Jamal's Seed Emporium claims that 75% of its lily seeds will germinate. Suppose the company's claim is true. Sierra buys a packet with 25 lily seeds from Jamal's Seed Emporium and plants them in her garden. What is the probability that exactly 18 seeds will germinate?
Answer:
P = 0.1654
Step-by-step explanation:
Binomial probability:
P = nCr pʳ qⁿ⁻ʳ
where n is the number of trials,
r is the number of successes,
p is the probability of success,
and q is the probability of failure (1−p).
P = ₂₅C₁₈ (0.75)¹⁸ (0.25)²⁵⁻¹⁸
P = 480,700 (0.75)¹⁸ (0.25)⁷
P = 0.1654
gina pasted 3 stickers in a book. if she added one sticker to her collection every day, what equation represents the relationship between x (number of days) and y (number of stickers)?
Answer:
The answer to your question is
Number of stickers = number of days + 3
Step-by-step explanation:
- To find the equation of the line that represents the situation, first, find the slope.
Slope = m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
m = [tex]\frac{4 - 3}{1 - 0} = \frac{1}{1} = 1[/tex]
- Find the equation of the line
y - y1 = m(x - x1)
y - 4 = 1(x - 1)
y - 4 = x - 1
y = x - 1 + 4
y = x + 3
y = number of stickers
x = days
Number of stickers = number of days + 3
Answer:
is x = y + 3
Step-by-step explanation:
A researcher is curious about the average IQ of registered voters in the state of FL. The entire group of registered voters in FL is an example of a(n) ___________.
a. sampleb. statisticc. populationd. parameter
Answer:
Option C) population
Step-by-step explanation:
We are given the following situation in the question:
A researcher is curious about the average IQ of registered voters in the state of FL.
Sample:
It is a part of a population. It is always smaller than the population.
Statistic:
Any numerical value or any other measure describing a sample of a population is known as statistic.
Population:
It is the universal data set. Every observation belongs to this group which is of interest. Sampling is done within population to obtain small groups of sample.
Parameter:
Any numerical value or any other measure describing the population is known as a parameter.
In this situation, the entire group of registered voters in FL is an example of a population because it contains all the individual for variable of interest.
Variable of interest:
Average IQ of registered voters in the state of FL.
Individual of interest:
Registered voters in the state of FL.
Which angles are coterminal with an angle drawn in standard position measuring 282°?
Select all correct angle measures.
−438∘
−78∘
78°
572°
642°
Answer:
−438°, -78°, 642°
Step-by-step explanation:
Given angle:
282°
To find the co-terminal angles of the given angle.
Solution:
Co-terminal angles are all those angles having same initial sides as well as terminal sides.
To find the positive co-terminal of an angle between 360°-720° we will add the angle to 360°
So, we have: [tex]282\°+360\°=642\°[/tex]
To find the negative co-terminal of an angle between 0° to -360° we add it to -360°
So, we have: [tex]282\°-360\°=-78\°[/tex]
To find the negative co-terminal of an angle between -360° to -720° we add it to -720°
So, we have: [tex]282\°-720\°=-438\°[/tex]
Thus, the co-terminal angles for 282° are:
−438°, -78°, 642°
The correct coterminal angles with 282° are -78° option(2) and 642° option(5). The angles -438°, 78°, and 572° are not coterminal with 282°.
In mathematics, coterminal angles are angles that share the same initial and terminal sides. To find coterminal angles for a given angle, we add or subtract multiples of 360° (a full rotation). For the angle 282°:
1. Subtracting 360°:
⇒ 282° - 360° = -78°
2. Adding 360°:
⇒ 282° + 360° = 642°
Therefore, the angle measures -78° and 642° are coterminal with 282°. The other values, -438°, 78°, and 572°, are not coterminal with 282° as they do not share the same position after full rotations.
In summary, the correct coterminal angles with 282° are -78° and 642°.
Complete question:
Which angles are coterminal with an angle drawn in standard position measuring 282°?
Select all correct angle measures.
−438°−78°78°572°642°How many different ways are there to select 24 donuts if there are 7 types of donuts available (and donuts are only distinguished by their type).?
Answer:
593,775 ways
Step-by-step explanation:
24 donuts have to be selected from 7 different varieties of donuts
n = 7
r= 24
Repetition is allowed
C(n+r-1, r) = C(7 + 24 - 1 , 24)
= C(30,24)
Recall that C(n,r) = n! /(n-r)! r!
C(30,24) = 30!/(30 - 24)! 24!
= 30!/(6!24!)
= 593,775 ways
Answer: 346,789 ways
Step-by-step explanation:
Using the formular for permutation to calculate :
P= n!/r!(n-r)!
We need to select 24 apples from 7 types of apples
n=24 ,r=7
Permutation =24!/7!(24-7)!
