Answers
ANSWER
[tex]\lim _{n\to\infty}\text{ }(\frac{3n^5^{}}{6n^6+1})\text{ = 0}[/tex]EXPLANATION
Step 1: Given that:
[tex]\sum ^{\infty}_{n\mathop=1}(\frac{3n^5^{}}{6n^6+1})[/tex]Step 2: Expand the limit
[tex]\begin{gathered} \lim _{n\to\infty}(\frac{3n^5^{}}{6n^6+1})\text{ } \\ \text{ = }\lim _{n\to\infty}\frac{n^5}{n^5}(\frac{3^{}}{6n^{}+\frac{1}{n^5}}) \\ \text{ = }\lim _{n\to\infty}(\frac{3^{}}{6n^{}+\frac{1}{n^5}}) \\ =\text{ }\lim _{n\to\infty}(\frac{3^{}}{6(\infty)^{}+\frac{1}{(\infty)^5}}) \\ \text{ = }\lim _{n\to\infty}(\frac{3^{}}{6(\infty)^{}+\frac{1}{\infty}}) \\ \text{ = }\lim _{n\to\infty}(\frac{3^{}}{6(\infty)^{}+0^{}}) \\ \text{ = }\lim _{n\to\infty}(\frac{3^{}}{6(\infty)^{}^{}})\text{ = 0} \\ \end{gathered}[/tex]Hence,
[tex]\lim _{n\to\infty}(\frac{3n^5}{6n^6+1})\text{ = 0}[/tex]Related Questions
Hi, i need assistance with question 2! need to graph all equations! Precalculus homework!
Answers
The graphs of the equations have been obtained.
We are given some equations.
We will find some points for the equations.
And then, we will graph them.
a) y = 2 x + 5
x 0 1
y 5 7
b) 2 x + 3 y = 6
x 0 3
y 2 0
c) y - 4 = 3(x + 2)
y - 4 = 3 x + 6
y = 3 x + 10
x 0 1
y 10 13
d) 4(y - 5) = 2(x + 1)
4 y - 20 = 2 x + 2
4 y = 2 x + 22
x 1 3
y 6 7
e) y = x - 3
x - 2 6
y - 5 3
Therefore, we get that, the graphs of the equations have been obtained.
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We can find s , the slant height using Pythagorean theorem , and since this solid is made of parts of simple solids , we can combine the formulas to find surface area and volume
Answers
EXPLANATION
Given that the slant represents the diagonal side of a solid, we can use the Pythagorean Theorem as shown as follows:
Thus, if we know the height and the base, we can compute the slant height by the Pythagorean as explained above.
The Pythagorean Theorem says:
Therefore, we can substitute the radius and the height in the Pytagorean Equation to obtain the slant height.
[tex]\text{radius}^2+\text{height}^2=\text{slant height\textasciicircum{}2}[/tex][tex]r^2+h^2=s^2[/tex]Pluggin in the given values into the equation:
[tex]5^2+7^2=s^2[/tex]Isolating the slant height:
[tex]\sqrt[]{5^2+7^2}=s[/tex]Now, if we need to compute the Surface Area, we need to combine the formulas for all the solids that form the figure.
Figure:
Thus, the surface area is:
[tex]Total\text{ Surface Area=}\frac{SurfaceArea_{\text{sphere}}}{2}+Surface\text{ Area of the Cone}-\text{ Surface Area of the Base}[/tex]Replacing terms:
[tex]=\frac{4\cdot\pi\cdot r^2}{2}+(\pi rs+\pi r^2)-\pi r^2[/tex]We can apply the same reasoning to the Volume:
[tex]Total\text{ Volume}=\frac{Volume\text{ Sphere}}{2}+Volume\text{ of the cone}[/tex][tex]=\frac{\frac{4}{3}\pi r^3}{2}+\frac{1}{3}\pi r^2h[/tex]Finally, just replacing the corresponding values, give us the appropiate surfaces and volumes.
