9. (a) Find the slope of the tangent to the curve [tex]y=3+4 x^{2}-2 x^{3}[/tex] at the point where [tex]x=a\text{.}[/tex]
Find the slope of the tangent to the curve [tex]y=3+4 x^{2}-2 x^{3}[/tex] at the point where [tex]x=a\text{.}[/tex]
Derivatives:The derivative of a function can be determined using different rules and formulations. One of the important rules here is the power rule. Power rule is used to differentiate functions in the form of [tex]f(x) = x^n[/tex].
[tex]\; \dfrac{d}{dx} (x^n) = nx^{n-1}[/tex]
Explanation:We are supposed to find the slope of the tangent to the curve [tex]y=3+4 x^{2}-2 x^{3}[/tex] at the point where [tex]x=a[/tex].
[tex]\implies \dfrac{d}{dx}(3+4x^2-2x^3)[/tex]
[tex]\implies \dfrac{d}{dx}(0+4(2x^{2-1})-2(3x^{3-1})[/tex]
[tex]\implies \dfrac{d}{dx}(0+4(2x)-2(3x^2)[/tex]
[tex]\implies \dfrac{d}{dx}(8x-6x^2[/tex]
Now plugging [tex]x=a[/tex] in the above equation, we obtain the following results:
[tex]\implies \boxed{8a -6a^2}[/tex]
Hence, this is our required solution for this question.
Tell me all of them pelase
Answer:
Step-by-step explanation:
A=1
B=41
C=3
The tax rate is 6.8% what is the tax on $9.95 round to the nearest hundredth
Answer:
$0.68
Step-by-step explanation:
you have to do:
9.95 x .068
or
9.95 x 6.8 ÷ 100
and you would get 0.6766 but rounded to the nearest hundredth would be $0.68
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
Step-by-step explanation:
I don't understand this question at all please help if you do
Answer:
Answer is [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
To find the interval of x. Use our equations to equal each other.
[tex]-x^2+2x=y,y=0[/tex]
[tex]-x^2+2x=0\\-x(x-2)=0\\-x=0 , (x-2)=0\\x=0 ,2[/tex]
[tex]\int\limits^2_0 {-x^2+2x} \, dx[/tex]
Integrate.
[tex]\frac{-x^3}{3}+x^2\\(\frac{-2^3}{3}+2^2)-[\frac{-0^3}{3}+0^2]\\-\frac{8}{3} +4-0\\-\frac{8}{3}+\frac{12}{3} =4/3[/tex]
Using Desmos I have Graphs of both of the equations you have provided. The problem asks us to find the shaded region between those curves/equations.
Proof Check your interval of x.
500,-100,20,-4 write an equation for the nth term
Answer:
500(-1/5)^(n-1)
Step-by-step explanation:
Each term after the first is obtained by multiplying by -1/5.
This is a geometric series.
The nth term = a1 r^n-1)
= 500(-1/5)^(n-1)
Jesse is making a sundae where she gets to choose one ice cream, one fruit topping, and one sauce. She can choose from chocolate, vanilla, and strawberry ice cream. She can choose from cherries or crushed pineapple as a fruit topping. Fudge and caramel are the sauces. How many outcomes?
Answer:
EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Identify the center and radius of each equation. (x - 1)² + y² +81
Write the mixed number as an improper fraction 2 1/6
Answer:
13/6 is the improper fraction
Step-by-step explanation:
Step 1: Convert the whole number into a fraction
2 is a whole number which replicates two 6/6's which adds up to 12/6
Step 2: Combine the two fractions
12/6 + 1/6
13/6
Answer: 13/6 is the improper fraction
Answer:
13/6
Step-by-step explanation:
6/6 = 1
12/6 = 2
12/6 + 1/6 =13/6
Daniel has a bag that contains pineapple chews, apple chews, and watermelon chews. He performs an experiment. Daniel randomly removes a chew from the bag, records the result, and returns the chew to the bag. Daniel performs the experiment 51 times. The results are shown below:
A pineapple chew was selected 21 times.
