Suppose [tex]x>0[/tex]; then the curves meet when
[tex]x^2 + \dfrac5{12} = 2 - \dfrac83 x \implies x^2 + \dfrac83 x - \dfrac{19}{12} = \left(x + \dfrac{19}6\right) \left(x - \dfrac12\right) = 0 \\\\ \implies x = \dfrac12[/tex]
By symmetry, they intersect at [tex]x=\pm\frac12[/tex].
We also see that [tex]\min\left\{f(x):|x|\le\frac34\right\} = \frac5{12}[/tex] and [tex]\max\left\{g(x):|x|\le\frac34\right\} = 2[/tex] at [tex]x=0[/tex]. [tex]f[/tex] and [tex]g[/tex] are continuous, so it follows that
[tex]\min\left\{f(x),g(x) :|x|\le\frac34\right\} = \begin{cases} f(x) & \text{if } |x| < \frac12 \\ g(x) & \text{if } |x| > \frac12 \\ f\left(\pm\frac12\right) = g\left(\pm\frac12\right) = \frac23 & \text{if } x = \pm\frac12 \end{cases}[/tex]
Compute the area [tex]\alpha[/tex]. Taking advantage of symmetry again, we have
[tex]\alpha = \displaystyle 2 \int_0^{1/2} \int_0^{f(x)} dy\,dx + 2 \int_{1/2}^{3/4} \int_0^{g(x)} dy \, dx \\\\ ~~~~ = 2 \int_0^{1/2} f(x) \, dx + 2 \int_{1/2}^{3/4} g(x) \, dx \\\\ ~~~~ = \left. 2 \left(\frac{x^3}3 + \frac{5x}{12}\right) \right\vert_0^{1/2} + \left. 2 \left(2x - \frac{8x^2}6\right) \right\vert_{1/2}^{3/4} \\\\ ~~~~ = \left(\frac12 - 0\right) + \left(\frac32 - \frac43\right) = \frac23[/tex]
and it follows that [tex]9\alpha = \boxed{6}[/tex].
If y’all can’t se it just zoom in because that’s the best I can get it please help me thank u please don’t comment on my stuff just for points I really need help with this
Answer:
the answer is 42
Step-by-step explanation:
you add 217+153+88=458
500-458=42
8. A fever is generally considered to be a body temperature greater than
100°F. Your friend has a temperature of 37°C. Does your friend have a
fever when the temperature increases by 1°F? 1°C?
The friend doesn't have a fever when the temperature increases by 1°C.
How to convert the temperature?To convert Celcius to Fahrenheit,we have to multiply by 1.8 and add 32°.
This will be:
37°C = (37 × 1.8) + 32
= 98.6
When we add 1°, we will get 99.6.
Therefore, the friend doesn't have a fever when the temperature increases by 1°C.
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In Fairbanks the temperature went down 20 degrees in 6 hours
Answer: 3.3 hours
Step-by-step explanation:
Given the recursive formula shown, what are the first 4 terms of the sequence?
f(n)=
f(1) = 3
(f(n)=f(n-1)+4 if n>1
OA) 3, 7, 11, 15
B) 4, 7, 10, 13
C) 3, 9, 11, 13
D) 3, 8, 10, 12
Answer:
Option A: 3, 7, 11, 15
Step-by-step explanation:
f(2) = f(1) + 4 = 3 + 4 = 7
f(3) = f(2) + 4 = 7 + 4 = 11
f(4) = f(3) + 4 = 11 + 4 = 15
f(5) = f(4) + 4 = 15 + 4 = 19
11. Descartes
has $9. He works 5 hours
and earns $8 each hour. Write an
expression
to represent the situation
Answer: y = 8x + 9
Step-by-step explanation: Descartes begins with only $9.00, so 9 is the y-intercept. He makes $8.00 every hour, so that is the slope.
y = mx + b
m is the slope, and b is the y-intercept.
y=8x + 9
The expression that represents the given situation is y = $49.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now it isgiven that,
Descartes has Money = $9
Each hour earning = $8
Total time of work = 5 hours
So, total money earned in 5 hours = 8*5 = $40
Let y be the total money Descartes has.
So total money Descartes has = Money + total money earned in 5 hours
⇒ y = $9 + $40
⇒ y = $49
This is the required expression for the present situation.
Thus, The expression that represents the given situation is y = $49.
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Solve the problem please.