Permutation =6.2×10^23/1.793×10^18
P= 346 ,789 ways
1. Given the below sequence: -1, -3, -5, -7, . . . (a) What are the next 3 terms? (b) Is this an arithmetic or geometric sequence? (c) Why? (d) What is the 27th term? (Show how to find it and tell me what the 27th term is.)
Answer:
(a) -7 , - 9 , - 11
(b) Arithmetic sequence
(c) There is a common difference of -2
(d) -53
Step-by-step explanation:
(a) To find the next three terms , we must firs check if it is arithmetic sequence or a geometric sequence . For it to be an arithmetic sequence , there must be a common difference :
check :
-3 - (-1) = -5 - (-3) = -7 - (-5) = -2
This means that there is a common difference of -2 , which means it is an arithmetic sequence.
The next 3 terms we are to find are: 5th term , 6th term and 7th term.
[tex]t_{5}[/tex] = a + 4d
[tex]t_{5}[/tex] = - 1 + 4 ( -2 )
[tex]t_{5}[/tex] = -1 - 8
[tex]t_{5}[/tex] = - 9
6th term = a +5d
[tex]t_{6}[/tex] = -1 + 5(-2)
[tex]t_{6}[/tex] = -1 - 10
[tex]t_{6}[/tex] = - 11
[tex]t_{7}[/tex] = a + 6d
[tex]t_{7}[/tex] = -1 + 6 (-2)
[tex]t_{7}[/tex] = -1 - 12
[tex]t_{7}[/tex] = -13
Therefore : the next 3 terms are : -9 , -11 , - 13
(b) it is an arithmetic sequence because there is a common difference which is -2
(c) Because of the existence of common difference
(d) [tex]t_{27}[/tex] = a + 26d
[tex]t_{27}[/tex] = -1 + 26 ( -2 )
[tex]t_{27}[/tex] = -1 - 52
[tex]t_{27}[/tex] = - 53
A rectangular box 4 meters long, 3 meters wide and 2 meters tall. On the box is a cat, and the box is floating in water such that half the box is under water. The density of the box is 300 kg/m³. What is the mass of the cat?
Answer:
Mass of the cat = 16800kg
Step-by-step explanation:
The volume of the box = its length * its breath * its height- 4m × 3m × 2m = 24[tex]m^{3}[/tex]
The standard density of water is 1000 Kg/[tex]m^{3}[/tex]
By Archimedes principle, the mass of a body floating body is equivalent to the mass of the volume liquid displaced
in this case we have
Mass of water displaced = Density of the water × Volume of the water displaced = 1000 Kg/[tex]m^{3}[/tex] × 24[tex]m^{3}[/tex] = 24000kg
The mass of the box = Box density × Box volume = 24[tex]m^{3}[/tex] × 300kg/[tex]m^{3}[/tex] = 7200 kg Hence the mass of water displaced = mass of the foating box + mass of th cat
24000kg = mass of cat +7200kg
mass of cat = 24000kg - 7200kg = 16800kg
The sum of two numbers is thirty seven. Using x to represent the larger of two numbers, translate "the difference between nine more than twice the larger number and the sum of the smaller number and three" into a variable expression
Answer:
Step-by-step explanation:
Let x represent the larger number.
Let y represent the smaller number.
The sum of two numbers is thirty seven. This means that the smaller number would be 37 - x
The translation into a variable expression for the the difference between nine more than twice the larger number and the sum of the smaller number and three would be
2x + 9 - (37 - x + 3)
Opening the parenthesis and putting the constants together, it becomes
2x + 9 - 37 + x - 3
2x + x + 9 - 37 - 3
3x - 31
simplifying inside parentheses first pt. 2
Answer:
The answer to your question is the second option
Step-by-step explanation:
Process
Simplify using exponents laws, first inside the parentheses and then outside the parentheses.
[tex][\frac{a^{-2}b^{2}}{a^{2}b^{-1}} ]^{-3}[/tex]
a) Simplify a
a⁻² a⁻² = a⁻⁴
b) Simplify b
b² b¹ = b³
c) Write the result
[tex][\frac{b^{3}}{a^{4}}]^{-3}[/tex]
d) [tex][\frac{a^{4}}{b^{3}}]^{3}[/tex]
e) Simplify
[tex]\frac{(a^{4})^{3}}{(b^{3})3}[/tex]
f) Result
[tex]\frac{a^{12}}{b^{9}}[/tex]
ASAP! I NEED THIS DONE AS QUICKLY AS POSSIBLE WITH WORKING OUT
After t seconds, a particle P has position vector
r = [(3t³- t + 3)i + (2t²+ 2t - 1)j] m
(a) Find an expression for the velocity of P in terms of t
(b) Find an expression for the acceleration of P in terms of t
Answer:
See explanation.
