Consider the following. g(x) = 4x2 − 2; h(x) = 1.6x Find thederivative of f(x) = g(x) · h(x) . f '(x) =
Answers
The derivative of f(x) = g(x) · h(x) is f'(x) = 12.8x^2 + 6.4.
To find the derivative of f(x) = g(x) · h(x), we can use the product rule, which states:
(f · g)' = f' · g + f · g'
Applying this rule to our function, we get:
f'(x) = g'(x) · h(x) + g(x) · h'(x)
To find g'(x), we need to take the derivative of g(x):
g(x) = 4x^2 - 2
g'(x) = 8x
To find h'(x), we need to take the derivative of h(x):
h(x) = 1.6x
h'(x) = 1.6
Now we can plug these values back into our original equation:
f'(x) = (8x)(1.6x) + (4x^2 - 2)(1.6)
Simplifying this expression, we get:
f'(x) = 12.8x^2 + 6.4
Therefore, the derivative of f(x) = g(x) · h(x) is f'(x) = 12.8x^2 + 6.4.
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Related Questions
Respond to the following question with either a TRUE or FALSE: "The following parabola opens down: f (x) = -x2 + 5"
O TRUE because the leading coefficient is negative.
O TRUE because the linear function is negative.
O FALSE because the 5 is.positive.
O FALSE because this function is actually linear and not a parabola.
O I'm not sure how to approach this problem...yet.
Answers
Answer: A) True because the leading coefficient is negative
Explanation:
The leading term is -x^2 since this term has the largest exponent.
The leading coefficient is -1 as it's the coefficient of the leading term.
It might help to write -x^2 as -1x^2
The negative leading coefficient makes the parabola open downward, so each endpoint goes off to negative infinity. The graph looks like a frowny face. You can think of a negative emotion going with a frowny face, so that negative emotion matches with the negative leading coefficient. There are probably other ways to remember but that's the trick I use.
plz help will mark as brainliest
Answers
Answer:
so the answer is = 210 beacuse u have multiply 5 times 6 times 7
Step-by-step explanation:
So, the area A of a triangle is given by the formula A=12bh where b is the base and h is the height of the triangle. Example: Find the area of the triangle. The area A of a triangle is given by the formula A=12bh where b is the base and h is the height of the triangle.
The time, in minutes, it took each of 11 students to complete a puzzle was recorded and is shown in the following list. 9, 17, 20, 21, 27, 29, 30, 31, 32, 35, 58 one of the students who completed the puzzle claimed that there were two outliers in the data set. Based on the 1. 5×iqr rule for outliers, is there evidence to support the student’s claim?.
Answers
Based on the 1.5 × IQR rule for outliers, there is no evidence to support the student's claim because there is only one outlier at 58 minutes.
What is an interquartile range of the data?The interquartile range is the difference between upper and lower quartiles. The semi-interquartile range is half the interquartile range. When the data set is small, it is simple to identify the values of quartiles.
Mathematically, interquartile range (IQR) is the difference between quartile 1 (Q₁) and quartile 3 (Q₃):
IQR = Q₃ - Q₁
The following interquartile ranges was calculated by using Excel:
Q₃ = 31.5
Q₁ = 20.5
Now, the interquartile range (IQR) is given by:
IQR = Q₃ - Q₁
IQR = 31.5 - 20.5
IQR = 11
Based on the 1.5 × IQR rule for outliers, we have:
1.5 × IQR = 1.5 × 11 = 16.5
Therefore, our fences will be 16.5 points below Q₁ and 16.5 points above Q₃:
Lower fence = 20.5 - 16.5 = 4.5
Upper fence = 4.5 + 31.5 = 36.
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What value of will make the triangles similar by the similarity theorem?
Answers
As similarity theorem, the value of x that will make the triangles similar by SSS similarity theorem is 77.
Similarity theorem:
In math, similarity theorem refers the line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.
Given,
Here we need to find the t value of will make the triangles similar by the similarity theorem.
For example, we are told that the 2 triangles are similar by SSS theorem.
Here we know that, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem
Therefore, in the triangles ,applying the SSS postulate gives;
=> x/35 = 44/20
Then by applying the multiplication property of equality, let us multiply both sides by 35 to get;
=> x = (44 * 35)/20
When we simplify this one then we get,
=> x = 77
Therefore, the value of x is 77.