A apple chew was selected 12 times.
A watermelon chew was selected 18 times.
Based on these results, express the probability that the next chew Daniel removes from the bag will be a flavor other than watermelon as a decimal to the nearest hundredth.
The probability that the next chew Daniel removes from the bag will be a flavor other than watermelon is 0.65
How to determine the probability?The distribution of the fruits is given as:
Pineapple = 21Apple = 12Watermelon = 18The probability that the next chew Daniel removes from the bag will be a flavor other than watermelon is:
P = (Apple + Pineapple)/Total
This gives
P = (12 + 21)/(21 + 12 + 18)
Evaluate
P = 0.65
Hence, the probability that the next chew Daniel removes from the bag will be a flavor other than watermelon is 0.65
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Which answer includes a function, its inverse, and a dashed line that verifies the relationship?
Answer:
A
Step-by-step explanation:
because that's the answer
The correct graph that includes a function, its inverse, and a dashed line that verifies the relationship is shown in option 1.
Used the concept of function that states,
A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable and another variable.
Ask about the function, its inverse, and a dashed line that verifies the relationship.
Now from the first graph;
The dashed line is y = x.
And the graph shows the functions and their inverse as both graphs are opposite to each other.
Therefore, option 1 is true.
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Glaucoma is a disease of the eye that is manifested by high intraocular pressure. The
distribution of intraocular pressure in the general population is approximately normal with
mean 16 mm Hg and standard deviation 3.2 mm Hg. If the normal range for intraocular
pressure is between 10 and 22 mm Hg, than what proportion of the general population would
fall within this range?
A z-table is also known as the standard normal distribution table. The percentage of the population that would fall in the 10 to 22 mm Hg range is 0.9386.
What is a Z-table?A z-table also known as the standard normal distribution table, helps us to know the percentage of values that are below (or to the left of the Distribution) a z-score in the standard normal distribution.
Given the mean and the standard deviation are 16mmHg and 3.2 mmHg, therefore, the percentage of the population whose blood pressure will fall in the range of 10 to 22 mm Hg are,
[tex]P(10 < x < 22) = P(\dfrac{10-16}{3.2} < Z < \dfrac{22-16}{3.2})[/tex]
[tex]= P(-1.875 < Z < 1.875)\\\\=P(Z < 1.875)-P(Z < -1.875)\\\\= 0.9693-0.0307\\\\= 0.9386[/tex]
Hence, the percentage of the population that would fall in the 10 to 22 mm Hg range is 0.9386.
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This Venn diagram shows the pizza topping preferences for 9 students. LIKES LIKES PEPPERONI OLIVES Joe Kalie Petal Noah Owen Let event A = Student likes pepperoni. Let event B = Student likes olives. What elements are in A and B? OA. (Maria, Zack, Bo} B. (Petal, Owen, Julia) C. (Joe, Kalie, Noah, Maria, Zack, Bo, Julia} OD. (Petal, Owen) Maria... Zack Bo Julia
The elements that are in A and B in the Venn diagram that represents the pizza topping preferences are (Maria, Zack, Bo).
What elements are in A and B?
A venn diagram represents information in a set using circles. The intersection of both circles represents those that like both pepperoni and olives. This is element A and B.
The names at the intersection of both circles are (Maria, Zack, Bo).
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A gardener is putting a fence around his garden. His garden is 6 feet long and 2 feet wide. How many feet of fence does he need?
Work Shown:
L = 6 = length
W = 2 = width
P = 2(L+W)
P = 2(6+2)
P = 2(8)
P = 16 feet of fencing is needed
An alternative formula is P = 2L+2W
6. Find the measure of each angle in the figure below and explain how you found each
measure.
Step-by-step explanation:
2 = 15
because it's Vertically opposite angle(VOA)
1 = 180 -15 because it is straight line
1 = 165
1 = 3
3 = 165
because it's Vertically opposite angle(VOA)
Solve for c I need answers bad please
Answer:
c = sqroot45
Put a 45 in the box under the square root.
Step-by-step explanation:
Use Pythagorean Theorem. See image.
