Find the average value fave of the function f on the given interval. f() = 5 sec2(/6), 0, 3 2
Answer:
[tex]f_{ave}[/tex] = [tex]{\frac{10 }{3\pi }[/tex]
Step-by-step explanation:
To find - Find the average value fave of the function f on the given interval. f(x) = 5 sec²(x/6), [0, 3[tex]\pi[/tex]/2]
Proof -
We know that,
Average value of f in the interval [a, b] is -
[tex]f_{ave}[/tex] = [tex]\frac{1}{b - a}\int\limits^b_a {f(x)} \, dx[/tex]
Now,
Here a = 0, b = [tex]\frac{3\pi }{2}[/tex], f(x) = [tex]5sec^{2}(\frac{x}{6} )[/tex]
Now,
[tex]f_{ave}[/tex] = [tex]\frac{1}{\frac{3\pi }{2} - 0}\int\limits^{\frac{3\pi }{2} }_0 {5sec^2 ({\frac{x}{6} }) } \, dx[/tex]
= [tex]{\frac{2 }{3\pi }}\int\limits^{\frac{3\pi }{2} }_0 {5sec^2 ({\frac{x}{6} }) } \, dx[/tex]
= [tex]{\frac{10 }{3\pi }}\int\limits^{\frac{3\pi }{2} }_0 {sec^2 ({\frac{x}{6} }) } \, dx[/tex]
= [tex]{\frac{10 }{3\pi }}[\ {tan({\frac{x}{6} }) }|^{\frac{3\pi }{2} }_0 \, ][/tex]
= [tex]{\frac{10 }{3\pi }}[\ {tan({\frac{x}{6} }) - tan({0) } \, ][/tex]
= [tex]{\frac{10 }{3\pi }}[ {1 - 0 } ][/tex]
= [tex]{\frac{10 }{3\pi }[/tex]
⇒[tex]f_{ave}[/tex] = [tex]{\frac{10 }{3\pi }[/tex]
HELP ILL GIVE BRAINLIEST what’s the shape of the
Base?
Answer:
circle
Step-by-step explanation:
Line segment JL is an altitude in triangle JKM. Triangle K J M is shown. Angle K J M is a right angle. An altitude is drawn from point J to point L on side K M to form a right angle. The length of K J is 13, the length of J L is 5, and the length of J M is 8. Which statement explains whether JKM is a right triangle? Round measures to the nearest tenth. JKM is a right triangle because KL + LM = 15.3. JKM is a right triangle because KL + LM = 18.2. JKM is not a right triangle because KL + LM ≠ 15.3. JKM is not a right triangle because KL + LM ≠ 18.2.
Answer:
JKM is not a right triangle because KL + LM ≠ 15.3.
Step-by-step explanation:
Given
[tex]JK = 13[/tex]
[tex]JL = 5[/tex]
[tex]JM = 8[/tex]
Required
Determine if JKM is right-angles or not
Calculate length KL using Pythagoras theorem.
[tex]JK^2 = JL^2 + KL^2[/tex]
[tex]13^2 = 5^2 + KL^2[/tex]
Collect like terms
[tex]KL^2 = 13^2 - 5^2[/tex]
[tex]KL^2 = 144[/tex]
[tex]KL = 12[/tex]
Calculate length LM using Pythagoras theorem.
[tex]JM^2 = JL^2 + LM^2[/tex]
[tex]8^2 = 5^2 + LM^2[/tex]
Collect like terms
[tex]LM^2 = 8^2 - 5^2[/tex]
[tex]LM^2 = 39[/tex]
[tex]LM = \sqrt{39[/tex]
[tex]LM = 6.2[/tex]
[tex]KM = KL + LM[/tex]
[tex]KM = 12 + 6.2[/tex]
[tex]KM = 18.2[/tex]
If JKM is right-angled, then:
[tex]KM^2 = JK^2 + JM^2[/tex]
[tex]KM^2 = 13^2 + 8^2[/tex]
[tex]KM^2 = 233[/tex]
[tex]KM = \sqrt{233[/tex]
[tex]KM = 15.3[/tex]
[tex]15.3 \ne 18.2[/tex]
i.e
[tex]KL + LM \ne 15.3[/tex]
Hence: JKM is not right-angled
Answer:
C-JKM is not a right triangle because KL + LM ≠ 15.3
Step-by-step explanation:
if right mark as brainliest
In ΔQRS, r = 6.9 inches, ∠Q=40° and ∠R=101°. Find the area of ΔQRS, to the nearest 10th of an square inch.
Answer:
9.8 in²
Step-by-step explanation:
If A, B and C are the angles of a triangle and a, b, c are the repective sides opposite the angles, then the area of the triangle is given as:
Area = (1/2)absin(C)
In ΔQRS, the area is:
Area = (1/2)rqsin(S)
∠S + ∠Q + ∠R = 180° (sum of angles in a triangle)
∠S + 40 + 101 = 180
∠S = 39°
Using sine rule to find q:
[tex]\frac{q}{sinQ} =\frac{r}{sinR} \\\\\frac{q}{sin40}=\frac{6.9}{sin101} \\\\q=\frac{6.9*sin40}{sin101} =4.52 \ inches\\\\Area\ of\ triangle \ QRS=\frac{1}{2}rqsin(S) =\frac{1}{2}*6.9*4.52*sin(39)=9.8\ in^2[/tex]
For this question, use the following functions.
f(x) = 2x + 6
g(x) = 4x2 – 9
Find a simplified expression for f(f(x)).
