now, let's recall that a geometric sequence is one that uses some "r" common ratio to get the next term, by simply multiplying the current term by it.
[tex]\bf \begin{array}{|cl|ll} \cline{1-2} term&value\\ \cline{1-2} a_1&\underline{\qquad }\\&\\ a_2&6\\&\\ a_3&\underline{6(r)}\\&\\ a_4&6(r)(r)\\&\\ &54\\ \cline{1-2} \end{array}\qquad \implies \begin{array}{llll} 54=6r^2\implies \cfrac{54}{6}=r^2\implies 9=r^2\\\\ \sqrt{9}=r\implies 3=r \end{array} \\\\[-0.35em] ~\dotfill\\\\ a_1=6\div 3\implies a_1=2~\hfill a_3=6(3)\implies a_3=18[/tex]
and of course, the next term or a₅ = 54(3) --> a₅ = 162.
The first five terms are 2, 6, 18, 54, 162
Given,
The second term is 6.
The fourth term is 54.
We need to find the first five terms of a geometric sequence.
What is a geometric sequence?A sequence where each term after the first is found by multiplying the previous one with a common ratio.
The sequence is given by:
a, ar, ar^2, ar^3, ar^4, ar^5,...
The nth term is given by:
a_n = ar^(n-1)
We have,
Second term = 6
a_2 = ar^(2-1)
6 = ar^1
6 = ar
a = 6/r _____(1)
Fourth term = 54
a_4 = ar^(4-1)
54 = ar^3
a = 54/r^3 ______(2)
From (1) and (2)
6/r = 54/r^3
r^3/r = 54/6
r^2 = 9
r = 3
Putting in (1)
a = 6/r
a = 6/3
a = 2
We have,
a = 2 and r = 3
Find the first five terms of a geometric sequence.
It is given by:
a, ar, ar^2, ar^3, ar^4
2, 2x3, 2x9, 2x27, 2x81
2, 6, 18, 54, 162
The first five terms are 2, 6, 18, 54, 162
Learn more about geometric sequence here:
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If you bought a stock last year for a price of $92, and it has gone down 4.4% since then, how much is the stock worth now, to the nearest cent?
Answer:
$87.95
Step-by-step explanation:
1. multiply the stock (92) time 4.4% (or 0.044)
92*0.044 = 4.048
2. subtract 4.048 from 92
92-4.048 = 87.952
3. Round to the nearest cent (2 in the thousandth place means the 5 stays the same)
87.95
simplify the sum or difference -6√10+5√90
A. 9√10 (CORRECT ANSWER)
B. -9√10
C -39√10
D - 10
Answer:
A. [tex]9\sqrt{10}[/tex]
Step-by-step explanation:
The given expression is [tex]-6\sqrt{10}+5\sqrt{90}[/tex]
Remove the perfect square from the second radical.
[tex]=-6\sqrt{10}+5\sqrt{9\times10}[/tex]
[tex]=-6\sqrt{10}+5\sqrt{9} \times \sqrt{10}[/tex]
This implies
[tex]=-6\sqrt{10}+15\sqrt{10}[/tex]
[tex]=(-6+15)\sqrt{10}[/tex]
[tex]=9\sqrt{10}[/tex]
The correct choice is A
Find a reasonable estimate of the limit
Answer:
The answer is (c) ⇒ the value is 6.6667
Step-by-step explanation:
∵ [tex]\lim_{x\to \2} _2\frac{x^{5}-32}{x^{3}-8}[/tex]
∵ 32 = 2^5 , 8 = 2³
∴ [tex]\lim_{x \to \2}_2 \frac{x^{5}-2^{5}}{x^{3}-2^{3} }[/tex]
* by using the rule:
[tex]\lim_{x\to\a}_a \frac{x^{n}-a^{n}}{x^{m}-a^{m}}=\frac{n}{m}(a)^{n-m}[/tex]
∴ [tex]\frac{5}{3}(2)^{5-3}=\frac{5}{3}(2)^{2}=\frac{20}{3}[/tex]
∴ 20/3 = 6.6667 ⇒ answer (c)
Answer:
The correct option is c.