Bud Graham owns property in Salinas assessed at $250,000 and pays a property tax rate of $1.96 per $100 of assessed value. He also owns property in Modesto assessedat the same $250,000 and pays property tax at a rate of $21.50 per $1,000 of assessed value. What is Bud's total property tax bill for properties in both towns?$10,275$9,965$11,045$10,996None of these choices are correct.
Answers
Ok so first we are gonna calculate the tax bill for each town independently and then we are gonna add their values. The tax rate in Salinas is $1.96 per $100 of assessed value and we know Mr. Graham's property is assessed at $250000 so we can use the rule of three:
$100-----------$1.96
$250000----------x
Where x represents his property tax bill for Salinas. According to the rule of three:
[tex]x=\frac{250000\cdot1.96}{100}=4900[/tex]So he has to pay $4900 in taxes for that property. Now we make the same process for his property on Modesto:
$1000-----------$21.5
$250000----------x
[tex]x=\frac{250000\cdot21.5}{1000}=5375[/tex]So he has to pay $5375 for his property in Modesto. Adding the two bills we know the total property bill: $4900 + $5375 = $10275
The cost (c), in dollars, charged by a car rental agency is calculated using the equation c = 12 +0.29m, where m represents the distancetraveled in miles.Calculate the distance traveled for the cost of $56. 37.
Answers
The distance taveled is 153 miles
Explanation:The cost function is given as:
c = 12 + 0.29m
Given cost of $56.37, the distance m is obtained from the following equation:
56.37 = 12 + 0.29m
0.29m = 56.37 - 12
0.29m = 44.37
m = 44.37/0.29
= 153
A sphere has a diameter of 4ft . what is its surface area ?The surface area of the sphere is _ ft 2(Type an exact answer in terms of pie .)
Answers
The formula of the surface area of an sphere is
[tex]SA=4\pi r^2[/tex]where r is the radius
the radius is half of the diameter
r=4/2
r=2 ft
we substitute the values
[tex]SA=4\pi(2)^2=4\cdot\pi\cdot4=16\pi ft^2[/tex]the surface area is 16pi ft^2
I'm kind of confused on this one I got some help but I'm still struggling to figure it out
Answers
Explanation
Step 1
the standard form of a quadratic equation is given by
[tex]f(x)=ax^2+bx+c[/tex]then, by the table, we have:
[tex]y=f(x)[/tex][tex]\begin{gathered} f(x)=ax^2+bx+c \\ f(-4)=a(-4)^2+b(-4)+c \\ f(-4)\rightarrow30=16a-4b+c\rightarrow\text{Equation}(1) \\ f(-3)=a(-3)^2+b(-3)+c \\ f(-3)=9a+-3b+c \\ f(3)=0=9a+-3b+c\rightarrow\text{Equation}(2) \\ \end{gathered}[/tex]now, we have 2 equations, and 3 variables ( a, b and c, so we need one more equation)
when x= 2
[tex]\begin{gathered} f(x)=ax^2+bx+c \\ f(2)=0=a2^2+b\cdot2+c \\ f(2)=0=4a+2b+c\rightarrow Equation\text{ (3)} \end{gathered}[/tex]Step 3
solve the equations
[tex]\begin{gathered} 30=16a-4b+c\rightarrow\text{Equation}(1) \\ 0=9a-3b+c\rightarrow\text{Equation}(2) \\ 0=4a+2b+c\rightarrow Equation\text{ (3)} \end{gathered}[/tex][tex]\begin{gathered} 0(eq2)=0(eq3) \\ \text{9a-}3b+c=4a+2b+c \\ \text{subtract c in both sides} \\ \text{9a-}3b+c-c=4a+2b+c-c \\ \text{9a-}3b=4a+2b \\ \text{subtract 4a in both sides} \\ \text{9a-}3b-4a=4a+2b-4a \\ 5a-3b=2b \\ \text{add 3b in both sides} \\ 5a-3b+3b=2b+3b \\ 5a=5b \\ \text{divide both sides by 5} \\ \frac{5a}{5}=\frac{5b}{5} \\ a=b \end{gathered}[/tex]Now, replace a=b in equation (1) and equation (2)