O 2x – 12
0 4x + 12
O 2x + 6
O 4x + 18
Answer:
4x + 18
Step-by-step explanation:
This is called a composite function, meaning passing the range of one function as a domain of another function.
For f(f(x)), the inner-function's range is passed as the domain of the outer function.
We can do so by substitution,
The range of f(x) can be written as 2x + 6 for any defined x values,
So we will substitute 2x + 6 as the 'x' of another function which is in this case
f(x) again, so it looks like this 2(2x+6) + 6 which can be simplified into
4x + 18
Grace earns $7 for each car she washes. She always saves $20 of her weekly earnings. This week, she wants to have at least $69 in spending money. How many cars must she wash? Enter and solve an inequality to represent this situation. Enter your value as a simplified mixed number, if necessary.
Answer:
She need to wash 9 cars
Step-by-step explanation:
The diagram shows a cuboid of volume Vcm (cubed)?
(a) Show that V = 15 + 16x-x(squared) - 2x (cubed)
Answer:
see explanation
Step-by-step explanation:
The volume (V) of the cuboid is calculated as
V = (2x + 5)(3 - x)(x + 1)
= (3 - x)(2x + 5)(x + 1) ← expand the pair of factors using FOIL
= (3 - x)(2x² + 7x + 5)
= 3(2x² + 7x + 5) - x(2x² + 7x + 5) ← distribute parenthesis
= 6x² + 21x + 15 - 2x³ -7x² - 5x ← collect like terms and rearrange
= 15 + 16x - x² - 2x³
The volume of the cuboid is 15 + 16x - x² - 2x³
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The volume (V) of the cuboid is calculated as
Volume of cuboid is length times width times height.
V = (2x + 5)(3 - x)(x + 1)
= (3 - x)(2x + 5)(x + 1)
Expand the pair of factors using FOIL
= (3 - x)(2x² + 7x + 5)
= 3(2x² + 7x + 5) - x(2x² + 7x + 5) ←
Distribute parenthesis
= 6x² + 21x + 15 - 2x³ -7x² - 5x
Combine like terms and rearrange
= 15 + 16x - x² - 2x³
Hence, the volume of the cuboid is 15 + 16x - x² - 2x³
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please help me. i'll give brainliest
The list that represents the simulation is (d) 8605 8378 5814 0101 2233 7198 6215 4903 4076 7964 9597 8078 4333 3033 3153
How to rearrange the list?The list is given as:
860583 785814 010122 337198 621549 034076 796495 978078 433330 333153
To illustrate the simulation of four free throws, then each number on the list must have 4 digits
So, we have:
8605 8378 5814 0101 2233 7198 6215 4903 4076 7964 9597 8078 4333 3033 3153
Hence, the list that represents the simulation of four free throws is (d)
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Gary is buying bananas at the grocery store. The bananas cost $0.89 per pound. What is the equation for the cost (y) of (x) pounds of bananas Gary buys?
a. y=0.89+x
b. y=0.89-x
c. y=0.89/x
d. y=(0.89)x
Answer:
d
Step-by-step explanation:
Find the
Width (in feet)
Answer
62
Step-by-step explanation:
Jonathan borrowed $5 from a friend who is charging him 5% interest every day on the $5. If his friend takes 4 weeks to pay Jonathan back, how much will he owe him. Use I= PRT
Answer:
$1.00
Step-by-step explanation:
5 (0.05) (4)= $1.00
hope this helps
I will give brainly
Find the probability that a randomly
selected point within the circle falls
in the red shaded area (square).
r = 4 cm
4√2 cm
[? ]%
Answer:
Step-by-step explanation:
This probability will be the area of the square divided by the area of the circle.
[tex]P=\frac{(4\sqrt{2})^2}{\pi 4^2}\\ \\ P=\frac{32}{16\pi}\\ \\ P=\frac{2}{\pi }\\ \\ \text{As a percentage}\\ \\ P=\frac{200}{\pi}\\ \\ P\approx 63.7\% [/tex]
Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression.
I need the bottom part
Answer:
y ≠ 9, y ≠ 3
Step-by-step explanation:
y² -12y +27 = (y - 9) (y - 3)
Denominator ≠ 0
y ≠ 9 or y ≠ 3
I need help I'm so confused
Answer:
Yeah me too buddy :(
Step-by-step explanation:
Shawn erned 5 dallors an hour mowing lawns pluse 10 welkly allounce from his parents what minmin number of hours he needs to mow in order to have enuf money to buy 75 dallars par of basketball sheows
Answer:
13 hours
Step-by-step explanation:
Since Shawn mows lawns at a rate of 5 dollars an hour, if he mows for t hours, he earns 5t dollars. Also, he gets 10 dollars weekly allowance from his parents. Thus, the total amount he earns per week is thus 10 + 5t.