Step-by-step explanation:
The given limit is
[tex]lim_{x\rightarrow 2}\frac{x^5-32}{x^3-8}[/tex]
It is can be written as
[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}[/tex]
According to the property of limits,
[tex]lim_{x\rightarrow a}\frac{x^n-a^n}{x^m-a^m}=\frac{n}{m}(a)^{n-m}[/tex]
In the given limit, a=2, n=5 and m=3. Using the above property of limits we get
[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=\frac{5}{3}(2)^{5-3}[/tex]
[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=\frac{5}{3}(2)^{2}[/tex]
[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=\frac{5}{3}(4)[/tex]
[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=\frac{20}{3}[/tex]
[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=6.6667[/tex]
Therefore the correct option is c.
What is 2|u| – |v|, if u = –9 and v = –2?
A. –18
B. 16
C. –20
D. 20
Answer:
B
Step-by-step explanation:
Note that the absolute value always returns a positive value, that is
| - 2 | = | 2 | = 2
given
2| u | - | v | with u = - 9 and v = - 2, then
2 | - 9 | - | - 2 |
= 2 × 9 - 2 = 18 - 2 = 16 → B
HELP ASAP PLEASE
A customer went to a garden shop and bought some potting soil for $17.50 and 4 shrubs. The total bill was $53.50. Write and solve an equation to find the price of each shrub.
4p + $17.50 = $53.50; p = $11.25
4(p + $17.50) = $53.50; p = $4.00
4p + $17.50 = $53.50; p = $9.00
4p + 17.5 p = $53.50; p = $2.49
You would need to multiply the quantity of shrubs bought by the price of each one, so 4p and add that to the price of the soil to get the total cost
The equation becomes 4p + 17.50 = 53.50
Now solve for p:
4p +17.50 = 53.50
Subtract 17.50 from both sides:
4p = 36
Divide both sides by 4:
p = 36/4
p = 9
The answer would be: 4p + $17.50 = $53.50; p = $9.00
I need help with this question.
For the right triangle shown match the equivalent expressions.
Answer:
The solution in the attached figure
[tex]sin(A)=\frac{12}{13}[/tex]
[tex]sin(B)=\frac{5}{13}[/tex]
[tex]cos(A)=\frac{5}{13}[/tex]
[tex]cos(B)=\frac{12}{13}[/tex]
[tex]sin(A)=cos(B)[/tex]
[tex]sin(B)=cos(A)[/tex]
Step-by-step explanation:
we know that
In the right triangle ABC
sin(A)=cos(B) and cos(A)=sin(B)
because
[tex]A+B=90\°[/tex] -------> by complementary angles
step 1
Find sin(A)
The function sine of angle A is equal to divide the opposite side angle A by the hypotenuse
[tex]sin(A)=\frac{BC}{AB}[/tex]
substitute the values
[tex]sin(A)=\frac{12}{13}[/tex]
step 2
Find sin(B)
The function sine of angle B is equal to divide the opposite side angle B by the hypotenuse
[tex]sin(B)=\frac{AC}{AB}[/tex]
substitute the values
[tex]sin(B)=\frac{5}{13}[/tex]
step 3
Find cos(A)
The function cosine of angle A is equal to divide the adjacent side angle A by the hypotenuse
[tex]cos(A)=\frac{AC}{AB}[/tex]
substitute the values
[tex]cos(A)=\frac{5}{13}[/tex]
[tex]cos(A)=sin(B)[/tex]
step 4
Find cos(B)
The function cosine of angle B is equal to divide the adjacent side angle B by the hypotenuse
[tex]cos(B)=\frac{BC}{AB}[/tex]
substitute the values
[tex]cos(B)=\frac{12}{13}[/tex]
[tex]cos(B)=sin(A)[/tex]
PLEASE HELP! I WILL MARK AS BRAINLIEST!! I REALLY NEED SOMEONES HELP!
