Answer:
[tex]\displaystyle b = -22[/tex]
Step-by-step explanation:
We are given the function:
[tex]\displaystyle f(x) = (x^3+bx+6)(g(x))[/tex]
Where b is a constant and g is a differentiable function.
And we want to determine the value of b such that f'(2) = 0.
Find f' using the product rule:
[tex]\displaystyle \begin{aligned} f'(x) & = \frac{d}{dx}\left[ (x^3+bx+6)(g(x))\right] \\ \\ & = \frac{d}{dx}\left[ x^3 + bx + 6\right] g(x) + (x^3+bx+6)\frac{d}{dx}\left[ g(x)\right] \\ \\ & = (3x^2+b)(g(x)) + (x^3 + bx + 6)(g'(x))\end{aligned}[/tex]
Substitute using known values and solve for b:
[tex]\displaystyle \begin{aligned}f'(2) = 0 & = (3(2)^2+b)(g(2)) + ((2)^3+b(2)+6)(g'(2)) \\ \\ 0 & = (12+b)(3) + (14+2b)(-1) \\ \\ 0 & = 22 +b \\ \\ b & = -22\end{aligned}[/tex]
In conclusion, the value of b is -22.
The function f is given b is a constant and g is a differentiable function the value b (-8.4),
Let's start by finding the derivative of the given function f(x) with respect to x:
f(x) = (x³ + bx + 6) × g(x)
Using the product rule for differentiation, the derivative of f(x) is:
f'(x) = (x³ + bx + 6) × g'(x) + g(x) × (3x² + b)
Now we are interested in finding the value of b for which f'(2) = 0. So, let's plug in x = 2 and use the information given about g(2) and g'(2):
f'(2) = (2³ + 2b + 6) × g'(2) + g(2) × (3 × 2² + b)
Since g(2) = 3 and g'(2) = -1,
f'(2) = (8 + 2b + 6) × (-1) + 3 × (3 × 4 + b)
= (2b + 14 - 8) + 3× (12 + b)
= 2b + 6 + 36 + 3b
= 5b + 42
Now, we want to find the value of b for which f'(2) = 0:
5b + 42 = 0
Subtracting 42 from both sides:
5b = -42
Dividing both sides by 5:
b = -8.4
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Complete question:
The function f is given by f(x)=(x^{3}+bx+6)(g(x)), where b is a constant and g is a differentiable function satisfying g(2)=3 and g′(2)=−1. For what value of b is f′(2)=0?
7
10
12
22
-8.4
How can multistep linear equations be written to represent different
scenarios?
Answer:
Linear equations use one or more variables where one variable is dependent on the other. Almost any situation where there is an unknown quantity can be represented by a linear equation, like figuring out income over time, calculating mileage rates, or predicting profit
help me please thanks
Answer:
9.25 would be the value of x
Explanation:
Perimeter = 2(l + w)
2(13.25 + 9.25)
= 45
The income elasticity is +2 and income increases by
20%. Sales were 5000 units, what will they be now?
Answer:
Step-by-step explanation:
The income elasticity is +2.5 and income increases by 20%. Sales were 5000 units, what will they be now? If the income elasticity is +2.5, income increases by 20% and sales were 5000 units, then the sales will increase by 20%*2.5 = 50% to 7500 units.
NEED HELP RELATIONSHIP IN TRIANGLES
We have: PT = NT <=> 4x - 17 = x + 10 <=> 3x = 27 <=> x = 9
=> NT = 4x - 17 = 4.9 - 17 = 19
Δ RNT have:
[tex]RT^2 = NT^2 -RN^2 =19^2 -14^2=165\\=>RT=\sqrt{165} [= 12.84523258][/tex]
Ok done. Thank to me :>
( 4 1 + 4 5 ) ^ 2 + 4 3 =
Answer: 7,439
Step-by-step explanation:
(86)^2 + 43
7396 + 43 = 7,439
I'm pretty sure that the other user has the same answer. (godlike74)
y=1/4x−2y=−2x+3 help solve problem.
Answer:
(x, y) = (2 2/9, -1 4/9)
Step-by-step explanation:
Equate the values of y and solve for x.
1/4x -2 = -2x +3
(2 1/4)x = 5 . . . . . . . . add 2+2x to both sides
x = 20/9 = 2 2/9 . . . multiply by 4/9
y = -2(2 2/9) +3 = -4 4/9 +3 . . . . substitute for x in the second equation
y = -1 4/9
The solution is x = 2 2/9, y = -1 4/9.
