The first derivative of the function f'(x) = 2 · [√(x + x²) + 3 · sin 3x]² · [(1 + 2 · x) / [2 · √(x + x²)] + 9 · cos 3x], whose value at x = 1 is - 35.909.
How to find the derivative of a given function
Herein we find a function whose first derivative has to be found. This can be done by using the following derivative rules:
Derivative of a power
f(x) = c · xⁿ → f'(x) = n · c · xⁿ ⁻ ¹
Chain rule
f[g(x)] = (df / dg) · (dg / dx)
Derivative of a sum of functions
d / dx [f(x) + g(x)] = df / dx + dg /dx
Derivative of the sine
d / dx [sin x] = cos x
Now we proceed to find the derivative of the function:
f'(x) = 2 · [√(x + x²) + 3 · sin 3x]² · [(1 + 2 · x) / [2 · √(x + x²)] + 9 · cos 3x]
And we evaluate the derivative at x = 1:
f'(1) = 2 · [√(1 + 1²) + 3 · sin 3]² · [(1 + 2) / [2 · √(1 + 1²)] + 9 · cos 3]
f'(1) = 2 · (√2 + 0.423)² · (3 / 2 - 8.910)
f'(1) = - 35.909
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A car travels 55 miles per hour for 2 hours
How much will it travel 1/2 per hour
How much will it travel in 1 1/2 per hour?
Answer:
2 hours 110
Step-by-step explanation:
Point C is an orthocenter. Solve for X
Look at pic thanks
In the triangle Point C is the orthocenter then the value of x will be equal to 42.
What is Orthocenter?The intersection of the cutting point of the triangle's three elevations is known as the orthocenter. The height in this instance is indeed the line to be drawn from the triangle's apex that is perpendicular to the other side.
As per the given diagram and data in the question,
The orthocenter is at Point C.
C = 3x - 36
3x - 36 = 90
3x = 90 + 36
3x = 126
x = 126/3
x = 42
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To practice for a competition, Barry swam 730 meters in the pool each day for 4 weeks. How many kilometers did Barry swim in those 4 weeks? 1 m = 0.001 km
Answer:
20.44 km
Step-by-step explanation:
The values are,
→ 730 m = 0.730 km
→ 4 weeks = 28 days
Now Barry swam in 28 days is,
→ 0.730 × 28
→ 20.44 km
Hence, answer is 20.44 km.
Question 12(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
A new gaming chair costs $455.95. You have already saved $136.45 and earn $35.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
35.5 + 136.45w = 455.95; w = 9
35.5w + 136.45 = 455.95; w = 9
35.5w − 136.45 = 455.95; w = 17
35.5w − 455.95 = 136.45; w = 17
The equation that represents the number of weeks that is needed to baby sit to buy gaming chair is 35.5w + 136.45 = 455.95; w = 9 , the correct option is (b) .
In the question ,
it is given that
the cost of the gaming chair = $455.95
amount of money already saved for the gaming chair = $136.45
amount of money earned by baby sitting each week = $35.50 .
let the number of weeks required to baby sit is " w " .
the equation can be represented by
cost of chair = money saved + money earned in w weeks
Substituting the values from above ,
we get
455.95 = 136.45 + 35.5w
On solving further ,
136.45 + 35.5w = 455.95
35.52w = 455.95 - 136.45
35.52w = 319.5
w = 319.5 / 35.52
w = 8.99
w ≈ 9
the number of weeks = 9
Therefore , The equation that represents the number of weeks that is needed to baby sit to buy gaming chair is 35.5w + 136.45 = 455.95; w = 9 .
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3. Solve for x: 2x+4=x-6.
a. x=-12
b. x = 10
C. X=-16
d. x=-10
Answer:
D. x = -10
Step-by-step explanation:
2x + 4 = x - 6
combine like terms
1x = -10
-10
Help me please its the last question before I finish.
