Answer:
You deposit $1000 in a savings account that earns ... Balance at. End of Year. = Principal + Annual. Interest. = $1000 + $1000(0.06) ... balance in an account that earns interest compounded annually after t years. P = Principal (initial deposit) ... 15. 4.8. —. 12. 16. 268.68 ⋅72. 17. MULTIPLE CHOICE Which graph represents ...
Step-by-step explanation:
please answer!! will give brainliest
Answer:
third option
Step-by-step explanation:
Differentiate using the product rule
Given f(x). g(x) then the derivative is
f(x). g'(x) + g(x). f'(x) ← product rule
Given
[tex]\frac{d}{dx}[/tex](x² secx )
with f(x) = x² and g(x) = secx , then
f'(x) = 2x and g'(x) = secxtanx, thus
[tex]\frac{d}{dx}[/tex](x² secx)
= x². secxtanx + secx. 2x ← factor out xsecx from each term
= xsecx(xtanx + 2) → third option
the class marks of a distribution are 37 42 and 47 the class limits corresponding to class mark 42 are
Answer:
[tex]39.5,44.5[/tex]
Step-by-step explanation:
[tex]Let\ the\ lower\ limit\ and\ the\ upper\ limit\ of\ the\ first\ interval\ be\ u_1,v_1.\\Let\ the\ lower\ limit\ and\ the\ upper\ limit\ of\ the\ second\ interval\ be\ u_2,v_2.\\Let\ the\ lower\ limit\ and\ the\ upper\ limit\ of\ the\ third\ interval\ be\ u_3,v_3.\\Hence,\\As\ the\ class\ marks\ are\ uniform\ with\ an\ a\ difference\ of\ 5, the\\ observation\ is\ continuous\ and\ the\ class\ size\ is\ 5\ too.\\Hence,\\v_1=u_2, v_2=u_3\\[/tex][tex]Now,\\Lets\ consider\ the\ first\ two\ classes.\\37=\frac{u_1+v_1}{2} \\42=\frac{u_2+v_2}{2}\\By\ adding\ the\ equations:\\79= \frac{u_1+v_1}{2}+\frac{u_2+v_2}{2}\\79=\frac{u_1+v_1+u_2+v_2}{2}\\79=\frac{(u_1+v_2)+(v_1+u_2)}{2}\\79=\frac{(u_1+v_2)}{2}+\frac{(v_1+u_2)}{2}\\Now,\\As\ the\ mid-point\ between\ two\ points\ can\ be\ calculated\ by\\ its\ average:\frac{u+v}{2} \\Hence,\\u_2\ lies\ in\ the\ mid-point\ of\ u_1\ and\ v_2.\\u_2=\frac{(u_1+v_2)}{2}\\[/tex]
[tex]Hence,\\By\ substituting\ u_2=\frac{(u_1+v_2)}{2},\\79=u_2+\frac{v_1+u_2}{2}\\As\ v_1=u_2[Proven],\\79=u_2+ \frac{u_2+u_2}{2}\\79=u_2+\frac{2u_2}{2}\\79=2u_2\\Hence,\\u_2=\frac{79}{2}\\u_2=39.5\\Now,\ as\ we\ already\ know\ that\ the\ class\ size=5,\\v_2-u_2=5\\Hence,\\v_2=5+u_2\\Here,\\v_2=5+39.5\\v_2=44.5\\Hence,\\The\ upper\ limit\ of\ the\ second\ interval=44.5\\The\ lower\ limit\ of\ the\ second\ interval=39.5\\[/tex]
10. A curve has the equation y = ax^3 + x + c, where a
and c are constants. The gradient of the curve at the
point (1, 2) is -2.
(i) Find the value of a and of c.
(ii) Hence, find the coordinates of the other point
on the curve where the gradient is -2.
Answer:
Part I)
[tex]a=-1\text{ and } c=2[/tex]
Giving the equation:
[tex]y=-x^3+x+2[/tex]
Part II)
(-1, 2)
Step-by-step explanation:
We have the equation:
[tex]y=ax^3+x+c[/tex]
Where a and c are constants.
We are given gradient/slope of the curve at the point (1, 2) is -2.
