Answer:
x = 5 ± √ 2
Step-by-step explanation:
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]
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
I need help I'm so confused
Answer:
Yeah me too buddy :(
Step-by-step explanation:
A bubble may be enclosed in a square whose side
length is equal to the bubble's diameter. Four bubbles
in squares collide and merge into one large bubble in
a square. The area of the large bubble is equal to the
sum of the areas of the small bubbles. How is the side
length of the large square related to the side length of
one small square?
Assume 1 small bub side = 2cm
area = 2 × 2
= 4 cm²
total area of small bub
4 × 4 = 16cm²
area of big bub = total area of small bub
= 16cm²
one side of big bub
16 ÷ 4 = 4
1 small bub side : 1 big bub side
2 : 4
1 : 2
the side length of the large square is 2 times bigger than the side length of one small square.
a.55.48.27.12.0
b.62.40.9.3.25.
c.1.8.13.29.42.
d.15.34.0.7.28
of the following shows an arrangement of an integer from least to greatest
Answer:
C
Step-by-step explanation:
a) 55 > 48 > 27 > 12 > 0 ×
b) 62 > 40 > 9 > 3 < 25 ×
c) 1 < 8 < 13 < 29 < 42 ✓
d) 15 < 34 > 0 < 7 < 28 ×
There are 640 calories in 4 scoops of ice cream. At this rate, how many calories would there be in 9 scoops of ice cream?
Answer:
1,440 calories
Step-by-step explanation:
Divide 640 by 4 to get how many calories there are per scoop.
640 calories ÷ 4 scoops = 160 calories per scoop
Then, we can multiple 160 by 9 to get the calories in 9 scoops.
160 calories per scoop × 9 scoops = 1,440 calories per 9 scoops
Answer:
1,440
Step-by-step explanation:
Use the net to find the surface area of the pyramid
Answer:
56
Step-by-step explanation:
5ft x 4ft = 20ft / 2 = area =10 10 x 4 triangles = 10 x 4 = 40 + square= area, so 4 x 4 = 16 + 40 = 56ft
Hope this helps!
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
Find 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!
Find the roots of f(x)=x^2 + 10x -96
I NEED YOUR OPINION PLEASE
okay , so I am 13 years old . I had gotten my cartilage pierced on both ears for my 13th birthday. Fast foward, I had asked my mom if I could get another cartilage piercing and my tragus pierced . She told me to ask my father. I did not . So I had pierced my tragus and my cartilage on my ear .. And my mom nor my dad has no clue I done it .
I just feel guilty hiding it from them , more so my mom ..
Can anyone give me advice on how to tell them PLEASEEEEEEEEEE
You're gonna get caught anyways, just come out. If you don't, figure out a way to undo it.
[tex]3 \sqrt{ - 125 - ( - {5)3}^{?} } [/tex]
A manager records the number of projects employees complete in one month. If the manager wants to summarize the data, which two statements are true?
The manager should use a measure of center to summarize how many projects the employees that complete the least projects complete.
The manager should use a measure of center to summarize how the number of projects employees complete differs.
The manager should use a measure of center to summarize the typical number of projects an employee completes.
The manager should use a measure of variability to summarize how the number of projects employees complete differs.
The manager should use a measure of variability to summarize the typical number of projects an employee completes.
Answer:
The manager should use a measure of center to summarize how many projects the employees that complete the least projects complete.
Step-by-step explanation:
Brand XYZ dog food cost $36 for 15 pounds of dog food. What is the cost per pound?
Answer:
2.4 per pound
Step-by-step explanation:
36÷15=2.4
how do i know this i used my brain
Please help this is timed!!
Answer:
can i see the rest of the problem...
Step-by-step explanation:
For the graph shown, the slope is changed to 1/5, but the y-intercept remains the same. What is the resulting equation for the new graph?
A)y = x + 15
B)y = x - 15
C)y = 15x + 1
D)y = 15x - 1
Answer: C. y=1/5x+1
Step-by-step explanation:
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:
5 b.) Bill swims 2/3 of a lap in 7 minute.
What is his speed in laps per minute?
Answer:
.095 laps per minute (if you need this answer as well 10.5 minutes per lap)
Step-by-step explanation:
(2/3)/7 =.095238 this is laps per min
7/(2/3)= 10.5 this is minutes per lap
I hope this is what you were looking for.
How many milligrams are in one-half a gram?
in your own words, describe what a horizontal asymptote is ?