Answer:5/2
Step-by-step explanation: Slope is rise (how far up or down) over run (how far left to right. Look for points where the line crosses a perfect grid line intersection. The graph goes up to 50 and right 20 (started at 10 and ended at 30). The rise/run is 50/20 or 5/2 reduced.
first, find two places on the line that intersects the grid boxed neatly. This occurs at (10 , 0) and (30 , 50).
slope = change in rise / change in run
slope = change in y / change in x
slope = ( 0 - 50) / (10 - 30)
slope = -50/-20
slope = 50/20
slope = 5/2
Adan is writing a comic book. His publisher has requested that he turned 50 pages draft by one day. If he's written 40 pages what percent does he still need to complete?
5 candy bars with 12 sections split between 3 friends equally. Must be in Fraction Form
Answer:
Well 5 candy bars with 12 sections would make 60 sections to divide among the 3 friends. (5 multiplied by 12)
60 sections divided by 3 friends is 20 sections each.
20/1
Solve for the missing measure of X
Answer:
x = 4
Step-by-step explanation:
4x+8 = 6x
6x-4x = 8
2x = 8
2/2 x = 8/2
x = 4
How can I solve 2/1 divided by 3/11 using the giant one method
Giant one method: It is the method in which we multiply any fraction and we get an equivalent fraction.
For example:
1/2 x 1 (giant one) can also be written as:
=> 1/2 x 8/8
=> 8/16
It is also the method in which we divide any fraction and we get an equivalent fraction.
For example:
21/30 ÷ 1 (giant one) can also be written as:
=> 21/30 ÷ 3/3
=> 7/10
Solving the question:
2/1 ÷ 3/11
Solving this we get
=> 2 x 11/3 = 22/3
Multiplying giant one (1) through the giant one method.
=> 22/3 x 1 (giant one)
Multiplying both numerator and denominator by 3.
=> 22/3 x 3/3
=> 66/9
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Stefan sells Jin a bicycle for $104 and a helmet for $17. The total cost for Jin is 110% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
The amount Stefan spent originally to buy the bike is; $100.91.
The amount Stefan made in profit by selling the bicycle and helmet to Jin is; $10.09.
How much did the bicycle cost originally?According to the task content;
Stefan sold the bicycle and helmet for a total of;
104 + 17 = $111.
Also, since the total cost ($111) for Jin is 110% of what Stefan spent to buy the bicycle and helmet, x originally; we have
110% × x = 111
x = (111 × 100) / 110
x = $100.91.
Therefore, Stefan spent $100.91 originally to buy the bike and helmet.
Consequently, the money Stefan made by selling the bicycle and helmet to Jin is; 111 - 100.91 = $10.09.
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Solve for m.
- 3/7 m = 12
Answer:
-28
Step-by-step explanation:
Isolate m in the equation first: m = 12 / (-3/7)
Simplify and solve: m = -84/3 = -28
Answer:
-28
Step-by-step explanation:
3/7=0.4285714285714
0.4285714285714 × 28 equals 11.99 which is estimated to 12.
ASAP 100 Points!!!!!
The table represents the amount of money in a bank account each month.
Month Balance ($)
1 3,600.00
2 3,960.00
3 4,356.00
4 4,791.60
5 5,270.76
What type of function represents the bank account as a function of time? Justify your answer.
This is an exponential function because there is a common difference in the balance between the months.
This is an exponential function because there is a common ratio in the balance between the months.
This is a linear function because there is a common difference in the balance between the months.
This is a linear function because there is a common ratio in the balance between the months.
Answer:
the second answer
Step-by-step explanation:
Answer:
This is an exponential function because there is a common ratio in the balance between the months.
Step-by-step explanation:
If we look at the first and second month of balance, we can see that the difference is 360. If we multiply that by 5, it equalls 1800. If we subtract 5270--3600, it equals 1670, meaning that there is not a linear function, nor a common difference, meaning that the second answer would be correct.
Kevin has a coin collection. He keeps 5 of the coins in his box, which is 25% of the collection. How many total coins are in his collection?
Answer:
20 coins
Step-by-step explanation:
[tex]\frac{5}{\frac{25}{100} }[/tex] = 20
Answer:
[tex]\huge\boxed{\sf Total\ collection = 20\ coins}[/tex]
Step-by-step explanation:
25% of the collection = 5 coins
Total collection = 100%So,
100% = 25% + 25% + 25% + 25%
100% = 5 + 5 + 5 + 5
100% = 20 coins
Total collection = 20 coins[tex]\rule[225]{225}{2}[/tex]
The area of square $ABCD$ is 100 square centimeters, and $AE = 2$ cm. What is the area of square $EFGH$, in square centimeters?
