The derivative of the given function is: f'(x) = sec(5x) / [5(sec(5x) + tan(5x))]
Using the first part of the Fundamental Theorem of Calculus, we can find the derivative of the function f(x) by evaluating its indefinite integral and then differentiating with respect to x.
First, we can evaluate the indefinite integral of the given function as follows:
[tex]\int\limits^x_0 2 sec(5t) dt[/tex]
Using the substitution u = 5t, du/dt = 5, we can simplify this to:
∫₀˵⁰ sec(u) du / 5
= 1/5 ln |sec(u) + tan(u)| from 0 to 5x
= 1/5 ln |sec(5x) + tan(5x)| - 1/5 ln |sec(0) + tan(0)|
= 1/5 ln |sec(5x) + tan(5x)| - 1/5 ln |1 + 0|
= 1/5 ln |sec(5x) + tan(5x)|
Next, we can differentiate this expression with respect to x to find the derivative of f(x):
f'(x) = d/dx [1/5 ln |sec(5x) + tan(5x)|]
= 1/5 (sec(5x) + tan(5x))^-1 * d/dx [sec(5x) + tan(5x)]
= 1/5 (sec(5x) + tan(5x))^-1 * 5sec(5x)
= sec(5x) / [5(sec(5x) + tan(5x))]
Therefore, the derivative of the given function is:
f'(x) = sec(5x) / [5(sec(5x) + tan(5x))]
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A shirt costs $5 less than a sweater. Together they cost
$25. How much does the sweater cost? _____
Answer:
$20
Step-by-step explanation:
25-5=20 that is your answer
Answer:
15 dollars
Step-by-step explanation:
El área cuadrada de un tablero de ajedrez mide 1681 cm².¿Cuál es la medida de cada uno de sus lados?
Los lados es = sqrt(1681)
=41cm
Simplify the followimg
(1 1/2) ^-2 step by step explanations plzzzzzzzz
Answer:
4/9
Step-by-step explanation:
sorry if wrong i don't know how to explain it also
Answer:
Convert 1 1/2 to an improper fraction.
3/2⋅2
Cancel the common factor of 2.
3
Approximately the distance d in miles that a person can see the horizon is represented by the
equation du
where h is the height where the person is. (1mile = 1609.3 m).
4
Step-by-step explanation:
bonjour quelqu'un peut-il se joindre à zo om Numéro d'identification 77974021488 le mot de passe 9taPHH
Mr. Hepworth bought a new refrigerator for $975 after a 25% discount, how much did the refrigerator cost originally?
Answer:
954
Step-by-step explanation:
Answer:
1218.75
Step-by-step explanation:
25% of $975 = 243.75
Discounted price + Discount = Original Price
$975 + 243.75 = 1218.75
can someone help please lol
Answer:
1. (an closed circle) on the negative 2 mark, then shade everything on the right. (Meaning anything greater than -2, such as -1, 0, 1, 2)
2. (an open circle) on the positive 3 mark, then shade everything right. (Meaning anything greater than 3, such as 4, 5, 6)
9. IS it possible to prove these triangles congruent by the HL Theorem?
Answer:
Yes, It is possible
Step-by-step explanation:
need help please
to find X
Answer:
[tex] \boxed{x = 86 \degree}[/tex]
Yoko's fish tank has 18 liters of water in it. She plans to add 5 liters per minute until the tank has more than 48 liters. What are the possible numbers of minutes Yoko could add water?
Answer:
7 minutes, 8 minutes, 9 minutes, or more
Really any minute more than 6 should do.
Step-by-step explanation:
48 - 18 = 30
30 ÷ 5 = 6
It says the tank should have more than 48 liters, so the answer should be more than 6 minutes.
WILL GIVE BRAINLIEST ASAP!!
1. Determine the area and perimeter of the quadrilaterals below.
Part A:
Part B:
Part C:
(see picture)
Answer: A) 1888 B) 664.225 C)?
Step-by-step explanation:
A= 42+76(1/2) = 59
59(32)=1888
A=163/10(163/4)=664.225
5 Which equation is equivalent to
3(2 x – 5) = 4( x + 3)?
