Answer:
Exterme Value: [tex](2,4)[/tex].
The bird reaches its minimum height which is 4ft affter covering a horizontal distance of 2 ft.
Step-by-step explanation:
The given function is [tex]y=x^2-4x+8[/tex].
We add and subtract the square of half the coefficient of x.
[tex]y=x^2-4x+(-2)^2-(-2)^2+8[/tex].
The first three terms form a perfect quadratic trinomial.
[tex]y=(x-2)^2+4[/tex].
This function is now written in the form [tex]y=a(x-h)^2+k[/tex], where (h,k) is the extreme value(vertex).
The extreme value or the vertex is [tex](2,4)[/tex].
Interpretation:
The bird reaches its minimum height which is 4ft affter covering a horizontal distance of 2 ft.
Answer: minimum at( 2,4)
Step-by-step explanation:
A p e x
Quest Manufacturing is building a product that costs $200 to start to build and $6.40 per unit sold. The company plans to sell each unit for $10.50. The company wrote an inequality to determine the minimum number of units (u) that it needs to sell to break even or make a profit on the product. 10.50u ≥ 200 6.40u What is the minimum amount of units that the company needs to sell to break even or make a profit on the product?
Answer:
49 units
Step-by-step explanation:
10.50u ≥ 200 + 6.40u solve for u....
4.10u ≥ 200 (subtract 6.40u to both sides)
u ≥ 200/4.10 (divide both sides by 4.10)
u ≥ 48.78
Any number of units greater than 48.78, but they can't sell parts of a unit, so 49 is the minimum number of units that need to be sold to make a profit
Water boils at 100 degree, C. This is 400 percent more than my room's temperature. What is my room's temperature?
Your room temperature is 25°C.
Step-by-step explanation:
hope this helps!
Use the laws of logarithms and the values given below to evaluate the logarithmic expression (picture provided)
Answer: option b.
Step-by-step explanation:
To solve the given exercise, you must keep on mind the following law of logaritms:
[tex]m*log(a)=log(a)^m[/tex]
Descompose 8 into its prime factors:
[tex]8=2*2*2=2^3[/tex]
Therefore, you can rewrite the expression given, as following:
[tex]log8=log2^3=3log2[/tex]
You know that [tex]log2=0.3010[/tex]
Then, when you substitute, you obtain:
[tex]3*0.3010[/tex]≈0.9030
Factor out 8 using 2.
log(8) = log(2^3)
Use the product rule [ log(xy) = log(x) + log(y) ] to simplify.
log(2^3) = 3 log(2)
Simplify using the given value for 2.
3(0.3010)
0.9030
Therefore, log(8) ≈ 0.9030 (Option B)
Best of Luck!
If 5 bags of apples weigh 12 1/7 pounds, how many pounds would you expect 1 bag of apples to weigh?
Answer:
2 and 3/7 pounds
Step-by-step explanation:
Convert the mixed number to an improper fraction
12 1/7 becomes 85/7
This represents 5 bags, so divide it by 5 to see what one bag should weigh...
(85/7)/5 becomes (85/7)/(5/1)
which becomes
(85/7)*(1/5) (division is the same as multiplying by the reciprocal)
85/35
17/7 (reduce the fraction by factoring out a 5 from top and bottom)
2 and 3/7 pounds
Example 5 suppose that f(0) = −8 and f '(x) ≤ 9 for all values of x. how large can f(3) possibly be? solution we are given that f is differentiable (and therefore continuous) everywhere. in particular, we can apply the mean value theorem on the interval [0, 3] . there exists a number c such that f(3) − f(0) = f '(c) − 0 so f(3) = f(0) + f '(c) = −8 + f '(c). we are given that f '(x) ≤ 9 for all x, so in particular we know that f '(c) ≤ . multiplying both sides of this inequality by 3, we have 3f '(c) ≤ , so f(3) = −8 + f '(c) ≤ −8 + = . the largest possible value for f(3) is .
[tex]f'(x)[/tex] exists and is bounded for all [tex]x[/tex]. We're told that [tex]f(0)=-8[/tex]. Consider the interval [0, 3]. The mean value theorem says that there is some [tex]c\in(0,3)[/tex] such that
[tex]f'(c)=\dfrac{f(3)-f(0)}{3-0}[/tex]
Since [tex]f'(x)\le9[/tex], we have
[tex]\dfrac{f(3)+8}3\le9\implies f(3)\le19[/tex]
so 19 is the largest possible value.
