Find the points on the curve y = 2x3 + 3x2 − 12x + 9 where the tangent line is horizontal.
the points on the curve [tex]y = 2x^3 + 3x^2 - 12x + 9 are (-2,29) \; and \; (1,2)[/tex]where the tangent line is horizontal.
Given :
The equation of the curve is [tex]y=2x^3\:+\:3x^2\:-\:12x\:+\:9[/tex]
Given tangent line is horizontal . Tangent line is horizontal when slope =0
Slope is nothing but the derivative.
So we find out x values where derivative =0
Lets take derivative for the given curve y
[tex]y=2x^3+3x^2-12x+9\\y'=2(3x^2)+3(2x)-12\\y'=6x^2+6x-12[/tex]
Now we set the derivative =0 and solve for
[tex]6x^2+6x-12=0\\Divide\; whole \; equation \; by \; 6\\x^2+x-2=0\\(x+2)(x-1)=0\\x+2=0, x=-2\\\\x-1=0, x=1[/tex]
So , the slope =0 when x=1 and x=-2
Now we find out the points . Use the original function
[tex]y=2x^3\:+\:3x^2\:-\:12x\:+\:9\\x=-2\\2\left(-2\right)^3+3\left(-2\right)^2-12\left(-2\right)+9=29\\(-2,29)\\\\x=1\\2\left(1\right)^3+3\left(1\right)^2-12\left(1\right)+9=2\\(1,2)[/tex]
the points on the curve [tex]y = 2x^3 + 3x^2 - 12x + 9 are (-2,29) \; and \; (1,2)[/tex]where the tangent line is horizontal.
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Determine if the functions are even, odd or neither. f(x) = -5x4 - 2 and g(x) = x3 + 2x
Complete the square to form a perfect square trinomial x^2-14x+
For which k will the graph of f(x)=x^2−kx+k^2 cross the x-axis twice?
What the complement of 54.6 degree
226Ra has a half-life of 1599 years. How much is left after 1000 years if the initial amount was 10 g?
how many rootes are in f(x)=(x^2-3x+1)^2
2
5
6
9
tickets for a football match are sold at $30 for adults and $15 for children a company bought 28 tickets if x of these tickets were for adults, write in terms of x a. the number of tickets for children b. the amount spent on tickets for adults c. the amount spent on tickets ...
The number of tickets for children is represented by '28-x' and the amount spent on tickets for adults is '$30x'. The amount spent on tickets for children is '$15*(28-x)'.
Explanation:We will use the concept of algebraic expressions to solve this question. If we represent the number of adult tickets as x, we know that the total number of tickets is 28. Hence, the number of children tickets can be represented as 28-x. The cost of a ticket for adults is $30, so the amount spent on adult tickets can be represented as $30x. Similarly, as the cost of a ticket for children is $15, the amount spent on children tickets can be represented as $15*(28-x).
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The number of ticket for children is (28 - x), the amount spent on tickets for adults would be $30x, and the total amount spent on tickets would be $30x + $15(28 - x).
Explanation:If a company bought 28 tickets and x of these tickets were for adults, then:
a. The number of tickets for children would be 28 - x. This is because from the total number of tickets purchased, we subtract the number of adult tickets to find the number of children's tickets.
b. The amount spent on tickets for adults would be $30x. This is because each adult ticket costs $30 and there are x number of adults.
c. To find out the total amount spent by the company, we will multiply the number of adult tickets by the price of an adult ticket ($30x) and add this to the product of the number of children tickets (28 - x) and the price of a child's ticket ($15). Therefore, the total spent would be $30x + $15(28 - x).
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what is the answer please
Robin randomly selects a number between 1 and 20. What is the probability that the number selected is the square of a natural number?
The probability that the number selected is the square of a natural number will be 0.20.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
Robin randomly selects a number between 1 and 20.
Then the total number of the events will be
Total events = 20 {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
The probability that the number selected is the square of a natural number will be
We know that natural numbers 1, 2, 3, 4, 5, and so on.
Then the square of the natural numbers will be
1, 4, 9, 16, 25, ....