∑ Hey, shadowwolf9764 ⊃
Answer:
x = - 7.5
Step-by-step explanation:
Given:
[tex]\frac{1}{5}x+\frac{1}{4}=\frac{1}{2}\left(x+5\right)[/tex]
Solution~:
[tex]\frac{1}{5}x+\frac{1}{4}=\frac{1}{2}\left(x+5\right)[/tex]
Distribute:
[tex]\frac{1}{5}x+\frac{1}{4}=\frac{1}{2}x+\frac{5}{2}[/tex]
Subtract 1/4 from both sides:
[tex]\frac{1}{5}x+\frac{1}{4}-\frac{1}{4}=\frac{1}{2}x+\frac{5}{2}-\frac{1}{4}[/tex]
[tex]\frac{1}{5}x=\frac{9}{4}+\frac{1}{2}x[/tex]
Subtract 1/2x from both sides:
[tex]\frac{1}{5}x-\frac{1}{2}x=\frac{9}{4}+\frac{1}{2}x-\frac{1}{2}x[/tex]
[tex]-\frac{3}{10}x=\frac{9}{4}[/tex]
Multiply both sides by 10:
[tex]10\left(-\frac{3}{10}x\right)=\frac{9\cdot \:10}{4}[/tex]
[tex]-3x=\frac{45}{2}[/tex]
Divide both sides by -3:
[tex]\frac{-3x}{-3}=\frac{\frac{45}{2}}{-3}[/tex]
x = -15/2
x = -7.5
xcookiex12
9/4/2022
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Josie has a 1,364-page book to read over summer vacation. She wants to read the
same number of pages each day for 62 days. What is the total number of pages
Josie will need to read each day?
A. 28
B. 27
C. 22
D. 17
10.
An airplane has economy and first class seating.
There are s seats in each row in economy.
There are t seats in each row in first class.
There are 9 rows in first class and 24 rows in economy.
Write down an expression, in terms of s and t, for the number of seats on the
airplane.
The expression, in terms of s and t, for the number of seats on the airplane is given by 24 s + 9 t.
We are given that there are 2 types of seating in an airplane which are economy and first class seating.
Also,
We are given that:
There are s seats in economy in each row and there are t seats in first class in each row.
Now, there are 24 rows in economy class seating.
So, number of seats in economy class = 24 × s = 24 s
And, there are 9 rows in first class seating.
So, number of seats in first class = 9 × t = 9 t
The total number of seats then will be = 24 s + 9 t
Therefore the expression, in terms of s and t, for the number of seats on the airplane is given by 24 s + 9 t.
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Solve for x can you help set up the problem for me to solve for x I have tried everything
As per the alternate angle property, alternate angles are equal hence, is x = 7.
What is the alternate angle property?
The alternate angle theorem states that when two resemblant lines are cut by a transversal, also the performing alternate interior angles or alternate surface angles are harmonious. To prove If two resemblant lines are cut by a transversal, also the alternate innards angles are equal. The Alternate Exterior Angles Theorem states that, when two resemblant lines are cut by a transversal, the performing alternate surface angles are harmonious. Then, the two angles of c and d are outside of the resemblant lines and so these are two exemplifications of alternate surface angles.Equating the alternate angles,
11x-2=10x+5,
11x - 10x = 5 + 2
x = 7
Since, as per the alternate angle property, alternate angles are equal.
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Pls help show work pamdas
Answer:
Answer is -4
Step-by-step explanation:
To solve this, you want to substitute the values of x and y. So, 2(-3)^2-5(-3)(-2)-(-2)^3 which will give you -4.
I do not remember how to solve this
Answer:
Your answer is correct
Step-by-step explanation:
Use the rules of exponents to simplify the expression.
(q⁶)²To raise a power to another power, multiply the exponents.
q⁶ˣ²Multiply 6 by 2.
q¹²The correct option is the third.
Skandar
7. Kiara baked 12 oatmeal cookies and 16 chocolate chip cookies to package in plastic containers for her
friends at school. She wants to divide the cookies into identical containers so that each container has the same
number of each kind of cookie. If she wants to have the greatest number of containers possible, how many
containers does she need? How many oatmeal and chocolate chip cookies will be in each container?
The greatest possible containers required by Kiara is 4.
The number of oatmeal and chocolate chip cookies in each container is 3 and 4 respectively.
What is defined as the highest common factor?The highest common factor, or HCF, is the greatest number that divides each of two or more numbers.HCF is also recognised as the Greatest Common Measure (GCM) and the Greatest Common Divisor (GCD) .For the given question;
The total number of oatmeal cookies = 12.
The total number of chocolate chip cookies = 16.
Taking the HCF of 12 and 16 (the largest multiple pf 12 and 16).
HCF = 4.
Thus, the number of boxes requires is 4.
The oat place in one box is 3. In 4 boxes it will be 12.
Similarly, the chocolate chip cookies placed in one box is 4. In 4 boxes it will be 16.
Thus, the oat placed in each box is 3 and the chocolate chip cookies placed is 4.
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What is the slope or pitch of this roof? 12 feet run rise 3 feet
Math 1332
Answer:
3/12 or 1/4 in simplest fraction form
Step-by-step explanation:
Slope is given by the formula rise/run
Here rise = 3, run = 12
So slope = 3/12 = 1/4
Write a linear cost function for the situation. Identify all variables used.
A parking garage charges 3 dollars plus 45 cents per half-hour.
Identify all variables used. Choose the correct answer below.
Part 2 of 2
O A. C(x) represents the number of hours the parking garage was used after paying x dollars.