Error analysis: describe the error in the way the difference of the two polynormials is set up and/or solved. Please be specific.
(6x^2 - 5x) - (2x^2 + 3x - 2)
= 6x^2 - 5x - 2x^2 + 3x - 2
= 4x^2 - 2x - 2
Solve the problem in the question above correctly. Please show your work!
Since this is subtraction, everything must be turned negative in the second polynomial.
(6x^2 - 5x) - (2x^2 + 3x - 2)
6x^2 - 5x - 2x^2 - 3x - (-2)
6x^2 - 5x - 2x^2 - 3x + 2
Now, reorder the terms to make it easier.
6x^2 - 2x^2 - 5x - 3x + 2
Now, just combine like terms.
4x^2 - 5x - 3x + 2
4x^2 - 8x + 2
There’s the answer!
Please consider marking this answer as Brainliest to help me advance.
50 POINTS PLEASE HELP ME!!!!!!!! HURRY!!!!
17. Evaluate
6!
8P5
12C4
Step-by-step explanation:
[tex]n!=\underbrace{1\cdot2\cdot3\cdot...\cdot n}\\\\6!=1\cdot2\cdot3\cdot4\cdot5\cdot6=720\\=======================\\_nP_r=\dfrac{n!}{(n-r)!}\\\\_8P_5=\dfrac{8!}{(8-5)!}=\dfrac{8!}{3!}=\dfrac{3!\cdot4\cdot5\cdot6\cdot7\cdot8}{3!}=4\cdot5\cdot6\cdot7\cdot8=6,720\\=======================\\_nC_r=\dfrac{n!}{r!(n-r)!}\\\\_{12}C_4=\dfrac{12!}{4!(12-4)!}=\dfrac{4!\cdot5\cdot6\cdot...\cdot12}{4!\cdot8!}=\dfrac{5\cdot6\cdot7\cdot8\cdot9\cdot10\cdot11\cdot12}{1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8}=495[/tex]
50 POINTS PLEASE HELP ME!!!!!!!! HURRY!!!!
Evaluate
6!
8P5
12C4
what are we supposed to evaluate, here? i dunno what your asking us to do
A game for $40 and the sales tax is two dollars what percent of the game price are you paying sales tax
Answer: 5%
Step-by-step explanation: In order to calculate the sales tax rate you divide the amount of the sales tax by the purchase price.
$2/40 = .05 = 5%
The interest rate is 5%.
Percy paid $24.10 for a basketball the price of the basketball was $22.99 what was the sales tax rate
To find the sales tax rate, you need to find what percentage of the base price the difference in cost is.
First, subtract 22.99 from 24.10:
24.1-22.99=1.11
Now, divide 1.11 by 22.99:
1.11/22.99=0.0483
Multiply 0.0483 by 100 to convert the decimal to a percentage:
0.0483*100=4.83
The sales tax rate was 4.83%.
Hope this helps!!
Which of the following equations is equivalent to 1/2x - 2/3y = 5?
x - 2y = 30
4x - 3y = 30
3x - 4y = 30
Answer:
[tex]\large\boxed{3x-4y=30}[/tex]
Step-by-step explanation:
[tex]\dfrac{1}{2}x-\dfrac{2}{3}y=5\qquad\text{multiply both sides by LCM(2, 3) = 6}\\\\6\!\!\!\!\diagup^3\cdot\dfrac{1}{2\!\!\!\!\diagup_1}x-6\!\!\!\!\diagup^2\cdot\dfrac{2}{3\!\!\!\!\diagup_1}y=6\cdot5\\\\(3)(x)-(2)(2y)=30\\\\3x-4y=30[/tex]
Find the are of a triangle (picture provided)
Answer:
B
Step-by-step explanation:
Use the Heron's formula for the area of the triangle:
[tex]A=\sqrt{p(p-a)(p-b)(p-c)},[/tex]
where a, b, c are lengths of triangle's sides and [tex]p=\dfrac{a+b+c}{2}.[/tex]
Since [tex]a=11.5,\ b=13.7,\ c=12.2,[/tex] then
[tex]p=\dfrac{11.5+13.7+12.2}{2}=18.7.[/tex]
Hence,
[tex]A=\sqrt{18.7(18.7-11.5)(18.7-13.7)(18.7-12.2)}=\sqrt{18.7\cdot 7.2\cdot 5\cdot 6.5}=\\ \\=\sqrt{11\cdot 1.7\cdot 9\cdot 4\cdot 0.2\cdot 5\cdot 5\cdot 1.3}=30\sqrt{11\cdot 1.7\cdot 0.2\cdot 1.3}=30\sqrt{4.862}\approx 66.1\ un^2.[/tex]
Answer:
Choice b is correct.