(Brainliest question) Which type of study best describes the following research most likely to be done? A researcher is trying to determine the effects of animal habitats and animal populations after forest fires. So she visits places that have had a naturally occurring Forest fire to study the area.
Experimental study
Observational study
Simulation study
Double blind study
Answer:
Observational study
Step-by-step explanation:
See the researcher visits the forest.She want to experience or observe the forest fire.She want to observe how it affects the animals.Hence it's observational study
Please help me simplify this answer.
Answer:
D
Step-by-step explanation:
if x =4 and y =5
the expression = 818.3396
and D the only expression done the same result
please help! will give brainliest:)
Solve the following system:
2x - z=14 a
10
3x - y + 5z = 0
(4x + 2y + 3z = -2
If your money doubles once every 30 minutes and your start with $12, how much money will you have in 1.5 day?
Answer:
$1728
Step-by-step explanation:
1.5 days is 36 hrs
36 hrs is 2160 mins
2160/30 = 72 (this is the amount of times our money will be doubled)
72*2 = 144
$12*144 = $1728
5. Which of the following linear expressions is a factor of the cubic polynomial x^3 + 9x² +16x-12?
(1) x+6
(3) r-3
(2) x-1
(4) x+2
Answer:
(1) x+6
Step-by-step explanation:
Possible rational zeroes include ±1, ±2, ±3, ±4, ±6, ±12
Check each answer choice with synthetic division:
1 | 1 9 16 -12
__1_10_26
1 10 26 | 14
-2 | 1 9 16 -12
__-2_-14_-4
1 7 2 | -16
-6 | 1 9 16 -12
__-6_-18_12
1 3 -2 | 0
Therefore, x+6 is a factor of the polynomial
Answer:
(1) x+6
Step-by-step explanation:
How to solve 22 – 3y > 7
Answer:
y < 5
Step-by-step explanation:
22 – 3y > 7
=> 22 – 7 > 3y
=> 15 > 3y
=> y < 5
Therefore, y < 5 is the solution.
Hoped this helped.
A vehicle was travelling at a speed of 72km per hour. What distance did it cover in 2 hours? A. 158km B. 148km C. 168km D. 144km
Answer:
D. 144km
Step-by-step explanation:
If the vehicle travels 72km every hour, in two hours, it will drive 144km. (72x2=144)
Y<-3 which is the solution:
A) 5
B) 0
C)-2
D)-5
Y needs to be less than -3 the larger the negative number the further from 0 it is so -5 would be less than -3
Answer: -5
Write a fraction with a denominator of 9 whose equivalent percent is less than 100%. In complete sentences, explain why the fraction is less than 100%.
The fraction is 8/9
Lets find percentage
8/9(100)800/988.89%Done!
witch expression an be placed on the right side of the equal sign to form an equation 5 + 2/3 ? K12 6 grade
Hanna has 16 pencils. She gets 3 new
pencils from Mrs. Lewis. She divides
the pencils equally between her 2
sisters. How many pencils does each
sister get?
Answer:
9.5
Step-by-step explanation:
If Hanna starts off with 16, and Mrs. Lewis GIVES(add) her 3 more, then she has 19 because 16+3=19. Then we divide by 2 because there are 2 sisters. so 19/2 = 9.5
Hello! I hope this helped you. If this is wrong please let me know. Thank you.
The weights of adult polar bears, the largest bear species in North America, have a mean of 950 pounds and standard
deviation of 84 pounds. What is the weight of a polar bear that has a z-score for weight of -1.50?
Find the Z-table here.
O 126 pounds
O 824 pounds
948.5 pounds
O 951.5 pounds
O 1,076 pounds
The weight of 824 pounds of a polar bear has a z-score of -1.50.
The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean,\sigma=standard\ deviation[/tex]
Given that μ = 950, σ = 84
For z = -1.50:
[tex]-1.50=\frac{x-950}{84}\\\\x-950=-126\\\\x=824[/tex]
The weight of 824 pounds of a polar bear has a z-score of -1.50.
