The answer is:
[tex]f'(2)=-1[/tex]
Why?To solve this problem, first we need to derivate the given function, and then, evaluate the derivated function with x equal to 2.
The given function is:
[tex]f(x)=\frac{4}{x}[/tex]
It's a quotient, so, we need to use the following formula to derivate it:
[tex]f'(x)=\frac{d}{dx}(\frac{u}{v}) =\frac{v*u'-u*v'}{v^{2} }[/tex]
Then, of the given function we have that:
[tex]u=4\\v=x[/tex]
So, derivating we have:
[tex]f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{x*(4)'-4*(x)'}{x^{2} }[/tex]
[tex]f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{x*0-4*1}{x^{2} }[/tex]
[tex]f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{0-4}{x^{2} }[/tex]
[tex]f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{-4}{x^{2} }[/tex]
Hence,
[tex]f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{-4}{x^{2} }[/tex]
Now, evaluating with x equal to 2, we have:
[tex]f'(2)=\frac{-4}{(2)^{2} }[/tex]
[tex]f'(2)=\frac{-4}{4}[/tex]
[tex]f'(2)=-1[/tex]
Therefore, the answer is:
[tex]f'(2)=-1[/tex]
Have a nice day!
ANSWER
[tex]f'(2) = -1[/tex]
EXPLANATION
The given function is
[tex]f(x) = \frac{4}{x} [/tex]
Recall that:
[tex] \frac{c}{ {a}^{ m} } = c {a}^{ - m} [/tex]
We rewrite the given function using this rule to obtain,
[tex]f(x) = 4 {x}^{ - 1} [/tex]
Recall again that,
If
[tex]f(x)= a {x}^{n} [/tex]
then
[tex]f'(x)=n a {x}^{n - 1} [/tex]
We differentiate using the power rule to obtain,
[tex]f'(x) = - 1 \times 4 {x}^{ - 1 - 1} [/tex]
[tex]f'(x) = - 4 {x}^{ - 2} [/tex]
We rewrite as positive index to obtain,
[tex]f'(x) = - \frac{4}{ {x}^{2} } [/tex]
We plug in x=2 to obtain,
[tex]f'(2) = - \frac{4}{ { (2)}^{2} } = - \frac{4}{4} = - 1[/tex]
Identify the volume of the hemisphere in terms of π. HELP PLEASE!!
Answer:
its D
Step-by-step explanation:
Find a function for the graph below.
Answer:
C
Step-by-step explanation:
From the graph you can see that y changes from -2 to 2, so the range of the function is [tex][-2,2].[/tex]
Since the range of the functions [tex]y=\cos x[/tex] and [tex]y=\sin x[/tex] is [tex][-1,1][/tex] and the range of the functions [tex]y=k\cos x[/tex] and [tex]y=k\sin x[/tex] is [tex][-k,k],[/tex] we can state that the correct option is C: [tex]f(t)=-2\cos 3t.[/tex]
Check the value at t=0:
[tex]f(0)=-2\cos 3\cdot 0=-2\cos 0=-2.[/tex]
Please help will give brainliest thank you.
Two events are dependent if the outcome of the first event affects the outcome of the second.
The last answer is the correct one.
PLEASE HELP!!:) need help with this question thanks
Answer:
30%
Step-by-step explanation:
24 of (40 +24 +16) = 3/10 of the turkey sandwiches were made with wheat bread. As a percentage, that is ...
3/10 = 30/100 = 30%
The function [tex]f(x)=3x^3+x^2+2x[/tex] rises as x grows very large.
A. True
B. False
Answer:
A. True
Step-by-step explanation:
The given function is;
[tex]f(x)=3x^3+x^2+2x[/tex]
The leading coefficient of this polynomial function is positive.
The degree of the polynomial is odd.
This implies that, the function will rise on the left and keep rising on the right.
Hence, the end behavior of the function tells us that, the function rises as x-values grow very large.
The correct option is True
Find the Area of the circle... PLEASE HELP
Answer: Is it 169? i think that wright maybe.
Answer: 530.92916
Step-by-step explanation:
A=πr2=π·132≈530.92916
If you multiply a number by five and then subtract negative ten, the difference is negative thirty. What is the number?
Answer:
-8
Step-by-step explanation:
Let n represent the number. The stated relationship is ...
5n -(-10) = -30
5n = -40 . . . . . . . add -10
n = -8
The number is -8.