Step-by-step explanation:
We have given the sides of triangle.
a = 11.5, b = 13.7 and c = 12.2
We have to find the area of the triangle.
The formula to find the area of the triangle when three sides are given is:
A = √p(p-a)(p-b)(p-c)
where p = (a+b+c) / 2
p = (11.5+13.5+12.2)/2
p = 18.7
A = √18.7(18.7-11.5)(18.7-13,7)(18.5-12.2)
A = 30√4.862 units²
A≈ 66.1 units²
Which of the following describes a situation in which a soccer player ends up 0 m from his starting point? The player runs 7 meters forward and then runs 7 meters in the opposite direction The player runs 3 meters forward and then runs 7 meters in the opposite direction The player runs 0 meters forward and then runs 7 meters in the opposite direction The player runs 7 meters forward and then runs 0 meters in the opposite direction
Answer:
Seven forward, seven opposite. It's like saying a footballer runs from 0 yd line to 50 yd line then turns around and runs 50 yards again, ends up right back at the 0.
Answer:
a
Step-by-step explanation:
got it right on test
If I have 2 quarters 12 dimes and 23 pennies how many more pennies will I need in order to have a toldal of $2.00
Answer:
You will need 7 more pennies.
Step-by-step explanation:
Answer:
7 more pennies.
Step-by-step explanation:
Quarters are .25 each and you have 2 so that is .50.
Dimes are .10 each and you have 12 so that is 1.20
Pennies are .01 each and you have 23 so that is .23.
Added together and you get 1.93. So all you need is 7 pennies to get 2 dollars.
Kat is painting the edge of a triangular stage prop with reflective orange paint. The lengths of the edges of the triangle are (3x – 4) feet, (x2 – 1) feet, and (2x2 – 15) feet. What is the perimeter of the triangle if x = 4?
Answer:
40 feet
Step-by-step explanation:
The perimeter of a triangle is the distance around the triangle. It can be found by adding all the sides together. First, find the amount each side is by substituting x = 4 and simplifying.
3x - 4 = 3(4) - 4 = 12 - 4 = 8
x² -1 = (4)² - 1 = 16 - 1 = 15
2x² - 15 = 2(4)² - 15 = 32 - 15 = 17
Add the sides together, 8 + 15 + 17 = 40 feet
An equation of a line through (0, 0) which is perpendicular to the line y=-4x + 3 has slope:
And y-intercept at:
perpendicular slopes are those that are flipped and opposite signs to the original slope
Please help a girl out (:
According to the rational root theorem, which answer is not a possible rational root of 4x^3+3x^2-2x+12=0?
A.) -4
B.) -1/3
C.) 1/2
D.) 3
Answer:
B.) -1/3
Step-by-step explanation:
According to the rational root theorem, rational roots will be of the form ...
±(divisor of the constant)/(divisor of the leading coefficient)
= ±(one of {1, 2, 3, 4, 6, 12})/(one of {1, 2, 4})
You will note that 3 is not among the possible denominators, hence -1/3 is not a possible rational root.
the answer is b cause its is correct
Solve for x.
x - 8 = -20
Answer:
x = -12
Step-by-step explanation:
x - 8 = -20
+8 +8
x = -12 Multiplying Polynomials Investigation:Arnold has a 6ftx6ft piece of cardboard to make a open box by cutting equal size squares from each corner,folding up the resulting flaps,and taping at the corners.Your task is to label dimensions on a sketch with the same size variable cut from each corner.