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PLEASE HELP!
Solve for x
Answers
Answer:
x=3
Step-by-step explanation:
local bank is using Winters' method with α = 0.2,
β = 0.1, and γ = 0.5 to forecast the number of
customers served each day. The bank is open Monday through Friday.
At the end of the previous week,
Answers
The exact forecasted number of customers to be served on each of the next five business days, rounded to one decimal place, are as follows:
Tuesday: 389.1
Wednesday: 368.7
Thursday: 326.5
Friday: 510.9
To forecast the number of customers served on each of the next five business days using Winters' method, we need to follow these steps:
Calculate the seasonal factor for each day by multiplying the seasonal index by the level.
Monday: 1.10 × 20 = 22
Tuesday: 0.95 × 20 = 19
Wednesday: 0.90 × 20 = 18
Thursday: 0.80 × 20 = 16
Friday: 1.25 × 20 = 25
Update the level and trend using the following formulas:
New Level = α × (Actual Value / Seasonal Factor) + (1 - α) × (Previous Level + Previous Trend)
New Trend = β × (New Level - Previous Level) + (1 - β) * Previous Trend
For Tuesday:
New Level = 0.2 × (30 / 22) + 0.8 × (20 + 1) = 20.3636
New Trend = 0.1 × (20.3636 - 20) + 0.9 × 1 = 0.0364
Forecast the number of customers served on each subsequent day using the formula:
Forecast = (New Level + Forecasted Trend) × Seasonal Factor
Tuesday Forecast = (20.3636 + 0.0364) × 19 = 389.0909
Wednesday Forecast = (20.3636 + 0.0364) × 18 = 368.7273
Thursday Forecast = (20.3636 + 0.0364) × 16 = 326.5455
Friday Forecast = (20.3636 + 0.0364) × 25 = 510.9091
Therefore, the forecasted number of customers to be served on each of the next five business days, rounded to one decimal place, are as follows:
Tuesday: 389.1
Wednesday: 368.7
Thursday: 326.5
Friday: 510.9
The question should be: A local bank is using Winters' method with α = 0.2, β= 0.1, and γ = 0.5 to forecast the number of customers served each day. The bank is open Monday through Friday. At the end of the previous week, the following seasonal indexes have been estimated: Monday, 1.10; Tuesday, 0.95; Wednesday, 0.90; Thursday, 0.80; Friday, 1.25. Also, the current estimates of level and trend are 20 and 1. After observing that 30 customers are served by the bank on this Monday, forecast the number of customers who will be served on each of the next five business days. Round your answers to one decimal place, if necessary.
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PLesea help with this yall i need to finish
Answers
The missing property is the distributive property of multiplication.
What is the distributive property of multiplication?
The distributive property of multiplication is a mathematical property that allows you to simplify expressions that involve multiplying a number or variable by a sum or difference of other numbers or variables.
For the addition of 5 terms with 1z, we have that the term 1 is common to all the factors in the expression, hence the expression can be written as follows:
1z + 1z + 1z + 1z + 1z = 1(z + z + z + z + z) = 5z.
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Question 43 please. I would also appreciate it if you could explain your steps. Thank you
Answers
Answer:
D. p is multiplied by 2
Step-by-step explanation:
43. We can simplify the formula a bit to better see the effect of changing 'a'.
\(p=\dfrac{\dfrac{1}{2}ary+a}{12y}=\dfrac{ary+2a}{2(12y)}=\dfrac{a(ry+2)}{24y}\)
This tells you that for unchanging values of r and y, the value of p is proportional to the value of a. That is, the formula is of the form ...
p = ka . . . . for k=(ry+2)/(24y)
If a is multiplied by 2, p is multiplied by 2.
Find two positive integers if their difference is 5
and the sum of their squares is 193.