The area of square EFGH is 68 square centimeters
What is the area of a geometric figure?The area of a geometric shape or figure is the area enclosed in its boundary.
Please find attached a possible drawing of the information in the question
The area of square ABCD = 100 square centimeters
Length of segment AE = 2 cm
Therefore;'
The side length of the square ABCD, s = √(100) = 10
The length of segment AB = 10 cm
AB = AE + EB (segment addition postulate)
10 = 2 + EB (substitution property of equality)
EB = 10 - 2 = 8
EB = 8 cm
∠CFG ≅ ∠AHE (alternate interior angles)
ΔCFG ≅ ΔAHE (ASA congruency postulate)
Similarly; ΔEBF ≅ ΔHAE (ASA congruency postulate)
BF = AE (CPCTC) = 2
[tex]\overline{EF}=\sqrt{\overline{EB}^2 +\overline{BF}^2}[/tex](Pythagorean theorem)
Therefore;
EF = √(8² + 2²) = √(68)
EF = √(68)
Area of a square = (Length of one side)²
Therefore, area of square EFGH = [tex]\overline{EF}^2[/tex]
Which gives; Area of square EFGH = (√(68))² = 68
The area of square EFGH is 68 square meters
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math geometry help help
Answer: w = 20 and the other side would be 16
Step-by-step explanation: based on the shortest side, it looks like all of the sides would be multiplied by 4 getting the answer above. The degree of all of the angels should be the same as the smaller triangle as it’s just a sized up version.
Sorry if it’s wrong, I’ve never used this program before. Good luck!
5 It is given that x2 - 5x + 6 and x3 - 6x² +11x + a have a common factor.
Find the possible value of a.
The possible value a using common factor is -6.
What is factors of the expression?
A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in a product, then the numbers we are multiplying are factors of the product because the product is divisible by them.
Here the given expression is,
=> [tex]x^2-5x+6=x^2-2x-3x+6[/tex]
=>x(x-2)-3(x-2)
=>(x-2)(x-3)
For the pair of polynomial have a common factor, 2 or 3 must be a root of the second polynomial.
If 2 is root then,
=> [tex]x^3-6x^2+11x+a[/tex] = 0 for x=2
=>8-24+22+a=0
=>6+a=0
=>a=-6.
If 3 is root then,
=> [tex]x^3-6x^2+11x+a[/tex] = 0 for x=3
=>27-54+33+a =0
=>6+a=0
=>a=-6.
Hence the possible value of a is -6.
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Babe Ruth, a professional baseball player known for hitting home runs, had a batting average of 0.342. Hank Aaron, another record home run hitter, had a batting average of 0.305.
3.7% greater was Babe Ruth's batting average than Hank Aaron's.
Given that, Babe Ruth, a professional baseball player known for hitting home runs, had a batting average of 0.342.
What is the average?In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
According to the question, 0.342-0.305
= 0.037
Now, 0.037 × 100
= 3.7%
Hence, 3.7% greater was Babe Ruth's batting average than Hank Aaron's.
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"Your question is incomplete, probably the complete question/missing part is:"
Babe Ruth, a professional baseball player known for hitting home runs, had a batting average of 0.342. Hank Aaron, another record home run hitter, had a batting average of 0.305. How much greater was Babe Ruth's batting average than Hank Aaron's?
98x972-67=??????????????????????????
Answer:
95,189
Step-by-step explanation:
98x972-67
95256-67
95189
Answer:95189
Step-by-step explanation: First you ave to multiply 98 x 972 which would equal to 95256 ten subtract 67 which would give you the answer 95189
The equation m=3b represents the times in minutes (m) it takes a chef to cook a certain number of bacon cheeseburgers (b) A: 3 B: 6 C:1/3 D: 1
For the given equation:
m = 3b
The constant of proportionality is 3, so the correct option is A.
How to determine the constant of proportionality?
After a small search on the internet, I've found that this question asks for the constant of proportionality.
Remember that a proportional relation is of the form:
y = k*x
Where k is the constant of proportionality, and x and y are the variables.