Given a differentiable function with f(0) = -8 and f'(x) ≤ 9 for all x, we use the Mean Value Theorem to find that f(3), at its largest, can be 1.
Explanation:In this mathematics problem, we are given that f is a differentiable function with f(0) = -8 and its derivative f'(x) ≤ 9 for all x. We aim to calculate the possible maximum value of f(3). To do this, we apply the Mean Value Theorem for the interval [0, 3]. By this theorem, there exists a number 'c' in this interval such that the derivative at that point is equal to the slope of the secant line through the points (0, f(0)) and (3, f(3)). Thus, we get the equation: f(3) - f(0) = f'(c). Rearranging this, we get f(3) = f(0) + f'(c). Substituting the given values, f(3) = -8 + f'(c).
Since we know f'(x) ≤ 9 for all x, this means f'(c) ≤ 9 as well. Replacing this in the equation we get f(3) ≤ -8 + 9 = 1. Hence, the largest possible value for f(3) is 1.
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?2300 is invested in 4 years at 5% per year simple interest work out the total interest
Answer:
460
Step-by-step explanation:
I=P x r x t
P is the principal amount, $2300.00.
r is the interest rate, 5% per year, or in decimal form, 5/100=0.05.
t is the time involved, 4....year(s) time periods.
So, t is 4....year time periods.
To find the simple interest, we multiply 2300 × 0.05 × 4 to get that:
The interest is: $460.00
There are two brands of Corn Flakes, Post and Kellogs. Each brand has the same size box. However, because of each brand’s filling procedure, they have different mean weights. The weights of a box of Post Corn Flakes is approximately normal with μ = 64.1 oz and σ = .5 oz while the weight of a box of Kellogs, which is also normally distributed, has μ = 63.9 oz and σ = .4 oz.
A box is selected from each brand and weighed. What is the probability that the Post box will outweigh the Kellogs box?
Probability of an event is the measure of its chance of occurrence. The probability that the post box will outweigh the Kellogs box is 0.4129 approximately.
How to get the z scores?If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z-score.
If we have
[tex]X \sim N(\mu, \sigma)[/tex]
(X is following normal distribution with mean [tex]\mu[/tex] standard deviation [tex]\sigma[/tex])
then it can be converted to standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
(Know the fact that in continuous distribution, probability of a single point is 0, so we can write
[tex]P(Z \leq z) = P(Z < z) )[/tex]
Also, know that if we look for Z = z in z-tables, the p-value we get is
[tex]P(Z \leq z) = \rm p \: value[/tex]
What is the distribution of random variable which is sum of normal distributions?Suppose that a random variable X is formed by [tex]n[/tex] mutually independent and normally distributed random variables such that:
[tex]X_i = N(\mu_i , \sigma^2_i) ; \: i = 1,2, \cdots, n[/tex]
And if
[tex]X = X_1 + X_2 + \cdots + X_n[/tex]
Then, its distribution is given as:
[tex]X \sim N(\mu_1 + \mu_2 + \cdots + \mu_n, \: \: \sigma^2_1 + \sigma^2_2 + \cdots + \sigma^2_n)[/tex]
If, for the given case, we assume two normally distributed random variables as:
X = variable assuming weights of boxes of Post Corn Flakes
Y = variable assuming weights of boxes of Kellogs
Then, as per the given data, we get:
[tex]X \sim N(\mu = 64.1, \sigma = 0.5)\\Y \sim N(\mu = 63.9, \sigma = 0.4)[/tex]
Then, the probability that the Post box will outweigh the Kellogs box can be written as:
[tex]P(X > Y)[/tex]
Or,
[tex]P(X -Y > 0)[/tex]
We need to know about the properties of X-Y.