A 2x= -27
B 2 x= 27
C 10 x=-27
D 10 x=-3
Answer:
I think its B
Step-by-step explanation:
Let's solve your equation step-by-step.
3(2x−5)=4(x+3)
Step 1: Simplify both sides of the equation.
3(2x−5)=4(x+3)
(3)(2x)+(3)(−5)=(4)(x)+(4)(3)(Distribute)
6x+−15=4x+12
6x−15=4x+12
Step 2: Subtract 4x from both sides.
6x−15−4x=4x+12−4x
2x−15=12
Step 3: Add 15 to both sides.
2x−15+15=12+15
2x=27
Step 4: Divide both sides by 2.
The equation is equivalent to given equation is 2x=27. Therefore, option B is the correct answer.
What is an equivalent equation?Algebraic equations with equivalent solutions or roots are called equivalent equations. An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation. An equation is equivalent if both sides are multiplied or divided by the same non-zero value.
The given equation is 3(2x-5)=4(x+3).
Now, 6x-15=4x+12
6x-4x=12+15
2x=27
The equation is equivalent to given equation is 2x=27. Therefore, option B is the correct answer.
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ANSWER ASAP GIVING BRAINLIEST FIVE STARS AND A HEART I ONLY NEED A FEW SENTENCES!
Please answer the following essay question:
An isosceles triangle has two congruent angles. Write an expression to represent the measure of the third angle of the triangle. Explain.
Answer:
third angle =180-two congruent angles. is expression.
Work out the sum of 1/6 , 4/5 and 2/3 Give your answer as a mixed number in simplest form.
Answer:
1 29/30
Step-by-step explanation:
First find the least common denominator of 1/6, 4/5, and 2/3. The least common denominator of that list is: 30.
So let's convert all of these fractions to a denominator of 30.
Here are the newly converted fractions:
5/30, 24/30, 20/30.
So now add all of them together. 5/30+24/30+20/30=(5+24+20)/30, which is equal to: 49/30 = 1 19/30.
Ifj. 1. what is the value of i
Answer:
i
Step-by-step explanation:
The square root of a negative number is identified as an imaginary number (i )
An imaginary number (i) with exponent 3 or any other exponent remains an imaginary number.
The answer is:
i
Q5) 60% of a number is 54. What is 50 % of the same?
Answer:
45
Step-by-step explanation:
we multiply 50 by 54 and divide 60 my the number you get after multiplying
so 50*54/60 that is 45
Encierra todo los números que sean menores para 25,000 003
how do you simplify 1/5 x 22
Answer:
The person above is correct
Step-by-step explanation:
Answer: 4 2/5
Step-by-step explanation:
PLS HELP!! BRAINLIEST!!
Answer:
Look below :)
Step-by-step explanation:
To find the relative frequencies, divide each frequency by the total number of students in the sample–in this case, 4 + 6 + 4 + 3 + 3. Which gives us 20. So for A grade, 4/20 people got it, which is 20%. We do that for the rest of them:
B = 6/20 = 30%
C = 4/20 = 20%
D = 3/20 = 15%
E = 3/20 = 15%
Now for the second question, the most is 30%, so most students got B. I hope this helps and please makr brainliest! <3
Find |14.06|= I'm having trouble with this.
Answer:
14.06
Step-by-step explanation:
The absolute value is the distance between a number and zero. The distance between 0 and 14.06 is 14.06.
Answer:
14.06
Step-by-step explanation:
|14.06| means the absolute value of 14.06, which is 14.06!
Hope that helps!
In a basketball game, Sally is the top scorer with 35% of the team's
points. If the team scored 120 points in total, how many points did Sally
score?
Answer:
she scored 42
Step-by-step explanation:
Answer:
vyvv6
Step-by-step explanation:
6g6t5g6g66ftce6tswftzadtxevyze
I need help with this problem Try not to answer this try to give me steps
Answer:
Step-by-step explanation:
80 inches = 6 feet and 8 inches
An equilateral triangle has a side length of 30.
Another side of the same triangle measures 3x + y.
The third side of the same triangle measures 4x - 2y.
