(1 point) Use the figure below to estimate the indicated derivatives. If a derivative does not exist, enter dne in the answer blank. The graph of f(x) is black and has a sharp corner at x=2. The graph of g(x) is blue.
Let j(x)=g(x)f(x). Find
j'(3)
Answers
Applying the quotient rule, the derivative of the given function at x = 3 is of -2/3.
What is the quotient derivative rule?A quotient function is defined as follows:
i(x) = g(x)/f(x)
Applying the quotient rule, the derivative of the function defined above is of:
i'(x) = [g'(x)f(x) - f'(x)g(x)]/f(x)².
Hence, at x = 3, the numeric value of the derivative is given as follows:
i'(3) = [g'(3)f(3) - f'(3)g(3)]/f(3)².
Function f(x) is a linear function with slope of -3/2, hence:
f'(3) = -3/2 (for a linear function, the derivative is constant).f(3) = 3/2 (from the graph).Function g(x) is a linear function with slope of -1/2, hence:
g'(3) = -1/2.g(3) = 1/2.Then the derivative is given as follows:
[tex]g^{\prime}(3) = \frac{-\frac{1}{2} \times \frac{3}{2} - \frac{3}{2} \times \frac{1}{2}}{\left(\frac{3}{2}\right)^2} = -\frac{\frac{6}{4}}{\frac{9}{4}} = -\frac{6}{9} = -\frac{2}{3}[/tex]
Hence the numeric value of the derivative at x = 3 is of -2/3.
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Related Questions
HELP QUICK
For each statement about owners of equity in a business, select True or False.
Answers
Question 1. Find the center and radius of the circunscribed circle.
Answers
In order to find the center of the circunscribed circle, we can use the midpoint theorem because the center point is in the middle of any two vertices
that is, if we take points (9,23) and (8,16) the midpoint C is given as
[tex]C=(\frac{8+9}{2},\frac{16+23}{2})[/tex]which gives
[tex]C=(8.5,19.5)[/tex]So the center of the circle is the point (8.5,19.5)
On the other hand, the radius is equal to the distance from any vertex to the center. If we take the vertex (8,16), we get
[tex]r=\sqrt[]{(8.5-8)^2+(19.5-16)^2}[/tex]which gives
[tex]\begin{gathered} r=\sqrt[]{0.5^2+3.5^2} \\ r=\sqrt[]{0.25+12.25} \\ r=\sqrt[]{12.5} \\ r=3.5355 \end{gathered}[/tex]so, the radius measure 3.54 units.
Now, lets prove that the answer are correct. In order to do that, we can choose the other vertices and apply the same procedure as above.
So the vertices are (5,20) and (12,19). Again, the center is the midpoint between these points and is given as
[tex]\begin{gathered} C=(\frac{5+12}{2},\frac{20+19}{2}) \\ C=(\frac{17}{2},\frac{39}{2}) \\ C=(8.5,19.5) \end{gathered}[/tex]which is the same center as above.
Now, the distance from the center to vertec (5,20) is
[tex]\begin{gathered} r=\sqrt[]{(8.5-5)^2+(20-19.5)^2} \\ r=\sqrt[]{3.5^2+0.5^2} \\ r=\sqrt[]{12.25+0.25} \\ r=\sqrt[]{12.5} \\ r=3.5355 \end{gathered}[/tex]which is the same radius obtained above. Then, the answers are correct.
2. Bob and Joy Salkind want to save $50,000 in 5 years for home improvement projects. If the
Bank of Aventura is paying 8% interest compounded quarterly, how much must they deposit
now to have the money for the project?
Answers
The amount of money should be invested to obtain interest of amount 50000$ is 34,000$(approximately)
What is the compound interest?The practice of adding interest to the principal amount of a loan or deposit is known as compound interest, sometimes known as interest on principal and interest. Reinvesting interest, or adding it to the lent capital rather than paying it out or seeking repayment from the borrower, results in interest being received on the principal amount plus interest collected previously.
How to calculate principal amount to get certain amount of interest?[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]
Where,A is the total sum.
P equals the initial principal amount.
The nominal yearly interest rate is r.
The compounding frequency is n.
t is the total amount of time that the interest is charged (expressed using the same time units as r, usually years).
The final value less the beginning investment yields the entire compound interest.
On substituting the values we get that initial investment of approximately 34000$
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00000 Replace the side length of this square with 4 in., and find the area. S
Answers
The area of the square is 16 square inches.
The area of a square is calculated by multiplying a side by itself.