Also, since [tex]E(aX) = aE(X), Var(aX) = a^2Var(X)[/tex], thus,
[tex]-Y \sim N(-63.9, 0.4)[/tex]
As both are independent(assuming), thus,
[tex]X - Y \sim N(\mu = 64.1 - 63.9, \sigma = 0.5 + 0.4) = N(0.2, 0.9)[/tex]
Using the standard normal distribution, we get the needed probability as:
[tex]P(X -Y > 0) = 1 - P(X - Y \leq 0) \\P(X -Y > 0)= 1- P(Z = \dfrac{(X-Y) - \mu}{\sigma} \leq \dfrac{0 - 0.2}{0.9})\\P(X -Y > 0) \approx 1 - P(Z \leq -0.22)[/tex]
Using the z-tables, the p-value for Z = -0.22 is 0.4129
Thus, [tex]P(X > Y) = P(X - Y > 0) \approx 0.4129[/tex]
Thus, the probability that the post box will outweigh the Kellogs box is 0.4129 approximately.
Learn more about standard normal distribution here:
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The probability that a randomly selected Post box outweighs a Kellogg's box is approximately 50%.
To find the probability that the Post box will outweigh the Kellogg's box, we need to calculate the difference in weights between the two brands and then determine the probability that this difference is positive.
Let X be the weight of a box of Post Corn Flakes and Y be the weight of a box of Kellogg's Corn Flakes.
We are given that:
- For Post Corn Flakes, X ~ N(μ = 64.1, σ = 0.5)
- For Kellogg's Corn Flakes, Y ~ N(μ = 63.9, σ = 0.4)
We want to find P(X > Y), which is the probability that a randomly selected box of Post Corn Flakes weighs more than a randomly selected box of Kellogg's Corn Flakes.
Now, let Z = X - Y. We are interested in finding P(Z > 0).
The mean and standard deviation of Z can be calculated as follows:
- Mean of Z: μ_Z = μ_X - μ_Y = 64.1 - 63.9 = 0.2 oz
- Standard deviation of Z: σ_Z =[tex]sqrt(σ_X^2 + σ_Y^2) = sqrt(0.5^2 + 0.4^2)= sqrt(0.25 + 0.16)= sqrt(0.41) = 0.64 oz[/tex]
Now, we standardize Z:
Z = (X - Y - μ_Z) / σ_Z
Therefore,
P(Z > 0) = P((X - Y - μ_Z) / σ_Z > 0)
= P((X - Y) > μ_Z)
= P((X - Y) > 0.2)
Now we look up the z-score corresponding to Z = 0.2:
z = (0.2 - μ_Z) / σ_Z
= (0.2 - 0.2) / 0.64
= 0
The probability that Z is greater than 0 is equal to the probability that the standardized Z-score is greater than 0, which is 0.5.
Therefore, the probability that the Post box will outweigh the Kellogg's box is 0.5 or 50%.
Estimate the limit, if it exists.
Answer:
0
Step-by-step explanation:
The given limit is
[tex]\lim_{x \to \infty} \frac{x^2+x-22}{4x^3- 13}[/tex]
Divide both the numerator and the denominator by the highest power of x in the denominator.
[tex]=\lim_{x \to \infty} \frac{\frac{x^2}{x^3}+\frac{x}{x^3}-\frac{22}{x^3}}{\frac{4x^3}{x^3}- \frac{13}{x^3}}[/tex]
This simplifies to;
[tex]=\lim_{x \to \infty} \frac{\frac{1}{x}+\frac{1}{x^2}-\frac{22}{x^3}}{4- \frac{13}{x^3}}[/tex]
As [tex]x\to \infty, \frac{c}{x^n} \to 0[/tex]
[tex]=\lim_{x \to \infty} \frac{0+0-0}{4- 0}=0[/tex]
The limit is zero
A cylinder with a radius of 1 cm and a height of 21 cm has the same volume as a cone with a height of 7 cm. What is the radius of the cone? A) 3 cm B) 5 cm C) 7 cm D) 9 cm
Answer:
A) 3 cmStep-by-step explanation:
The formula of a volume of a cylinder:
[tex]V=\pi r^2H[/tex]
r - radius
H - height
We have r = 1cm and H = 21cm. Substitute:
[tex]V=\pi(1^2)(21)=21\pi\ cm^3[/tex]
The formula of a cone:
[tex]V=\dfrac{1}{3}\pi r^2H[/tex]
r - radius
H - height
We have V = 21π cm³ and H = 7cm. Substitute:
[tex]\dfrac{1}{3}\pi(r^2)(7)=21\pi[/tex] divide both sides by π
[tex]\dfrac{1}{3}(7)(r^2)=21[/tex] divide both sides by 7
[tex]\dfrac{1}{3}r^2=3[/tex] multiply both sides by 3
[tex]r^2=9\to r=\sqrt9\\\\r=3\ cm[/tex]
Answer:
A 3cm
Step-by-step explanation:
9 minutes left to finish this!! I need help!
