First, we observe that
[tex]4x-x^2 = x(4-x) = 0 \implies x=0 \text{ or } x = 4[/tex]
and
[tex]4x-x^2 = 4-(x-2)^2 \le 4[/tex]
so that [tex]R[/tex] is in the first quadrant. Any line [tex]y=mx[/tex] that slices this region into two pieces must then have a slope between [tex]m=0[/tex] and [tex]m=4[/tex] (which is the slope of the tangent line to the curve through the origin).
The parabola and line meet at the origin, and again when
[tex]4x - x^2 = mx \\\\ ~~~~ \implies x^2 + (m-4)x = x (x + m - 4) = 0 \\\\ ~~~~\implies x = 4-m[/tex]
with [tex]4x-x^2\ge mx[/tex] for [tex]0\le x\le4-m[/tex].
Now, the total area of [tex]R[/tex] is
[tex]\displaystyle \int_0^4 (4x-x^2) \, dx = \left(2x^2 - \frac{x^3}3\right)\bigg|_0^4 = \frac{32}3[/tex]
so that half the area is 16/3.
The area of the left piece (containing the origin) is
[tex]\displaystyle \int_0^{4-m} ((4x-x^2) - mx) \, dx = \left(\frac{4-m}2 x^2- \frac{x^3}3\right)\bigg|_0^{4-m} = \frac{(4-m)^3}6[/tex]
Solve for [tex]m[/tex].
[tex]\dfrac{(4-m)^3}6 = \dfrac{16}3[/tex]
[tex](4-m)^3 = 32[/tex]
[tex]4 - m = \sqrt[3]{32} = 2\sqrt[3]{4}[/tex]
[tex]\boxed{m = 4 - 2\sqrt[3]{4} \approx 0.825}[/tex]
Find the maximum revenue for the revenue function R(x) = 395x − 0.9x2
The maximum revenue obtained for the given revenue function is 43340.
What is termed as maxima and maximum value?Maxima and minima are the highest and lowest values of a function within a given set of ranges.
The maximum value of the function under the entire range is known as the absolute maxima, and the minimum value is recognized as the absolute minima.Range refers to the difference between both the maximum and minimum values of observations in a data set.Now, as per the given question;
The given revenue function is; R(x) = 395x − 0.9x²
Differentiate the given function with respect to x.
dR/dx = 395 − 2×0.9x
dR/dx = 395 - 1.8x
Put the given equation equal to zero and find the critical point for which the function will become maximum.
395 - 1.8x = 0
x = 219.44
x ≈≈ 220.
Substitute the obtained value of x in the revenue function to find its maximum value.
R(x) = 395x − 0.9x²
R(220) = 395×220 − 0.9(220)²
R(220) = 86900 - 43560
R(220) = 43340.
Therefore, the maximum revenue calculated for the given revenue function is 43340.
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C
After concluding his research, which statements would Virchow agree with? Check all that apply.
Living things come from nonliving things.
Cells can come from nonliving materials.
Frogs can come from mud.
Living things can only come from living things.
Cells come from pre-existing cells.
Answer:
Cells come from pre-existing cells.
Answer:
(A) Living things can only come from living things.
(B) Cells come from pre-existing cells.
Step-by-step explanation:
i just answered this on e d g e n u i t y.
hope this helps <3
Please help me out!!!
Answer:
Shifts 4 units down ---> [tex]g(x)=2x-10[/tex]
Stretches f(x) by a factor of 4 away from x-axis--->[tex]g(x)=8x-6[/tex]
Shifts f(x) 4 units right---> [tex]g(x)=2x-14[/tex]
Compress f(x) by a factor of 1/4 toward the y-axis ---> [tex]g(x)=1/2x-3/2[/tex]
Step-by-step explanation:
We are given [tex]f(x)=2x-6[/tex]
We need to match the transformations.
1) shifts f(x) 4 units down.