In this case, the side S is replaced by 4 in, then:
[tex]\begin{gathered} \begin{cases}A=S\cdot S \\ S=4in\end{cases} \\ A=4in\cdot4in=16in^2 \end{gathered}[/tex]The National Opinion Research Center administered the General Social Surve
persons in the United States who were 18 years of age or older. One question asked
respondents for their highest grade of school completed (Respondent's Years of Education).
Another question asked respondents for the highest grade of school that their father had
completed (Father's Years of Education).
The equation for the least squares regression line for predicting a respondent's years of
education, ý, from the years of education for the respondent's father, x, is:
ý = 9.996 + 0.355x
Predict the years of education for a person whose father had 14 years of education. Round to
the nearest whole number.
Answers
The years of education as per the given equation, for a person whose father had 14 years of education is 14.966 years.
What is education?
A planned activity, education has objectives like knowledge transmission or character and skill development. The development of understanding, reason, kindness, and honesty may be some of these goals.
As given in the question,
respondent's years of education is represented by y, and
respondent's father years of education is represented by x,
The equation for the least squares regression line for predicting a respondent's years of education is given as:
y = 9.996 + 0.355x
The year of education of respondent's father is given as 14
So putting the value of x in the given equation as 14:
we get,
y = 9.996 + 0.355(14)
y = 14.966
Hence, the years of education for a person whose father had 14 years of education is 14.966 years.
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What quadrant is 0 And. . -1 1/2 in or is it on a y- axis or x-axis.
Answers
The coordinate pair is between the third and fourth quadrants, on the y-axis.
In which quadrant is the coordinate point?Remember that the quadrants are:
First quadrant: x > 0, y > 0.
Second quadrant: x < 0, y > 0.
Third quadrant: x < 0, y < 0.
Fourth quadrant: x > 0, y < 0.
In this case our coordinate pair is (0, -1/2).
So it will be between the third and fourth quadrants.
And yes, because one of the variables is zero, it is on the y-axis (just between the two quadrants).
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(3)/(4)[(-15+4)+(6+7)-:(-3)]
Answers
Answer:
The answer is -23/2 or -11.5
Step-by-step explanation:
Which of the following sets of numbers could represent the three sides of a righttriangle?Submit AnswerO {9, 12, 14}O {48, 55,73}O {11, 59, 61}{8, 40, 41}
Answers
Answer:
{48, 55,73}
Explanation:
To determine if any three side lengths can form a right triangle, we check if it satisfies the Pythagorean Theorem.
[tex]\begin{gathered} c^2=a^2+b^2 \\ c\text{ is the longest side, the hypotenuse} \end{gathered}[/tex][tex]\begin{gathered} 14^2=9^2+12^2 \\ 196\neq225 \end{gathered}[/tex][tex]\begin{gathered} 73^2=48^2+55^3 \\ 5329=5329 \end{gathered}[/tex]Therefore, the side lengths that could form a right triangle are {48, 55,73}.
During a basketball game, you made 11 shots of either 2 or 3 points. You scored atotal of 25 points. How many shots of each point value did you make?
Answers
During a basketball game, you made 11 shots of either 2 or 3 points. You scored a
total of 25 points. How many shots of each point value did you make?
Let
x -----> number of shots of 2 points
y -----> number of shots of 3 points
we have that
x+y=11
x=11-y -----> equation A
and
2x+3y=25 -----> equation B
substitute equation A in equation B
2(11-y)+3y=25
solve for y
22-2y+3y=25
y=25-22
y=3
Find the value of x
x=11-3
x=8
therefore
number of shots of 2 points is 8number of shots of 3 points is 3Which of the following is the correct mathematical expression for:
The difference between three times a number and 4
A. 3x + 4
B. 3x - 4
C. 1/3x + 4
D. 1/3x - 4
Answers
Answer:
B
Step-by-step explanation:
if the number is x then 3 times the number is 3x
the difference is the subtraction of 3x and 4 , that is
3x - 4
A tanker truck fills the gas station’s reservoir at the rate of 1212 gallons per minute.
If the reservoir was empty and it is now 35 gallons full, how long has the tanker been filling the reservoir?
Answers
The tanker has been filling the reservoir for 0.0288 minutes or 1.728 seconds as the rate of filling is 1212 gallons per minute using the estimation concept.
As per the question statement, A tanker truck fills the gas station’s reservoir at the rate of 1212 gallons per minute and the reservoir was empty and it is now 35 gallons full. We are supposed to find out for how long has the tanker been filling the reservoir. We will use the concept of estimation.
Rate of filling gas = 1212 gallons per minute
i.e., 1212 gallon of gas taken 1 minute for transfer.