What are the values of x and y that would keep the triangle equilateral?
Answer:
x=9
y=3
Step-by-step explanation:
since all three sides of an equlateral triangle are equal:
3x+y=30 then y=30-3x
4x-2y=30
4x-2(30-3x)=30
4x-60+6x=30
10x=90
x=9
3x+y=4x-2y
x=3y
y=3
Katie wants to collect over 100 seashells. She already has 34 seashells in her collection. Each day, she finds 12 more seashells on the beach. Katie can use fractions of days to find seashells. Write an inequality to determine the number of days, d, it will take Katie to collect over 100 seashells.
Answer:
34+12x=100 12x=66 x=66/12=11/2 answer:11/2
Step-by-step explanation:
Answer:
[tex]12n+34>100[/tex]
Step-by-step explanation:
Let d be the number of days.
We have been that each day Katie finds 12 more seashells on beach, so after collecting shells for d days Katie will have 12d shells.
We are also told that Katie already has 34 seashells in her collection, so total number of shells in Katie collection after d days will be: [tex]12n+34[/tex]
As Katie wants to collect over 100 seashells, so the total number of shells collected in d days will be greater than 100.
Jesse wants to have $ 500,000 in his IRA when he retires in 40 years. He is able to invest in an IRA that will yield 2 % compounded monthly. How much will Jesse need to invest into his IRA each month to reach his goal?
P=B(r/n)/(1+r/n)^nt-1
A. $ 374.69
B. $ 436.72
C. $ 556.69
D. $ 680.79
Answer:
Your answer is D.
Step-by-step explanation:
Which postulate or theorem proves that triangle JHG and
triangle EFG are congruent?
•HL Congruence Theorem
• ASA Congruence Postulate
•SAS Congruence Postulate
• AAS Congruence Theorem
Answer:
The answer is AS A Congruence Postulate.
Step-by-step explanation:
What is the position
number of the term
125 in the sequence
f(n) = 2n+3?
Answer:
61st term in the sequence
Step-by-step explanation:
125 = 2n + 3
122 = 2n
n = 61
To rent a limousine, Theo must pay an initial fee of
$
45
in addition to
$
12
for every hour (
h
) he has the limousine reserved. To calculate the final cost (
c
), Theo wrote the following equation.
c
=
45
+
12
h
If the final bill amounts to
$
123
, how many hours did Theo have the limousine reserved
Answer:
6.5 hours
Step-by-step explanation:
123-45=78
78/12=6.5
Theo had the limousine reserved for 6.5 hours.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Theo's equation for the cost of renting a limousine is:
c = 45 + 12h
where c is the total cost,
and h is the number of hours reserved.
If the final bill amounts to $123,
we can set c equal to 123 and solve for h:
123 = 45 + 12h
Subtracting 45 from both sides:
78 = 12h
Dividing both sides by 12:
h = 6.5
Therefore, Theo had the limousine reserved for 6.5 hours.
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6. If ABCD is a square and AD = 11. find each missing value.
B
BC=
mZDAB =
AC =
m2AEB =
BD =
mZCBD =
EC =
mZBAC =
D
Answer:
All sides will be 11 and all angles will be 90 degrees.
Step-by-step explanation:
As all sides of square are equal. And all angles are right angled.
Hope it helped!!
a straight line has equation 4y-5x=2 work out the gradient of this line
Answer:
gradient = [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope (gradient) and c the y- intercept )
Given
4y - 5x = 2 ( add 5x to both sides )
4y = 5x + 2 ( divide the terms by 4 )
y = [tex]\frac{5}{4}[/tex] x + [tex]\frac{1}{2}[/tex] ← in slope- intercept form
with gradient m = [tex]\frac{5}{4}[/tex]
Your friend's house is 6 miles south and 14.4 miles east of the bank. How far is your friend's house from the bank?
Answer: 15.6 miles
Step-by-step explanation:
If you draw it out it makes a triangle which you can then use the pythagorean theorem to find the actual distance between the house and the bank. Your equation should be sqroot of 6^2+14.4^2 which equals 15.6 miles. Hope this helps. :)