When function f(x) shifts k units down the new function becomes f(x)-k
In our case
[tex]g(x)=2x-6-4\\g(x)=2x-10[/tex]
So, Shifts 4 units down ---> [tex]g(x)=2x-10[/tex]
2) Stretches f(x) by a factor of 4 away from x-axis
When function f(x) is stretched by a factor of b away from x-axis the new function becomes f(bx)
[tex]g(x)=2(4x)-6\\g(x)=8x-6[/tex]
So, Stretches f(x) by a factor of 4 away from x-axis--->[tex]g(x)=8x-6[/tex]
3) Shifts f(x) 4 units right
When function f(x) shifts h units right the new function becomes f(x-h)
[tex]g(x)=2(x-4)-6\\g(x)=2x-8-6\\g(x)=2x-14[/tex]
So, Shifts f(x) 4 units right---> [tex]g(x)=2x-14[/tex]
4) Compress f(x) by a factor of 1/4 toward the y-axis
When function f(x) is compressed by h factor of a toward the y-axis the new function becomes h.f(x)
[tex]g(x)=1/4(2x-6)\\g(x)=1/2x-3/2[/tex]
Compress f(x) by a factor of 1/4 toward the y-axis ---> [tex]g(x)=1/2x-3/2[/tex]
(Option Not given)
(If we compress f(x) by a factor of 4 towards y-axis we get g(x)=8x-24)
A small drink holds 50% as much as a large drink. If the large drink holds 24 ounces, how much does the small drink hold?
Answer:
12
Half of 24 is 12
I hope this helps C:
Answer:
23.5
Step-by-step explanation:
i hope this is helpful :)
plzz i need fasssssst
Answer: 1. a) 0 b) -4 2. a) 3 b) -9 3. a) -80 b) -339 c) -14 4. a) 110 b) -87
Step-by-step explanation: This took forever
Given the points below, find XY. Round to
the nearest hundredth.
X(-9, 2) and Y(5, -4)
The distance between X(-9,2) and Y(5,-4) is 15.23 units.
The distance formula states that if there are 2 points A(x1, y1) and B(x2, y2), then the distance between the two points is given by the formula-
[tex]\sqrt{(x1-x2)^{2} + (y1-y2)^{2} }[/tex]
Here, we are given that there are 2 points- X(-9, 2) and Y(5, -4)
So here we can say that,
x1 = -9, y1 = 2
and x2 = 5, y2 = -4
Now, plugging in the values given above in the distance formula we will find XY as follows-
XY = [tex]\sqrt{(-9-5)^{2} + (5+4)^{2} }[/tex]
XY = [tex]\sqrt{(-14)^{2} + (9)^{2} }[/tex]
XY = [tex]\sqrt{196+ 81 }[/tex]
XY = [tex]\sqrt{277 }[/tex]
The square root of 277 is approximately 15.23.
Thus, XY = 15.23
Therefore the value of XY to the nearest hundredth is 15.23 units.
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Monday
American Industries charges
$5 a day and $3.50 and hour
to rent a drill. Write and solve
an equation to show how
much it will cost you to rent a
drill for 6 hours.
Answer:
Step-by-step explanation:
so the equation will be: y = 5 + 3.50x. y is the total cost, and x is the number of hours. To solve for 6 hours, just plug 6 into the equation so: y = 5 + 3.50(6) = 26. So the answer is: it costs $26.00 to rent a drill for 6 hours.
Suppose that the functions q and r are defined as follows.
q (x)=–2x+1
r(x) = 2x²+2
Find the following.
(r og)(-1) = 0
0/6
Х
(q or)(-1) = 0
5
?
Answer:
(r o q)(-1) = 20
(q o r)(-1) = -11
Step-by-step explanation:
Given
[tex]q(x) = -2x + 1[/tex]
[tex]r(x) = 2x^2 + 2[/tex]
Solving (a): (r o q)(-1)
In function:
(r o q)(x) = r(q(x))
So, first we calculate q(-1)
[tex]q(x) = -2x + 1[/tex]
[tex]q(-1) = -2(-1) + 1[/tex]
[tex]q(-1) = 2 + 1[/tex]
[tex]q(-1) = 3[/tex]
Next, we calculate r(q(-1))
Substitute 3 for q(-1)in r(q(-1))
r(q(-1)) = r(3)
This gives:
[tex]r(x) = 2x^2 + 2[/tex]
[tex]r(3) = 2(3)^2 + 2[/tex]
[tex]r(-1) = 2*9 + 2[/tex]
[tex]r(-1) = 20[/tex]
Hence:
(r o q)(-1) = 20
Solving (b): (q o r)(-1)
So, first we calculate r(-1)
[tex]r(x) = 2x^2 + 2[/tex]
[tex]r(-1) = 2(-1)^2 + 2[/tex]
[tex]r(-1) = 2*1 + 2[/tex]
[tex]r(-1) = 6\\[/tex]
Next, we calculate r(q(-1))
Substitute 6 for r(-1)in q(r(-1))
q(r(-1)) = q(6)
[tex]q(x) = -2x + 1[/tex]
[tex]q(6) = -2(6) + 1[/tex]
[tex]q(6) =- 12 + 1[/tex]
[tex]q(6) = -11[/tex]
Hence:
(q o r)(-1) = -11
help, I need help. please
Answer:
4 1/2 and 7 1/4
Step-by-step explanation:
Please answer this correctly without making mistakes
Answer:
The second coupon
Step-by-step explanation:
Answer:
First coupon ($250.00)
Step-by-step explanation:
Figure out the new price with first coupon:
$453.00 - $250.00 = $203.00Figure out the new price with second coupon:
55% of $453 = [tex]\frac{55}{100}[/tex] × [tex]\frac{453}{1} = \frac{24915}{100} = 249.15[/tex] Because we now know that 55% ($249.15) is less than $250.00, we automatically know that the first coupon will save Braden more moneyI hope this helps!