[tex]\begin{gathered} 30=16a-4b+c\rightarrow\text{Equation}(1) \\ 30=16a-4a+c \\ 30=12a+c\rightarrow\rightarrow equation\text{ (4)} \\ 0=9a-3b+c\rightarrow\text{Equation}(2) \\ 0=9a-3a+c \\ 0=6a+c\rightarrow\rightarrow equation(5) \end{gathered}[/tex]Step 3
use equations (4) and (5) to find a and c
[tex]\begin{gathered} 30=12a+c\rightarrow\rightarrow equation\text{ (4)} \\ 0=6a+c\rightarrow\rightarrow equation(5) \end{gathered}[/tex]a)isolate c in both equations and equal the expressions to find a
[tex]\begin{gathered} 30=12a+c\rightarrow\rightarrow equation\text{ (4)} \\ 30-12a=c \\ c=30-12a \\ 0=6a+c\rightarrow\rightarrow equation(5) \\ -6a=c \\ c=c \\ 30-12a=-6a \\ \text{add 6a in both sides} \\ 30-12a+6a=-6a+6a \\ 30-6a=0 \\ \text{subtract 30 in both sides} \\ 30-6a-30=0-30 \\ -6a=-30 \\ \text{divide both sides by -6} \\ \frac{-6a}{-6}=\frac{-30}{-6} \\ a=5 \end{gathered}[/tex]we have a= 5,
now, replace in equation (4) to find x
[tex]\begin{gathered} 30=12a+c\rightarrow\rightarrow equation\text{ (4)} \\ 30=12\cdot5+c \\ 30=60+c \\ \text{subtrac 60 in both sides } \\ 30-60=60+c-60 \\ -30=c \\ c=-30 \end{gathered}[/tex]Therefore we have
a=5 b=5 c=-30
Step 4
finally, rewrite the equation
[tex]\begin{gathered} f(x)=ax^2+bx+c \\ f(x)=5x^2+5x-30 \end{gathered}[/tex]I hope this helps you
A small tabletop is 3/4 ft by 3 1/2 ft. Rita solves 3/4⋅3 1/2 to find the area of the tabletop in square feet. Choose numbers to complete Rita's calculations for the area.
Answers
Number which represents the area of table top which has measures of 3/4 ft by 3 1/2 ft is equal to 21/8 square feet.
As given,
Measures of a small tabletop is equal to 3/4 ft by 3 1/2 ft
length=3 1/2 ft
=7/2 ft
Width=3/4 ft
Formula used to measure area of the small tabletop is equal to
=Length ×width
Substitute the values in formula to get a number which represents the area of small tabletop :
Area=(3/4) × (7/2)
=21/8 square feet
Therefore, number which represents the area of table top which has measures of 3/4 ft by 3 1/2 ft is equal to 21/8 square feet.
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Find the height of a cylinder with a volume of 36pie cm with an exponent of 3 and a base with a radius of 3 cm.h = ???cmv \: is \: 36\pi \: cm ^{3}vis36πcm3r \: is \: 3cmris3cm
Answers
Data
Volume = 36 cm3
radius = 3 cm
Formula
Volume of a cylinder = pi x r2 x h
Solve for h
h = Volume / (pi x r2)
Substitution
h = 36 / (3.1416 x (3)2)
Simplification
h = 36 / (3.1416 x 9)
h = 36 / 28.2744
Result
height = 1.27 cm
Lisa used [tex] \frac{1}{4} [/tex]cup of milk in her muffin recipe. How can you write I as a decimal? 0 A. 0.2 B. 0.25 C. 0.4 OD 1.4
Answers
Answer:
1/4 = 0.25
Option B
Step-by-step explanation:
To write 1/4 as a decimal, we use a division, dividing 1 by 4.
