If g(x)=x4−3x3−x, the value of x such that g′(x)=12 is x = 2.67
The given function is:
[tex]g(x)=x^4-3x^3-x[/tex]
The derivative of the function g(x) is calculated below
[tex]g'(x)=4x^3-9x^2[/tex]
The question indicates that g'(x) = 12
This means that we are going to equate the derivative of g(x) gotten above to 12
[tex]4x^3-9x^2=12[/tex]
Solving the cubic equation above
The only real valid value of x is 2.67
Therefore, the value of x such that g′(x)=12 is x = 2.67
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Thanksgiving Dinner Logic Grid Puzzle
Answer:
Step-by-step explanation:
Ella buys a computer for $785 her local tax rate is 7% how much does Ella pay for the computer
Answer:
$839.95
Step-by-step explanation:
There are 2 ways to go about this. First, the logical method is to calculate the tax and then add it to the price:
7%=7/100=0.07
7% “of” the amount says to multiply. The word “of” in maths means multiply:
0.07×$785=$54.95. The tax is $54.95
The computer costs $785. Plus the tax $54.95: $785+$54.95=$839.95
She pays $839.95 for the computer, including tax.
You can do this calculation in 1 step. If you are like me, I like to do my math as quickly and as efficiently as possible. What we did above is this:
100% of the computer price plus 7% of the computer price to get the total cost taxes in.
100% + 7% = 107%. And 107% = 1.07
So we have the following:
$785×1.07=$839.95
Hope this helps :)
Answer:
$839.95
Step-by-step explanation:
From the question, we are informed that Ella buys a computer for $785 and that her local tax rate is 7%. The amount that Ella pay for the computer, including tax will be:
= $785 + (7% × $785)
= $785 + (0.07 × $785)
= $785 + $54.95
= $839.95
help me graph this plzzzzzz mate
Answer:
Should look like this
Step-by-step explanation:
y-intercept = 2
slope = 1
how many times can 10 go into 5228
Find the perimeter. Simplify your answer.
Answer:
28w + 12Step-by-step explanation:
Perimeter = 9w + 1 + 8w + 3 + 6w + 8 + 5w
= 28w + 12...ans
Hope it Helps you!!HELPPPPPPPPPPPPPPPPPP
a farmer takes 1 week to fill 6 bins of squash. At this rate,how long will it take to fill 360 bins
Answer:
60 weeks
Step-by-step explanation:
Setup a proportion.
[tex] \frac{weeks}{bins} \frac{1}{6} = \frac{w}{360} [/tex]
cross multiple
[tex]6w = 360[/tex]
now divide by 6
[tex] \frac{6w}{6} = \frac{360}{6} [/tex]
[tex]w = 60[/tex]
Answer/Step-by-step explanation:
Important Information:
1 Week to fill 6 Bins
Question to answer:
How Long will it takes to fill 360 Bins
Solution/Explanation:
360 Divided by 6 =
60 Week
A rectangle measures 2 2/5 inches by 4 1/8 inches. What is its area
Answer:
A = 9 9/10 sq inches
Step-by-step explanation:
A = lw
A = 12/5 x 33/8
A = 396/40
A = 9 9/10 sq inches
Adding & Subtracting Decimals
Add the decimals using the table.
46.9 + 14.74
+
Answer:
19.43
Step-by-step explanation:
This is a trick for you.
Make the numbers to become whole numbers(1474+469)
After adding the whole numbers,the decimal point were 2 so,move 2jumps from the right to the left which will give you 19.43 as your answer.
A soap manufacturing company packs 5252 soap bars per carton.
Find the number of soap bars that can be packed in 99 cartons, using a direct variation model.
If this is the question in picture below.
Answer:
468
Step-by-step explanation:
A company that manufactures golf balls produces a new type of ball that is supposed to travel significantly farther than the company’s previous golf ball. To determine this, 40 new-style golf balls and 40 original-style golf balls are randomly selected from the company’s production line on a specific day. The balls are then placed in a bag and shaken. A golf pro then selects a ball and hits it. The distance the ball travels is then measured. The bag is shaken again, and the golf pro selects another ball to hit. She continues this procedure until all 80 of the golf balls are hit.
Has the principle of comparison been addressed in this experimental design?
Yes, because the balls are randomly selected, the distances of the new ball can be compared to the distances of the original ball.
Yes, because the original ball type is included in this experiment, the distances the different balls travel can be accurately compared.
No, because a placebo ball was
The design of the experiment is such that the knowledge of the type of
ball being hit does nit influence the outcome of the experiment.