Use a parametrization to express the area of the surface as a double integral. Then evaluate the integral. The portion of the cylinder x^2+y^2=16 between the planes z=4 and z=5
Let u=z and v=θ and use cylindrical coordinates to parameterize the surface. Set up the double integral to find the surface area.
Answer:
The answer is "[tex]8\pi[/tex]"
Step-by-step explanation:
[tex]\to r(v,u) =(4 \cos v, 4 \sin v,u) \\\\0\leq v \leq 2\pi, \ \ 4\leq u\leq 5\\\\\to r_v= (-4 \sin v, 4 \cos v, 0)\\\\\to r_u=(0,0,1)[/tex]
[tex]\to r_v\times r_u = \left|\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\-4 \sin v& 4 \cos v& 0\\0&0&1\end{array}\right| \\\\[/tex]
[tex]= (4 \cos v, -4 \sin v, 0)[/tex]
[tex]|r_v \times r_u| = \sqrt{16 \cos^2 v +16 \sin^2 v}\\\\[/tex]
[tex]= \sqrt{16( \cos^2 v + \sin^2 v)}\\\\= \sqrt{16(1)}\\\\= \sqrt{4^2}\\\\=4[/tex]
Calculating the surface area:
[tex]=\int^{2\pi}_{0} \int^{5}_{4} 4 \ du \ dv \\\\=\int^{2\pi}_{0} 4[4]^{5}_{4} \ dv \\\\=\int^{2\pi}_{0} 4[5-4] \ dv \\\\=\int^{2\pi}_{0} 4 \ dv \\\\=4 [v]^{2\pi}_{0}\\\\= 4 \times 2\pi\\\\= 8\pi[/tex]
This question is based on the parametrization. Therefore, 8[tex]\pi[/tex] is the surface area as a double integral by using parametrization.
Given:
The portion of the cylinder [tex]x^{2} +y^{2} = 16[/tex] between the planes z=4 and z=5.
Let u=z and v=θ and use cylindrical coordinates to parameterize the surface.
We need to express the area of the surface as a double integral.by using parametrization.
According to the question,
It is given that u=z and v=[tex]\theta[/tex],
Therefore, r(v,u) = (4 Cos v,4 Sin v, u)
Range of v : 0 [tex]\leq[/tex] v [tex]\leq[/tex] 2[tex]\pi[/tex]
Range of u : 4 [tex]\leq[/tex] u [tex]\leq[/tex] 5
[tex]\rightarrow r_v= (-4 \;sin\; v,4\;cos\; v,0)\\\rightarrow r_u=(0,0,1)[/tex]
[tex]\rightarrow r_u \times r_v =\begin{bmatrix} \hat{i}& \hat{j} & \hat{k}\\ -4\; sin\;v & 4\; cos\; v & 0 \\ 0 & 0 & 1\end{bmatrix}\\\\=(4 cos v,\;-4 sin v ,0)\\\\\left | r_v \times r_u \right | = \sqrt{16cos^{2}v+16sin^2v } \\\\= \sqrt{16(cos^{2}v+sin^2v) }\\\\=\sqrt{16}\\\\=4[/tex]
Now calculating the surface area,
[tex]=\int\limits^{2\pi}_0\int\limits^5_4 4 du\; dv\\\\=\int\limits^{2\pi}_0 4[u]^5_4 dv\\\\=\int\limits^{2\pi}_0 4[5-4] dv\\\\\\=\int\limits^{2\pi}_0 4dv\\\\\\=4[v]^{2\pi}_0 = 4(2\pi-0)= 8\pi[/tex]
Therefore, 8[tex]\pi[/tex] is the surface area as a double integral by using parametrization.