So
1/4 = 0.25
Oliver puts 600.00 into an account to use for school expenses the account earns 3% interest compounded annually how much will be in the account after 6 years
Answers
$600.00
3% interest = 0.03
compund anually
How much in 6 years
P = 600
r = 0.03
n = 1
t = 6
[tex]A\text{ = 600(1 + }\frac{0.03}{1})^{(1)(6)}=600(1.03)^{6\text{ }}\text{ = 600(1.1940) = 716.40}[/tex]Answer:
$716.40
My math teacher has the answer as -1/4. I got 1/4 and cannot figure out the negative part.
Answers
To find the limit we need to rationalize the function, we achieve this by multiplying by a one written in an appropiate way:
[tex]\begin{gathered} \lim_{h\to0}\frac{2-\sqrt{4+h}}{h}=\lim_{h\to0}\frac{2-\sqrt{4+h}}{h}\cdot\frac{2+\sqrt{4+h}}{2+\sqrt{4+h}} \\ =\lim_{h\to0}\frac{(4-(\sqrt{4+h})^2)}{h(2+\sqrt{4+h})} \\ =\lim_{h\to0}\frac{4-(4+h)}{h(2+\sqrt{4+h})} \\ =\lim_{h\to0}\frac{4-4-h}{h(2+\sqrt{4+h})} \\ =\lim_{h\to0}\frac{-h}{h(2+\sqrt{4+h})} \\ =\lim_{h\to0}\frac{-1}{2+\sqrt{4+h}} \\ =-\frac{1}{2+\sqrt{4+0}} \\ =-\frac{1}{2+\sqrt{4}} \\ =-\frac{1}{2+2} \\ =-\frac{1}{4} \end{gathered}[/tex]Therefore:
[tex]\lim_{h\to0}\frac{2-\sqrt{4+h}}{h}=-\frac{1}{4}[/tex]which values are solution to the inequality below. Check all applyX^2<64A. 65B. 64C. 7D. -8E> 0F. NO SOLUTION
Answers
Answer:
[tex]C\text{ and E.}[/tex]Step-by-step explanation:
[tex]x^2<64[/tex]Take the square root of both sides:
*A positive number has two square roots, one positive, and one negative, which are opposite to each other.
[tex]\begin{gathered} x<\pm\sqrt[]{64} \\ -8Therefore, 0 and 7 are solutions to inequality.Find the next two terms in this
sequence.
20, 32, 42, 50, 56, [ ? ], [ ? ]
Answers
The next two digits in the sequence are 60 and 62 and the sequence looks like this: 20, 32, 42, 50, 56, 60, 62
What do we mean by sequence?Sequences are ordered collections of numbers, also known as "terms," such as 2,5,8. There are some sequences that adhere to a particular pattern that allows for an endless extension. For instance, 2,5,8 adheres to the "add 3" pattern, so we can now continue the sequence. There are formulas for sequences that show us where to find any given term. You should be familiar with the following four main categories of sequences: arithmetic sequences, geometric sequences, quadratic sequences, and special sequences.So, the next to numbers will be:
20, 32, 42, 50, 56, [ ? ], [ ? ]We can observe that:
20 + 12 = 3232 + 10 = 4242 + 8 = 5050 + 6 = 56Similarly,
56 + 4 = 6060 + 2 = 62Therefore, the next two digits in the sequence are 60 and 62 and the sequence looks like this: 20, 32, 42, 50, 56, 60, 62
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State the order and type of each transformation of the graph of the function f(X)=4(X+9)^2 as compared to the graph of the base function
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Using translation concepts, the function f(x) was evaluated by comparing to the graph of a base function g(x) = x².
stretched vertically by a factor of fourShifted 9 units to the left.What exactly is a translation?In mathematics, a translation is the movement of a shape to the left or right and/or down or up. The translated shapes appear to be the same size as that of the original shape, and thus the shapes are congruent. They were simply shifted in one or even more directions. There's no change in shape because it is simply moved from one location to another.A translation is signified by a change with in function graph, based on operations in its definition including such multiplication or sum/subtraction.