1 gallon of gas will take = (1/1212) minutes
Hence 35 gallons of gas will take = (1/1212)*35 minutes = 0.0288 min.
So, the tanker has been filling the reservoir for 0.0288 minutes or 1.728 seconds as the rate of filling is 1212 gallons per minute.
Estimation: Having an approximate estimate of something's worth, number, size, or extent is referred to as estimation in mathematics.To learn more about Estimation click on the link given below:
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Pls help
Alyssa's algebra test score was 8 points lower than Jennifer's. The total of their two tests was 180. What did each girl receive?
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A kite is shown below. What is the length of LINE AC? (image attached)A. 4B. 6C. 9D. 10
Answers
The length of AC is given by AE + EC
According to the Pythagorean Theorem, we know that:
AE² = AD² - ED²
AE² = 5² - 3²
AE² = 25 - 9
AE² = 16
AE = 4
EC² = DC² + ED²
Since DC = BC, we have:
EC² = BC² + ED²
EC² = 45 - 9
EC² = 36
EC = 6
Therefore, AC = 4 + 6 = 10
Answer: D. 10
plesehelppppppppppppppppppp!
Answers
Answer:
54 x 5
Step-by-step explanation:
the first figure out the brackets, then multiply by 5.
plss mark me as brainlist
Answer:
the answer is 6 ^ 15 you are very welcom
What is the length of a side of an equilateral triangle whose altitude is 5?
Answers
To make things easier to understand, let's see this figure, which represents the given situation:
According to this diagram, to find x, which is the length of the side of the triangle, we can use pythagorean theorem, this way:
[tex]\begin{gathered} x^2=(\frac{x}{2})^2+5^2 \\ x^2=\frac{x^2}{4}+25 \\ x^2-\frac{x^2}{4}=25 \\ \frac{3}{4}x^2=25 \\ x^2=\frac{25}{3}\cdot4^{} \\ x=\sqrt[]{33.3333} \\ x=5.77 \end{gathered}[/tex]Select all the intervals where if is increasing
Answers
The given function is increasing over these following intervals:
B. -2 ≤ x ≤ -1.
C. 0 < x < 1.
Where to find where a function is increasing, from it's graph?Considering the graph of the function, we get that a function f(x) is increasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when x increases, y increases.Conversely, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down the graph, meaning that when x increases, y decreases.Considering the given definitions on the bullet points above, the behavior of the function can be separated as follows:
Increasing on -2.5 ≤ x ≤ 2.5.Decreasing on all other intervals except the one above.Items B and C have subsets of the interval -2.5 ≤ x ≤ 2.5, hence the function is increasing on those intervals, and they are the correct options for this problem.
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A triangle has sides of lengths 11 in., 59 in., and 61 in. Is the triangle a right triangle?
O yes
O no
O There is not enough information to tell.
Answers
Felix is making a pattern with tiles shaped like parallelograms. He needs 5 black tiles
and 5 white tiles. The tiles cost $0.50 per cm².
What is the total area of the tiles Felix needs
to buy?
A =
? cm²
27
2.4 cm
2 cm
4 cm
Answers
Answer:
first one is 80
Step-by-step explanation:
i did it
The total area for the parallelogram-shaped tiles Felix needs to buy exists 80cm² at the price of $40.
What is meant by the area of parallelogram?In calculating the area of a parallelogram, the base exists multiplied by the height, in an exact way as computing the area of a rectangle.
Given that, the base of one parallelogram-shaped tile exists 4cm with a height of 2 cm.
Area of one parallelogram shaped tile = 4cm × 2cm
Area of one parallelogram-shaped tile = 8cm²
Total area for the 5black and 5white tiles = 10 × 8cm²
Total area for the 5black and 5white tiles = 80cm²
Therefore, Felix must buy a total area of 80cm² of 10 parallelogram-shaped tiles.
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A triangle, ABC, has angle measures of 45°, 45°, and 90° and two congruent (equal) sides. How would this triangle be classified?
O Isosceles acute
O Scalene acute
O Scalene right
O Isosceles right
Answers
Answer:
(d) Isosceles right
Step-by-step explanation:
You want to know the classification of a triangle with angles 45°-45°-90°.
ClassificationThe largest angle is 90°, a right angle. Any triangle containing a right angle is a right triangle.
Two of the angles have the same measure. This means the triangle is an isosceles triangle.
The triangle is classified as an isosceles right triangle.
__
Additional comment
A triangle whose largest angle is less than 90° is an acute triangle. If the largest angle is greater than 90°, it is an obtuse triangle.