- How does each variable expression relate to length,width,and height of the box when folded?
-Based upon the variables you used,write a product for the volume?
-expand the product to write a volume function?
- what domain makes sense for the volume?
guess and check values to find the size cut that produces a maximum volume
*lgth ( )width ( ) hght ( ) volume ( )
you have to have 5 guesses
i don't think so.....
sorry
This answer explains how to determine the volume of an open box created by cutting squares from each corner of a piece of cardboard, discussing the relations between variables, volume calculation, domain restrictions, and a guess-and-check method for maximizing volume.
Variables: In the open box scenario, let's assume the size of the square cut from each corner is 'x'.
Relation to Dimensions: After cutting and folding, the length of the box would be (6ft - 2x), the width would be (6ft - 2x), and the height would be 'x'.
Product for Volume: The volume formula is length x width x height. Substituting the expressions, we get V = x(6 - 2x)(6 - 2x).
Domain: The domain for the volume function would be 0 < x < 3 (as the size of the cut cannot exceed half of the side length).
Guess and Check: To find the maximum volume, you can test values within the domain like x = 1, 1.5, 2, 2.5, and 3 to determine the optimal cut size and corresponding dimensions and volume.
Determine any asymptotes (Horizontal, vertical or oblique). Find holes, intercepts and state it's domain.
[tex]g(x) = \frac{(2x+1)(x-5)}{(x-5)(x+4)^{2} }[/tex]
Answer:
1.
Horizontal Asymptote is y = 0
2.
Vertical Asymptote is x = -4
3.
No Slant Asymptote
4.
Hole at (5, 0.14)
5.
x-intercepts:
x-intercept [tex](-\frac{1}{2},0)[/tex]
y-intercepts:
y-intercept [tex](0,\frac{1}{16})[/tex]
6.
Domain is [tex]{x|x\neq -4,5}[/tex]
Step-by-step explanation:
1. Horizontal Asymptotes
* If the degree of the numerator is less than the degree of the denominator (this is our case since multiplying will give the numerator a degree of 2 and denominator a degree of 3), then y = 0 is the only horizontal asymptote
Horizontal Asymptote is y = 0
2. Vertical Asymptotes
* To get VA (vertical asymptote), we set the denominator equal to zero.
Before doing this, we see that we can cancel out (x-5) from both numerator and denominator so the denominator becomes (x+4)^2. Now we find VA:
[tex](x+4)^2=0\\x+4=0\\x=-4[/tex]
Vertical Asymptote is x = -4
3. Oblique asymptotes
* If the degree of numerator is less than the degree of the denominator (this is our case as explained above), then there is no slant asymptote.
No Slant Asymptote
4. Holes
There is hole in a rational function if there is the same factor in both numerator and denominator (before simplifying, only after factoring). Set that equal to 0 and solve. Then, cross out the common factor and put the x-value into the function and get the y-value of the hole.
We can see that there is a factor of (x-5) in both the numerator and denominator. We set it equal to 0 and solve for x:
[tex]x-5=0\\x=5[/tex]
Putting x = 5, we get:
Y value of hole = [tex]g(x)=\frac{2x+1}{(x+4)^2}\\g(5)=\frac{2(5)+1}{(5+4)^2}\\g(5)=0.14[/tex]
Hole at (5, 0.14)
5. Intercepts
To get x-intercepts, we set y = 0 (g(x) = 0) and for y-intercepts we set x = 0.
x-intercepts:
[tex]0=\frac{2x+1}{(x+4)^2}\\2x+1=0\\2x=-1\\x=-\frac{1}{2}[/tex]
x-intercept [tex](-\frac{1}{2},0)[/tex]
y-intercepts:
[tex]y=\frac{2x+1}{(x+4)^2}\\y=\frac{2(0)+1}{(0+4)^2}\\y=\frac{1}{16}[/tex]
y-intercept [tex](0,\frac{1}{16})[/tex]
6. Domain
This is the set of allowed x-values of the function. We simply disregard any value that would make the denominator equal to 0.
