f(x)=a⁵+cos⁵x, find f′(x)
We need to find the derivative of the function f(x) = \(a^5\) + \(cos^5\)(x). The derivative of f(x) is f'(x) = 5\(a^4\) - 5\(cos^4\)(x) * sin(x). We can use the power rule and chain rule.
To find the derivative of f(x), we use the power rule and the chain rule. The power rule states that if we have a function g(x) =\(x^n\), then the derivative of g(x) with respect to x is given by g'(x) = n*\(x^(n-1)\).
Applying the power rule to the term \(a^5\), we have:
(\(a^5\))' = 5\(a^(5-1)\) = 5\(a^4\)
To differentiate the term \(cos^5\)(x), we use the chain rule. Let u = cos(x), so the derivative is:
(\(cos^5\)(x))' = 5(\(u^5\)-1) * (u')
Differentiating u = cos(x), we get:
u' = -sin(x)
Substituting these derivatives back into the expression for f'(x), we have:
f'(x) = 5\(a^4\)+ 5\(cos^4\)(x) * (-sin(x))
Simplifying further, we have:
f'(x) = 5\(a^4\) - 5\(cos^4\)(x) * sin(x)
Therefore, the derivative of f(x) is f'(x) = 5\(a^4\) - 5\(cos^4\)(x) * sin(x).
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a food manufacturer recently developed a new preservative to extend the shelf life of its perishable food items. It makes two batches of the perishable items. The preservative is added only to the second batch. After some time, researcher compares the shelf life of the batches. which method is the researcher applying?
Answer:
The researcher is using the Experiment method
Step-by-step explanation:
Plato
Answer:
Experiment
Step-by-step explanation:
PLATO/Edmentum
I GOT IT RIGHT!!!
Which of the following is correct? 1. cosh? x +sinn?x=1. II. sinh x cosh y = sinh (x + y) + sinh (x - y). a. Neither I nor II O b.I only O c. ll only O d.I and II
b. I only. The equation cosh(x) + sinn(x) = 1 is a trigonometric equation involving hyperbolic functions. Since statement I is incorrect and statement II is correct, the correct option is b. I only.
It does not hold true for all values of x and n. Therefore, statement I is not correct.
On the other hand, the equation sinh(x) cosh(y) = sinh(x + y) + sinh(x - y) is an identity involving hyperbolic functions. It holds true for all values of x and y. Therefore, statement II is correct.
Since statement I is incorrect and statement II is correct, the correct option is b. I only.
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Which expressions are equivalent to -9
x + 1 ? Check all that apply.
-9
* +9(1)
-ox-91
)
- 1
-6x +1
-6x + 9
-6x -9
Answer:
I think this right but I got it right on edge
Step-by-step explanation:
Hope fsdjgsdthisthis this psshelps
Answer:
F : –6x – 9 and B : -9( 2/3x ) - 9(1)Step-by-step explanation:
if you are on a school computer and dont have access to the image.. pls trust me is F and B for Expanding Expressions Assignment in edge... pls give brainlest :3
f(x)=(x+2)^2-6plot the vertex and the axis of symmetry of this function on the provided graph
first of all, we need to open the bracket and simplify it before proceeding to plot the graph
\(\begin{gathered} f(x)=(x+2)^2-6 \\ f(x)=x^2+4x+4-6 \\ f(x)=x^2+4x-2 \end{gathered}\)now, we plot for the equation
20 POINTS: Mr. Holland wants to buy a suit marked $235. He receives a 25% discount, and then there is 7% sales tax. How much will Mr. Holland actually spend on the suit?
Don't forget to round your answer to the nearest hundredth!
Answer:
$235 - 25% = $176.25
$235x 7% = $16.45
176.25
16.45
+______
( $192.7 )
Pls pls help it's urgent. Due in another few minutes!!
which statement is true?
1. y=csc x and y=sec x intersect at y = 1.
2. the period of y =tan x is doubled the period of y=csc x.
3. the zeros of y= tan x and y= cos x are the same.
4. the local maximum points of y = sec x is the same as the absolute minimum points of y = sin x.