The base function g(x) = x² in this problem was.Multiplied by 4, such that, stretched vertically by a factor of four.Shifted 9 units to the left.Thus, the resultant function is obtained as (X)=4(X+9)²
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A sprinkler waters a circular region in Jason's yard that has a radius of 15 feet. Rounded to the nearest square foot, what is the area of the circular region that is watered by the sprinkler?
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A sprinkler waters a circular region in Jason's yard that has a radius of 15 feet. Rounded to the nearest square foot, what is the area of the circular region that is watered by the sprinkler?
the area of the circular region is
A=pi*r^2
we have
pi=3.14
r=15 ft
substitute
A=3.14*(15^2)
A=707 ft2There are two parts ill send the second part after the first part is answered. Please!
Answers
A dog breeder recorded the weight of a puppy during the first eight months after it was born. The breeder created the equation w = 0.25m + 8.3, where w is the weight of the puppy in pounds and m is the number of months since the puppy was born. What is the meaning of the slope from the breeder's equation?
When the puppy is born, the total weight is 0.25 pounds.
When the puppy is born, the total weight is 8.3 pounds.
For every month after the puppy is born, the weight increases by 8.3 pounds.
For every month after the puppy is born, the weight increases by 0.25 pounds.
Answers
Answer:
For every month after the puppy is born, the weight increases by 0.25 pounds.
Step-by-step explanation:
A dog breeder recorded the weight of a puppy during the first eight months after it was born. The breeder created the equation w = 0.25m + 8.3, where w is the weight of the puppy in pounds and m is the number of months since the puppy was born. What is the meaning of the slope from the breeder's equation?
When the puppy is born, the total weight is 0.25 pounds.
When the puppy is born, the total weight is 8.3 pounds.
For every month after the puppy is born, the weight increases by 8.3 pounds.
For every month after the puppy is born, the weight increases by 0.25 pounds.
the equation is: w = 0.25m + 8.3
slope for this = 0.25 so the answer is: For every month after the puppy is born, the weight increases by 0.25 pounds.
Answer:
For every month after the puppy is born, the weight increases by 0.25 pounds.
Step-by-step explanation:
A dog breeder recorded the weight of a puppy during the first eight months after it was born. The breeder created the equation w = 0.25m + 8.3, where w is the weight of the puppy in pounds and m is the number of months since the puppy was born. What is the meaning of the slope from the breeder's equation?
When the puppy is born, the total weight is 0.25 pounds.
When the puppy is born, the total weight is 8.3 pounds.
For every month after the puppy is born, the weight increases by 8.3 pounds.
For every month after the puppy is born, the weight increases by 0.25 pounds.
the equation is: w = 0.25m + 8.3
slope for this = 0.25 so the answer is: For every month after the puppy is born, the weight increases by 0.25 pounds.
14. Pick the corner point below that maximizes the following objective function: p=22x+14y (6,5)(0,0)(0,12)(15,0)(11,13)
Answers
Okay, here we have this:
Considering the provided function, we are going to replace the coordinate pairs one by one in the function, to observe which of the pairs maximizes the function, so we obtain the following:
(6, 5):
p=22x+14y
p=22(6)+14(5)
p=132+70
p=202
(0,0):
p=22x+14y
p=22(0)+14(0)
p=0+0
p=0
(0, 12):
p=22x+14y
p=22(0)+14(12)
p=0+168
p=168
(15, 0):
p=22x+14y
p=22(15)+14(0)
p=330+0
p=330
(11, 13):
p=22x+14y
p=22(11)+14(13)
p=242+182
p=424
Finally we obtain that the corner point that maximizes the function p=22x+14y is the last option (11, 13).
Marshall has 3 bottles of water. Together, Marshall and Scott have at most 12 bottles of water. Let x represent the number of bottles Scott may have.