B. C(x) represents the number of half-hours the parking garage was used after paying x dollars.
C. C(x) represents the cost for using the parking garage for x half-hours.
OD. C(x) represents the cost for parking x cars in the parking garage.
A linear cost function for the situation is C(x) =
(Use integers or decimals for any numbers in the expression.)
4
Albert made $54.25 bagging groceries for 5 hours last week. What was Albert's hourly wage? '
Answer:
$10.85
Step-by-step explanation:
Divide 54.25 by 5 and you get 10.85.
can someone help me with this
Step-by-step explanation:
so it starts with
182 = 182 × 3 / p
as the price is inversely related to D.
(a)
so, in general
D = 182 × 3/p = 546/p
(b)
D = 546/3.25 = 168 bags
if the price increases to $3.25, then they will sell only 168 bags.
I am sure, the function will not stay linear for every value of p. for example, if they increase the price to $546 per bag, they would still sell 1 bag. but I am certain, they would fall to 0 sold bags much, much earlier than that ...
132891 rounded to the nearest thousand is?
Answer:
132, 900.
Step-by-step explanation:
The 9 is in the tens, so it tells the hundreds to go up by 1 to 9 & add 2 zero's beside. The answer would be 132, 900.
Tina Charlie and Amber have Matchbox cars each car has 4 wheels . how many wheels do their cars have altogether .
Answer:
I think its 12
Step-by-step explanation:
I think its 12 bc 4+4+4=12 Sorry if its wrong! ):)
What is the number of combinations on a lock. (for a 40-number lock, no successive repeating numbers)
(permutations or combinations).
the peremiter of a parallelogram is 56 meters The width of the parallelogram is 4 meters less than its length find the length and the width of the parallelogram
The length of the parallelogram is 16 m and the width of the parallelogram is 12 m.
We are given that the perimeter of a parallelogram is 56 m.
Let the length of the parallelogram be x meter.
So, we get that the width of the parallelogram will be = x - 4 meter.
We also know that:
Perimeter of parallelogram = 2 ( l + b )
Substituting the values in this, we get that:
56 = 2 ( x + x - 4 )
56 = 2 ( 2 x - 4 )
28 = 2 x - 4
2 x - 4 = 28
2 x = 28 + 4
2 x = 32
x = 16
Length = 16 m
Width = 16 - 4 = 12 m
Therefore, the length of the parallelogram is 16 m and the width of the parallelogram is 12 m.
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Please help on the middle!!
Answer: I just points so rate this a 10
Step-by-step explanation:
Answer:
owi4w85e963696w95witote5iw47e
Divide. Please help 10 points.
Answer:
The answer to the question is the third answer
Estimate the quotient of
68)6080
Express any remainder beginning with an R.
What ia the answer for 4.5 gl to dl
Answer: 45,000,000,000 dl
Step-by-step explanation:
10,000,000,000 dl=1 gl
4.5 gl * 10,000,000,000 dl/1 gl =
4.5 * 10,000,000,000 dl = 45,000,000,000 dl
whats the meaning of literature
Answer:
literature most commonly refers to works of the creative imagination, including poetry, drama, fiction, nonfiction, and in some instances, journalism, and song.
|2w + 12| = |4x|
Hvghvvhvgbvgh
Answer:
No solutions.
Step-by-step explanation:
[tex]\left|2w\left(x\right)+12\right|=\left|4x\right|[/tex]
[tex]x < 0,\:\:x\ge \:0 = No Solutions[/tex]
A spinning disk with radius 10 cm rotates at 120 rpm.
1. Find the angular speed:
2. Find the linear speed of a point on the edge of the disk:
1) The angular speed is approximately 12.566 radians per second.
2) The linear speed of a point on the edge of the disk is 1.257 meters per second.
What are the angular speed and the linear speed of a spinning disk?
1) Herein we have a disk that spins at constant angular speed (ω), in radians per second, whose magnitude is found dimensional analysis and unit conversions:
ω = 120 rev / min × (2π rad / 1 rev) × (1 min / 60 s)
ω ≈ 12.566 rad / s
The angular speed is approximately 12.566 radians per second.
2) The linear speed (v), in meters per second, on the edge of the disk is described by the following formula:
v = R · ω
Where R is the radius of the spinning disk, in meters.
If we know that R = 0.1 m and ω ≈ 12.566 rad / s, then the linear speed is:
v = (0.1 m) · (12.566 rad / s)
v = 1.257 m / s
The linear speed of a point on the edge of the disk is 1.257 meters per second.
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Find the square root of: 2 + sqrt5
Answer:
3.65
Step-by-step explanation:
The square root of 2 is 1.4 and the square root of 5 is 2.2 adding that together you get 3.6
evaluate |3-5+7|
a-15
b-5
c- -15
d- -5
Please type the answers please help
Answer:
Step-by-step explanation:
哇，我喜歡吃很多食物，因為我喜歡並喜歡它。
Wa, wǒ xǐhuān chī hěnduō shíwù, yīnwèi wǒ xǐhuān bìng xǐhuān tā.