Final answer:
To solve the equation given in the student's question, convert the operation of subtracting a negative number into addition, subtract 10 from both sides to isolate the term with x, and then divide by 5 to find that the number in question is -8.
Explanation:
The student's question is a linear algebra problem, which can be turned into a simple equation to find the unknown number.
According to the question, we multiply a number by five and then subtract a negative ten to get a difference of negative thirty.
Mathematically, this can be expressed as the equation 5x - (-10) = -30, and we can solve for x. First, we should simplify the equation by turning the subtraction of a negative number into an addition. This makes our equation 5x + 10 = -30.
To find the value of x, we then subtract 10 from both sides of the equation, which gives us 5x = -40.
Finally, we divide both sides by 5 to solve for x, leading us to an answer of x = -8.
All the students in the sixth grade either purchased their lunch or brought their lunch from home on Monday 24% of the students purchased their lunch 190 students brought their lunch from home how many students ante in the sixth grade?
I believe it is 60 but I’m not sure
Joe ran 3 miles yesterday and wanted to run at least 12 miles this week. Write an inequality that can be used to determine the additional number of days joe must run this week if each run is 3 miles. Then solve the inequality .
Answer:
if you take into consideration the run from yesterday,
Joe needs to run at least three more days
y > = 3
if you don't take into consideration the 3 mile run from yesterday,
The answer is
He needs to run 4 or more days toachieve his goal
y > = 4
Step-by-step explanation:
12 miles as a minimum
that means
let x be the total amount of miles ran
x > = 12
Let y be the number of days in which Joe runs
3*y > = 12
y > = 4
Joe needs to run for at least 3 more days to meet his goal of running at least 12 miles this week, considering that each run is 3 miles.
We can set up an inequality. Joe has already run 3 miles, so we need to find out how many more miles he needs to run. If Joe runs 3 miles each day, the inequality representing the situation is 3d + 3 \\geq 12, where d is the number of additional days Joe must run.
We can solve the inequality as follows:
Subtract 3 from both sides of the inequality: 3d \\geq 9.Divide both sides by 3: d \\geq 3.This means Joe needs to run for at least 3 more days to meet his goal of 12 miles.
The Flat Rock auto assembly plant in Detroit, Michigan, produces three different makes of automobiles. In two years, the plant constructed a total of 390,000 cars. If 90,000 more cars were made in the first year than in the second year, how many cars were made in each year?
a. first year: 90,000
second year: 180,000
b. first year: 300,000
second year: 90,000
c. first year: 240,000
second year: 150,000
d. first year: 180,000
second year: 90,000
Answer:
c. first year: 240,000
second year: 150,000
Step-by-step explanation:
We let the number of cars made in the second year be X. Consequently, the number of cars made in the first year would be X+90000 since we are told that 90,000 more cars were made in the first year than in the second year. Furthermore, we are also told that the total number of cars constructed in these two years is 390,000, implying that;
X+X+90000=390000
2X+90000=390000
2X=390000-90000
2X=300000
X=150000; number of cars made in second year
The number made in the first year is thus;
150000+90000 = 240000
Answer:
Option c is correct
So, the cars made in 1st year = x = 240,000
and the cars made in 2nd year = 150,000
Step-by-step explanation:
in this question we have to find the number of cars made in each year by The Flat Rock auto assembly plant.
Given:
the plant constructed a total of 390,000 cars and 90,000 more cars were made in the first year than in the second year
Let cars made in 1st year = x
and cars made in 2nd year = y
then the plant constructed a total of 390,000 will be :
x+ y = 390,000 (i)
and
90,000 more cars were made in the first year than in the second year can be written as:
x=90,000 +y (ii)
Solving equation (i) and (ii) we can find the values of x and y
Putting value of x from eq (ii) into eq(i)
(90,000 + y) + y = 390,000
90,000 +y +y =390,000
2y = 390,000 - 90,000
2y= 300,000
y= 150,000
Putting value of y in equation (ii) we can find the value of x
x= 90,000 + y
x= 90,000 + 150,000
x= 240,000
So, the cars made in 1st year = x = 240,000
and the cars made in 2nd year = 150,000.
The first section of a newspaper has 16 pages. Advertisements take up 3 3/8 of the pages. How many pages are not advertisements?
Answer:
12.62
Step-by-step explanation:
you divide 3 by 8, then add the quotient of that to 3, then subtract that from 16
Answer:
Givens
The first section has 16 pages.Advertisements take up 3 3/8 of the pages.First, we need to the number of pages dedicated to advertisements.