Favorable event = 3 {1, 4, 9, 16}
Then the probability will be
P = 4 / 20
P = 1/5
P = 0.20
The probability that the number selected is the square of a natural number will be 0.20.
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How much would $500 invested at 7% interest compounded annually be worth after 5 years?
Find the inverse of this 3x3 matrix. [1 5 2]
[ 1 1 7]
[0 -3 7]
Answer:
A
Step-by-step explanation:
⎡−25 26 −33⎤
⎥ 4 −4 5 ⎥
⎥ 3 −3 4 ⎦
You were just approved for a $32,000 car loan at an APR of 1.99% for 60 months. As you make payments over time: your payment is , the amount of interest you will pay each month , and the amount of principal you pay each month .
What it Means...
If you borrow $32,000 at 1.99% for 5 years, your monthly payment will be $560.75.
The payments do not change over time. The loan amortizes over the repayment period, meaning the proportion of interest paid vs. principal repaid changes each month. As the loan amortizes, the amount of monthly interest paid decreases while the amount of principal paid increases.
Loan Amount: $32,000Cheryl paid $3 for each pin in her collection. She bought 32 pins in March and 56 pins in April.
How much did Cheryl spend on pins in April?
A.
What is the total amount of money Cheryl spent buying pins?
B.
How many pins did Cheryl add to her collection in March and April?
C.
What is the total cost of the pins that Cheryl bought in April?
D.
What is the difference between the number of pins bought in March and April?
Assume that when adults with smartphones are randomly selected, 48% use them in meetings or classes. If 55 adult smartphone users are randomly selected, find the probability that at least 22 of them use their smartphones in meetings or classes.
whats the distance between (-8,-7) (8,-4)
Look at the figure. How can you prove ∆ABD and ∆ACD are congruent?
A. ∆ABD ≅ ∆ACD by the SAS Postulate.
B. It is not possible to determine if the triangles are congruent.
C. ∆ABD ≅ ∆ACD by the SSS Postulate.
Answer: The correct option is (B). It is not possible to determine if the triangles are congruent.
Step-by-step explanation: We are given to select the correct option by which we can prove that ∆ABD and ∆ACD are congruent.
As shown in the figure,
In ∆ABD and ∆ACD, we have
∠ADB = ∠ADC = 90°,
AD is the common side.
So, one angle and the adjacent side of one triangle are congruent to the corresponding angle and the adjacent side of the other triangle.
That is, to prove that the two triangles are congruent, we need one of the following two conditions:
(i) BD = CD
or
(ii) ∠BAD = ∠CAD.
Since none of these two are given, so we cannot determine the congruence of the two triangles.
Therefore, it is not possible to determine if the triangles are congruent.
Thus, option (B) is correct.
PLZZZZZZ HELPPPP
Solve the system of equations using the substitution method.
{2x+8y=4x=−3y+5 Enter your answers in the boxes.
The method of substitution is a three step method to solve the equations. In this method , one equation for one of the variables is solved and in the first step.
The outcome is then substituted to the second equation in the second step for solving the equation.The value is re-substituted to the original equation to find the outcome in the third step.
On solving the equations by substitution method we get x=14 and y=-3
Calculation:Given equations:
[tex]\rm 2x+8y = 4[/tex] (1)
[tex]\rm x=-3y+5[/tex] (2)
On substituting [tex]x=-3y+5[/tex] in equation 1:
[tex]\begin{aligned}\rm 2(-3y+5)+8y&=4\\\\-6y+10+8y&=4\\\\2y+10&=4\\\\2y&=4-10\\\\ 2y &= -6\\\\y&=\dfrac{-6}{2}\\\\y&=-3\end[/tex]
Substituting [tex]\rm y=-3[/tex] in equation 2:
[tex]\rm x&=-3y+5\\\\x&=-3(-3)+5\\\\x=9+5\\\\x=14[/tex]
Therefore the values of x and y for the given equations is 14 and -3 respectively.
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Write the explicit formula for the geometric sequence.
64, 32, 16, 8, ...