Joey is 17 years older than his sister Pat. In 6 years, Joey will be 7 more than twice Pat’s age then. How old are Joey and Pat today?
Answer:
p = 4
j = 21
Step-by-step explanation:
Joey = j
Pat = p
j = p + 17
(j+6) = 2*(p + 6) + 7 Simplify this. Remove the brackets.
j + 6 = 2p + 12 + 7 combine like terms
j + 6 = 2p + 19 Subtract 6 from both sides
j +6-6 = 2p +19-6
j = 2p + 13
================
Equation j = 2p + 13 and j = p + 17
2p + 13 = p + 17 Subtract p from both sides
2p-p+13 =p-p + 17
p + 13 = 17 Subtract 13 from both sides
p = 17-13
p = 4
============
j = p + 17
j = 4 + 17
j = 21
Answer:
Joey is 21; Pat is 4
Step-by-step explanation:
The problem statement supports two equations in Joey's age (j) and Pat's age (p):
j - p = 17
(j +6) -2(p +6) = 7
Subtracting the second equation from the first, we have ...
(j -p) -((j +6) -2(p +6)) = (17) -(7)
p +6 = 10 . . . . . simplify
p = 4 . . . . . . . . . subtract 6
J = 17 +4 = 21
Joey is 21; Pat is 4.
HELPPPPP ... Question 18
Answer:
Part a) The volume of the prism Q is two times the volume of the prism P
Part b) The volume of the prism Q is two times the volume of the prism P
Step-by-step explanation:
Part 18) we know that
The volume of a rectangular prism is equal to
[tex]V=Bh[/tex]
where
B is the area of the base
h is the height of the prism
a) Suppose the bases of the prisms have the same area, but the height of prism Q is twice the height of prism P. How do the volumes compare?
Volume of prism Q
[tex]VQ=B(2h)=2(Bh)[/tex]
Volume of prism P
[tex]VP=Bh[/tex]
Compare
[tex]VQ=2VP[/tex]
so
The volume of the prism Q is two times the volume of the prism P
b) Suppose the area of the base of prism Q is twice the area of the base of prism P. How do the volumes compare?
Volume of prism Q
[tex]VQ=(2B)h=2(Bh)[/tex]
Volume of prism P
[tex]VP=Bh[/tex]
Compare
[tex]VQ=2VP[/tex]
The volume of the prism Q is two times the volume of the prism P
I need help on #20 please
Answer:
P = 10x³ + 4x² + 8x + 6
Step-by-step explanation:
The perimeter of a rectangle is twice the sum of length and width.
P = 2(L+W) = 2((x³ +2x² -6x +12) +(4x³ +10x -9))
= 2(5x³ +2x² +4x +3) . . . . collect terms inside parentheses
P = 10x³ +4x² +8x +6
Write the augmented matrix for each system of equations.
9x-4y-5z=9
7x+4y-4z=-1
6x-6y+z=5
Answer:
a. [tex]\left[\begin{array}{cccc}9&-4&-5&|9\\7&4&-4&|-1\\6&-6&1&|-5\end{array}\right][/tex]
Step-by-step explanation:
The given system of equation is
[tex]9x-4y-5z=9[/tex]
[tex]7x+4y-4z=-1[/tex]
[tex]6x-6y+z=-5[/tex]
The coefficient matrix is :
[tex]\left[\begin{array}{ccc}9&-4&-5\\7&4&-4\\6&-6&1\end{array}\right][/tex]
The constant matrix is
[tex]\left[\begin{array}{c}9\\-1\\-5\end{array}\right][/tex]
The augmented matrix is obtained by combining the coefficient matrix and the constant matrix.
[tex]\left[\begin{array}{cccc}9&-4&-5&|9\\7&4&-4&|-1\\6&-6&1&|-5\end{array}\right][/tex]
The correct choice is A
Melinda spent 4 Hours Reviewing for Her Midterm exams. She spent 1/4 Of The Time studying for social studies.How Many Hours Did she spend on social studies
Answer:
1 hour
Step-by-step explanation:
1/4 of 4 is 1
Answer:one hour
Step-by-step explanation:
Solve the equation. Round to the nearest hundredth. Show work.