Here the relation is:
m = 3*b
Where m and b are the variables, then the remaining coefficient is the constant of proportionality, which is 3.
In this way, we can see that the correct option is A.
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19. Number Sense A company had
9 x 106 dollars in sales last year. Explain
how to find the product 9 × 106.
Answer: 954
Step-by-step explanation:
9x106 = 954
Given the function h(x)=-x^2+x+4, determine the average rate of change of the function over the interval −1≤x≤4
The average rate of change of the function h(x) = - x² + x + 4 is equal to 22 / 5.
How to determine the average rate of change of a function
In this problem we find the definition of a function and its interval regarding an average rate of change. Graphically speaking, the average rate of change of the function over an interval is represented by the slope of a secant line that passes through two function points related to the interval limits.
The average rate of change is represented by the following formula:
m = [h(b) - h(a)] / (b - a), for a ≤ x ≤ b
If we know that h(x) = - x² + x + 4, a = - 1 and b = 4, then the average rate of change is:
m = [h(4) - h(- 1)] / [4 - (- 1)]
m = [h(4) - h(- 1)] / 5
m = (- 4² + 4 + 4 + (- 1)² - (- 1) - 4) / 5
m = (17 + 5) / 5
m = 22 / 5
The average rate of change is equal to 22 / 5.
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Please help, 50 points & brainiest if you answer all 3!!!
9. The plane's speed would be of 340 and 350 miles per hour.
10. She runs the downhill portion of the course at a rate of 10 miles per hour.
11. The total time would be of 24 minutes.
How to obtain the velocity?
Velocity is distance divided by time, hence the equations is:
v = d/t.
For the first plane, the velocity and the distances are given by:
v = v + 10, d = 495.
Hence:
v + 10 = 495/t
t = 495/v + 10
For the second plane, the velocity and the distance are:
v = v, d = 510.
Hence:
v = 510/t
t = 510/v
The time is equal, hence the velocity of the slower plane is obtained as follows:
495/v + 10 = 510/v
Applying cross multiplication:
510v + 5100 = 495v
15v = 5100
v = 5100/15
v = 340 mph
For the runner, we have two parts, as follows:
First part: distance of 3 miles, velocity of v - 5, time of t.Second part: distance of 4 miles, velocity of v, time of 1 - t.Hence the equations are given as follows:
v - 5 = 3/t.v = 4/(1 - t).From the first equation, we have that:
v = 5 + 3/t.
Replacing in the second, we have that:
5 + 3/t = 4/(1 - t)
(5t + 3)/t = 4/(1 - t)
Applying cross multiplication, we have that:
(5t + 3)(1 - t) = 4t
-5t² + 2t + 3 = 4t
5t² + 2t - 3 = 0.
The positive solution, as time is a positive measure, of the quadratic equation is given by:
t = 0.6.
Hence the velocity of the downhill part is given by:
v = 4/(1 - t) = 4/0.4 = 10 miles per hour.
What is the together rate?The together rate is the sum of each separate rates.
The rates in this problem are given as follows:
Jason: 1/30.Kevin: 1/120.Together: 1/x.Hence:
1/x = 1/30 + 1/120
1/x = 5/120
x = 120/5
x = 24 minutes.
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1/5X+8=1/10X+9
What’s the answer to this question?
1/5x+8=1/10x+9.
We move all terms to the left:
1/5x+8-(1/10x+9.)=0
The domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 10x+9.)!=0
x∈R
We add all the numbers together, and all the variables
1/5x-(1/10x+9)+8=0
We get rid of parentheses
1/5x-1/10x-9+8=0
We calculate fractions
10x/50x^2+(-5x)/50x^2-9+8=0
We add all the numbers together, and all the variables
10x/50x^2+(-5x)/50x^2-1=0
We multiply all the terms by the denominator
10x+(-5x)-1*50x^2=0
Wy multiply elements
-50x^2+10x+(-5x)=0
We get rid of parentheses
-50x^2+10x-5x=0
We add all the numbers together, and all the variables
-50x^2+5x=0
a = -50; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-50)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use the following formulas to calculate our solutions:
x1=−b−Δ√2ax2=−b+Δ√2a
Δ−−√=25−−√=5
x1=−b−Δ√2a=−(5)−52∗−50=−10−100=1/10
x2=−b+Δ√2a=−(5)+52∗−50=0−100=0
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Waskahat wants to make a pair of earrings of different sized circles. The diameter of the first circle is 10 cm and that of the second is 6 cm. For his project, Waskahat determines that 35 beads will cover an area of 1 cm². How many beads in total will he need to make BOTH circles? Please answer with a whole number.
