Answer:
19+a
Step-by-step explanation:
The sum of three consecutive integers is 42. Determine the value of the smallest
integer.
Answer:
13.
Step-by-step explanation:
[tex]42 = a + (a+1) + (a+2) = 3a + 3 = 3(a+1)[/tex]
Then, [tex]a+1 = 14[/tex], so [tex]a=13.[/tex]
How do you do this question?
=======================================================
Explanation:
f(x) is continuous when x >= 1. The only discontinuity for f(x) is when x = 0, but 0 is not part of this interval.
f(x) is positive for any valid x value in the domain since x^6 is always positive. In general, x^n is positive for all x when n is any even number.
f(x) is decreasing. You can see this through a table of values or through a graph. For anything in the form 1/(x^k), it will be a decreasing function because x^k gets larger, so 1/(x^k) gets smaller, when x goes to infinity.
--------------------
The conditions to use the integral test have been met. So we have to see if [tex]\displaystyle \int_1^{\infty}f(x)dx[/tex] converges or not.
Let's integrate and find out
[tex]\displaystyle \int \frac{1}{x^6} dx = \int x^{-6} dx\\\\\\ \displaystyle \int \frac{1}{x^6} dx = \frac{1}{1+(-6)}x^{-6+1}+C\\\\\\ \displaystyle \int \frac{1}{x^6} dx = \frac{1}{-5}x^{-5}+C\\\\\\ \displaystyle \int \frac{1}{x^6} dx = -\frac{1}{5}*\frac{1}{x^5}+C\\\\\\ \displaystyle \int \frac{1}{x^6} dx = -\frac{1}{5x^5}+C\\\\[/tex]
So we have
[tex]\displaystyle g(x) = \int f(x) dx\\\\\\\displaystyle g(x) = \int \frac{1}{x^6} dx\\\\\\\displaystyle g(x) = -\frac{1}{5x^5}+C\\\\\\[/tex]
Meaning that,
[tex]\displaystyle \int_{a}^{b} f(x) dx = g(b)-g(a)\\\\\\\displaystyle \int_{a}^{b} \frac{1}{x^6} dx = \left(-\frac{1}{5b^5}+C\right)-\left(-\frac{1}{5a^5}+C\right)\\\\\\\displaystyle \int_{a}^{b} \frac{1}{x^6} dx = -\frac{1}{5b^5}+\frac{1}{5a^5}\\\\\\[/tex]
If we plug in a = 1 and apply the limit as b approaches positive infinity, then the expression [tex]-\frac{1}{5b^5}+\frac{1}{5a^5}[/tex] will turn into [tex]\frac{1}{5}[/tex]
Therefore,
[tex]\displaystyle \int_{1}^{\infty} \frac{1}{x^6} dx = \frac{1}{5}\\\\\\[/tex]
Because this integral converges, this means the series [tex]\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^6}[/tex] also converges as well by the integral test.
please gyus help me out ..... urgent need......for 20 points please gyus answer it .....
Answer:
I wish I could help you but i have not learn yhat yet. so sorrry :( pleaser forgive jme....... please i beg u plase
Step-by-step explanation:
If the expression 4x+3 is equal to 1 to the same value of x, what is the expression 4x+8 equal to for the same value of x？
Answer:
6
Step-by-step explanation:
4x + 3 = 1
4x =-2
x = -1/2 so 4x +8 =4(-1/2) +8=6
What are the zeros of x (3 - 18x) = 0 ?
Answer:
x=3⋅± 2
=±4.2426
x=0
Step-by-step explanation:
Which equation has no solution
Answer:
d
Step-by-step explanation:
Zeke's birthday party will cost $6 if he invites 3 guests. If there are 8 guests,
how much will Zeke's birthday party cost? Assume the relationship is
directly proportional. *
Which answer choices fit in the pattern below? Select all that apply.
18, 28, 38, ___, ___, ___
BTW I DONT WANT TO DO THIS SO TY FOR WHOEVER DOES IT
Answer:
18,28,38,48,58,68
Step-by-step explanation:
You are adding by 10 every time
What is the prime number?
Answer:
In math, prime numbers are whole numbers greater than 1, which have only two factors – 1 and the number itself. Prime numbers are divisible only by the number 1 or itself. For example, 2, 3, 5, 7, and 11 are the first few prime numbers.
Step-by-step explanation:
hope this helps :)
Bella is in school at math class. Her teacher, Mrs. Williams asks her "What's 9-3 divided by 1/3 + 1 equal to?" help Bella answer the question without using a calculator.
A mixture requires 4 cups of water for every 7 cups of flour used. How many cups of water should be used with 28 cups of flour
Answer:
16 cups of water
The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.74
before the discount, and they leave a 20% tip. If the tip applies to the cost of the meal before the
discount, what is the total cost of the meal? Round your intermediate calculations and answer to thenearest cent.