If no sides are the same length, the triangle is scalene. If two sides are the same length, the triangle is isosceles. If all three sides are the same length, it is an equilateral triangle.
Larger angles are opposite longer sides, so if angles are the same, their opposite sides are the same.
It can be worthwhile to remember that the side length ratios in an isosceles right triangle are 1 : 1 : √2.
Help i need an answer.
Answers
There are 2.54 centimeters in 1 Inch. There are 100 centimeters in 1 meter. To the nearest inch, how many inches are in 7 meters? Enter the answer in the box. inches
Answers
Based on the given equivalences, you have:
7 m = 7(100 cm) = 700 cm
700 cm = 700 (2.54 in) = 1,778 in
Hence, there are 1,778 inches in 7 meters
The nutty professor sells cashews for $6.20 per pound and Brazil nuts for $4.30 per pound. How much of each type should be used to make a 32 pound mixture that sells for $5.37 per pound?
Answers
Let's call C the weight of the Cashews and B the weight of the Brazil nuts.
Since the professor wants to sel a 32 pound mixture, we have the following equation:
[tex]C+B=32.[/tex]Now, since the price of the mixture will be $5.37 per pound, this means the price of the whole mixture will be
[tex]32\cdot5.37=171.84.[/tex]This leads us to the followin equation:
[tex]6.20C+4.30B=171.84.[/tex]Now we have a system of equations:
[tex]C+B=32[/tex][tex]6.20C+4.30B=171.84.[/tex]To solve it, let's isolate one of the variables in the first equation by subtracting B from both sides of it:
[tex]C=32-B\text{.}[/tex]Now, let's use this value of C in the second equation:
[tex]6.20(32-B)+4.30B=171.84,[/tex][tex]198.4-6.20B+4.30B=171.84,[/tex][tex]198.4-1.9B=171.84.[/tex]To solve this equation, let's subtract 198.4 from both sides of it:
[tex]-1.9B=-26.56.[/tex]Then, let's divide both sides by -1.9:
[tex]B\approx13.98.[/tex]Using this value of B in the first equation will give us:
[tex]C=32-13.98=18.02.[/tex]These would be the values of B and C round to two decimals. If we want, we can also write them as integer numbers. so the mix would need to have 18 pounds of cashews and 14 pounds of Brazil nuts.
Find sin(2x), cos(2x), and tan(2x) from the given information.
tan(x) = − 4/3 , x in Quadrant II
Answers
Answer:
Step-by-step explanation:
Starting from tan x, you can find sec x, because of the trigonometric identity 1 + tan2 x = sec2 x.
1 + (-4/3)2 = 1 + 16/9 = 25/9 = sec2 x.
So sec x = ±√(25/9) = ±5/3. But since x is in Quadrant II, sec x has to be negative. That's because sec x has the same sign as cos x, because sec x = 1 / cos x. We know that cos x is negative is Quadrant II, therefore so is sec x. So sec x = -5/3.
Since sec x and cos x are reciprocals of each other, cos x = 1/sec x = -3/5.
Now use the identity sin2 x + cos2 x = 1, to find sin x:
sin2 x + (-3/5)2 = 1
sin2 x + 9/25 = 1
sin2 x = 16/25
sin x = ±4/5
Again, we know that sin x is positive in Quadrant II, so sin x = 4/5.
Now that we know sin x and cos x, we can use the double angle formulas to find sin 2x and cos 2x.