Part I)
We know that the gradient of the curve exactly at the point (1, 2) is -2.
So, we will differentiate our equation. We have:
[tex]\displaystyle y=ax^3+x+c[/tex]
Differentiate both sides with respect to x:
[tex]\displaystyle y^\prime=\frac{d}{dx}\big[ax^3+x+c\big][/tex]
Expand the right:
[tex]\displaystyle y^\prime=\frac{d}{dx}\big[ax^3]+\frac{d}{dx}\big[x\big]+\frac{d}{dx}\big[c\big][/tex]
Since a and c are simply constants, we can move them outside:
[tex]\displaystyle y^\prime=a\frac{d}{dx}\big[x^3]+\frac{d}{dx}\big[x\big]+c\frac{d}{dx}\big[1\big][/tex]
Differentiate. Note that the derivative of a constant is simply 0.
[tex]\displaystyle y^\prime=3ax^2+1[/tex]
We know that at the point (1, 2), the gradient/slope is -2.
Hence, when x is 1 and when y is 2, y’ is -2.
So (we don’t have a y so we can ignore it):
[tex]-2=3a(1)^2+1[/tex]
Solve for a. Simplify:
[tex]-2=3a+1[/tex]
Subtract 1 from both sides yield:
[tex]-3=3a[/tex]
So, it follows that:
[tex]a=-1[/tex]
Therefore, our derivative will be:
[tex]y=-3x^2+1[/tex]
Now, we can go back to our original equation:
[tex]y=ax^3+x+c[/tex]
Since we know that a is -1:
[tex]y=-x^3+x+c[/tex]
Recall that we know that a point on our curve is (1, 2).
So, when x is 1, y is 2. By substitution:
[tex]2=-(1)^3+1+c[/tex]
Solve for c. Simplify:
[tex]2=-1+1+c[/tex]
Then it follows that:
[tex]c=2[/tex]
Hence, our entire equation is:
[tex]y=-x^3+x+2[/tex]
Part II)
Our derivative is:
[tex]y^\prime=-3x^2+1[/tex]
If the gradient is -2, y’ is -2. Hence:
[tex]-2=-3x^2+1[/tex]
Solve for x. Subtracting 1 from both sides yields:
[tex]-3=-3x^2[/tex]
So:
[tex]x^2=1[/tex]
Then it follows that:
[tex]x=\pm1\\[/tex]
Since we already have the point (1, 2) where x is 1, our other point is where x is -1.
Using our equation:
[tex]y=-x^3+x+2[/tex]
We can see that our second point is:
[tex]y=-(-1)^3+(-1)+2[/tex]
Simplify:
[tex]y=1-1+2=2[/tex]
So, our second point where the gradient is -2 is at (-1, 2).
What is the slope of this line?
Enter your answer as a whole number or a fracion in simplest
forn in the box
the altitude H of cylinder with a constant volume V is inversely proportional to the square of its radius R. write the related variation equation
Answer:
The related variation will be:
H = V/R²Step-by-step explanation:
We know that when 'y' varies inversely with 'x', we get the equation
y ∝ 1/x
y = k × 1/x
Here 'k' is the constant of proportionality
Given that the altitude H of a cylinder with a constant volume V is inversely proportional to the square of its radius R.
so the equation can be mapped as
H ∝ 1/R²
H = k/R²
In this case, the k is the constant volume. i.e. V = k
Thus, the equation becomes
H = V/R²
where H is the altitude, V is the constant volume and R is the radius.
Therefore, the related variation will be:
H = V/R²The variation equation showing the relationship between H, V and R is given by H = VR²
A direct proportional relationship is that in which as one variable increases the other variable increases and vice versa.
An indirect proportional relationship is that in which as one variable increases the other variable decreases and vice versa.
Let H represent the altitude and R represent the radius.
H ∝ R²
H = VR²; V (volume) is the constant of proportionality
The variation equation showing the relationship between H, V and R is given by H = VR²
Find out more at: https://brainly.com/question/13977805
Please help on timer ill give 15 brainlist
Answer:
B
Step-by-step explanation:
if 5/x = 15/x+20, what is the value of x/5?
Answer:
x = 1/2 or 0.5
Step-by-step explanation:
Brainliest Please!!
