Answer: W
Step-by-step explanation: I remember learning this in school> you can tell it’s a function because no numbers repeat themselves etc .
Someone please help me with this thank you!
Answer:
50°
Step-by-step explanation:
Note EFGH is an isosceles trapezoid.
∠HGF=77° (base angles of an isosceles trapezoid are congruent)
∠EGH=27° (angles in a triangle add to 180°)
∠FGE=50° (angle subtraction postulate)
Use the drop-down menus to complete each equation so the statement about its solution is true.
No Solutions 2x+5+2x+3x= x +
One Solution 2x+5+2x+3x= x +
Infinitely Many Solutions 2x+5+2x+3x= x +
Since there is only one value of x, hence the equation given has only one solution
Equations and expressionsEquations are expressions separated using mathematical operations. Given the equation below;
2x+5+2x+3x = x
Collect the like terms
2x+2x+3x -x = -2
7x -x = -2
Simplify
6x = -2
x = -2/6
x = -1/3
Since there is only one value of x, hence the equation given has only one solution
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Show that the function f(x)=sin3x + cos5x is periodic and it’s period.
The period of [tex]f(x)[/tex] is [tex]\boxed{2\pi}[/tex].
Recall that [tex]\sin(x)[/tex] and [tex]\cos(x)[/tex] both have periods of [tex]2\pi[/tex]. This means
[tex]\sin(x + 2\pi) = \sin(x)[/tex]
[tex]\cos(x + 2\pi) = \cos(x)[/tex]
Replacing [tex]x[/tex] with [tex]3x[/tex], we have
[tex]\sin(3x + 2\pi) = \sin\left(3 \left(x + \dfrac{2\pi}3\right)\right) = \sin(3x)[/tex]
In other words, if we change [tex]x[/tex] by some multiple of [tex]\frac{2\pi}3[/tex], we end up with the same output. So [tex]\sin(3x)[/tex] has period [tex]\frac{2\pi}3[/tex].
Similarly, [tex]\cos(5x)[/tex] has a period of [tex]\frac{2\pi}5[/tex],
[tex]\cos(5x + 2\pi) = \cos\left(5 \left(x + \dfrac{2\pi}5\right)\right) = \cos(5x)[/tex]
We want to find the period [tex]p[/tex] of [tex]f(x)[/tex], such that
[tex]f(x + p) = f(x)[/tex]
[tex] \implies \sin(3x + p) + \cos(5x + p) = \sin(3x) + \cos(5x)[/tex]
On the left side, we have
[tex]\sin(3x + p) = \sin(3x + 2\pi + p - 2\pi) \\\\ ~~~~~~~~ = \sin(3x+2\pi) \cos(p-2\pi) + \cos(3x+2\pi) \sin(p-2\pi) \\\\ ~~~~~~~~ = \sin(3x) \cos(p-2\pi) + \cos(3x) \sin(p - 2\pi)[/tex]
and
[tex]\cos(5x + p) = \cos(5x + 2\pi + p - 2\pi) \\\\ ~~~~~~~~ = \cos(5x+2\pi) \cos(p-2\pi) - \sin(5x+2\pi) \sin(p-2\pi) \\\\ ~~~~~~~~ = \cos(5x) \cos(p-2\pi) - \sin(5x) \sin(p-2\pi)[/tex]
So, in terms of its period, we have
[tex]f(x) = \sin(3x) \cos(p - 2\pi) + \cos(3x) \sin(p - 2\pi) \\\\ ~~~~~~~~ ~~~~+ \cos(5x) \cos(p - 2\pi) - \sin(5x) \sin(p - 2\pi)[/tex]
and we need to find the smallest positive [tex]p[/tex] such that
[tex]\begin{cases} \cos(p - 2\pi) = 1 \\ \sin(p - 2\pi) = 0 \end{cases}[/tex]
which points to [tex]p=2\pi[/tex], since
[tex]\cos(2\pi-2\pi) = \cos(0) = 1[/tex]
[tex]\sin(2\pi - 2\pi) = \sin(0) = 0[/tex]
Find y'' y = 3 cot x/8
If y = 3 cot x/8, the double differentiation of y gives,
y'' = (3/32) (cosec x/8)(cot x/8)
Given value of y is,
y = 3 cot x/8
Differentiation of the above equation will give us the following,
y' = d(3 cot x/8) / dx
y' = 3d(cot x/8) / dx ........... (1)
Now, we know that the differentiation of cot x is -cosec²x
Therefore, d(cot x/8) / dx = -(cosec²x/8)/8
Thus, equation (1) transforms as follows,
y' = -3(cosec²x/8)/8
Taking differentiation of the above equation, we get,
y'' = -3d((cosec²x/8)/ 8dx
y'' = -6d(cosec x/8) / 8dx [Using chain rule] .......... (2)
As we know, the differentiation of cosec x is -(cosec x)(cot x),
d(cosec x/8) / dx = -(cosec x/8)(cot x/8) / 8 [Using chain rule]
Therefore, equation (2) can be written as,
y'' = -(-6(cosec x/8)(cot x/8) / (8×8)
∴ y '' = 3(cosec x/8)(cot x/8) / 32
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In the diagram, angle ADE ≈ angle ABC the ratios blank and blank are equal.