Answer:
it is 82.53 round to 82.50 ithink
What is X- y= 3 in a graph
Answer:
You must first put the equation into slope-intercept form (y = mx + b). To do this, subtract x from both sides to isolate y. Then, since y will be negative, divide each side by -1, resulting in y = x - 3. Since a 1 is understood to be in front of the x, the slope is 1
How to graph:
x-0 y- -3 or (0,-3)
x- 3 y-0 or (3,0)
If you graph these points you should get your graph
How can i use multiplication/division to calculate a percent of a number?
Answer:
for example you are given a percentage and numbers you cross multiply
Step-by-step explanation:
hope it helps cause I don't know how to explain the answer
Find the distance between the points (3, 2) and (15,-3).
Please help me this is a big grade for me and I’m very confused on this whole page
Answer: 5) 2, -8, 32, _,_
I believe that it would be -64, then 128
Step-by-step explanation:
Bc its positive then negative and its being multiplied by -4 each time so when you mutiply a negative to a negative its a positive which is were the positives and negatives come from. :)
Find the area of the figure. (Sides meet at right angles.)
9 in
in
5 in
B in
4 in
Answer:
48 in²Step-by-step explanation:
A1 = 9 x 4 = 36
A1 = 4 x 3 = 12
Total = 36 + 12
= 48 in²
3. Select two numbers that have 4 as their greatest
common factor. Mark all that apply.
12
Part
A 2,4
B
4,8
C
8. 12
D 8. 16
E
12. 24
I’m
Answer:
B and C
Step-by-step explanation:
All others have higher factors than 4
Answer:
B,(4,8) &C,(8,12)
Step-by-step explanation:
A,(2,4)=2=2
4=2^2(GCF of 2&4 is 2)
B,(4,8)=4=2^2
8=2^3(GCF of 4&8 is 4)
C,(8,12)=8=2^3
12=2^2*3(GCF of 8&12 is 4)
D,(8,16)=8=2^3
16=2^4(GCF of 8&16 is 8)
E,(12,24)=12=2^2*3
24=2^3*3(GCF of 12&24 is 12).
i hope it helps you
2. Mr. Winter is putting away
48 chairs. He can put away
the chairs in stacks of 10 or
as single chairs. What are all
of the ways Mr. Winter can put
away the chairs?
Wh
he can make 4 stacks, leaving 8 chairs as single chairs
4. The cost of a long-distance telephone call is $.50 for making the call and $.10 per minute. What is the slope? What does it represent?
$$$$$$$$$$$$$$$$$$$$$$$$$$
A class of 28 students has four more than two times as many
boys as girls. How many of the students are girls?
Answer:
there are 8 girl students
Step-by-step explanation:
28-4= 24
28 divided by 3 is 8
8x2=16
16+4=20
20+8= 28
therefore... there are 8 girls in the class
A factory makes sheets of metal that are 4 5/8 inches thick. If a worker at the factory makes
a stack of 5 of the sheets, how many inches thick will the stack be?
Write your answer as a fraction or as a whole or mixed number.
what do you mean by '^' next to everything?
Answer:
power of for example 4 to the power of 2. 2 means square
what is three times three
Answer:
9
Step-by-step explanation:
3x3=9
its nine bruhhhhhhhhhhhhh
formula for calculating average speed
The width of a rectangle is 5 times the length. If the perimeter is 72, find the dimensions of the rectangle.
Answer:
l=6
b=30
Step-by-step explanation:
b=5l
perimeter= 72
2(l+b)= 72
l+b= 36
l+5l= 36
6l= 36
l= 6
b=5l= 6*6= 30
Determine the range of the function.
y=1/4x^2 - 5
a.All real numbers.
b.All integers less than or equal to -5.
c.All integers greater than or equal to -5.
d.All real numbers greater than or equal to -5.
Answer:
[tex]Solution: f(x)\ge-5\\Interval:[-5,\infty)[/tex]
Step-by-step explanation:
Equation: [tex]\frac{1}{4} x^2-5 = y[/tex]
1). [tex]\frac{1}{4} x^2-5 = y[/tex] →[tex]\frac{x^2}{4}-5=y[/tex]
2). [tex]\frac{x^2}{4}-5=y[/tex] ∴ [tex]a=\frac{1}{4}, b=0, c=-5[/tex]
3). [tex]x_v=-\frac{b}{2a}[/tex]
[tex]=-\frac{0}{2(\frac{1}{4})}[/tex]
[tex]=0[/tex]
4). now plug [tex]x_v[/tex] into [tex]y_v[/tex]
[tex]y_v=\frac{0^2}{4}-5[/tex]
[tex]=-5[/tex]
5). Minimum (0,-5) ∴ [tex]f(x)\ge-5[/tex]
the question is in the picture can someone PLSSS answer!!!
i will mark brainliest!!
Answer:
the third one im pretty sure
Step-by-step explanation:
While I was walking to schoed this morning I saw 2 ants and 2 butterflies.
My teacher taught me that an insect has 6 legs. Ants one butterflies are
both intects! How many legs were there all together?
Answer:
it would me 24 legs
Step-by-step explanation:
hope that helps
Solve 4,000 ÷ 80 = what
Answer:
50
Step-by-step explanation:
i asked alexa so yeaaa