Let's transform the mixed number into a fraction
[tex]3\frac{3}{8}=\frac{27}{8}[/tex]
Now, let's multiply this fraction with the number of pages
[tex]\frac{27}{8} \times 16= 54[/tex]
That is, there are 54 pages dedicated to advertisements.
Pages without advertisements are 5/8, which is
[tex]\frac{5}{8} \times 16=5(2)=10[/tex]
What is the 6th value in the sequence with the explicit formula
an= −2n−14?
Answer:
a6 = -26
Step-by-step explanation:
Fill in n=6 and do the arithmetic.
a6 = -2·6 -14 = -12-14 = -26
Solution:
Given, Tn = -2n - 14
To Find : What is the 6th value in the sequence
Solution: Simply Substitute the value of n as 6 .
Tn = -2n-14
Tn = -2(6) -14
Tn = -12 - 14
Tn = -14 - 12
Tn = -26
Therefore -10 is the 6th value in the sequence.
Decima is a spanish song form that is a style of poetry. how many lines does it have?
The spanish song Decima has ten lines
Final answer:
A decima is a Spanish form of poetry that consists of ten lines per stanza, with a fixed rhyme pattern of ABBAACCDDC, representing a distinct structure from other forms like sonnets or haikus.
Explanation:
The decima is a form of Spanish poetry. Unlike a sonnet, which typically comprises fourteen lines and may follow various rhyme schemes such as the Shakespearian or Petrarchan forms, the decima is characterized by its ten-line stanzas. These stanzas adhere to a specific rhyme pattern and are traditionally written in eight-syllable lines. Each line in a decima ends with a rhyme following the pattern ABBAACCDDC. The form is quite popular in Spanish literature and folk music, and it is distinct in its total line count from other forms like the sonnet, sestina, and haiku.
What is the surface area of the cube below?
A. 486 units^2
B. 729 units^2
C. 405 units^2
D. 508 units^2
The formula of the surface area of a cube is 6 x s²
→ s = 9
→ s² = 9²
→ s² = 81
→ 6 x 81 = 486
So, the surface area of the cube is 486 units².
Which description means the same as the limit expression? (Image attached)
A. The graph falls on the left side.
B. The graph rises on the left side.
C. The graph falls on the right side.
D. The graph rises on the right side.
Answer:
B. The graph rises on the left side.
Step-by-step explanation:
The limit provided on the image is interpreted as; The limit of the function f(x) as x approaches negative infinity is infinity.
X is approaching negative infinity, this means that along the x-axis we are moving towards the left where the values of x become increasingly negative.
On the other hand, f(x) is approaching positive infinity, meaning that along the y-axis we are moving upwards where the values of y become increasingly positive.
This typically implies that as we move towards the left the graph of f(x) is moving upwards or basically the graph rises on the left side.
Answer:
b. the graph rises on the left side
WILL GIVE BRAINLIEST
Answer:
(x,y) --> (x, y-5)
Step-by-step explanation:
the y-intercept of f(x) = (0,2)
the y-intercept of g(x) = (0, -3)
-3 - 2 = -5
Convert 90 degrees to radians.
π radians
2π/3radians
π/3 radians
π/2 radians
The answer is the last one . =
π
2
For quadrilateral abcd, determine the most precise name for it. A(-2,3),B(9,3),C(5,6)D(2,6). Show your work and explain.
Answer:
ABCD is an isosceles trapezoid.
Step-by-step explanation:
The line AB will be horizontal (parallel to the x axis), because the y values are both 3. It is 9--2 = 11 units long.
CD is also parallel to the x axis because the y values of C and D are both 6. Itis 5 - 2 = 3 units long.
The x values of the four points are all different so ABCD is a trapezoid.
Let's check the lengths of the line segments AC and BD:
AC = √((5--2)^2 + (6-3)^2 = √58.
BD = √((9-2)^2 + (3-6)^2 = √58.
They are equal in length so:
ABCD is an isosceles trapezoid.
in the triangle determine the value of c
Answer: The answer is A: 8.6
Step-by-step explanation: In this case, the side you're trying to figure out is the opposite and the side measurement given is the hypotenuse.
This means that out of the sin, cos, and tan we will be using sin.