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7. A boutique is offering a 25% discount on purchase made in cash. Calculate the cash price Janelle paid for articles totaled to $465.
solve the system using substitution x+5y=0 3y+2x=-21
Answer:
[tex]\left \{ {{x = -15} \atop {y=3}} \right.[/tex]
Step-by-step explanation:
[tex]\left \{ {{x + 5y = 0} (1) \atop {3y + 2x = -21}(2)} \right. <=> \left \{ {{x = -5y} \atop {3y + 2x = -21}} \right. <=> \left \{ {{x = -5y} \atop {3y + 2*(-5y) = -21}} \right. <=> \left \{ {{x = -5y} \atop {3y - 10y = -21}} \right. \\<=> \left \{ {{x = -5y } \atop {-7y = -21}} \right. <=> \left \{ {{x = -5y} \atop {y= 3 }} \right. <=> \left \{ {{x = -5 * 3} \atop {y=3}} \right.=> \left \{ {{x=-15} \atop {y=3}} \right.[/tex]
Todd drinks 4 liters of water every day. There are approximately 29.6 Milliliters in 1 fluid ounce. Which measurement is closest of to the number of fluid ounces in 4 liters/
A.7 fl oz
B. 34 fl oz
C. 118 fl oz
D. 135 fl oz
Answer:
D is the closest. The exact is 135.256
Determine if the sequence is geometric . If it is , find the common ratio , the explicit formula and the recursive formula .
1. -40 , 20 , -100 , 500
2. 4 , 20 , 100 , 500
3. 4 , 24 , 144, 864
5. 3 , -12 , 48 , -192
Step-by-step explanation:
if it is a geometric sequence, then
sn = sn-1 × r
with r being the common ratio.
1.
s2 = s1 × r
20 = -40 × r
r = 20/-40 = -1/2
but the same r has to apply to all other terms, if it is geometric.
s3 = s2 × r
-100 = 20 × -1/2 = -10
this is wrong, so, it is not geometric.
2.
s2 = s1 × r
20 = 4 × r
r = 20/4 = 5
but the same r has to apply to all other terms, if it is geometric.
s3 = s2 × r
100 = 20 × 5 = 100
s4 = s3 × r
500 = 100 × 5 = 500
this is all correct, so, it is geometric.
sn = sn-1 × 5
sn = s1 × 5^(n-1) = 4 × 5^(n-1)
3.
s2 = s1 × r
24 = 4 × r
r = 24/4 = 6
but the same r has to apply to all other terms, if it is geometric.
s3 = s2 × r
144 = 24 × 6 = 144
s4 = s3 × r
864 = 144 × 6 = 864
this is all correct, so, it is geometric.
sn = sn-1 × 6
sn = s1 × 6^(n-1) = 4 × 6^(n-1)
5.
s2 = s1 × r
-12 = 3 × r
r = -12/3 = -4
but the same r has to apply to all other terms, if it is geometric.
s3 = s2 × r
48 = -12 × -4 = 48
s4 = s3 × r
-192 = 48 × -4 = -192
this is all correct, so, it is geometric.
sn = sn-1 × -4
sn = s1 × (-4)^(n-1) = 3 × (-4)^(n-1)
Sarah walked ½ mile yesterday morning and ¾ mile yesterday afternoon. What was the total distance walked by Sarah?
Answer:
1.25 miles or 5/4
Step-by-step explanation:
Take the two distances and add them together and simplify.
Answer: 1 & 1/4 mile
Explanation:
1/2 = 2/4
She walked 2/4 of a mile in the morning and 3/4 of a mile in the afternoon. The total she walked is 5/4 of a mile. We add the numerators and place the sum over the common denominator.
The improper fraction 5/4 converts to the mixed number 1 & 1/4, since,
5/4 = (4+1)/4 = 4/4 + 1/4 = 1 + 1/4 = 1 & 1/4
A recipe for lemonade called for 1 cup of sugar and 5cups of water.How much sugar is used per cup of water
Which side lengths form a right triangle?
Choose all answers that apply
(Choice A)
A
3
,
27
,
6
3,
27
,63, comma, square root of, 27, end square root, comma, 6
(Choice B)
B
8
,
15
,
17
8,15,178, comma, 15, comma, 17
(Choice C)
C
Answer:
4, 7.5, 8.54,7.5,8.5
Step-by-step explanation:
We can use the Pythagorean Theorem to see if the side lengths will form a right triangle.
The equation for the Pythagorean Theorem is
a^2 + b^2 = c^2a
2
+b
2
=c
2
a, squared, plus, b, squared, equals, c, squared
where aaa and bbb are the lengths of the two legs of the triangle, and ccc is the length of the hypotenuse.
[How can I tell which side is the hypotenuse?]
Hint #22 / 5
Let's check each set of numbers:
\begin{aligned} a^2 + b^2 &= c^2 \\\\ 4^2 +\sqrt8^2 &\stackrel{\large?}{=} 24^2 \\\\ 16 + 8&\stackrel{\large?}{=} 576\\\\ 24&\neq 576\\\\ \end{aligned}
a
2
+b
2
4
2
+
8
2
16+8
24
=c
2
=
?