Based on the angle-angle similarity theorem (AA), the pair of ratios that are equal is: AE/EC = AD/DB.
What is the Angle-angle Similarity Theorem (AA)?The angle-angle similarity theorem (AA) states that two triangles are similar to each other if they have two corresponding congruent angles, and therefore, the ratios of their corresponding side lengths are equal. This means their corresponding side lengths are proportional in measure.
Given that angle ADE ≅ angle ABC, we also know that:
Angle EAD ≅ CAB.
Thus, this implies that triangle EAD is similar to triangle CAB based on the angle-angle similarity theorem (AA). Therefore, the ratios of their corresponding side lengths are equal.
Thus, the ratios that are equal to each other would be:
AE/EC = AD/DB.
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P: 2,012
1) El volumen de un cubo de arista 1 es Vc = 1³ y el
Volumen de una esfera de radior es
JE
V₁ = πr ²³ Entonces si en un cubo de arista 4cm
3
y se introduce una pelota de diametro 4 cm, al Calcular
aproximación con cuatro cifras decimales, por exceso.
Calcular el volumen que queda entre la esfera y el cubo.
(toma π =
3,141592654)
El volumen que queda entre la esfera y el cubo es: 30.49cm^3
¿Como calcular el volume sobrante?
El volumen sobrante será simplemente la diferencia entre el volumen del cubo y el volumen de la esfera.
Para el cubo que tiene una arista de 4cm, el volumen es:
V = (4cm)^3 = 64 cm^3
Para la esfera con un diametro de 4cm, el radio es:
R = 4cm/2 = 2cm
Y el volumen será:
V' = (4/3)*3.141592654*(2cm)^3 = 33.51 cm^3
El volumen que queda entre la esfera y el cubo es:
V - V' = 64 cm^3 - 33.51 cm^3 = 30.49cm^3
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50 POINTS PLEASE HELP I NEED ANWSER NOW what would the reflection look like
Answer:
Point C will be at (3,1), Point B will be at (7,1) and Point A will be at (7,5)
Step-by-step explanation:
f(x)=4x+1 and g(x)=2x2+1, find (f∘g)(x) and (g∘f)(x)
The value of the composite functions (g∘f)(x) and (f∘g)(x) are 32x^2 + 16x + 3 and 8x^2 + 5 respectively
Composite functionsComposite function is also known as function of a function. They are determined by representing x with the other function.
Given the following functions
f(x)=4x+1
g(x)=2x^2+1
(f∘g)(x) = f(g(x))
(f∘g)(x) = f(2x^2+1)
(f∘g)(x) = 4(2x^2+1) + 1
(f∘g)(x) =8x^2 + 5
For the composite function (g∘f)(x)
(g∘f)(x) = g(f(x))
(g∘f)(x) = g(4x+1)
Replace x wit 4x+1 to have:
(g∘f)(x) = 2(4x+1)^2 + 1
(g∘f)(x)= 2(16x^2+8x+1) + 1
(g∘f)(x) = 32x^2 + 16x + 3
Hence the value of the composite functions (g∘f)(x) and (f∘g)(x) are 32x^2 + 16x + 3 and 8x^2 + 5 respectively
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Find m/1 and m/2 in the kite.
help asap
The measure of angle 1 (m ∠1) is 28° and the measure of angle 2 (m ∠2) is 62°
Calculating anglesFrom the question, we are to determine the measure of angle 1 and the measure of angle 2
The given diagram is a kite and the diagonals intersect at right angles
Thus,
m ∠2 + 28° + 90° = 180°
m ∠2 = 180° - 28° - 90°
m ∠2 = 62°
Hence, the measure of angle 2 is 62°
For the measure of angle 1
Consider ΔADB
ΔADB is an isosceles triangle
Thus,
In the triangle, m ∠D = m ∠B
Then, we can write that
m ∠1 + 62° + 90° = 180°
m ∠1 = 180° - 62° - 90°
m ∠1 = 28°
∴ The measure of angle 1 is 28°
Hence, the measure of angle 1 (m ∠1) is 28° and the measure of angle 2 (m ∠2) is 62°
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18. What is the probability that the student plays football?