Also, sqroot45 can be simplified. It 3root5, just in case they ask that next.
Answer:
c=√45
Step-by-step explanation:
I'm assuming this question is before Pythagorean theorem so.
Find the total area of the big square.Find the total area of the four right-angled triangles.Subtract the big square with the four right-angled triangles to find the area of the smaller square with sides 'c'.Lastly, square root (√) the value to find c. Because c²=area of smaller square.Big square area:
[tex](3 + 6) \times (3 + 6) = 81[/tex]
All four right-angled triangles area:
[tex]4( \frac{1}{2} \times 3 \times 6) = 36[/tex]
Smaller square area:
[tex]81 - 36 = 45[/tex]
Value of c:
[tex] {c}^{2} = 45 \\ c = \sqrt{45} [/tex]
What is the area of Vivian's backyard
What percent of 29 is 3? Round to the nearest tenth or tenth of a percent
the answer is 10.3, just search up how to solve percentage word problems
Please help with this question
What is the measure of each angle in Megan’s triangle?
m∠A =
°
m∠B =
°
m∠C =
°
Answer:
A, C and D are true statements.
Step-by-step explanation:
Megan constructed triangle ABC.
In Megan’s triangle, m∠A is represented by x°.
Therefore, ∠A = x°
For m∠B is 4 times greater than m∠A
Therefore, ∠B = 4x°
For m∠C is 30° less than 5 times m∠A.
Therefore, ∠C = 5x°-30°
ABC is a triangle.
Sum of all angles of a triangle is 180°. Angle sum property of triangle.
m∠A + m∠B + m∠C = 180°
x° + 4x° + 5x°-30° = 180°
x° = 15°
True Statements are:
A) m∠A = x°
C) m∠B = (4x)°
D) m∠C = (5x – 30)°
A right triangle has side lengths 9, 40, and 41 as shown below.
B
40
Use these lengths to find cosB, tanB, and sin B.
9
Answer:
cos B = 9/41
tan B = 40/9
sin B = 40/41
Step-by-step explanation:
There is no picture, so I am making a few assumptions.
I am assuming that angle C is the right angle and is opposite 41.
I am also assuming that angle B is formed by the sides that measure 9 and 41. The hypotenuse is 41.
For angle B, the adjacent leg is 9, and the opposite leg is 40.
cos B = adj/hyp = 9/41
tan B = opp/adj = 40/9
sin B = opp/hyp = 40/41
At a flea market, used computer games are sold at the prices shown in the table below.
Number of Games Price ($)
2 9.00
5 22.50
7 31.50
Do the number of games and price form a proportional relationship?
Choose the correct response.
A.
Yes. There is a constant of proportionality of $11.25.
B.
Yes. There is a constant of proportionality of $4.50.
C.
No. There is not a constant of proportionality.
D.
No. The slope is 4.5.
Answer:
This is the answer I understood and got.
B. Yes. There is a constant of proportionality of $4.50.
Step-by-step explanation:
When you divided 9/2, you get 4.5
When you divide 22.5/5, you get 4.5
When you divide 31.5/7, you get 4.5
* REMEMBER IT'S ASKING DO THE NUMER OF GAMES AND PRICE FOR A PROPORTIONAL RELATIONSHIP *
So, y= 4.5x
The area of rectangle is ( 30x²y + 20xy ) cm² and its breadth is 10xy cm .Find its length.
Subtract the quotient when 20x⁴y² is divided by 5x³y from the product of 2x and 3y.
Step-by-step explanation:
1) The area of rectangle is ( 30x²y + 20xy ) cm² and its breadth is 10xy cm .Find its length....
= Solution ,
Length ( L ) = ?
breadth ( b ) = 10xy cm
area ( a ) = ( 30x² + 20xy )
Now ,
area ( a ) = l × b
or, ( 30x²y + 20xy ) = L × 10xy cm
[tex]or,\frac{30 {xy + 20xy}^{2} }{10xy} = l \\ [/tex]
[tex]or, \: l = 3 {x}^{2 - 1} + 2cm[/tex]
[tex]\boxed{\sf{l = (3x+2)cm}}[/tex]
2) Subtract the quotient when 20x⁴y² is divided by 5x³y from the product of 2x and 3y.