Susan read 130 pages of a book in 2.5 days. If she read the same amount each day, how many pages did she read each day ?
A 5.2
B 5.6
C 52
D 56
Answer:
c.52
Step-by-step explanation:
if susan reads 130 pages in 2.5 days then we have to divide 130 and 2.5 which gives us 52 which kinda means she reads 52 pages per day i hope that clear
mr. jaw needs 1 bag of sand for every 5 square feet of the sandpit. of bags of sand cost $8 each, about how much will mr. jaw spends on sand use ~ 3.14
Answer:
$125.60
Step-by-step explanation:
3.14*5 = 15.7
15.7*$8 = $125.60
HOPE THIS HELPS!!!! <3333
-Silver
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.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ6
A mix of factoring by grouping. Factor the exressions. 17ax+17a-x-1 Please explain/show steps on how to do this!
*edit: I know the answer to the problem because it was said aloud in a class, but I am not sure the steps to get there!
Answer:
[tex](x+1)(17a-1)[/tex]
Step-by-step explanation:
We are given that
[tex]17ax+17a-x-1[/tex]
We have to factorize the given expression.
Pair up the terms
[tex](17ax+17a)+(-x-1)[/tex]
Now, taking common factor
[tex]17a(x+1)-1(x+1)[/tex]
Taking common (x+1)
[tex](x+1)(17a-1)[/tex]
Now, we get
[tex](x+1)(17a-1)[/tex]
This is required factors of given expression.
4x + 7y = 12
-8x - 14y = -24
Answer:
x = 3
y = 0
Step-by-step explanation:
4(3) + 7(0) = 12
-8(3) - 14(0) = -24
y= 1/2x - 1
what's the slope and intercept.
Answer:
The slope is 1/2. The x-intercept is (2,0). The y-intercept is (0,-1)
Answer:
The slope is 1/2x and -1 is the (y) intercept
Step-by-step explanation:
Since y= 1/2x - 1 is already a linear equation (y=mx+b) you can use y=mx+b to find the slope and (y) intercept.m is the slope and b is the intercept
Find the
Width (in feet)
Answer
62
Step-by-step explanation:
Select all the correct descriptors for the relationship
Answer:
Options (1), (3) and (5)
Step-by-step explanation:
Coordinates of D → (2, 2)
Coordinates of E → (1, 6)
Coordinates of F → (5, 7)
Coordinates of G → (6, 3)
Length of ED = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
= [tex]\sqrt{(2-1)^2+(2-6)^2}[/tex]
= [tex]\sqrt{17}[/tex]
Length of FG = [tex]\sqrt{(5-6)^2+(7-3)^2}[/tex]
= [tex]\sqrt{17}[/tex]
Length of GD = [tex]\sqrt{6-2)^2+(3-2)^2}[/tex]
= [tex]\sqrt{17}[/tex]
Length of EF = [tex]\sqrt{(1-5)^2+(6-7)^2}[/tex]
= [tex]=\sqrt{17}[/tex]
Since, all sides of the given quadrilateral are equal in length, quadrilateral will be a square.
Therefore, diagonals EG and DF will be perpendicular, equal in measure, congruent and will bisect each other.
Options (1), (3) and (5) are the correct options.
A factory produces 80,000 candies each day.They produce equal quantity of four flavors:cherry,lemon,orange and strawberry. The candies are mix together during packaging. What is the probability of selecting orange.
Answer:
1 /4
Step-by-step explanation:
Total number of candies produced per day = 80,000
Number of flavors made = 4
Since the number of each flavor produced are equal ;
Number of each flavor produced :
80000 /4 = 20000
Probability of selecting orange flavor :
Number of orange flavor / total candies produced
= 20000 / 80000
= 1/4
Jaime drew the number line below to show 2/3 4/5. Explain how the number line shows 2/3 times 4/5. What is the product?
Answer:
[tex]\frac{2}{3} * \frac{4}{5} = \frac{6}{15}[/tex]
Step-by-step explanation:
Given
[tex]\frac{2}{3} * \frac{4}{5} =[/tex]
The number line is missing from the question.
So, I will answer the question and also draw the number line to show the product.
[tex]\frac{2}{3} * \frac{4}{5} =[/tex]
[tex]\frac{2}{3} * \frac{4}{5} = \frac{6}{15}[/tex]
To represent this on a number line;
We draw a number line of 15 points, and place a dot on the 6th point.
This represents 6/15
See attachment