[tex]4^{-5x-7} = 6^{2x-1}[/tex]
Answer:
[tex]x=-0.75[/tex]
Step-by-step explanation:
The given equation is
[tex]4^{-5x-7}=6^{2x-1}[/tex]
We take logarithm of both sides to base 10.
[tex]\log(4^{-5x-7})=\log(6^{2x-1})[/tex]
[tex](-5x-7)\log(4)=(2x-1)\log(6)[/tex]
We expand the brackets to get;
[tex]-5x\log(4)-7\log(4)=2x\log(6)-\log(6)[/tex]
Group similar terms;
[tex]-7\log(4)+\log(6)=2x\log(6)+5x\log(4)[/tex]
[tex]-7\log(4)+\log(6)=(2\log(6)+5\log(4))x[/tex]
[tex]\frac{-7\log(4)+\log(6)}{(2\log(6)+5\log(4))}=x[/tex]
[tex]x=-0.752478[/tex]
To the nearest hundredth.
[tex]x=-0.75[/tex]
Ms. Thomas buys 3 pounds of sliced ham to make sandwiches. It takes 1 3 lb of ham for each sandwich. How many ham sandwiches can Ms. Thomas make with the ham she's purchased? A) 3 sandwiches B) 6 sandwiches C) 9 sandwiches D) 12 sandwiches
Answer:
Option C [tex]9\ sandwiches[/tex]
Step-by-step explanation:
we know that
using proportion
[tex]\frac{1}{(1/3)}\frac{sandwich}{pounds}=\frac{x}{3}\frac{sandwiches}{pounds}\\ \\x=3*3\\ \\x=9\ sandwiches[/tex]
Answer:
9
Step-by-step explanation:
I got the answer from USATestprep
The length of a rectangular field is 7 m less than 4 times the width. The perimeter is 136m ?. Find the width and the length of the rectangle
➷ The perimeter is the total of all the lengths / widths
The lengths can be represented by 4x - 7
The width can be represented by x
2 times the length + 2 times the width would equal the perimeter
2(x) + 2(4x - 7) = 136
Simplify:
2x + 8x - 14 = 136
10x - 14 = 136
Add 14 to both sides:
10x = 150
Divide both sides by 10:
x = 15
The width is equal to 15m
The length is 4(15) - 7 = 53m
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
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A picture measuring 4" high by 6" wide is to be enlarged so that the width is now 9”. How tall will the picture be?
The original width was 6 inches, the new width is 9 inches.
Divide the new width by the original width to find the scale factor:
9/6 = 1.5
Now multiply the original height by the scale factor to find the new height:
4 x 1.5 = 6 inches.
An experiment consists of rolling a die, flipping a coin, and spinning a spinner divided into 4 equal regions. The number of elements in the sample space of this experiment is
12
3
6
48
Answer:
48
Step-by-step explanation:
There are 3 events that are taking place.
Rolling a die which has 6 possible outcomes.
Flipping a coin which has 2 possible outcomes.
Spinning a spinner which has 4 possible outcomes.
Since the outcome of each event is independent of the other, the total possible outcomes will be equal to the product of outcomes of each event.
i.e.
Total outcomes = 6 x 2 x 4 = 48
The sample space of the experiment contains all the possible outcomes. so the number of elements in the sample space of this experiment will be 48
Answer:
The correct answer option is 48.
Step-by-step explanation:
Here in this experiment, three events are taking place that include rolling a die, flipping a coin and spinning a spinner.
The possible outcomes of each of these events are:
Rolling a die - 6
Flipping a coin - 2
Spinning a spinner - 4
Therefore, we can find the number of elements in the sample space of this environment by multiplying their possible outcomes.