Answers
Answer:
7 & 12
Step-by-step explanation:
7²=49
12²=144
144+49=193
12-7=5
STEP BY STEP EXPLANATION
The strength, S, of a wooden beam depends on the width and depth of the rectangular cross-section of the beam, but not on the length of the beam. For a particular type of wood, the value of S of a beam is proportional to the product of the width and the square of the depth of its cross-section. Suppose the strength of an oak beam is 69 , when the beam is 7 inches wide and 3 inches deep. Determine the strength, S, of the largest rectangular beam that can be cut from a 28 -inch-diameter oak tree, given that the beam must be 14 inches wide. Remember y is proportional to x if there is a constant k such that y=kx. The constant k is known as the constant of proportionality. a) S=9016 b) S=2231 c) S=8232 d) S=392
Answers
The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.
Given,The strength, S, of a wooden beam depends on the width and depth of the rectangular cross-section of the beam, but not on the length of the beam.
For a particular type of wood, the value of S of a beam is proportional to the product of the width and the square of the depth of its cross-section.
The strength of an oak beam is 69, when the beam is 7 inches wide and 3 inches deep.Thus, we can conclude that k, a constant of proportionality exists, such that: S=k(W x D²), where W is the width, D is the depth of the rectangular cross-section and S is the strength of the beam.
Let's use this to calculate k: When the beam is 7 inches wide and 3 inches deep, S=69. Thus, we get:k = S/W x D²=69/(7 x 3²)=1.
Thus, the equation for S becomes:S = W x D²The radius of the oak tree is 28/2 = 14 inches and the beam must be 14 inches wide.
This implies that the rectangular cross-section of the beam must be square (or the largest rectangular cross-section is a square). Let the side of the square cross-section be x.
Thus, we can write:S = x²Diameter, d = 28 inches => radius, r = 14 inchesWe need to determine the depth of the beam. The depth of the beam is half the height of the cylindrical log from which the beam is cut. The cylindrical log has a diameter of 28 inches. The beam has a width of 14 inches.
The largest rectangular cross-section is a square with sides of length x. This cross-section can be obtained by cutting the log at a height of x/2 from its center.Since the diameter is 28 inches, the radius is 14 inches. The height at which the beam is cut is h = 14 - x/2.
Thus, the depth of the rectangular beam cut from the cylindrical log is given by: D = 2(h) = 2(14 - x/2) = 28 - x.Using the relationship S = W x D² with S = 69, W = 14 and k = 1, we can write:x² (28 - x)² = 69Simplifying the above equation,x⁴ - 56x³ + 784x² - 69 = 0.
Using polynomial long division, we get:(x² + 16x - 69)(x² - 40x + 1) = 0The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.Therefore, the answer is (b) S = 2231.
The strength, S, of a wooden beam depends on the width and depth of the rectangular cross-section of the beam, but not on the length of the beam. Let the side of the square cross-section be x. Thus, we can write:S = x²Diameter, d = 28 inches => radius, r = 14 inches. Using the relationship S = W x D² with S = 69, W = 14 and k = 1, we can write:x² (28 - x)² = 69.The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.
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A spring is attached at one end to support B and at the other end to collar A represented in the figure. Collar A slides along the vertical bar between points C and D. In the figure, the angle is the angle created as the collar moves between points Cand D. When the spring is stretched and the distance from point A to point Bis 5.3 feet, what is the value of e to the nearest tenth of a degree? 3 ft B 00000 А
Answers
The Distance from point A to point B is: 3.4 ft when θ = 28° and The value of θ is: 54.8°
Given,
A spring is attached at one end to support B and at the other end to collar A.
Part A: Reference angle (θ) = 28°
We have to find out the distance of point A to point B.
Adjacent = 3 ft (given)
Apply the trigonometry function to find AB
cos θ = adj / hypotenuse
Substituting all the values ,
cos 28°= 3/AB
AB = 3/cos 28°
AB = 3.4 ft (nearest tenth of a foot)
Part B:
It is given that Distance from point A to point B is 5.2 feet
We have to calculate the Value of θ
adjacent = 3 ft
hypotenuse = AB = 5.3 ft
To find θ , We will again apply the trigonometry function
cos θ = adjacent/hypotenuse
Substituting all the given values
cos θ = 3/5.3
θ = cos⁻¹ ( 3 / 5.3)
θ = 54.8°
That is,
The length of point A to point B is 3.4 feet
The value of θ is 54.8°
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Angle Q measures 30 degrees. If angle Q is rotated 45 degrees, what is the measure of angle Q'?