So we have:
x - 5 = 0, x = 5
and
(x+4)^2 = 0, x = -4
Domain is the set of all real numbers x EXCEPT x = -4 and x = 5
Domain is [tex]{x|x\neq -4,5}[/tex]
Steven bought 8 shirts. The least expensive was $8.95, and the most expensive was $15.79, which is the most reasonable estimate of the total cost of the shirts before tax was added?
A- between $36.00 and $64.00
B- between $64.00 and $76.00
C- between $76.00 and $120.00
D- between $120.00 and $200.00
The answer is C because you multiply 8×8.95 to get your lowest range, and 8×15.79 to get your highest range.
If both coordinates of a point are negative,in which quadrantis the point located?
Determine the graph of the polar equation r =6/2-2cos theta.
Answer:
Choice D is correct
Step-by-step explanation:
The first step is to write the polar equation of the conic section in standard form by dividing both the numerator and the denominator by 2;
[tex]r=\frac{3}{1-cos(theta)}[/tex]
The eccentricity of this conic section is thus 1, the coefficient of cos θ. Thus, this conic section is a parabola since its eccentricity is 1.
The value of the directrix is determined as;
d = k/e = 3/1 = 3
The denominator of the polar equation of this conic section contains (-cos θ) which implies that this parabola opens towards the right and thus the equation of its directrix is;
x = -3
Thus, the polar equation represents a parabola that opens towards the right with a directrix located at x = -3. Choice D fits this criteria
Answer:
D
Step-by-step explanation:
edge
Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .005 significance level.
The null and alternative hypothesis would be:
H0:pM=pFH0:pM=pF
H1:pM
H0:μM=μFH0:μM=μF
H1:μM>μFH1:μM>μF
H0:pM=pFH0:pM=pF
H1:pM>pFH1:pM>pF
H0:μM=μFH0:μM=μF
H1:μM<μFH1:μM<μF
H0:μM=μFH0:μM=μF
H1:μM≠μFH1:μM≠μF
H0:pM=pFH0:pM=pF
H1:pM≠pFH1:pM≠pF
The test is:
two-tailed
right-tailed
left-tailed
Based on a sample of 40 men, 25% owned cats
Based on a sample of 40 women, 35% owned cats
The test statistic is: (to 2 decimals)
The p-value is: (to 2 decimals)
Based on this we:
Fail to reject the null hypothesis
Reject the null hypothesis
Answer:
The null and alternate hypothesis would be
H0: pm = pf
H1: pm < pf
Test is left tailed
The test statistic: z = -0.98
The p-value: 0.1365
We fail to reject the null hypothesis
Conclusion: There is not enough evidence to support the claim that the proportion of men who own cats is less than the proportion of women who own cats
Step-by-step explanation:
The null and alternate hypothesis would be
H0: pm = pf
Ha: pm < pf
because they say that the test claim is the proportion of men is smaller less than the proportion of women. The null hypothesis always get the statement of equality (the equals sign). In this case, the alternate hypothesis is the claim.
The test is left tailed because the alternate hypothesis has a < sign. It's strictly less than a value, so it's one tailed, and the < or > sign points to the area of rejection, so in this case, it's pointing left
The test statistic is calculation is attached as a photo
The p-value is found by looking it up on the chart using z = -0.98
Since 0.1365 > 0.005, we fail to reject the null hypothesis
Because we fail to reject the null, there is not enough evidence to support the claim
We perform a hypothesis test for the difference between two proportions. The null hypothesis states the proportion of men owning cats equals the one of women, while the alternative hypothesis says it's smaller. We do a one-tailed test, and if the p-value<=0.005, we reject the null hypothesis.