Number of elements = 6 × 2 × 4 = 48
2x+3x+4x=180
9x=180
x=20
how did they get 20, am i missing something
➷ We'll work from here:
9x = 180
To isolate x, you would need to divide both sides by 9
x = 180/9
Solve:
x = 20
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer: ❤️Hello!❤️ x = 20
Step-by-step explanation: Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
2*x+3*x+4*x-(180)=0
Step 1 :
Pulling out like terms :
1.1 Pull out like factors :
9x - 180 = 9 • (x - 20)
Step 2 :
Equations which are never true :
2.1 Solve : 9 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
2.2 Solve : x-20 = 0
Add 20 to both sides of the equation :
x = 20
Which line contains the point (2, 1)?
a)4x-y=7
b)2x+5y=4
c)7x-y=15
d)x+5y=21
If Seven cookies are shared equally by four people how many cookies will each person get
Final answer:
Each person will get 1 cookie and there will be 3 cookies leftover.
Explanation:
In this scenario, we have 7 cookies that are being shared equally among 4 people. To find out how many cookies each person will get, we divide the total number of cookies by the number of people.
So, 7 cookies divided by 4 people = 1.75 cookies per person.
Since we can't divide a cookie into fractions, each person will get 1 cookie and there will be 3 cookies leftover.
The trail is 2982 miles long.It begins in city A and ends in city B.Manfred has hiked 2/7 of the trail before.How many miles has he hikes?
Answer:
852
Step-by-step explanation:
PLEASE HELP 15 POINTS Sphere A is similar to sphere B.
If the radius of sphere A is 3 times the radius of sphere B, then the volume of sphere A is____ times the volume of sphere B.
3
6
9
27
81
Answer:
27
Step-by-step explanation:
We figure out the scale factor first, which is the number of times one radius is of the other. We call the scale factor, k.
To get how many times larger is the volume of similar spheres, we will need to cube the scale factor.
Since it is given that radius of Sphere A is 3 times that of Sphere B, we can say that the scale factor (k) = 3. Hence, the volume of Sphere A would be k^3 times the volume of Sphere B.
So, [tex]k^3\\=(3)^3\\=27[/tex]
Hence, the volume of sphere A is 27 times the volume of sphere B.
Plz help me..
WILL GIVE BRAINLIEST
Answer:
B, 3x - 5
Step-by-step explanation:
Factor by grouping to get (3x - 5)(2x + 3).
Factor 6x2−x−15
6x2−x−15
=(3x−5)(2x+3)
Answer:
(3x−5)(2x+3)
The volume of a rectangle or prism is 72 m? the prism is 2 cm wide and the 4 cm high what is the length of the prism
Answer:
9 cmStep-by-step explanation:
The formula of a volume of a rectangle prism:
[tex]V=lwh[/tex]
l - length
w - width
h - height
We have V = 72 cm³, w = 2 cm and h = 4 cm. Substitute:
[tex](2)(4)l=72[/tex]
[tex]8l=72[/tex] divide both sides by 8
[tex]l=9\ cm[/tex]
Solve for x in the given interval.
sec x= -2√3/3, for π/2 ≤x≤π
Answer:
b. [tex]x=\frac{5\pi}{6}[/tex]
Step-by-step explanation:
The given function is
[tex]\sec x=-\frac{2\sqrt{3} }{3},\:\:for\:\:\frac{\pi}{2}\le x \le \pi[/tex]
Recall that the reciprocal of the cosine ratio is the secant ratio.
This implies that;
[tex]\frac{1}{\cos x}=-\frac{2\sqrt{3} }{3}[/tex]
[tex]\Rightarrow \cos x=-\frac{3}{2\sqrt{3} }[/tex]
[tex]\Rightarrow \cos x=-\frac{\sqrt{3}}{2}[/tex]
We take the inverse cosine of both sides to obtain;
[tex]x=\cos^{-1}(-\frac{\sqrt{3}}{2})[/tex]
[tex]x=\frac{5\pi}{6}[/tex]
write an explicit formula formula for the sequence 2, 8, 14, 20, 26,...
a. a_n= 2n-2
b. a_n= 2n+2
c. a_n=4n+2
d. a_n = 6n-4
Answer:
d. a_n = 6n - 4.
Step-by-step explanation:
The common difference (d) is 8-2 = 14-8 = 20-14 = 26-20 = 6.
This is an Arithmetic Sequence with the first term (a1) is 2.
The general form of the explicit formula is a_n = a1 + d(n - 1) so this sequence has the formula:
a_n = 2 + 6(n - 1)
a_n = 2 + 6n - 6
a_n = 6n - 4.