A) an = 8 · 4n-1
B) an = 8 · 2n-1
C) an = 32 · 0.5n-1
D) an = 64 · 0.5n-1
Answer:
D) [tex]a_{n}[/tex][tex]=64[/tex]×[tex]0.5^{n-1}[/tex]
Step-by-step explanation:
The answer is D because it is the only answer that has an=64 and a decimal, 64 is your first term and the sequence is getting smaller
AND OR
Answer:
D) [tex]a_{n}[/tex][tex]=64[/tex]×[tex]0.5^{n-1}[/tex]
Step-by-step explanation:
Explicit Formula: an = a1 · dn-1
a1 = 64, d = 0.5
an = 64 · 0.5n-1
Evaluate the integral. (use c for the constant of integration.) 7 ln(x)/ x sqrt(5 + (ln(x))^2) dx
The expression for the integral [tex]\int\frac{7ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex] after the evaluation is [tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex].
Given an integral expression:
[tex]\text{I}=\int\frac{7ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex]
This can be written as:
[tex]\text{I}=7\int\frac{ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex]
It is required to find the integral value.
Let u = 5 + (ln (x))²
Differentiate.
[tex]du=2ln(x)*\frac{1}{x} dx[/tex]
Or [tex]\frac{du}{2} =\frac{lnx}{x} dx[/tex]
Substitute the values.
[tex]\text{I}=7\int\frac{1}{\sqrt{u} } \frac{du}{2}[/tex]
[tex]\text{I}=\frac{7}{2} \int\frac{1}{\sqrt{u} }du[/tex]
[tex]\text{I}=\frac{7}{2} (2\sqrt{u} )+C[/tex]
Substitute back the value of u.
[tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex]
Hence the value of the integral is [tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex].
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A 2 liter drink costs $0.10 per deciliter. How much does the drink cost?
The price of drink is given as 0.10 dollars per deciliter.
It says to find the cost of 2 liters of drink.
We need to convert the units from liters to deciliters.
We know 1 liter = 10 deciliters.
then 2 liters = 20 deciliters.
So we need to find the cost of 20 deciliters of drink at rate of 0.10 dollars per deciliter.
1 deciliter of drink cost = 0.10 dollars.
20 deciliter of drink would cost = 20 x 0.10 dollars = 2.00 dollars.
Hence, 2 liters of drink would cost 2 dollars.
J is 25 more than 3 help???
if x2 = 49 the only possible answer for x is 7
While the equation x² = 49 suggests that x = 7, it also has a negative solution, x = -7. Both solutions can be verified by substitution into the original equation, proving they are correct through resulting identities.
The equation x² = 49 has two solutions in the realm of real numbers, not just x = 7. To find the values of x that satisfy the equation, we take the square root of both sides. Since the square root of a number has both a positive and a negative value, the solutions are x = 7 and x = -7. To verify these solutions, we can substitute them back into the original equation to confirm that they work, demonstrating identities such as 7² = 49 and (-7)² = 49.
I WILL GIVE U BRAINLY!!!
Which substance has been changed most over time from its original plant material?
A.
peat
B.
anthracite coal
C.
bituminous coal
D.
lignite
Treys online music club charges a monthly rate of $20 plus $0.80 per song download. Debs online music club charges a monthly rate of $21 plus $0.60 per song download. For what number of songs will the monthly charge be the same for both clubs? How much will it cost?
Answer:
For 5 songs the monthly charge be the same for both clubs.
It will cost $ 24.
Step-by-step explanation:
Let, for x songs, the monthly charges are same for both clubs,
Given,
For Treys online music club,
Monthly rate = $ 20,
Additional Charges for a song = $ 0.80,
⇒ Additional Charges for x song = $ 0.80x,
Thus, the total monthly charges for x songs = Monthly rate + Additional Charges for x song
= 20 + 0.80x
Now, for Debs online music club,
Monthly rate = $ 21,
Additional Charges for a song = $ 0.60,
⇒ Additional Charges for x song = $ 0.60x,
Thus, the total monthly charges for x songs = Monthly rate + Additional Charges for x song
= 21 + 0.60x
Hence, we can write,
[tex]20 + 0.80x = 21 + 0.60x[/tex]
[tex]0.80x - 0.60x = 21 - 20[/tex]
[tex]0.20x = 1[/tex]
[tex]\implies x = \frac{1}{0.20}=5[/tex]
Hence, for 5 songs the monthly charge be the same for both clubs.