sin 2x = 2 sin x cos x = 2 (4/5) (-3/5) = -24/25
cos 2x = cos2 x - sin 2 x = (-3/5)2 - (4/5)2 = 9/25 - 16/25 = -7/25
Finally use the identity tan x = sin x / cos x to find tan 2x:
tan 2x = sin 2x / cos 2x = (-24/25) / (-7/25) = -24/-7 = 24/7
Write an equation in slope - intercept form for the line that passes through the given paint andis perpendicular to the given equation.7.(-5, 2), y =1/2x-3
Answers
You have to find a line perpedicular to the line y=1/2x-3 that passes through the point (-5,2)
Given one line, to find another one perpedicular to it, you have to keep in mind that the slope of the perpedicular line is the negative inverse of the slope of the first one, that is:
Let the given line be:
[tex]y_1=mx+b[/tex]And the perpendicular line
[tex]y_2=nx+c[/tex]The slope of the perpendicular line will be:
[tex]n=-\frac{1}{m}[/tex]So for the line
[tex]y=\frac{1}{2}x-3[/tex]The slope is
[tex]m=\frac{1}{2}[/tex]For the perpedicular line it will be:
[tex]\begin{gathered} n=-\frac{1}{\frac{1}{2}}=-1\cdot\frac{2}{1} \\ n=-2 \end{gathered}[/tex]Now that the slope of the perpendicular is determined, use the point slope form to find the equation of the perpedicular line:
[tex]y-y_1=m(x-x_1)[/tex]Replace the with m=-2 and (-5,2)
[tex]\begin{gathered} y-2=-2(x-(-5)) \\ y-2=-2(x+5) \\ y-2=-2x-10 \\ y=-2x-10+2 \\ y=-2x-8 \end{gathered}[/tex]The equation perpendicular to
[tex]y=\frac{1}{2}x-3[/tex]is
[tex]y=-2x-8[/tex]Now you can draw both lines:
a tiling of the plane occurs when we fill the entire infinite playing with a repeated pattern . the image to the right shows a portion of one such tiling. The pattern extends forever in all directions. A give all angles of rotational symmetry between 0 and 360 degrees about the two marked points. point A: Point B:
Answers
EXPLANATION
Let's see the facts:
The angles of symmetry in point A is 60 degrees because the plane in point A is divided in 6 parts, so dividing 360° by 6 give us 60°. The same reasoning applies for the point B dividing it by 3 parts.
The angles of symmetry in point B is 120 degrees.
Study the spinner below. If the wedges 2 and 5 are twice the area of the otherwedges what is the likelihood of landing on 4 or 6?23416/5A.NIO.B.A-OC.100oD. There is not enough information provided.
Answers
As we can see, there are 8 parts in our circle but 4 parts belong to wedge 2 and 5. Then, the probability of landing on 4 or 6 is given by
[tex]P(4\cup5)=P(4)+P(5)[/tex]because part 4 and part 5 are disjoint sets. Since there are 8 parts in our circle, we have
[tex]\begin{gathered} P(4\cup5)=P(4)+p(5) \\ P(4\cup5)=\frac{1}{8}+\frac{1}{8} \end{gathered}[/tex]which gives
[tex]P(4\cup5)=\frac{2}{8}=\frac{1}{4}[/tex]which corresponds to option B
Describe the expression.Cuad2 * 5+7jog vollsynsinontbnilo++7(3 + 13) evollarWhich of the following describes (7 in the expression above?A. factorB.(B, sumC. quotientD. product
Answers
Answer:
The expression is given below as
[tex]2\times5+7(3+13)[/tex]Concept:
We will have to explain the options so we can figure out what the final answer is
Sum:
The result is obtained by adding numbers
Quotient:
a quotient is a quantity produced by the division of two numbers.
Product:
A product is the result of multiplication,
Factor:
factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder.
Step 1:
[tex]2\times5=10(represents\text{ the product of 2 and 5\rparen}[/tex]We will then have to deal with the parenthesis
[tex]3+13=16(sum\text{ of 3 and 13\rparen}[/tex]We will then have to multiply 7 by 16 before adding to 10
Hence,
7 in the expression above represents a factor because after adding 3 and 13, you would need to multiply 2 and 5. Then, you will multiply 7 and 16 which shows that 7 in the expression above represents a factor. 7 is a factor common to both 3 and 16
Therefore,
The final answer is OPTION A
20 students started the class. Then 2 students dropped the
class.
What percent of the students have dropped the class?
Answers
Pls help if someone can solve for me 7-15. Thank you!
Answers
Given:
Set U: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
Set P: {2, 3, 5 7, 9, 11, 13, 17, 19}
Questin 7.
Complement of set P.
The complement of set P will be the set that contains the elements present in set U but not in P.
Hence, we have:
ANSWER:
P' = {1, 4, 6, 8, 10, 12, 14, 15, 16, 18, 20}
A car loan totaling 13,456.44 paid off in 36 equal monthly payment can afford no more than $350 per month can she or down explain
Answers
She cannot afford to buy the car with monthly instalments of $350. She needs to make a downpayment of $856.44 to afford the car
The total amount of the car loan = 13456.44
Number of instalments = 36 monthly payments
Affordable installment per month = $350
EMI: A fixed payment is made by a borrower to a lender at a specific time each month, known as an equated monthly instalment (EMI). The loan is repaid in full over a predetermined period of time by making equal monthly payments to the principal and interest.
Total payment that can be made using the instalments = Monthly instalments * Number of instalments
= 350*36
Total payment that can be made using the instalments = 12600
The amount remaining after paying instalments = 13456.44 - 12600
= 856.44
Downpayment required = $856.44
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