5. None of the above are true.
Answer:
5
Step-by-step explanation:
none of the above are true
1. intersect at x=45
so y=sqrt(2)
2. y=cscx period is doubled y=tanx
3. not the same
4. no local maximum of y=secx
minimum point of y=sinx is -1
so none of the above are true
Which expression is equivalent to 3(3x + 8) ? A B С C D 9x = 21
Answer: it would be D.
Step-by-step explanation: you'd multiply the 3 by the 3x then multiply the 3 with the 8.
Solve for xx. Leave your answer in simplest radical form.
3
8
x
2
ANSWER ) x = sqrt51
Write and solve a word problem that can be solved using decimals addition that requires regrouping the 10th
Lets suppose we used an example of two children, one of them having $7.50 and other one having $8.40, and the total money will be the addition i.e., $15.9 using decimal operations.
As per the question statement, we are supposed to write and solve a word problem for decimal addition. Let the statement be : Two children, one of them have $7.50 and other one having $8.40, the sum total money would be____".
We are supposed to add both decimal numbers:
Total money = $7.50 + $8.40
Total money = $15.9
Hence, the sum total of the money of both the children is $15.9 using the decimal operations.
Decimal: A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole amounts.To learn more about decimals, click on the link given below:
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HELPPPP
please help me answer this question-
Answer:
\( \displaystyle GH = 2 \sqrt{30} \)
\( \displaystyle FH = 2 \sqrt{10} \)
\( \displaystyle m \angle G = {30}^{ \circ} \)
Step-by-step explanation:
QUESTION-2:we are given a right angle triangle
it's a 30-60-90 triangle of which FH is the shortest side
remember that,in case of 30-60-90 triangle the the longest side is twice as much as the shortest side thus
our equation is
\( \displaystyle 2FH=4\sqrt{10}\)
divide both sides by 2
\( \displaystyle\frac{2FH}{2}= \frac{ 4 \sqrt{10} }{2}\)
\( \displaystyle FH =2 \sqrt{10}\)
Question-1:in order to figure out GH we can use Trigonometry because the given triangle is a right angle triangle
as we want to figure out GH we'll use sin function
remember that,
\( \displaystyle \sin( \theta) = \frac{opp}{hypo} \)
let our opp, hypo and \(\theta\) be GH, 4√10 and 60° respectively
thus substitute:
\( \displaystyle \sin( {60}^{ \circ} ) = \frac{GH}{4 \sqrt{10} } \)
recall unit circle:
\( \displaystyle \frac{ \sqrt{3} }{2} = \frac{GH}{4 \sqrt{10} } \)
cross multiplication:
\( \displaystyle 2 GH = 4 \sqrt{10} \times \sqrt{3} \)
simplify multiplication:
\( \displaystyle 2 GH = 4 \sqrt{30} \)
divide both sides by 2:
\( \displaystyle GH = 2 \sqrt{30} \)
QUESTION-3:Recall that, the sum of the interior angles of a triangle is 180°
therefore,
\( \displaystyle m \angle G + {60}^{ \circ} + {90}^{ \circ} = {180}^{ \circ} \)
simplify addition:
\( \displaystyle m \angle G + {150}^{ \circ} = {180}^{ \circ} \)
cancel 150° from both sides
\( \displaystyle m \angle G = {30}^{ \circ} \)
Two sides of a triangle are 8 inches and
10 inches in length and the angle θ between
them is increasing at a rate of 1/10 radians
per second.
Find the rate at which the area of the tri-
angle is increasing when θ = π/3.
When the angle θ of a triangle, with sides measuring 8 inches and 10 inches, is increasing at a rate of 1/10 radians per second, the rate at which the area of the triangle is increasing when θ = π/3 is approximately 6.43 square inches per second.
To find the rate at which the area of the triangle is increasing, we can use the formula for the rate of change of the area with respect to time:
dA/dt = (1/2) * a * b * dθ/dt * sin(θ),
where A is the area of the triangle, a and b are the lengths of the sides, θ is the angle between the sides, and dθ/dt is the rate of change of θ with respect to time.
In this case, a = 8 inches, b = 10 inches, and dθ/dt = 1/10 radians per second. We are interested in finding the rate of change of the area when θ = π/3.
Plugging in these values into the formula, we have:
dA/dt = (1/2) * 8 * 10 * (1/10) * sin(π/3).