(a) 35 /66 (b) 20 /33 (c) 13 /33 (d) 3 /22
The probability that the student plays football is 20/33.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
The probability that the student plays football = total number of students who play football / total number of students
total number of students who play football = 26 + 3 + 5 + 6 = 40 total number of students = 26 + 3 + 5 + 6 + 9 + 7 + 10= 66The probability that the student plays football = 40/66 = 20/33
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The medical assistant weighs patients each month. Mrs. Smith weighed 120 pounds last month.
Over the last 2 months she gained 1½ and 1/4 pounds. What is Mrs. Smith's current weight?
13) 120 + 1.5 + 0.25 = 121.75 pounds
14) 4 - 1.5 = 2.5 pints
15) (2.25)(32)= $72
As per the unitary method, Mrs. Smith's current weight is 121 pounds and 3 ounces.
To find Mrs. Smith's current weight, we need to add the weight she gained over the last two months to her initial weight. First, we will convert the mixed fractions to improper fractions for easier calculations.
1½ pounds can be written as (2 * 1) + 1/2 = 3/2 pounds.
1/4 pound remains as it is.
Now, let's add the weight gained in the last two months:
3/2 pounds + 1/4 pound = (3/2) + (1/4) = (6/4) + (1/4) = 7/4 pounds.
Next, we add the total weight gained to Mrs. Smith's initial weight:
120 pounds + 7/4 pounds = (120 * 4/4) + (7/4) = (480/4) + (7/4) = 487/4 pounds.
To express the answer in pounds, we convert the improper fraction back to a mixed fraction:
487/4 pounds can be written as (4 * 121) + 3 pounds.
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A certain insecticide kills 60% of all insects in laboratory experiments. A sample of 7 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 4 insects will survive? Round your answer to four decimal places.
Step-by-step explanation:
the probability of 1 tested insect is killed is 60% or 0.6.
the probability that it is not killed is then 1-0.6 = 0.4.
when we test 7 insects and exactly 4 survive is the event that
3 insects are killed, 4 insects survive.
the probability for one such case is
0.6×0.6×0.6 × 0.4×0.4×0.4×0.4
how many such cases do we have ?
as many as ways we can select 4 insects out of the given 7.
these are 7 over 4 combinations :
7! / (4! × (7-4)!) = 7! / (4! × 3!) = 7×6×5/(3×2) = 7×5 = 35
so, the probability that exactly 4 out of 7 tested insects survive is
35 × 0.6³ × 0.4⁴ = 0.193536 ≈ 0.1935
Find an equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): − 3 , 4 , − 3 . Assume the leading coefficient is 1.
f(x) = x³ + 2x² - 15x - 36 is the equation of a degree 3 polynomial (in factored form) with the given zeros of f(x) are − 3 , 4 , − 3 assuming that the leading coefficient is 1. This can be obtained by formula of polynomial function.
Find the required equation:The zeroes or roots of a polynomial function are x values for which f(x) = 0If the zeroes or roots are r₁, r₂, r₃,... then possible polynomial function is⇒ f(x) = a(x - r₁)(x - r₂)(x - r₃)
where a is the leading coefficient
Here in the question it is given that,
Polynomial should be with degree 3zeros of f(x) are − 3 , 4 , − 3By using the formula of polynomial function we get,
⇒ f(x) = a(x - r₁)(x - r₂)(x - r₃)
⇒ f(x) = 1(x - (-3))(x - (4))(x - (-3))
⇒ f(x) = 1(x + 3)(x - 4)(x + 3)
⇒ f(x) = (x + 3)(x² - x - 12)
⇒ f(x) = x³ - x² - 12x + 3x² - 3x - 36
⇒ f(x) = x³ + 2x² - 15x - 36
Hence f(x) = x³ + 2x² - 15x - 36 is the equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): − 3 , 4 , − 3 assuming that the leading coefficient is 1.
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a man borrowed GHC 1200 at the bank for 4 months at the rate of 5%.Calculate a. his simple interest
there are 12 months in a year, so then 4 months is really 4/12 of a year.
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & 1200\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=\to \frac{4}{12}years\dotfill &\frac{1}{3} \end{cases} \\\\\\ I = (1200)(0.05)(\frac{1}{3})\implies I=20~GHC[/tex]
Find the simple interest.
$2000 at 6% for 6 months
The simple interest is $____
(Round to the nearest cent as needed.)
Answer:
I think it's 120 dollars sorry if i get it wrong but I am sure it is right tell me when you get the right answer byeeee.
Can u guys please give me the correct answer
Answer:
27°Step-by-step explanation:
in the smallest triangle (BCD) you have an angle of 90° and one of 63°, the sum of the internal angles in a triangle is 180°, remove the known angles from 180 ° and you will have the measure of the CBD angle
180 - 63 - 90 =
27°
Answer:
27°
Step-by-step explanation:
180°-90°-63° = 27°
Find the value of z such that 0.8664 of the area lies between −z and z. Round your answer to two decimal places.