The sequence is an illustration of an arithmetic sequence.
The explicit formula is: (d) [tex]a_n = 6n - 4[/tex]
We have:
[tex]a_1 = 2[/tex] -- the first term
Next, we calculate the common difference (d)
[tex]d = a_2 - a_1[/tex]
So, we have:
[tex]d = 8 -2[/tex]
[tex]d = 6[/tex]
The explicit formula is calculated using:
[tex]a_n = a_1 + (n - 1)d[/tex]
So, we have:
[tex]a_n =2 + (n - 1) \times 6[/tex]
Open bracket
[tex]a_n = 2 + 6n - 6[/tex]
Collect like terms
[tex]a_n = 6n - 6 + 2[/tex]
[tex]a_n = 6n - 4[/tex]
Hence, the explicit formula is: (d) [tex]a_n = 6n - 4[/tex]
Read more about arithmetic sequence at:
https://brainly.com/question/18109692
Two numbers total 14 ,and their differences is 12 .find two numbers
Answer:
12+2 =14
Step-by-step explanation:
Answer: 1 and 13.
Step-by-step explanation: Because of the total, we know that the first number has to be less than 5, but greater than 0. to start in the median, let's use 3.
3+12 = 15.
That won't work, so let's try 2.
2+12 = 14.
There's the answer.
Solve using proper methods. Show work. (25 POINTS)
Initially a tank contains 10,000 liters of liquid at the time t = 0 minutes a tap is opened, a liquid then follows out of the tank. The volume of the liquid V liters, which remains in the tank after t minutes is given by V = 10,000(0.933)^t
a) Find the value of V after 5 minutes.
b) Find how long, to the nearest second, it takes for half of the initial amount of liquid to follow out of the tank.
c) The tank is regarded as effectively empty when 95% of the liquid has flowed out. Show that it takes almost three quarters of an hour for this to happen.
d) (i) Find the value of 10,000 - V when t = 0.001 minutes
(ii) Hence or otherwise, estimate the initial flow rate of the liquid. Give your answer in liters per minute, correct to two significant figures.
Answer:
a) 7069.82 Liters
b) 600 seconds
c) Shown below
d) (i) 0.6935 liters (ii) Since 0.6935 liters in 0.001 minute, so 693.5 liters per minute is as estimate (in liters per minute)
Step-by-step explanation:
a)
We simply put 5 into t of the equation and get the value of V. So:
[tex]V=10,000(0.933)^t\\V=10,000(0.933)^5\\V=7069.82[/tex]
So after 5 minutes the amount remaining is 7069.82 Liters
b)
half of the initial amount is half of 10,000 which is 5000. So we substitute 5000 into V and solve for t using logarithms.
Note: [tex]ln(a^b)=blna[/tex]
Thus, we have:
[tex]V=10,000(0.933)^t\\5000=10,000(0.933)^t\\0.5=(0.933)^t\\ln(0.5)=ln((0.933)^t)\\ln(0.5)=tln(0.933)\\t=\frac{ln(0.5)}{ln(0.933)}\\t=9.99[/tex]
Thus, t = 9.9949 minutes.
To get answer in seconds, we multiply by 60. Thus 9.9949*60= 600 seconds
c)
95% empty means 5% remaining. 5% of 10,000 = 0.05 * 10,000 = 500. We plug in 500 into V and solve for t as the previous step. Shown below:
[tex]V=10,000(0.933)^t\\500=10,000(0.933)^t\\0.05=0.933^t\\ln(0.05)=ln(0.933^t)\\ln(0.05)=tln(0.933)\\t=\frac{ln(0.05)}{ln(0.933)}\\t=43.1972[/tex]
So it takes around 43.1972 minutes to empty 95%. Since three-quarters of an hour is [tex](\frac{3}{4})(60)=45[/tex] minutes, we have shown that the time it takes (43.1972 minutes) is very close to three-quarters of an hour.
d)
We plug in 0.001 into t and find V. Then we subtract that value from 10,000. This is just finding how much water has been removed in 0.001 minutes. Let's do this:
[tex]V=10,000(0.933)^t\\V=10,000(0.933)^{0.001}\\V=9999.3065\\Now\\10,000 - 9999.3065 = 0.6935[/tex]
So, 0.6935 liters