Step-by-step explanation:
Let us first analyze some principle theory. By definition we know that the velocity ( [tex]v[/tex] ) is a function of a distance ( [tex]d[/tex] ) covered in some time ( [tex]t[/tex] ), whilst acceleration ( [tex]a[/tex] ) is the velocity achieved in some time. These can also been expressed as:
[tex]v = \frac{d}{t}\\[/tex] and [tex]a=\frac{v}{t}[/tex]
We also know that both velocity and acceleration are vectors (therefore they are characterized by both a magnitude and a direction). Finally we know that given a position vector we can find the velocity and the acceleration, by differentiating the vector with respect to time, once and twice, respectively.
Let us now solve our problem. Here we are givine the Position vector of a particle P (in two dimensional space of [tex]i-j[/tex] ) as:
[tex]r=(3t^3-t+3)i+(2t^2+2t-1)j[/tex] Eqn.(1)
Let us solve.
Part (a) Velocity: we need to differentiate Eqn.(1) with respect to time as:
[tex]v(t)=\frac{dr}{dt}\\\\ v(t)=[(3)3t^2-1]i+[(2)2t+2]j\\\\v(t)=(9t^2-1)i+(4t+2)j[/tex] Eqn.(2)
Part (b) Acceleration: we need to differentiate Eqn.(2) with respect to time as:
[tex]a(t)=\frac{dv}{dt}\\ \\a(t)=[(2)9t]i+4j\\\\a(t)=(18t)i+4j[/tex]
Thus the expressions for the velocity and the acceleration of particle P in terms of t are
[tex]v(t)=(9t^2-1)i+(4t+2)j[/tex] and [tex]a(t)=(18t)i+4j[/tex]
Julia purchased a new car and traveled 356 miles before refueling. If she needed 15.6 gallons of gas to fill the car's tank, estimate her gas mileage.
Answer:
22.8 MPG
Step-by-step explanation:
356 divided by 15.6 = 22.8
If y = e^5t is a solution to the differential equation d^2 y/dt^2 - 13 dy/dt + ky = 0, find the value of the constant k and the general form y = Ae^5t + Be^at of the solution to the above equation, (i.e. find a). (Use constants A, B, etc., for any constants in your solution formula.)
Answer:
k = -12/5
A = 125/12
B = -325/12
a = 5
Step-by-step explanation:
y = e^5t
Dy/dt = 5e^5t
d2y/dt2 = 25e^5t
Inputting the values of dy/dt and d2y/dt2 into the equation above, we have:
25e^5t - 13e^5t + 5k(e^5t) = 0
12e^5t + 5k(e^5t) = 0
e^5t(12 + 5k) = 0
12 + 5k = 0
k = -12/5
The equation becomes,
d2y/dt2 - 13dy/dt -12/5y = o
So rearranging the equation,
-5/12d2y/dt2 + 65/12dy/dt + y = 0
y = 5/12(25e^5t) - 65/12(5e^5t)
y = 125/12e^5t - 325/12e^5t
Therefore,
k = -12/5
A = 125/12
B = -325/12
a = 5
The value of the constant k is 40. The general form of the solution is y = A[tex]e^{5t}[/tex] + B[tex]e^{8t}[/tex]
Let's start by recognizing that if y = [tex]e^{5t}[/tex] is a solution to the differential equation d²y/dt² - 13 dy/dt + ky = 0, we need to find the value of the constant k and the general form y = A[tex]e^{5t}[/tex] + B[tex]e^{at}[/tex] of the solution. To do this, we need to determine k and a.
1. First, calculate the first and second derivatives of y = [tex]e^{5t}[/tex]
First derivative: dy/dt = 5[tex]e^{5t}[/tex]Second derivative: d²y/dt² = 25[tex]e^{5t}[/tex]2. Substitute these into the differential equation:
d²y/dt² - 13 dy/dt + ky = 0
3. Substituting, we get:
25[tex]e^{5t}[/tex] - 13(5[tex]e^{5t}[/tex]) + k[tex]e^{5t}[/tex] = 0
25[tex]e^{5t}[/tex] - 65[tex]e^{5t}[/tex] + k[tex]e^{5t}[/tex]= 0
(25 - 65 + k)[tex]e^{5t}[/tex] = 0
(-40 + k)[tex]e^{5t}[/tex] = 0
4. For this to hold true, the following must be true:
k - 40 = 0
Thus:
k = 40
The general solution to the differential equation can be expressed as:y = A[tex]e^{5t}[/tex] + B[tex]e^{at}[/tex]
1. To find a, substitute y = [tex]e^{at}[/tex] into the equation:
d²([tex]e^{at}[/tex])/dt² - 13 d([tex]e^{at}[/tex])/dt + 40[tex]e^{at}[/tex] = 0
We get:
a²[tex]e^{at}[/tex]- 13a[tex]e^{at}[/tex] + 40[tex]e^{at}[/tex]= 0
(a² - 13a + 40)[tex]e^{at}[/tex] = 0
2. The characteristic equation is:
a² - 13a + 40 = 0
3. Solve for a using the quadratic formula:
a = [13 ± √(13² - 4⋅40)] / 2
a = [13 ± √(169 - 160)] / 2
a = [13 ± √9] / 2
a = [13 ± 3] / 2
4. The roots are:
a = 8a = 5Since y = [tex]e^{5t}[/tex] is a solution already, the other root a = 8 is the additional solution. Thus, the general solution to the differential equation is:
y = A[tex]e^{5t}[/tex] + B[tex]e^{8t}[/tex].