24
2
=
?
576
=576
The side lengths 4, \sqrt8, 244,
8
,244, comma, square root of, 8, end square root, comma, 24 do not form a right triangle.
Hint #33 / 5
\begin{aligned} a^2 + b^2 &= c^2 \\\\ 5^2 + 5^2 &\stackrel{\large?}{=} 5^2 \\\\ 25+ 25&\stackrel{\large?}{=} 25\\\\ 50&\neq 25\\\\ \end{aligned}
a
2
+b
2
5
2
+5
2
25+25
50
=c
2
=
?
5
2
=
?
25
=25
The side lengths 5, 5, 55,5,55, comma, 5, comma, 5 do not form a right triangle.
Hint #44 / 5
\begin{aligned} a^2 + b^2 &= c^2 \\\\ 4^2 + 7.5^2 &\stackrel{\large?}{=} 8.5^2 \\\\ 16+ 56.25&\stackrel{\large?}{=} 72.25\\\\ 72.25&\stackrel{\checkmark}{=} 72.25\\\\ \end{aligned}
a
2
+b
2
4
2
+7.5
2
16+56.25
72.25
=c
2
=
?
8.5
2
=
?
72.25
=
✓
72.25
Answer:
4, 7.5, 8.5
Step-by-step explanation:
I had this question on Khan, and it was right (:
ROCKETS The height in feet of a rocket t seconds after launch is modeled
by h(t) =–16t2 + 72t. Find its average speed from 3 to 4 seconds.
F-56 ft/s
G40 ft/s H 40 ft/s
J 56 ft/s
The average speed of the rocket from 3 to 4 seconds after launch is: -40 ft/s
Given the equation as a model, h(t) =–16t² + 72t.
Average speed from 3 to 4 seconds = [tex]\frac{h(4) - h(3)}{4 - 3}[/tex]
Find h(4):
h(t) =–16t² + 72t
Substitute 4 for t in the equation h(t) =–16t² + 72th(4) = -16(4)² + 72(4)
h(4) = -256 + 288
h(4) = 32
Find h(3):
h(t) = -16t² + 72t
Substitute 3 for t in the equation h(t) =–16t² + 72th(3) = -16(3)² + 72(3)
h(3) = -144 + 216
h(3) = 72
Plug in the value into [tex]\frac{h(4) - h(3)}{4 - 3}[/tex]:
average speed from 3 to 4 secs = [tex]\frac{32 - 72}{4 - 3} = -40[/tex]
Therefore, the average speed of the rocket from 3 to 4 seconds after launch is: -40 ft/s
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[tex]Simplify..... \\ \\ \frac{6x ^{4} {y}^{2} \times 4 {x}^{6} {y}^{3} }{12 {x}^{5} {y}^{4} } [/tex]
..............................
Hope it helps.
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15. Kate plays a card game with two friends. She gives 5 cards to each player. Ten plus what number is equal to the total number of cards Kate gives out? Write an equation to show and solve the problem.
Answer:
i believe it would be 0
Step-by-step explanation:
2*5 = x
2*5 = 10
x = 10
10 + y = x
10 + y = 10
-10 -10
-----------------
y = 0
the number is 0
hope this helps! :D
have a miraculous day!! <3
Solve for X
2/3 x +10/60 =100/60
Answer:
2 1/4
Step-by-step explanation:
subtract 10/60 from each side to get:
2/3x = 90/60
multiply each side by 3/2 to get:
x = 270/120
x = 27/12 or 2 1/4
Determine the center and radius of the following circle equation:
x? + y2 - 2x - 12y +36 = 0
Step-by-step explanation:
x²+ y² -12x - 18y +17 = 0 means : (x²-12x+36)-36+(y²-18y+81)-81-27 =0
(x-6)²+(y-9)² =12²....standard form when the center is (-6 , 9) and radius 12
Answer:
The center is at (1, 6) and the radius is 1.
Step-by-step explanation:
x^2 + y^2 - 2x - 12y +36 = 0
Convert to standard form:
x^2 - 2x + y^2 - 12y = -36
(x - 1)^2 - 1 + (y - 6)^2 - 36 = -36
(x - 1)^2 + (y - 6)^2 = -36 + 36 + 1
(x - 1)^2 + (y - 6)^2 = 1
The center is at (1, 6) and the radius is 1.