Also, the cost for 5 songs = 20 + 0.80 × 5 = 20 + 4 = $ 24
2x - y + 3z = -9
x + 3y - z = 10
3x + y - z = 8
find the ordered triple
Quadrilateral ABCD is inscribed in a circle. What is the measure of angle A? Enter your answer in the box. m∠A= ° A quadrilateral inscribed in a circle. The vertices of the quadrilateral lie on the edge of the circle and are labeled as A, B, C, D. The interior angle A is labeled as left parenthesis 3 x plus 6 right parenthesis degrees. The angle C is labeled as left parenthesis x plus 2 right parenthesis degrees.
The measure of angle A in a cyclic quadrilateral ABCD, where the measure of angle A is (3x + 6) degrees and the measure of angle C is (x + 2) degrees, is determined to be 135 degrees.
Explanation:Given that quadrilateral ABCD is inscribed in a circle, it follows from the properties of cyclic quadrilaterals that the sum of the opposite angles of such a quadrilateral is always 180 degrees. Therefore, if the measure of angle A is represented by the expression (3x + 6) degrees and the measure of angle C is represented by the expression (x + 2) degrees, then we can set up an equation that (3x + 6) + (x + 2) = 180. Solving this equation gives x = 43. Using x = 43, substitute it into 3x + 6 to get the value of angle A, which is equal to 135 degrees.
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PLEASE HELPS NEED THIS DONE BEFORE 3 O CLOCK
1)Jerome noticed the following house numbers on his street:
305, 318, 331, 344
The house numbers follow a pattern. Which expression can be used to determine the nthnth house number on his street?
A) 292 +13n
B) 292n
C) 292n + 13
D) 13(n + 292)
2) A polynomial expression is shown below.
(mx+8)(2x−4)
The expression is simplified to:
−6x2+28x−32-6x2+28x-32
What is the value of m?
A) 3
B) 4
C) -3
D) -4
3) What is the domain of the function shown below? (PICTURE AT BOTTOM)
A) 2
B) −8 ≤ x <3and 4 ≤ x <8
C) −8 ≤ x < 8
D) −7 ≤ x ≤ 7
Answer:
Jerome noticed the following house numbers on his street:
Answer 292 +13n
A polynomial expression is shown below. What is the value of m?
Answer -3
What is the domain of the function shown below
Answer −8 ≤ x <3and 4 ≤ x <8
The formula for the volume of a cube is V(s) = s3 where s is the side length of the cube. In which quadrant(s) is the graph of the function V(s)?
Answer:
The answer is A: Quadrant 1
Step-by-step explanation:
On Edge :)
What is the volume of the figure below if a = 3.9 units, b = 5.7 units, and c = 3 units?
A. 157.95 cubic units
B. 351.351 cubic units
C. 124.605 cubic units
D. 113.49 cubic units
Final answer:
The volume of the parallelepiped with sides of lengths a = 3.9 units, b = 5.7 units, and c = 3 units is given by the formula V = a × b × c. After performing the calculation, the volume comes out to be 66.87 cubic units.
Explanation:
To find the volume of the parallelepiped with edges of lengths a, b, and c, you can multiply the length of each edge together. The volume (V) of a parallelepiped (a three-dimensional figure formed by six parallelograms) is given by the product of the lengths of its three dimensions. In this case, the formula to calculate the volume is V = a × b × c.
By plugging in the values provided:
a = 3.9 units
b = 5.7 units
c = 3 units
We get:
V = 3.9 units × 5.7 units × 3 units
Doing the multiplication:
V = 66.87 cubic units
Therefore, the volume of the figure is 66.87 cubic units.