Answers
Substituting Q = 30 degrees, we get:
Q' = 30 degrees + 45 degrees
Q' = 75 degrees
Therefore, the measure of angle Q' is 75 degrees.
What exactly does a degree angle mean?Acute angles are those that range in degree from 0 to 90. Obtuse angles (90°–180°) are those that fall within this range. • A right angle is one with an angle of 90 degrees (= 90°).
If angle Q measures 30 degrees and is rotated 45 degrees, we can find the measure of the new angle Q' as follows:
Q' = Q + 45 degrees
Substituting Q = 30 degrees, we get:
Q' = 30 degrees + 45 degrees
Simplifying, we get:
Q' = 75 degrees
Therefore, the measure of angle Q' is 75 degrees.
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Solve by factoring: x2+3x-18=0
Answers
Answer:
x^2 +3x- 18=0
x^2 +6x -3x - 18 =0
x( x+6) - 3(x +6) =0
(x-3) + ( x+6) =0
therefore, x= -6,3
Solve the equations X = -6 X = 3 The equation has 2 solutions Solution
2 X + 6x-3x- 18 = 0 Factor the expressions xx (x + 6) -3 (x + 6) = 0 Factor the expression (x + 6) x (x-3) = 0 Separate into possible cases X + 6 = 0 X-3 = 0 Solve the equations X = -6 X = 3 The equation has 2 solutions Solution X4 = -6, x, = 3>
3x^2-2x+1 when x is 4
Answers
Answer: I got 29
Step-by-step explanation:
You would plug in 4 in all the spots where the x's are and then solve the problem
The answer is 21
sum of the digits of a two- digit number is 9. the number obtained by interchanging the digits exceeds the given number by 27 . then the given number is
Answers
Answer:
18,36,45
Step-by-step explanation:
sum if the two numer is 9
ex:1+8=9
Does someone mind helping me with this? Thank you!
Answers
For all values of x greater than or equal to -2, the function f(x) = √(x + 2) + 2 will yield real outputs. So, x = -2.
How to find the Output Value of a Function?To determine the input value at which the function f(x) = √(x + 2) + 2 begins to have real outputs, we need to find the values of x for which the expression inside the square root is non-negative. In other words, we need to solve the inequality x + 2 ≥ 0.
Subtracting 2 from both sides of the inequality, we get:
x ≥ -2
Therefore, the function f(x) = √(x + 2) + 2 will have real outputs for all values of x greater than or equal to -2.
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whoch expression is equivalent to -20 - (-4)
Answers
Answer:
D
Step-by-step explanation:
-(-4)=+4
so it is -20+4
Answer:
D) -20 + 4 is the answer.
Step-by-step explanation:
1) Record the terms .
\(4 - 20\)
2) Use this rule: a - b = -(b - a)
\( - (20 - 4)\)
3) Use algorithm method.
(see the attached picture)
4) After simplifying, we have:
\( -(20 - 4) = - 16\)
5) therefor, -20 + 4 = -16
\( - 16\)
Find the area of this parallelogram.
Answers
Answer:
Step-by-step explanation:
THE ANSWER IS 2,520 I HOPE THS HELPED :) !!!!!
A sample of 30 observations is selected from a normal population. The sample mean is 59, and the population standard deviation is 8. Conduct the following test of hypothesis using the 0.02 significance level.
H0: μ = 62
H1: μ ≠ 62
a. Is this a one- or two-tailed test? One-tailed test Two-tailed test
b. What is the decision rule? Reject H0 if z 2.326 or Reject H0 if -2.326 < z < 2.326
c. What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)
d. What is your decision regarding H0? Fail to reject H0 Reject H0 e. What is the p-value? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Answers
a. Two-tailed test b. Reject H0 if z < -2.33 or z > 2.33 (using a z-table for a 0.01 tail area) c. The test statistic is calculated as: z = (sample mean - population mean) / (population standard deviation / sqrt(sample size)) z = (59 - 62) / (8 / sqrt(30)) = -2.47 d. Reject H0 e. The p-value is calculated as the probability of observing a test statistic as extreme as -2.47 or more extreme, assuming H0 is true. Using a z-table, the area in the tail beyond -2.47 is 0.0069. Since this is a two-tailed test, the p-value is twice this value, or p = 0.0138.