I half dozen cupcakes cost $15. What constant of proportionality relates to the numbers of cupcakes and the total cost? Write an equation that represents its relationship
Answer:
The constant of proportionality is 2.5 dollar per cupcake and then the required equation would be [tex]y=2.5x[/tex].
Step-by-step explanation:
Given:
Let the number of cupcakes be represent by [tex]'x'[/tex]
Also let the total cost be represented by [tex]'y'.[/tex]
We know that two proportional quantities are in for;
[tex]y=kx[/tex]
where, k⇒ represents constant of proportionality.
Now we know that;
1 dozen = 12
Half dozen = 6
Now Given:
half dozen cupcakes cost $15.
So Let us substitute [tex]x=6[/tex] and [tex]y=15[/tex] in above equation we get;
[tex]15 =k \times 6[/tex]
Dividing both side by 6 we get;
[tex]\frac{15}{6}=\frac{k6}{6}\\\\k= 2.5 \ \$/cupcake[/tex]
Hence the constant of proportionality is 2.5 dollar per cupcake and then the required equation would be [tex]y=2.5x[/tex].
Final answer:
The constant of proportionality relating the number of cupcakes to the cost is $2.50 per cupcake. The equation representing the relationship is C = $2.50 × n.
Explanation:
To find the constant of proportionality for the number of cupcakes and total cost, we use the given information: half a dozen cupcakes (which is 6 cupcakes) cost $15. Therefore, we can divide 15 by 6 to find the cost per cupcake.
C = k × n
Where C is the total cost, n is the number of cupcakes, and k is the constant of proportionality (cost per one cupcake). First, find the constant:
k = C/n = $15/6 cupcakes = $2.50 per cupcake
The equation that represents the relationship between the number of cupcakes (n) and the total cost (C) is:
C = $2.50 × n
THE NUMBER OF STUDENTS FRON SCHOOL LAST WEEK WAS 145. This week there were only 110 students sick. What was the percent decrease of the number of students home sick?
The percent decrease of the number of students home sick is 24.14%.
Solution:
The number of students home this last week was 145
This week there were only 110 students home sick
To find: Percent decrease
The percent decrease is given by formula:
[tex]\text{Percent Decrease } = \frac{\text{Final value-initial value}}{\text{Initial value}} \times 100[/tex]
Here given that,
Initial value = last week = 145
Final value = this week = 110
Substituting the values in formula, we get,
[tex]\text{Percent Decrease } = \frac{110-145}{145} \times 100\\\\\text{Percent Decrease } = \frac{-35}{145} \times 100\\\\\text{Percent Decrease } = -24.14[/tex]
Here negative sign denotes decrease in percent
Thus the percent decrease of the number of students home sick is 24.14%.
Solve the system using elimination.
3x – 4y = 9
–3x + 2y = 9
(–27, –9)
(3, 9)
(–3, –6)
(–9, –9)
Answer:
(-9,-9)
Step-by-step explanation:
Answer:
(-9,-9)
Step-by-step explanation:
50 POINT QUESTION!! A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, the angle of depression to the boat is 16°23'. When the boat stops, the angle of depression is 49°29'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.
This has already been answered but something seemed off so if u could answer it for that would be great thx
See the attached picture.
Answer could change slightly depending on how all the steps are rounded.
Scott and Tom rent a boat at Stow Lake. They start at 10:15 and end at 11:45. The boat rental costs $1.50 for every 15 minutes. How much will they pay?
Answer:they would pay a total amount of $9
Step-by-step explanation:
Scott and Tom rent a boat at Stow Lake. They start at 10:15 and end at 11:45. The number of hours for which they rented the boat would be
11:45 - 10:15 = 1 hour 30 minutes = 1.5 hours.
Converting to minutes, It becomes
60 + 30 = 90 minutes.
The boat rental costs $1.50 for every 15 minutes. Therefore, the total amount of money that they would pay is
90/15 × 1.5 = $9