Sin(Ф)= opposite/hypotenuse
Plug in the numbers you know: Sin(35)=x/15
Take the 15 to the other side to get x by itself
Then plug into your calculator 15Sin(35)=x
This gives you 8.6
Find the value of the csc 40° using your calculator.
(A)1.342
(B)0.745
(C)1.556
(D)0.643
The answer is:
C. 1.556.
[tex]csc(40\°)}=1.556[/tex]
Why?To solve the problem using our calculator we need to set it to "Degree" mode in order to avoid miscalculations.
Also, we need to remember that the cosecant (csc) is the inverse function of the sine, so:
[tex]csc(40\°)=\frac{1}{sin(40\°)} =\frac{1}{0.6427}=1.556[/tex]
Hence, the answer is C. 1.556.
Have a nice day!
Charles went to a restaurant for dinner and paid a tip of 15% on the total bill amount. He then had an ice cream that cost $13 less than the total restaurant bill excluding the tip.
If he spent $43 in all, how much was the total restaurant bill excluding the tip?
A.
$13.95
B.
$26.05
C.
$48.69
D.
$24.89
Answer:
B. $26.05
Step-by-step explanation:
Since this was a multiple choice question, I used process of elimination. I got rid of A because $13.95 - the ice cream ($13) would be no where near $43. For B, i did ($26.05) + ($26.05 - $13) which equals $39.10 and then i did ($39.10 + ($26.06 x 0.15) and that gave me $43 in all.
June has 42 sports books, 85 mystery books, and 69 nature books. She arranged her books equally on 7 shelves. How many books are on each shelf.
Answer:
28
Step-by-step explanation:
Add 42, 85, and 69 together and you get 196 but you need to divide that by 7 and you get 28
Answer:
28
Step-by-step explanation:
We are given that
June has sports books=42
June has mystery books=85
June has nature books=69
Total number of shelves=7
We have to find the number of books are on each shelf.
Total number of books=42+85+69=196
To find the number of books on each shelf we will divide the total number of books by 7.
Number of books on each shelf=[tex]\frac{196}{7}[/tex]
Number of books on each shelf=28
Hence, number of books on each shelf=28
A plywood template for a kitchen breakfast bar is cut from a circle.
Answer:
25
Step-by-step explanation:
The radius of the circle, which is the perpendicular bisector of a 48-inch diameter kitchen breakfast bar template, is 30 inches. The correct option is C).
Let's break down the information given in the problem:
PQ is the perpendicular bisector of VW, and Q is the midpoint of VW. This means that PQ passes through the center of the circle.
The length of PQ (perpendicular bisector) is 18 inches.
VW is 48 inches in diameter, which means its radius is half of that, i.e., 48 inches / 2 = 24 inches.
Since PQ is the radius of the circle, and it is also the perpendicular bisector of VW, it divides VW into two equal parts, each measuring 24 inches (as VW has a diameter of 48 inches, and Q is the midpoint).
Now, we have a right-angled triangle, with PQ as the hypotenuse and two legs measuring 18 inches and 24 inches. We can use the Pythagorean theorem to find the length of PQ (the radius of the circle):
PQ² = 18² + 24²
PQ² = 324 + 576
PQ² = 900
PQ = √900
PQ = 30 inches
So, the radius of the circle is 30 inches.
The correct answer is option c) 30 inches.
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Please help me with this
Answer:
8 ft
Step-by-step explanation:
The area (A) of a triangle = [tex]\frac{1}{2}[/tex] bh
where b is the base and h the perpendicular height
Using b = 20 and h = 12, then
A = 0.5 × 20 × 12 = 120 ft²
Using b = 30 and perpendicular height = h, then
0.5 × 30 × h = 120
15h = 120 ( divide both sides by 15
h = 8
According to lots of Pythagorean theorem,
h=7
I really don’t want to show my work because it took a while to solve this lol but if you want me to show my work just comment
You're baking a cake with a ratio of 3:4. If you use 2 cups of flour,how many cups of sugar will you use?
Answer:
2 2/3 cups of sugar
Step-by-step explanation:
If your ratio is 3 flour to 4 sugar, and you use 2 cups of flour, set up your proportion as follows:
[tex]\frac{3}{4}=\frac{2}{x}[/tex]
Cross multiply to get 3x = 8 and x = 8/3 which is 2 and 2/3 cups of sugar.
The cups of sugar used is 3/2 corresponding to 2 cups of flour.