- Hermionia
Answer:
The answer is -1/2
Step-by-step explanation:
5/x = 15/x+20
5/x-15/x=20
-10/x=20
-10=20x
x= -10/20
x= -1/2
1. A man walks for 12 hours. The table shows his
total distance, in miles, for several walking
times
3
5
8
10
12
Distance
6.3 9.2 15.7
19.5
24.5
|(Miles)
What does the correlation coefficient for the
data indicate about the strength of the linear
association between the time and the distance?
Answer:
Weak positive correlation
Step-by-step explanation:
Just trust me
Also it’s positive in a graph but it’s not changing that much so it’s weak
PLEAS HELP. EASY. HIGH POINTS
Phoebe surveyed T E E N S and A D U L T S to find the average number of hours of sleep they get during the week. Her results are shown below. Which statement regarding her survey results is true?
Hours of Sleep for T E E N S
A box-and-whisker plot. The number line goes from 1 to 12. The whiskers range from 2.5 to 12, and the box ranges from 5 to 8.5. A line divides the box at 7.
Hours of Sleep for A D U L T S
A box-and-whisker plot. The number line goes from 1 to 12. The whiskers range from 3 to 11, and the box ranges from 5 to 7.5. A line divides the box at 7.
A D U L T S get more hours of sleep on average than T E E N S
A D U L TS have less variability in the hours of sleep.
T E E N S have less variability in the hours of sleep.
T E E N S get less sleep on average than adults.
Answer:
Phoebe surveyed teens and adults to find the average number of hours of sleep they get during the week. Her results are shown below. Which statement regarding her survey results is true?
Hours of Sleep for Teens
A box-and-whisker plot. The number line goes from 1 to 12. The whiskers range from 2.5 to 12, and the box ranges from 5 to 8.5. A line divides the box at 7.
adult have less variability in the sleep hours because well they work more then us and us teens we have school starting at 7:45 am and the adult have to wake up to go to work or having to stay up
hope this can help
what is the slope of the line that passers through the point(9,-1)and(4,-11)
Answer:
slope is 2
Step-by-step explanation:
-11-(-1) =-10
4-9=-5
-10/-5
=2
Slope-2x
WILL MARK BRAINLIEST!!!! BRAINLIEST!
Write 206 in base 7
Answer:
104
Step-by-step explanation:
Answer:
appreciate it man
Step-by-step explanation:
best of luck
Complete the table showing the price of different amounts of grapes at this rate
jacks mom purchased a savings bond for jack. the value of the savings bond increases by 5% each year. one year after it was purchased, the value of the savings bond was $210. find the value of the bond when jacks mom purchased it.
Answer:
Step-by-step explanation:
Find the fifth term in the geometric
sequence, given the first term and
the common ratio.
a1 = 2 and r = 3
a5 = [ ?]
The fifth term is 162 in the geometric sequence.
What is geometric sequence?The geometric sequence defined as a series represents the sum of the terms in a finite or infinite geometric sequence. The successive terms in this series share a common ratio.
The nth term of a geometric progression is expressed as
Tₙ = arⁿ⁻¹
Where a is the first term, r is the common ratio
What is arithmetic sequence?A arithmetic sequence is defined as an arrangement of numbers which is particular order.