The correct option is; Yes, because the balls are randomly selected, the distance of the new ball can be compared to the distances of the original ball.Reasons:
The aim of the experiment is to determine if the new type of ball travels farther than the company's previous golf ball.
The design of the experiment is as follows;
Number of the previous golf ball in the experiment = 40
Number of the new type of golf ball used in the experiment = 40
The order in which the ball are selected from the bag = Randomly
The subject of the experiment = A golf pro
The sample size of each sample is larger than 30, and therefore, the
distribution can be taken as approximately normal.
The principle of comparison has been addressed in the experiment
because the golf pro that is subject to the treatment will react more
accurately to the change in the variable, given that, the previous golf ball
serves as a placebo in the study and after all the balls are hit, the distance
travelled by each set can be determined.
The correct option is therefore;
Yes, because the balls are randomly selected, the distance of the new ball can be compared to the distances of the original ball.Learn more experimental design here:
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what is the square of 0.81?
Answer:
0.9 or 9/10Step-by-step explanation:
what is the square of 0.81?
0.9
The square root of 0.81 is equal to 0.9 or 9/10
--------------
check
0.9 * 0.9 = 0.81
the answer is good
Help me someone please my teacher needs this soon or I’m going to fail school
Answer:
A. 9π/3 · 2Step-by-step explanation:
Use the equation of circumference and substitute the value of radius:
C = 2πrC = 2π*3 = 6π inchesCompare the answer choices to find the correct one, which is:
9π/3 · 2 = 3π · 2 = 6π[tex]\\ \sf\longmapsto Circumference=2\pi r[/tex]
[tex]\\ \sf\longmapsto Circumference=2(3)(π)=6\pi[/tex]
Now
Check 1st option
[tex]\\ \sf\longmapsto \dfrac{9\pi}{3}.2=6\pi[/tex]
What is the product? (5r − 4)(r2 − 6r 4) 5r3 − 34r2 44r − 16 5r3 − 4r2 14r − 16 5r3 − 6r − 16 5r3 10r − 16.
Answer:
5r³ - 34r² + 44r - 16
Step-by-step explanation:
use the distributive property
5r × (r² − 6r + 4) - 4× (r² − 6r + 4)
5r³ - 30r² + 20r - 4r² + 24r - 16
combine like terms
5r³ - 30r² - 4r² + 20r + 24r - 16
5r³ - 34r² + 44r - 16
Hope this helped!!
Answer:
A. 5r3 − 34r2 + 44r − 16
Step-by-step explanation:
The distance from Jason's house to school is 0.9 kilometer. What is this distance in meters?
The distance from Jason's house to school is
meters.
Answer:
900 meters
In 0.9 move the decimal two times to the right
That makes it 900 meters
After a baby was born, she began to gain weight at a rate of 1.5 pounds per month. The weight of the baby at birth was 12 pounds. Write an equation for W,W, in terms of t,t, representing weight, in pounds, of the newborn baby tt months after birth.
What we know:
The baby gains 1.5 pounds per month.
Its weight at birth is 12 pounds.
Therefore, when looking to find the weight after t time, we have to take the constant and the rate of change and place them into the equation. This means our equation will look something like this:
W(t) = Rate of Change x number of months + weight at birth.
Or
W(t) = 1.5(t) + 12
So if in 4 months we look at the weight, the baby will be:
1.5 (4) + 12 = W(t)
6 + 12 = W(t)
18 = W(t)
After 4 months the baby is 18 pounds.
Answer: W(t) = 1.5(t) + 12
I hope this helps! :)
Gigi graphs the parabola (x+1)2=2(y−3).
How does she proceed?
Drag a value, coordinates, equation, or word to the boxes to correctly complete the statements.
After graphing the parabola [tex](x+1)^2=2(y-3)[/tex], she can fill the boxes as follows:
Gigi identifies that the vertex of the parabola is [tex](-1, 3)[/tex]. The parabola opens up, and the focus is [tex]\frac{1}{2}[/tex] unit away from the vertex. The directrix is [tex]1[/tex] unit from the focus. The focus is the point [tex](-1, \frac{7}{2})[/tex]. The directrix of the equation is [tex]y=\frac{5}{2}[/tex].