Since he needs to earn enough to buy 75 dollars pair of basketball shoes, the amount he earns must equal the price of the shoes. So,
10 + 5t = 75
We now solve for t to find the amount of hours if takes him to earn enough to buy the shoes.
So,
10 + 5t = 75
Subtracting 10 from both sides, we have
10 - 10 + 5t = 75 - 10
5t = 65
dividing both sides by 5, we have
t = 65/5
t = 13 hours
So, it takes Shawn 13 hours to earn enough to buy the shoes.
Find the missing sides of each triangle. Leave your answers in radical form
Answer:
youbhave give me more information.
Answer:
incomplete question
please write the whole question or diagram of the question
How many milligrams are in one-half a gram?
HELP ! How long is segment AB ?
Answer:
square root of (2+10)²+(-5+3)²
square root of 144+4
square root of 148
PLEASE HELP ME- In the diagram below,
Answer:
Step-by-step explanation:
What is the equation of the line that passes through the point (-6,7) and has a slope of -5? Write the equation in slope intercept form
Answer:
y = -5x - 23
Step-by-step explanation:
Write it in point - slope form:
y - 7 = -5(x + 6)
rearrange:
y - 7 = -5x - 30
y = -5x - 23
PLEASE PLEASE PLEASE HELP HELP ME ME!!!!
Answer:
The answer for question 3 is D, number 4 is C
Some one plesae heelp!1
Option (b) 1.00
Step-by-step explanation:
3.4×1.00 = 3.4
Answer:
1.00
Step-by-step explanation:
1.00 equals one therefore the actual equation is 3.4x 1 = 3.4
Or 3.4x1.00=3.4
Hope this helps.
Identify a transformation of the function ƒ(x) = x^2 by observing the equation of the function g(x) = (x – 1)^2
Answer:
f(x) is translated 1 units left to give g(x)
Step-by-step explanation:
Given
[tex]f(x) = x^2[/tex]
[tex]g(x) = (x - 1)^2[/tex]
Required
How does f(x) transform to g(x)
[tex]f(x) = x^2[/tex]
When translated by b units left, it gives:
[tex]g(x) = f(x - b)[/tex]
In this case:
[tex]b = 1[/tex]
So:
[tex]g(x) = f(x - 1)[/tex]
If [tex]f(x) = x^2[/tex], then
[tex]f(x - 1) = (x - 1)^2[/tex]
Hence:
[tex]g(x) = (x - 1)^2[/tex]
This implies that; f(x) is translated 1 units left to give g(x)
math (not too hard answer asap) :)
Answer:
A and CStep-by-step explanation:
A. 134 is the mode, correct, repeated 5 timesB. 111 is appears 3 times, incorrect , this number is not part of data setC. There are more data values between 130 and 139, correct, there are 8 of themD. There are 20 data values, incorrect , there are 23Find the measure of the indicated angle. (image included)
I'm sorry I keep posting these it's just cause I don't understand still but i'm learning.
Answer: 88
The unknown angle in the left triangle is 80 since the sum of the angles in a triangle is 180.(180-60-40=80)
The unknown angle (the one that doesn't have a "?") is 36 since there's a straight angle which equals 180.(180-80-64)
Therefore the angle with the "?" is 88 since the sum of the angles in a triangle are 180(180-36-56)
Hope this helps!
PLS HELP 20 points
Triangle ABC is a right triangle with right angle B and altitude BD. If DC =54, AC=60, find AB (x) and BD (y)
Answer:
Hey Mate!
tis is ur answrr!
Alexa took a taxi from her house to the airport. The taxi company charged a pick-up fee of $4.20 plus $0.25 per mile. The total fare was $6.20, not including the tip. How many miles was the taxi ride?
Answer:
8
Step-by-step explanation: 6.20-4.20=2.00 2.00 divide by 25 for each mile = 8
Mhanifa can you please help? Look at the picture attached. I will mark brainliest!
Answer:
Sum of exterior angles of a polygon is 360°#8
2x + 2(64°) + 36° + 48° = 360°2x + 212° = 360°2x = 360° - 212°2x = 148°x = 74°#9
x + 73° + 109° + 90° = 360°x + 272° = 360°x = 360° - 272°x = 88°Write 4x10 to the power of 6 in decimal notation.
Answer:
Since the exponent of the scientific notation is positive, move the decimal point 66 places to the right.
4000000
The expression 4 x [tex]10^6[/tex] in decimal notation is 4,000,000.
We have,
In scientific notation, a number is expressed as a product of a decimal number and a power of 10.
In the given expression, 4 x [tex]10^6[/tex], the base number is 4, and it is multiplied by 10 raised to the power of 6.
To convert this into decimal notation, we need to multiply the base number (4) by the power of 10 ([tex]10^6[/tex]), which means moving the decimal point six places to the right.
Starting with 4, we move the decimal point six places to the right, resulting in 4,000,000.
Thus,
The expression 4 x [tex]10^6[/tex] in decimal notation is 4,000,000.
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Find the roots of f(x)=x^2 + 10x -96