= Solution,
[tex] = \frac{20 {x}^{4} {y}^{2} }{5 {x}^{3} y} \\ [/tex]
[tex] = 4xy[/tex]
The product of 3x and 4y = 6xy
= 6x - 4xy
[tex] = \boxed{\sf {2xy}}[/tex]
hope it helped !!!!
Ignore the other questions I just need help with numbers 18 and 25 how do you work it out please help me out I would of have helped you
Answer:
25. -7/5 [tex]\leq[/tex] x [tex]\leq[/tex] 1
Step-by-step explanation:
18:
[tex]5-|x|\leq 2\\-|x| \leq -3\\|x|\leq 3\\x\geq -3[/tex]or [tex]x\leq 3[/tex]
25:
[tex]3|5x+1|-6\geq 12\\3|5x+1|\geq 18\\|5x+1|\geq 6\\x\leq -7/5[/tex]or [tex]x\geq 1[/tex]
[tex]-7/5\leq x\leq 1[/tex]
I don't think I explained this well let me know if you need more explanation.
4 1/4 - 5/6 I don’t understand pls help
Answer:
1/6 or 0.167
Step-by-step explanation:
First understand that 4 x 1/4 is equal to 1, then replace it in the equation
1 - 5/6
Turn the whole number into a fraction that can be computed
6/6 - 5/6
Solve the equation
6/6 - 5/6 = 1/6
If you need it as a decimal enter it in a calculator and get
0.16666666667
Since the 6 is repeating you can just round that to
0.167
A customer buys a different book for a selling price of 38$.The book is discounted 25%.The customer must pay 6% sales tax on the disocounted price of the book.How much does the customer pay for the book including tax.
Answer:
$30.21
Step-by-step explanation:
Fraction of
[tex] \frac{200}{350} [/tex]
please give ans
4/7
Step-by-step explanation:
[tex] \hookrightarrow \sf \frac{200}{350} [/tex]
[tex]\hookrightarrow \sf \: \frac{ \sout{200}}{ \sout{350}} = \frac{\sout{100}}{\sout{175}} = \frac{4}{7} [/tex]
Therefore, [tex] \rm \frac{200}{350} [/tex] = [tex] \sf \frac{4}{7} [/tex]
A cone with a height of 15 yards has a volume of
475.17 yd³. Find the diameter of the cone.
Answer:
11
Step-by-step explanation:
h = 15 yards
Volume = 475.17 cubic yards
Diameter = 5.5*2 = 11.0 = 11 yards
Please help!!! I will give Brainliest!!!! :_D
Write an equation for each situation!
Just remember that 100% = 1.00 !
y = .78x
y = 108.5x
y = .946x
Lynn filled each of three bags with
2 kilograms 450 grams of sand. Is the
mass of 2 bags greater than or less than
5 kilograms? Explain how you know.
10
The mass of 2 bags, which is filled by Lynn each with 2 kilograms 450 grams of sand, is less than 5 kilograms.
How to measure the weight?Weight measurement is the measurement of the heaviness of a object. The units of weight measurement are pounds, grams, kilograms etc.
There is total 1000 grams in one kilogram of weight measurement.
Lynn filled each of three bags with 2 kilograms, 450 grams of sand. There is total 1000 grams in one kilogram of weight measurement. Thus, the kilogram in 450 grams is,
[tex]x=\dfrac{450}{1000}\\x=0.45\rm\; kg[/tex]
Thus, weight in one bag is,
[tex]W=2+0.45\\W=2.45\rm\; kg[/tex]
The weight in two bags is,
[tex]2W=2.45+2.45\\2W=4.9\rm\; kg[/tex]
The weight of 4.9 kg is less than the 5 kilogram..
Thus, the mass of 2 bags, which is filled by Lynn each with 2 kilograms 450 grams of sand, is less than 5 kilograms.
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