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75a ²c– 45a ²d - 30bc + 18bd
Answer:
(25a2c - 15a2d - 10cb + 6db)
Step-by-step explanation:
Equation at the end of step 1: (((75•(a2))•c)-((32•5a2)•d))-30cb)+18db
STEP 2:Equation at the end of step2: ((((3•52a2) • c) - (32•5a2d)) - 30cb) + 18db
STEP3:
STEP 4:Pulling out like terms
4.1 Pull out like factors :
75a2c - 45a2d - 30cb + 18db =
3 • (25a2c - 15a2d - 10cb + 6db)
Write an equation to model each situation and solve. Be sure to label the solution.
7. A rectangle has a length of 2x - 12 units and a width of 3 units. The value of the
rectangle's area is equal to the value of its perimeter. Write an equation to represent this
situation. Then, solve the equation.
Need a equation and a solution.
Answer:
A. 3(2x - 12) = 2(3 + 2x - 12)
B. Length = 6, width = 3
Step-by-step explanation:
l = 2x - 12
w = 3
Area = 3(2x - 12)
Perimeter = 2(3 + 2x - 12)
if A = P
3(2x - 12) = 2(3 + 2x - 12)
6x - 36 = 6 + 4x - 24
6x - 4x = 6 - 24 + 36
2x = 18
x = 9
Length = 2x - 12 = 2(9) - 12 = 18 - 12 = 6
What is an equation of the line that passes through the point ( 6 , − 2 ) (6,−2) and is perpendicular to the line 6 x + y = 2 6x+y=2?
Answer:
An equation of the line that passes through the point (6, − 2) and is perpendicular to the line will be:
[tex]y=\frac{1}{6}x-3[/tex]Step-by-step explanation:
We know that the slope-intercept form of the line equation is
y=mx+b
where m is the slope and b is the y-intercept.
Given the line
6x+y=2
Simplifying the equation to write into the slope-intercept form
y = -6x+2
So, the slope = -6
As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line.
Thus, the slope of the perpendicular line will be: -1/-6 = 1/6
Therefore, an equation of the line that passes through the point (6, − 2) and is perpendicular to the line will be
[tex]y-y_1=m\left(x-x_1\right)[/tex]
substituting the values m = 1/6 and the point (6, -2)
[tex]y-\left(-2\right)=\frac{1}{6}\left(x-6\right)[/tex]
[tex]y+2=\frac{1}{6}\left(x-6\right)[/tex]
subtract 2 from both sides
[tex]y+2-2=\frac{1}{6}\left(x-6\right)-2[/tex]
[tex]y=\frac{1}{6}x-3[/tex]
Therefore, an equation of the line that passes through the point (6, − 2) and is perpendicular to the line will be:
[tex]y=\frac{1}{6}x-3[/tex]Need help asap plz will give brainliest
Answer:
[tex]z - 0.05z = 236.60[/tex]
Step-by-step explanation:
Given
[tex]Discount = 5\%[/tex]
[tex]Total\ Cost = 236.60[/tex]
Represent the cost of goods bought with z
When the coupon is applied, the discount becomes
[tex]Discount = 5\% * z[/tex]
This gives:
[tex]Discount = 0.05 * z[/tex]
[tex]Discount = 0.05z[/tex]
The discount subtracted from the cost of good will gives the total amount paid.
So, we have:
[tex]Cost\ of\ Goods - Discount = Total\ Cost[/tex]
This gives:
[tex]z - 0.05z = 236.60[/tex]
Hence, option (a) is correct
A bag contains coins consisting of quarters and dimes.
The total value of the coins is $8.65. There are 6 more
dimes than quarters. Which system of equations can be
used to determine the number of quarters, x, and the
number of dimes, y, in the bag?
x = y + 6 & 25x + 10y = 865
y = x + 6 & 10x + 25y = 8.65
10 = x +y & .25x + .10y = 8.65
y = x + 6 & 25x + 10y = 8.65
A (i think)
Step-by-step explanation:
Cómo resuelvo esta ecuación 14-8=10- __
Answer:
4
Step-by-step explanation:
14-8=6
10-4=6
14-8=10-4
14-8=10-???
6=10-???
6=10-4
6=6
???=-4
Simplify 42 ⋅ 48.
416
410
1616
1610
Choose the model that represents the same function as the graph of f (x)
y=1/2x-3
The graph shows that the line moves up 1 and right 2, up 1 and right 3, etc., and that b is the y intercept. It denotes a positive 1/2 slope.
The y intercept is -3 because the line crosses the y axis at -3. The shaded region has to be below the line. Our response is the second graph in the first row.
so
y= 1/2x -3
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If a position vector v has a magnitude of 5 and is located in the first quadrant, then which of the following could be the terminal point of 2v?