Since Gigi's parabola has the x-term squared, then the parabola has the general formula
[tex](x-h)^2=4p(y-k)[/tex]
So,
[tex]x-h=x+1 \implies h=-1[/tex]
[tex]y-k=y-3\implies k=3[/tex]
The vertex is
[tex](h,k)=(-1,3)[/tex]
The focus is
[tex](h,k+p)=(-1,3+\frac{1}{2})\\=(-1,\frac{7}{2})[/tex]
The directrix is
[tex]y=k-p=3-\frac{1}{2}=\frac{5}{2}[/tex]
The other values can be computed as follows;
Direction the parabola opens: Since the value of p is positive, the parabola opens up.
Distance of focus from vertex: The focus and vertex both have the same x position, so the distance will be in terms of the y-coordinates only. The distance from the focus to the vertex is
[tex]\frac{7}{2}-3=\frac{1}{2}\text{ unit}[/tex]
Distance of directrix to focus: The directrix is the line [tex]y=2.5[/tex]. The distance of the directrix to the focus will be
[tex]\frac{7}{2}-\frac{5}{2}=1 \text{ unit}[/tex]
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Answer:
I took the quiz.
Step-by-step explanation:
Mike can type 1/2 page in 1/6 of an hour. What is Mike's rate per hour
Answer:
4/6
Step-by-step explanation:
change 1/2 to 3/6 because of the common denominator and add 1/6 + 3/6
If you made equal monthly payments how much would you need
Answer:
For example, a borrower takes a $100,000 loan with a 6% annual interest rate for three years.
Step-by-step explanation:
Have a GREAT DAY !
what is the unit rate of gallons used per minute
What is the base of the expression 6^-4?
Answer:
The 6 is the base of the expression
Step-by-step explanation:
The base number is the number in front of the exponent.
So [tex]6^{-4}[/tex] the 6 is the base of the expression
a person whose height is 6 feet is walking away from the base of a streetlight
H,200 feet per hour. What is the speed in miles per hour?
Answer:
0.0378788 mph is the correct answer here
Richard buys a balance being priced at 799 shipping and handling or an additional 30% of the price how much shipping and handling will Richard pay
what does coplanar mean?
Answer:
Step-by-step explanation:
Co-planer
When points are in the same plane it means that the points are co-planer.
Answer:
In geometry, a set of points in space are coplanar if there exists a geometric plane that contains them all.
find the area of the parallelogram with the given information:
Answer:
There is a area of triangle and there is two trapezium so 8×17=136
solve the mean of 4,5,3,4,3,1
Answer:
3.333 recurring
Step-by-step explanation:
Add and divide for the mean
Answer:
refer to the pic attached for steps
What is 25/9 as a mix fraction?
Answer: 2 7/9
Step-by-step explanation:
Answer: 2 7/9
Step-by-step explanation:
First divide 25 by 9. You should get the answer of 2.7777777777778 which equals 2. Then to find the new numerator, you do 25-(9x2)=7. You keep the original denominator (9) and there it is. 2 7/9.
help me please i’ll give you a brain list thingy thank youu
Answer:
Are the triangles similar?
1) Both triangles are congruent by SAS ( Side Angle Side ) Postulate
2) SAS Postulate
3) congruent by ASA Postulate
4) SSS Postulate
5) congruent by AAS Postulate
6) SAS Postulate
Isosceles and Equilateral Triangles
1) by isosceles something triangle theorem
if two angles of opposite sides are congruent the sides opposite of those are congruent.
4x-12=20
x=8
2) Triangle Sum Theorem - all angles add up to 180.
with Isosceles triangle theorem.
x= 70 degrees
y= 40 degrees
3) 2x-14 = x+17 ( I think )
x=34
4) The picture is cut out.
Step-by-step explanation:
100 POINTS!!!!! WILL GIVE BRAINLIEST!!!!!!!
Show that: (a + bi)^2 = (a + b)(a − b) + 2abi
Step-by-step explanation:
(a + bi)^2 = (a + b)(a − b) + 2abi
= a² + (bi)² + 2 * a * bi
= a² + b²i² + 2abi
= as i² = -1
= a² - b² + 2abi
= (a + b) (a - b) + 2abi
The equation ( a + bi )² is simplified as A = ( a + b ) ( a - b ) + 2abi
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = ( a + bi )² be equation (1)
On simplifying the equation , we get
A = ( a )² + ( ib )² + 2iab
Now , the value of i² = -1
A = a² + i²b² + 2iab
Substituting the value of i in the equation , we get
A = a² - b² + 2iab
Now , the value of ( a² - b² ) = ( a + b ) ( a - b )
Substituting the values in the equation , we get
A = ( a + b ) ( a - b ) + 2iab
Therefore , the value of A is ( a + b ) ( a - b ) + 2iab
Hence , the equation is ( a + b ) ( a - b ) + 2abi
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