The formula to find the general term of an arithmetic sequence is,
aₙ = a₁ + (n-1)d
Given data :
First term of sequence geometric (a₁) = 2
The common ratio of geometric (r) = 3
To determine the fifth term of geometric sequence
Let the fifth term of sequence = a₅
The nth term of a geometric sequence is expressed as :
Tₙ = a₁rⁿ⁻¹
Substitute the values of n = 5, a₁ =2 and r = 3 in the formula,
T₅ = (2)(3)⁵⁻¹
T₅ = (2)(3)⁴
T₅ = (2)(81)
T₅ = 162
Hence, the fifth term is 162 in the geometric sequence
Learn more about geometric sequence here :
https://brainly.com/question/11266123
#SPJ5
Someone, please help me fill this out
Answer:
Here is the summary:
y = 13x+5 satisfies the points (0, 5) and (-2, -21)y = -3x satisfies the points (0, 0), (-5, -15) and (-3, 9)y = x-10 satisfies the points (8, -2)Step-by-step explanation:
Given the equation
y = 13x+5y = -3xy = x-10The points which satisfy the equation y=13x+5
y = 13x+5
Checking the point (0, 5)
5 = 13(0)+5
5 = 0 + 5
5 = 5
TRUE
Checking the point (-2, -21)
-21 = 13(-2)+5
-21 = -26 + 5
-21 = -21
TRUE
The points which satisfy the equation y=-3x
y = -3x
Checking the point (0, 0)
0 = -3(0)
0 = 0
TRUE
Checking the point (-5, -15)
y = -3x
-15 = -3(-5)
-15 = -15
TRUE
Checking the point (-3, 9)
y = -3x
9 = -3(-3)
9 = 9
TRUE
The points which satisfy the equation y=x-10
y = x-10
Checking (8, -2)
-2 = 8 - 10
-2 = -2
TRUE
Therefore, from the above calculations we conclude the summary:
Here is the summary:
y = 13x+5 satisfies the points (0, 5) and (-2, -21)y = -3x satisfies the points (0, 0), (-5, -15) and (-3, 9)y = x-10 satisfies the points (8, -2)find perimeter of semicircle if radius is 22 cm (π=22/7)
Answer:
To calculate the perimeter of a circle we have this formula:
[tex]P = 2\pi r[/tex]
And, if we're going to calculate for a semicircle, we should divide it by 2
We should also take into account the diameter, as, if it's a semicircle, we also have to add the base of it, which will have the diameter length
Knowing this, we can see the formula to calculate this specific perimeter
[tex]\frac{2\pi r}{2} + 2r[/tex]
Now, we can replace r by 22:
[tex]\frac{2\pi *22}{2} + 2*22 \approx 113.12[/tex]
So the perimeter is approximately 113.12 cm
Find the solution of the systems of equations
Answer:
-2,-2
Step-by-step explanation:
-
Answer:
................(-2,-2)
i need an opinion, what do y'all think about this note I wrote. I have another one for another person.
Dear Sierra
I know I have made mistakes in the past
And the happiness inside of me will never last
I'm sorry for all the things I have done
Everything I do was so you will have fun
I'm sorry I'm not there for you
Through all the rough stuff that you been through
I'm sorry I'm not there to help you with your homework
I'm sorry I'm not there to praise your artwork
I've been trying to be there for some time now
Thinking I can be there some how
But as it turns out I'm just a failure
No one noticed my sad behavior
Not Evan you, I mean who would
No one can help, nobody ever could
I geuss I'm just stuck here on this Earth
You don't need me, I mean what am I worth
Nothing, right. It won't hurt because it's the truth
My life is like court now that everyone voted at the booth
It's time for me to go, the majority rule
I'm tierd of being here looking like a fool
Times running out, it's funny how it just flyes by
I love you Sierra and this is Goodbye
Answer:
this is really good but very sad so if thats what you're going for then you did a really good job!! :(
Step-by-step explanation:
Answer:
i love it!!! very cool
Step-by-step explanation:
Solve the system by substitution -4-y=17 and 4y=x
Answer:
x = -84
y = -21
Step-by-step explanation:
4 - y = 17
4y = x
Use the first equation to solve for y
4 - y = 17
y = 4 - 17
y = -21
In the second equation, get y on its own.
4y = x
y = x/4
Substitute the new second equation into the new first equation
-21 = x/4
-21 * 4 = x
x = -84
Someone please answer these questions I need help!! :(
Answer:
4. the answer is 20
5. x=12 y=30
6. MLV = TUV bySSS
7. ABC=HGF by SSS
to show work:
4. 15/12=25/x (cross multiply)
=15x=300 (divide both sides by 15)
= x=20
5. the triangle is equilatieral so all the angles are the same. this means 60=2y.
if you isolate the variable and divide both sides by 2, you get y=30
6. 49/14 = 28/8 ?
if you solve both the division problems, they both equal 3.5, meaning the side lengths are the same so the rule would be SSS or side side side
and you do the same thing with the next triangle too
hope this helps!! also brainliest would be nice but you dont have to
4.8n + 3.2n simply the expression mathematics
What is the solution set for this quadratic equation 2(x-3)^2-4=28
Answer: x₁=7, x₂=-1
Step-by-step explanation:
(x-3)^2= x^2-6x+9
2(x^2-6x+9)=28+4
x^2-6x+9=16
x^2-6x-7=0
you use the quadratic equation will give you 2 roots,
x₁=7, x₂=-1
25 points-
Please help me-
Answer:
alr i tried, i hope i got them right! <3 pls let me know if i got them wrong.