(4, 6)
(2, 8)
(6, 8)
(10, 10)
Answer:
I think its (6,8) if im wrong i will write the correct answer here or i will right it in the comments
Step-by-step explanation:
I GIVE BRAINLIEST!
Someone explain please!
Answer: 7 8 9 7 6 12 2 0
Step-by-step explanation:
Answer:
1) -8m +4+p
2) 10-3t
3)im not sure for the rest
Step-by-step explanation:
When tomás simplified the expression -2.6 + [-5.4], he got2.8. What mistake did tomás likely make?
Answer: he probably didn't pay attention to the - sign on -5.4
What number is 75%of32
Answer: 24
I am bad at explaining so i wouldn't help there
Answer:
24
Step-by-step explanation:
75% is also 3/4. 3/4 out of 32 can be 3 x 32/4 which is 3 x 8, or 24.
Rudy invested $2460 in a money market account for 3 and 1/2 years. He earned $452 in simple interest. Which best represents the annual interest rate?
A. 3 and 3/5 percent
B. 5 and 1/4 percent
C. 5 and 3/4 percent
D. 6 and 2/5 percent
Answer:
B. 5 and 1/4 percent
Step-by-step explanation:
Step one:
given
principal= $2460
time= 3 and 1/2 years= 3.5 years
SI= $452
Required
The rate
Step two:
we know that
SI= PRT/100
substituting our data we have
452= 2460*R*3.5/100
452=8610R/100
cross multiply
452*100= 8610R
divide both sides by 8610
45200/8610= R
R= 5.25%
R= 5 and 1/4 percent
A man has mislaid his wallet. He thinks there is a 0.4 chance that the wallet is somewhere in his bedroom, a 0.1 chance it is in the kitchen, a 0.2 chance it is in the bathroom, and a 0.15 chance it is in the living room. What is the probability that the wallet is a) somewhere else? b) in either the bedroom or the kitchen?
Answer:
a. Probability = 0.15
b. Probability = 0.3
Step-by-step explanation:
Given
[tex]P(Bedroom) = 0.4[/tex]
[tex]P(Kitchen) = 0.1[/tex]
[tex]P(Bathroom) = 0.2[/tex]
[tex]P(Living\ room) = 0.15[/tex]
Solving (a): Probability of being somewhere else
This is calculated by subtracting the sum of given probabilities from 1.
[tex]Probability = 1 - (0.4 + 0.1 + 0.2 + 0.15)[/tex]
[tex]Probability = 1 - 0.85[/tex]
[tex]Probability = 0.15[/tex]
Solving (b): Probability of being in bedroom or kitchen
This is calculated as:
[tex]Probability = P(Bedroom) + P(Kitchen)[/tex]
[tex]Probability = 0.2 + 0.1[/tex]
[tex]Probability = 0.3[/tex]
What is the discriminant of the quadratic equation 5x^2-8x+4=0?
The first equation from the system of equations is graphed. Graph the second equation to find the solution of the system of equations. y = –x, y = 2x + 6 What is the point of intersection? (2, 1) (–1, 2) (0, 6) (–2, 2)
Answer:D
Step-by-step explanation:
just took it on edge
Answer:
The answer is d
Step-by-step explanation:
Solve | =
711.6Y/
K²
for K².
The answer is K^2 = 711.6Y on solving the given equation.
Given that, 1 = 711.6Y/K^2 and we have to solve it for the value of K^2. For this we simply have to solve the given equation steps wise. So, let's proceed to solve the equation.
1 = 711.6Y/K^2
Now, multiply K^2 with 1, we get
K^2 = 711.6Y
So, the value of k^2 will be equal to Y times 711.6 and further we can solve it for the various value of Y.
Let us suppose, we have to solve the above equation for the specific value of Y.
So, put Y = 1
On solving, we get
K^2 = 711.6x1
K^2 = 711.6
K = (711.6)^(1/2)
K = 26.67
∴ K^2 = 711.6Y is the equation we will get on solving the equation given to us in the question.
Hence, K^2 = 711.6Y is the required answer.
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How many edges does this shape have?
Answer:8
Step-by-step explanation:
It has the same number of edges, planes, and vertices as a cuboid. Therefore, there are 12 edges in the shape.
What is the rectangular prism?A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.
A rectangular prism has 12 edges.
It has the same number of edges, planes, and vertices as a cuboid.
The shape can be a rectangular prism or cuboid.
Therefore, there are 12 edges in the shape.
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Which is the best estimate for 6,193 ÷ 48 using compatible numbers?
A. 100
B. 120
C. 150
D. 160
Round 6193 to 6000
Round 48 to 40
6000/50 = 120
The answer is B. 120