Answers
Answer:
If you need to find out how many bottles of water Dave has then at the most it would be 9 bottles
Step-by-step explanation:
Scott has 9 number of bottles.
The total number of bottles is 12
Marshall has 3 bottles of water
let the number of bottles Scott is having is x
using the above data:
3+x=12
x=9
Scott has 9 number of bottles.
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Divide (41°48') = 4.
Answers
The division of 41°48' by 4 gives the result 10°27'.
What is termed as the division?Multiplication is the inverse of division. If 3 groups of 4 add up to 12, 12 divided into 3 equal portions adds up to 4 in each group in division. Each component of a division eqn has its own name.Dividend: A dividend is indeed the number divided during the division process.Divisor: The divisor is the number in which the dividend is divided.Quotient: A quotient is an outcome of the division process.Remainder: We can't always divide things exactly. There could be an extra number. The leftover number is known as the remainder.The following describes the relationship between such four parts:
Dividend = Divisor x Quotient + Remainder
For the given expression,
(41°48') divided by 4.
= 41°48' / 4
= 10°27'.
Thus, the division of the expression 41°48' by 4 gives 10°27'.
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A basketball team scored a total of 97 points in a basketball game. They made a total of 42 2-point and 3-point baskets. How many 2-point baskets did they make? How many 3-point baskets did they make? Let the number of 2-point baskets = and the number of 3-point baskets = .
Answers
If a basketball team scored a total of 97 points in a basketball game and they made a total of 42 2-point and 3-point baskets. then they made 29 two points basket and 13 three point baskets.
The total points scored by the basketball team = 97 points
Consider the number of 2 points basket they scored as x and number of 3 point basket they scored as y
Then the equation will be
2x+3y = 97
They made a total of 42 2-point and 3-point baskets.
Therefore
x+y = 42
x = 42-y
Use the substitution method on the first equation
Substitute the value of x on the first equation.
2(42-y) +3y = 97
84-2y +3y = 97
y = 97-84
y = 13
Substitute the value of y in the equation
x = 42-y
x = 42-13
x = 29
Hence, If a basketball team scored a total of 97 points in a basketball game and they made a total of 42 2-point and 3-point baskets. then they made 29 two points basket and 13 three point baskets.
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Patrick rolls a die. What is the probability that he rolls an 1, 3 or 5?
Answers
The total possible outcomes of a dice are: 1,2,3,4,5 and 6.
There are 6 possible outcomes, all with equal probability.
Then, as all the outcomes have the same probability, we have to calculate what is the probability of having one ot three specific outcomesout of the possible 6 outcomes.
We can calculate this as:
[tex]P=\frac{\#\text{success outcomes}}{\#\text{possible outcomes}}=\frac{3}{6}=\frac{1}{2}=0.5=50\text{ \%}[/tex]Answer: P(1,3, or 5) = 1/2 = 0.5 = 50%
please help me out quickly
Answers
Answer:
take the first 1 an flip it to the other side and with the second row put that 1 on the other side an switch the other two the same way
Using the imagine below, find the measure of angle y.
Answers
y+ (5x-10)= 180 º
Due to the lines are parallels
[tex]\alpha=\beta[/tex]So then
(5x-10)= (x+86)
5x - x = 86 + 10
4x = 96
x = 24
__________________
Checking
(5x-10= 5*24-10= 110º
(x+86) = 24+ 86= 110º
__________________________
y+ (5x-10)= 180 º
y+ 110º = 180 º
y= 180-110º
y= 70º
how to find the answer for 15x-9y=-9
Answers
The value of "x" in the given linear equation of two variable 15x - 9y = -9 will be x = 0.6(-1+y).
As per the question statement, we are given a linear equation of two variable 15x - 9y = -9 and we are supposed to solve it for the variable "x"
First step would be to isolate "x" from the given equation
15x - 9y = -9
15x = -9 + 9y
15x = 9(-1+y) [Distributive property]
x = 9(-1+y)/15
x = 3(-1+y)/5 [Simplified]
or x = 0.6(-1+y)
Hence, the value of "x" in the given linear equation of two variable 15x - 9y = -9 will be x = 0.6(-1+y).