Simplifying the expression, we get:
dA/dt = 4 * sin(π/3) = 4 * (√3/2) = 2√3.
Therefore, when θ = π/3, the rate at which the area of the triangle is increasing is approximately 2√3 square inches per second. Evaluating this expression, we find that the rate is approximately 6.43 square inches per second.
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how to tell if a variable is discrete or continuous
To determine whether a variable is discrete or continuous, you need to consider the nature and characteristics of the variable.
Here are some guidelines to help you make the distinction:
1. Discrete Variables:
- Discrete variables have a countable or finite number of possible values.
- The values of a discrete variable are often whole numbers or integers.
- Examples of discrete variables include the number of children in a family, the number of cars in a parking lot, or the number of customers in a store at a given time.
2. Continuous Variables:
- Continuous variables can take on any value within a certain range or interval.
- The values of a continuous variable can be infinitely divisible and can include decimal fractions.
- Examples of continuous variables include height, weight, time, temperature, or the amount of rainfall.
However, it's worth noting that some variables may fall in a gray area and can be considered both discrete and continuous depending on the context.
For example, age can be treated as a discrete variable when only whole numbers are considered (e.g., number of years), but it can be treated as continuous when fractional values (e.g., age in years and months) are considered.
When determining if a variable is discrete or continuous, it's important to consider the level of measurement and the nature of the values being observed. Discrete variables typically involve counts or distinct categories, while continuous variables involve measurements along a continuum.
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At layla's beading boutique, 7 out of the 14 beads on clearance are plastic. what percentage of beads on clearance are plastic? write your answer using a percent sign (%).
At layla's beading boutique, 50% beads on clearance are plastic.
What is percentage?A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement. It has no unit of measurement.
Formula-
(\(\frac{value}{Total value}\))×100%
Given Data
7 out of 14 beads are plastic
Putting values in the Formula-
=(\(\frac{value}{total value}\))×100%
= \(\frac{7}{14}\)(100%)
= ½(100%)
=50%
At layla's beading boutique, 50% beads on clearance are plastic using percentage formula.
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Multiple Choice An equation of the line
whose slope is 3 and whose y-intercept is 8 is
? ?
A y = 8x + 3
C y = – 3x + 8
Ey = 3x - 8
B y = 3x + 8
D y = - 3x – 8
Answer:
y = 3x + 8
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 3 and c = 8 , thus
y = 3x + 8 ← equation of line
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
x=17 degrees
Step-by-step explanation:
All 3 angles = 180 degrees
So 90 + 54 + (x+19) = 180
Combine like terms
163 + x = 180
Subtract 163 from both sides
x = 180-163
x = 17
What percentage of the shape is pink?
Write your answer using a percent sign (%).
Answer:
Step-by-step explanation:
It is 20% because there is 5 squares. So we need to make this a fraction. So the fraction would be 1/5. So we then have to find a multiple for 1/5 because it is out of 100. So 20x5=100. So we have to multiply the top and the bottom part of the fraction by 20. So 5x20=100 and 1x20=100. So then we get 20/100. So the top number is your percent. So 20% is your answer. Good luck.
HELP MEEEEE! I can't do this all aloooone!
Answer:
the first one is the answer
Which angle is complementary to COD?
АOB
AOE
BOC
AOC
Answer:Then since ∠BOD = 90°, we know that ∠BOC + ∠COD = 90°. In other words, ∠BOC and ∠COD are complementary. Thus, the answer is angle BOC
Step-by-step explanation:
Answer:
The person above is correct! The answer is C. <BOC
Step-by-step explanation:
Hope u have a great rest of your day/night! <3333
How many solutions does the equation
-1/2(-8x+14) = 3x +9+x have?
The no: of solutions that the equation -1/2(-8x+14) = 3x +9+x has is 1
What is an example of an equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
What are the 3 types of equations?There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.
The no: of solutions that the equation is -1/2(-8x+14) = 3x +9+x is 1
as the equation is 1 degree polynomial.
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What is the slope of the line through (-7,-8) and (0,4)?
Gene's bucket holds 1/3 of a pound of
soil. Gene needs to move 10 2/3 pounds
of topsoil to his grandmother's garden.