What is proportion in ratio?If we are using the ratio of 3 flour to 4 sugar.
We have 2 cups of flour.
Let us consider the amount of sugar be 'y'.
By writing the proportion /as follows:
[tex]\frac{3}{4} = \;\frac{2}{y}[/tex]
4y =6
y =3/2
Thus, the amount of sugar used is 3/2.
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Please help me out!!!
Answer:
y = 30.
Step-by-step explanation:
As they are similar corresponding sides are in the same ratio.
So (y + 20) / 20 = 100/40
(y + 20) / 20 = 5/2
2(y + 20) = 5*20
y + 20 = 50
y = 30 (answer).
The number 0.9967 represents the area under the standard normal curve below a particular z-score.
What is the z-score?
Enter your answer, as a decimal to the nearest hundredth, in the box.
Answer:
2.72
Step-by-step explanation:
Here, we use a z-score table or calculator to look up the probability and find the corresponding z-score.
P(z < ?) = 0.9967 at z = 2.72.
Using the normal distribution principle, the Zscore which corresponds to the area under the normal curve at P(Z < z) = 0.9967 is 2.716
To obtain the Zscore in this scenario, which is the number of standard deviations from the mean value for a given score ; we make use of Zscore calculator or a normal distribution table ;
Using a normal distribution table;
Zscore at P(Z < z) = 0.9967 is 2.716Therefore, the Zscore value is 2.716
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Write 7x^5/11 in radical form. (Show steps please)
Answer:
[tex]7\sqrt[11]{x^{5}}[/tex]
Step-by-step explanation:
we know that
[tex]a^{\frac{n}{m}}=\sqrt[m]{a^{n}}[/tex]
In this problem we have
[tex]7x^{\frac{5}{11}}[/tex]
therefore
[tex]7x^{\frac{5}{11}}=7\sqrt[11]{x^{5}}[/tex]
Prove the converse of the Pythagorean theorem using similar triangles. The converse of the Pythagorean theorem states that when the sum of the squares of the links of the legs of the triangle equals the shared length of the hypotenuse, the triangle is a right triangle. Be sure to create and name the appropriate geometric figures. HELPPP
Answer:
Step-by-step explanation:By AA similarity postulate
△ADB∼△ABC∼△BDC
therefore the sides of the triangles are proportional, in particular
ADAB=ABAC ACBC=BCDC
By algebra we have the following equations
AD⋅AC=AB⋅ABAC⋅DC=BC⋅BC
this is the same as
AD⋅AC=AB2AC⋅DC=BC2
"Equals added to equals are equal" allows us to add the equations
AD⋅AC+AC⋅DC=AB2+BC2
By distributive property
AC(AD+DC)=AB2+BC2
but by construction AD+DC=AC.
Substituting we have
AC⋅AC=AB2+BC2
this is equivalent to
AB2+BC2=AC2
which is what we wanted to prove
The Pythagorean theorem uses similar triangles, This is equivalent to AB^2+BC^2=AC^2.
We have given that,
the converse of the Pythagorean theorem using similar triangles.
The converse of the Pythagorean theorem states that when the sum of the squares of the links of the legs of the triangle equals the shared length of the hypotenuse, the triangle is a right triangle.
What is the Pythagorean theorem?
[tex]hypotenuse ^2=side^2+side^2[/tex]
By AA similarity postulate
△ADB∼△ABC∼△BDC
Therefore the sides of the triangles are proportional, in particular
ADAB=ABAC ACBC=BCDC
By algebra, we have the following equations
AD⋅AC=AB⋅ABAC⋅DC=BC⋅BC
This is the same as
AD⋅AC=AB^2AC⋅DC=BC^2
Equals added to equals are equal allows us to add the equations
AD⋅AC+AC⋅DC=AB^2+BC^2
By distributive property
AC(AD+DC)=AB^2+BC^2
but by construction AD+DC=AC.
Substituting we have
AC⋅AC=AB^2+BC^2
This is equivalent to
AB^2+BC^2=AC^2
Hence the proof.
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The quotient of three divided by the sum of two and four
The sum is the answer to an addition problem. 2+4=6. so, 3÷6=0.5
The quotient of three divided by the sum of two and four will be 0.5.
What is a number system?The number system is a way to represent or express numbers.
Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
As per the given,
Three divided by the sum of two and four
3/(2 + 4) = 3/6 = 0.5
Hence "The quotient of three divided by the sum of two and four will be 0.5".
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