Explanation:In order to test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at a .005 significance level, we need to perform a hypothesis test for the difference between two proportions.
The null hypothesis (H0) is that the proportion of men who own cats (pM) equals the proportion of women who own cats (pF), while the alternative hypothesis (H1) is that pM smaller than pF. So they are:
H0: pM = pF
H1: pM < pF
Basing on the samples, 25% of 40 men and 35% of 40 women owned cats. We are making a one-tailed (left-tailed) test because we want to know if pM is less than pF.
The test statistic and p-value have to be calculated using these formulas or a statistical software. If the p-value is less or equal to .005 (our alpha), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Learn more about Hypothesis Testing here:https://brainly.com/question/34171008
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Water is leaking out of an inverted conical tank at a rate of 8300.0 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 13.0 meters and the diameter at the top is 3.5 meters. If the water level is rising at a rate of 15.0 centimeters per minute when the height of the water is 3.0 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute. Note: Let "R" be the unknown rate at which water is being pumped in. Then you know that if V is volume of water, dV/dt=R−8300.0. Use geometry (similar triangles?) to find the relationship between the height of the water and the volume of the water at any given time. Recall that the volume of a cone with base radius r and height h is given by 1/3πr^2h.
this is super confusing
Takeru has 444 birdfeeders. It takes \dfrac43 3 4 ? start fraction, 4, divided by, 3, end fraction bags of birdseed to fill each feeder. What is the minimum number of bags of birdseed Takeru needs to fill all the feeders?
Answer:
6 bags
Step-by-step explanation:
Please answer this multiple choice question!
Point C must be the center of the circle, since all of the radii connect there.
Identify the area of a regular nonagon with side length 18 cm. Round to the nearest tenth. HELP ASAP PLEASE!!
Answer:
[tex]A=2,002.9\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of a regular polygon is equal to
[tex]A=\frac{1}{2}rP[/tex]
where
r is the apothem
P is the perimeter
step 1
Find the perimeter
The perimeter of a regular nonagon is
[tex]P=ns[/tex]
where
n is the number of sides (n=9)
s is the length side (s=18 cm)
substitute
[tex]P=9*18=162\ cm[/tex]
step 2
Find the apothem
The apothem in a regular polygon is equal to
[tex]r=\frac{1}{2}(s)cot(180\°/n)[/tex]
we have
[tex]s=18\ cm[/tex]
[tex]n=9[/tex]
substitute
[tex]r=\frac{1}{2}(18)cot(180\°/9)[/tex]
[tex]r=9cot(20\°)=24.73\ cm[/tex]
step 3
Find the area of the regular nonagon
[tex]A=\frac{1}{2}rP[/tex]
substitute
[tex]A=\frac{1}{2}(24.73)(162)=2,002.9\ cm^{2}[/tex]
How do you do this problem?
Answer:
Step-by-step explanation:
Remarks
They want only the exponential equation, here's the point.
You need to be dividing by a number barely over one. You need to reflect the idea that every 500 ft. the % is going to go down by approximately 1.8%. The model for an exponential result is not as good as a linear one (this is really better done a s a linear result, but I will be obedient to what is asked for).You ought to try so values just to see if the equation works.Equation
[tex]\text{Amount the pressure becomes} = \dfrac{101 kpa}{(1+\dfrac{ 1.8}{100} )^\frac{h}{500} }[/tex]
What this gives you is the equation for a rise every 500 feet. To figure out the %
Use
[tex]\text {\% =} \frac{\text{101 - answer from above equation}}{101}*100\%[/tex]
Example
Let h = 1000 feet
101 / (1 + 1.8/100) ^ (1000/500)
101 / (1.018)^2
101 / 1.036324
97.46
Now take this number and use the second formula
% = (101 - 97.46)/101 * 100%
% = 3.54%
The answer should be 3.6% (2 * 1.8%)
This is close enough. The question does say approximately.
1500 feet will give you 5.2% which is close to 5.4 (1.8 * 3). The higher you go, the more it is going to be out, but the results will always be close.