The number of beads needed to make both pair of earrings is 3090.
What is Unitary method?In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.
Given that,
The diameter of first circle is 10 cm.
The diameter of second circle is 4 cm.
And, the area covered by 35 beads is 1 cm².
Now, the area of first and second circle is given by substituting the diameters in the expression for area πD²/4 as,
Area of the first circle = (π × 10²)/4
= 25π cm².
Area of the second circle = (π × 4²)/4
= 4π cm²
The total area is 25π + 4π = 29π cm².
Now, the number of beads can be determined using the unitary method as below,
Number of beads for 1 cm² area is 35.
So, the beads for 29π cm² area is 35 × 29π = 3090.
Hence, the number of beads required for both the circles is 3090.
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A rectangle is placed around a semicircle as shown below. The length of the rectangle is 8ft Find the area of the shaded region.
Use the value 3.14 for PI , and do not round your answer. Be sure to include the correct unit in your answer.
it wont let me paste the picture but please help
Answer: 6.88 cm sq.
1. Find the area of the rectangle
A=l *w
L=8cm
the width=the radius of the semicircle
Width=8/2=4
8*4=32
A=32cm sq
2. find area of the semicircle
area=pi times the radius squared divided by 2
r=4cm
A=(3.14)*4^2/2. The area =25.12 cm sq.
Area of the shaded region=32-25.12=6.88cm sq.
Complete (assume $100,000 of overhead to be distributed): (Enter amount of overhead allocated as whole dollar amounts. Round your ratio answers to the nearest hundredth.) Sq. Ft. Ratio Amount of Overhead Allocated Dept. A 25,000 A B Dept. B 75,000 C D
The completion of the ratios, resulting from the square feet occupied by Departments A and B, and the amounts of allocated overhead costs to the two departments are as follows:
Ratio Amount
Department A 0.25 $25,000
Department B 0.75 $75,000
What is the ratio?Ratios show the relative values or proportions of the whole shared by two or more numbers.
Ratios are fractional values like proportions and are depicted in fractions, decimals, and percentages.
Total distributable overhead = $100,000
Ratios = 25,000:75,000
= 25:75
= 5: 15
= 1:3
Sum of Ratios = 4
OR
= 0.25:0.75
Sum of Ratios = 1
Overhead Allocation:Department Square Feet Ratio Amount of Overhead Allocated
Dept. A 10,000 A = 1 B = $25,000 ($100,000 x 0.25)
Dept. B 30,000 C = 3 D = $75,000 ($100,000 x 0.75)
Thus, based on the cost driver ratios, Department A bears $25,000, while Department B will be allocated $75,000 of the allocated overhead costs.
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A bag contains 18 red marbles. The ratio of red marbles to blue marbles is 6 to 9. Find the number of blue marbles in the bag. Please explain!
Answer:
Step-by-step explanation:
is enough to think it will work with the new system but not the new one that is already working on the old one
The midpoint of AB is M(1,-4). If the coordinates of A are (-3, -6), what are
the coordinates of B?
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-6})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -3}{2}~~~ ,~~~ \cfrac{ y -6}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(1~~,~~-4)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -3}{2}=1\implies x-3=2\implies \boxed{x=5} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -6}{2}=-4\implies y-6=-8\implies \boxed{y=-2}[/tex]
PLEASE HELP ME I’ll GIVE 20 PTS!!! The pizza shop offers a 15 percent discount for veterans and senior citizens. If the price of a pizza is $12, how would you find the discounted price?
Answer:
10.2
Step-by-step explain:
Subtract 15 from 100, you should get 85. Then move the decimal 2 times to the left from 85, then 12 and .85 and that is you answer.
Answer:
10.20
Step-by-step explanation:
12-15%= $10.20
And that's it just subtract with the % sign and you'll get the same