How many times will he need to fill
his bucket if he wants to move the
entire pile of topsoil to the garden?
Answer:
32 TIMES
Step-by-step explanation:
do 10 *3 ( because there are three thirds in each number) and then add 2 beacuse there are 2 thirds in 2/3
What is the sum of the measures of the exterior angles of this triangle
Answer:
180°
Step-by-step explanation:
because because that's how much the angle of this triangle is
The sum of the exterior angles is always 360. This applies to any polygon.
note: If you wanted to sum up the interior angles, then the answer would be 180.
Evaluate the function. f(x)=−x^2 Find f(−5)
Answer:
25
Step-by-step explanation:
put -5 from x so (-(-5))²=25
Solution:
For each occurence of x in f(x) substitute 4 and clculate the result
f(x)=-x^2+5 becomes
f(4)=-(4)^2+5
f(4)=-16+5
f(4)=-11
Find the measure of each angle. ZCBA ZDAB ZEAB ZCAF ZDAF ZEAF
Answer:
CAB = 36 degrees, DAB = 107 degrees, EAB = 162 degrees, CAF = 144 degrees, DAF = 73 degrees, EAF = 18 degrees.
Step-by-step explanation:
Find the angle you are trying to figure out and then look at numbers on the protractor. The angle depends on where the 3rd point is (B or F). If it is B it would be the second row of numbers, if it was F, it would be the 1st row.
Hope this helps!! :)
Given the points (2, 2) and (-1, -7) find the slope.
Slope is change in y over the change in x.
Slope = (-7 - 2) / (-1 -2)
Slope = -9/-3
Slope = 3
PLEASE HELP
(r + 2)(r - 3) = 0?
A. 6
B. 0
C. 2
D. -3
E. -6
Answer:
hope it helps you see the attachment for further information
1. makenzie's favorite clothes include four t-shirts, three pairs of designer jeans, and two pairs of sandals. how many days in a row could she wear a different outfit using her favorite clothes?
The number of days in a row Makenzie could wear a different outfit using only her favorite clothes is 24 days.
How do you prove that?Solving this problem would involve combinations. In mathematics, combination refers to a mathematical technique used to determine the number of possible arrangements in a collection of items, irrespective of the arrangements.
We are given that the number of t-shirts is four, the number of pairs of designer jeans is three, and the number of pairs of sandals is two. The number of days in a row Makenzie could wear a different outfit using only her favorite clothes is calculated as follows:
(4C₁) (3C₁) (2C₁) =
4 × 3 × 2 =
24
We have confirmed that the number of days in a row Makenzie could wear a different outfit using only her favorite clothes is indeed 24 days.
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It cost jose $8.70 to send 87 text messages. How much would it cost to send 10 text messages?
Answer:
One dollar
Step-by-step explanation:
So you divide 8.70 by 87 to get 0.10. So then you multiply 0.10 by 10 to get a dollar
Sending 87 text messages cost $8.70. Sending 10 text messages would cost $1.00.
Use the concept of fraction defined as:
A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.
Given that,
Cost to send 87 text messages: $8.70
Number of text messages: 87
To find out how much it would cost to send 10 text messages,
Use a proportion.
If it cost Jose $8.70 to send 87 text messages,
Set up the proportion:
$8.70 / 87 messages = x / 10 messages
To solve for x,
Cross-multiply and divide:
($8.70 x 10) / 87 = $1.00
Therefore, it would cost $1.00 to send 10 text messages.
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The steepness of a road is called its grade. The higher the grade, the steeper the road is. For example, an interstate highway is considered out of standard if its grade exceeds 7%. Interpret a grade of 7% in terms of slope. Use feet to explain the meaning for a driver.
Answer:
A grade of 7% = 7 / 100 ;
This means that the elevation or vertical heighy of the interstate highway changes 7 feets for every 100 feets of horizontal distance moved
Step-by-step explanation:
Given that :
A road has a grade of 7%. This means that the slope of the of the highway is 7%. The slope is the proportion of rise and run. Hence the change in vertical distance with horizontal distance moved.
A grade of 7% = 7 / 100 ;
This means that the elevation or vertical heighy of the interstate highway changes 7 feets for every 100 feets of horizontal distance moved