1. 108 | 6x12 = 72 9x12 = 108 |
2. 91 | 13x7 = 19
3. 19 | 108/6 90/6 = 19/15 |
4. 50. 400/8 = 50
5. 50. 300/6
hope this helped! <3
Step-by-step explanation:
please help me on this!
Answer:
1- no
2- yes
3- no
4- yes
the ones that are no are because they either have x-values that repeat or they have y-values that repeat
Step-by-step explanation:
How do I solve this equation?
Answer:
[tex]x<3[/tex]
Step-by-step explanation:
STEP 1: Move all terms not containing [tex]x[/tex] to the right side of the inequality.
[tex]5x<15[/tex]
STEP 2: Divide each term by [tex]5[/tex] and simplify.
[tex]x<3[/tex]
STEP 3: The result can be shown in multiple forms.
Inequality Form:
[tex]x<3[/tex]
Interval Notation:
[tex](-[/tex]∞[tex],3)[/tex]
Is 8 a solution to 1/2 x + 9= 13 ?
Answer:
yes the solution is 8
Step-by-step explanation:
subtract 9 from both sides
1/2x+9-9=13-9
simplify
1/2x=4
multiply both sides by 2
2 x 1/2=4 x 2
simplify
x=8
20 points, please help I really bloody need it
2. The equation x+2= v-----3x+10 is of the form x+a=v------bx+c ,where a, b, and c are all positive integers and b>1. Using this equation as a model, create your own equation that has extraneous solutions.
(a) Using trial and error with numbers for a, b, and c, create an equation of the form x+a=v-----bx+c, where a, b, and c are all positive integers and b>1 such that 7 is a solution. (Hint: Substitute 7 for x, and choose a value for a. Then square both sides so you can choose a, b, and c that will make the equation true.)
(b) Solve the equation you created in Part 2a.
(c) If your solution in Part 2b did not have an extraneous solution, revise your equation so that 7 is one solution and there is an extraneous solution. If your solution in Part 2b did have an extraneous solution, create another equation with different values of a, b, and c that also has 7 as one solution and an extraneous solution.
Answer:
x plus 3y minus 63
Step-by-step explanation:
50 PTS Please help me answer this asap!
Answer:
1. 2x + 1 ≤ 3
2. 1 + 3x ≥ -5
3. 5x - 7 ≥ 17
4. 5 - 3x ≥ 11
Step-by-step explanation:
Ok
5x - 7 ≥ 17
subtract 7 and u get 5x ≥ 10
divide that and you get ≥ 2
so 3 goes with that one
1 + 3x ≥ -5
subtract 1 and you get 3x ≥ -6
divide that and youll get x ≥ -2
so 2 goes with this one
2x + 1 ≤ 3
subtract 1 and u get 2x ≤ 2
divide them and you get x ≤ 1
so 1 goes with this one
5 - 3x ≥ 11
subtract 5 and u get -3x ≥ 6
divide it and u get x ≥ -2
so 4 goes with this one
Hoped this helps :)
also btw Brainly steals half the points you give out so instead of 15 ur giving me 25.
A movie lasts 2 1/3 hours james watches 3/4 of the movie then pauses it while he eat dinner how long did he spend watching the movie. And how did you solve it.
Rewrite the length of the movie as an improper fraction.
2 1/3 = 7/3
Now multiply the length of the movie by 3/4
7/3 x 3/4 = (7 x3) / (3 x 4) = 21/12 = 1 3/4 hours
I REALLY NEED HELP I FORGOT HOW TO DO THIS :(
Answer:
117.8
Step-by-step explanation:
i used heron's formula
√s(s-a)(s-b)(s-c)
s= (20+16+33)/2 = 34.5
√34.5(34.5-20)(34.5-16)(34.5-33)
= 117.8