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A few days later, the American tourist went to a bank in Plymouth and exchanged 150 American dollars for British pounds. How many pounds did she receive? (Round your answer to two decimal places.)
Answers
The amount of money that the American tourist will receive will be 132.74 pounds.
What is money?It should be noted that money is the medium of exchange. In this case, it should be noted that 1 pound = 1.13 dollar
The American tourist went to a bank in Plymouth and exchanged 150 American dollars for British pounds, the pound received will be:
= Amount / rate
= 150 / 1.13
= 132.74 pounds.
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What is the range of this function?O A. ys-9OB. y2-9C. All real numbersD. x 1
Answers
Given the function:
[tex]y=x^2-2x-8[/tex]The function above is a quadratic function, the graph is a parabola
The standard form of a quadratic function is given by:
[tex]\begin{gathered} ax^2+bx+c=0 \\ \text{for a parabola with }a\text{ vertex (h, k)} \\ If\text{ a<0},\text{ the range is y}\leq k \\ \text{if a>0},\text{ the range is y}\ge k \end{gathered}[/tex]From the given graph and function,
[tex]\begin{gathered} The\text{ vertex (h, k) = (}1,\text{ -9)} \\ a\text{ =1} \\ \sin ce,\text{ a>0, the range is y}\ge-9 \end{gathered}[/tex]Therefore, the range of the function is:
[tex]undefined[/tex]Which number line shows the solution of 5x-25>-15
Answers
The solution to the inequality 5x - 25 > -15 in inequality and interval notation form are x > 2 and (2,∞)
How to solve linear inequality problems?A linear inequality is simply an expression where two values are compared by the inequality symbols <, >, ≤ or ≥.
Given the data in the question;
5x - 25 > -15
To solve for x, bring all terms containing the variable to the left side of the equation and the terms without variables to the right side of the equation.
5x - 25 > -15
Add 25 to both sides
5x - 25 + 25 > -15 + 25
5x > -15 + 25
5x > 10
Divide each term in 5x > 10 by 5 and simplify.
5x > 10
5x/5 > 10/5
x > 2
Therefore, the solution to inequality is x > 2.
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Cooper, Sha'NiyaThe sum of three consecutive integers is 177. What is the largest of the integers, and why?
Answers
We can represent the sum of the three consecutive integers as:
[tex]n+(n+1)+(n+2)=177[/tex]Then, we need to solve the equation for n, then:
[tex]3n+3=177_{}\Rightarrow3n=177-3\Rightarrow3n=174\Rightarrow n=\frac{174}{3}\Rightarrow n=58[/tex]Then, the largest of the integers is n + 2 or 58 +2 = 60.
The reason is that the other integers are 58, 58 + 1 = 59, that is, 58 and 59.
We can check that:
58 + 59 + 60 = 177.
Use the sum and difference identities to determine the exact value of the following expression. If the answer is undefined, write DNE.tan17724tan1110241751 + tantan1172424
Answers
The Solution:
Given the expression below:
We are required to determine the exact value of the above expression.
Recall:
By Trigonometric identity,
[tex]\frac{\:tan\left(\frac{17\pi\:}{24}\right)-tan\left(\frac{11\pi\:}{24}\right)}{1+\:tan\left(\frac{17\pi\:}{24}\right)tan\left(\frac{11\pi\:}{24}\right)}=\tan (\frac{17\pi}{24}-\frac{11\pi}{24})[/tex]This becomes:
[tex]\tan (\frac{17\pi}{24}-\frac{11\pi}{24})=\tan (\frac{17\pi-11\pi}{24})=\tan (\frac{6\pi}{24})=1[/tex][tex]undefined[/tex]Therefore, the correct answer is 1