In hypothesis testing, the p-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample data, assuming that the null hypothesis is true. If the p-value is less than the significance level, we reject the null hypothesis. The significance level is a predetermined threshold used to determine whether the results of a test are statistically significant. If the p-value is greater than or equal to the significance level, we fail to reject the null hypothesis. In other words, we do not have enough evidence to conclude that the alternative hypothesis is true. The p-value is commonly used to report the results of hypothesis tests because it provides a measure of the strength of evidence against the null hypothesis.
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How to find the missing side of angles if each pair of figures are similiar
Answers
Answer:
To find missing sides you subtract the angle from 180.
Step-by-step explanation:
If you have 40 and 30 you subtract them from 180 to find the missing lengh
What is the area of a right triangle that measure 8” high and has a 4” base?
Answers
Answer:
the answer is 16 im pretty sure
Step-by-step explanation: hope this helps :)
A bag contains 5 red marbles, 3 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue
Answers
Write an equation in point-slope form for the line through the two points. Then change it toslope-intercept form. Rewrite the equation in standard form.10. (1, 2) and (3, 12)11. (6, 2) and (-2,-2) 12. (4,1) and (1,4)Please help I have sooo many assignments (:
Answers
For the point 13. we have that the line passes through the points (-1,-2) and (0,1) then the slope is
\(m=\frac{-2-1}{-1-0}=\frac{-3}{-1}=3\)and the line equation will be:
\(y-1=3x\Rightarrow y=3x+1\)For the point 14: we have that the line passes through the points (-1,0) and (0,-1) then the sslope is:
\(m=\frac{-1-0}{0-(-1)}=\frac{-1}{1}=-1\)and the line equation will be:
\(y=-1(x-(-1))\Rightarrow y=-x-1\)For the point 15: the line equation is y=-3 because the y coordinate will be always the same (-3) and the slope of the line will be equal to zero
A princess is standing 38 feet from the base of a 217 foot tall tower. What is the angle of elevation from him to the ogre who has his princess held captive
Answers
Answer:
Angle of elevation = 80°
Step-by-step explanation:
A princess is standing 38 feet from the base of a 217 foot tall tower. What is the angle of elevation from him to the ogre who has his princess held captive?
To solve for angle of elevation, we use the Trigonometric function of Tangent.
tan θ = Opposite side/Adjacent side
Opposite side = Height of the tower = 217 ft
Adjacent side = 38ft
tan θ = 217/38
tan θ = 5.6315789474
θ = arc tan 5.6315789474
= 79.930937301°
Approximately = 80°
Based on this definition, which sentence is the best use of the word contemplative'??
O We watched the contemplative television show before heading to bed for the night
O Her contemplative speech was rather unfocused
O We were not very contemplative about the unfamiliar subject
O He was seated in a contemplative pose in the quiet library
Answers
Answer:
look thoughtfully for a long time at.
Step-by-step explanation:We watched the contemplative television show before heading to bed for the night
Question 11 < > For a confidence level of 98% with a sample size of 18, find the critical t value. Add Work > Next Question
Answers
The critical t-value is 2.898.
Given data:
The confidence level = 98%Sample size = 18Formula used: T-distribution formula is given as;$$t=\frac{x-\mu}{s/\sqrt{n}}$$ Where,x = the sample meanµ = the population means = the sample standard deviation n = sample size.
Calculation: Degree of freedom = n - 1 = 18 - 1 = 17 The significance level (α) = 1 - 0.98 = 0.02 From the T-distribution table, the critical t-value for the degree of freedom of 17 and a significance level of 0.02 is 2.898. Adding these values to the above formula, we get;$$t=\frac{x-\mu}{s/\sqrt{n}}$$$$2.898=\frac{x-\mu}{s/\sqrt{18}}$$
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if point OR=20 and PR=5, would OP=15?
Answers
Answer:
No
Step-by-step explanation:
If OR = 20,
PR = 5
OP would be:
=> 20+5
=> 25
When a correlation is found between a pair of variables, this always means that there is a direct cause and effect relationship between the variables.
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find the value of x:x 12 =5:4
Answers
What is the range of the number of minutes that employees commute to work?
Answers
Answer:
Need more information to this question.
Step-by-step explanation:
Answer: need way more information
Step-by-step explanation:
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