Using the normal distribution, the value of z is of z = 1.5.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For this problem, considering the symmetry of the normal distribution, the area above the mean is given by:
0.8664/2 = 0.4332.
Hence z has a p-value of 0.5 + 0.4332 = 0.9332, hence the value of z is z = 1.5.
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5:
will give brainliest
The focal length of the given ellipse is given as (±6, 0)
Equation of an ellipseAn ellipse is defined as a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant or when a cone is cut by an oblique plane which does not intersect the base.
The standard equation of an ellipse is expressed as;
x^2/a^2 + y^2/b^2 = 1
The formula for calculating the focus of the ellipse is given as:
c^2 = b^2 - a^2
Given the equation of an ellipse
(x-7)^2/64 + (y-5)^2/100 = 1
This can also be expressed as:
(x-7)^2/8^2 + (y-5)^2/10^2 = 1
Comparing with the general equation
a = 8 and b = 10
Substitute
c^2 = 10^2 - 8^2
c^2 = 100 - 64
c^2 = 36
c = 6
Hence the focal length of the given ellipse is given as (±6, 0)
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A store is having a sale on trail mix and jelly beans. For 3 pounds of trail mix and 8 pounds of jelly beans, the total cost is $29. For 5 pounds of trail mix and 2 pounds of jelly beans, the total cost is $20. Find the cost for each pound of trail mix and each pound of jelly beans.
Answer:
the price of one pound of trail mix is $3
the price of one pound of jelly beans is $2.5
Step-by-step explanation :
let t be the price of one pound of trail mix.
and b be the price of one pound of jelly beans.
This statement:
“For 3 pounds of trail mix and 8 pounds of jelly beans,
the total cost is $29”
Can be translated mathematically like this :
3t + 8b = 29
This statement:
“For 5 pounds of trail mix and 2 pounds of jelly beans,
the total cost is $20”
Can be translated mathematically like this :
5t + 2b = 20
We obtain a system of two equations :
3t + 8b = 29
5t + 2b = 20
Solving the system:
3t + 8b = 29 (equation 1)
5t + 2b = 20. (equation 2)
3t + 8b = 29
20t + 8b = 80 [4×(equation 2)]
3t + 8b = 29
17t = 51 [4×(equation 2) - equation 1]
3t + 8b = 29
t = 51/17 = 3
9 + 8b = 29
t = 3
8b = 20
t = 3
b = 20/8 = 5/2
t = 3
b = 5/2
t = 3
Therefore ,the solution to our system is (3 , 2.5)
Please hurry quick I need an answer
Answer:
slope is 4
Step-by-step explanation:
Slope is rise/run
for every 4 units it rises it runs 1 unit
4/1=4
1. What is the measure of angle x?
Answer: 60
Step-by-step explanation:
Almost everything in this picture is irrelevant to finding the measure of x.
x = 180 - 90 - 30 = 60
A board, 74 cm long is cut into three pieces such as the second board is twice as long as first board and the third is 4 cm longer than second. Find length of shorter piece
Answer:
The shortest piece is the first piece and it is 14 cm long.
Step-by-step explanation:
We have three unknowns so we need 3 equations.
Let x = the length of the first piece
Let y = the length of the second piece
Let z = the length of the third piece.
x + y + z = 74 y = 2x z = y + 4
There are a number of ways to solve this. I am going to plug in 2x for y into the first and the third equation to get:
x + y + z = 74
x + 2x + z = 74 Combine the x terms
3x + z = 74
Next, I am going to substitute 2x in for y in the third equation above.
z = y + 4
z = 2x + 4 I am going to put both variable on the left side of the equation
z - 2x = 4
I can know take the two bold equations that I have above and solve for the either x or z. I am going to solve for z. I need one of the equation to have a z and the other equation to have -z so that they will cancel one another out. I am going to multiple z - 2x = 4 all the way through by -1 to get:
z - 2x = 4
-1(z - 2x) = 4(-1)
-z +2x = -4
I am going to rearrange 3x + z = 74 so that the z term is first and add it to -z + 2x = -4
z + 3x = 74
-z + 2x = -4
5x = 70 divide both sides by 5
x = 14 This is the length of the first piece.
y = 2x
y = 2(14) = 28
y = 28 This is the length of the second piece.
z = y+4
z = 28 + 4 = 32
or
x + y + z = 74
14 + 28 + z = 74
42 + z = 74 Subtract 42 from both sides.
z = 32
Which polygon does not belong with the others?
DETAILS BASSELEMMATH7 9.PP1.035. 0/1 Submissions Used The measure of the smallest angle of a right triangle is 10° less than the measure of the other small angle. Find the measures of all three angles in degrees. smallest angle largest angle.
Answer:
40°, 50°, and 90°
Step-by-step explanation:
Let the smallest angle be x.
Then, the other small angle is x+10.
The acute angles of a right triangle are complementary, so x+x+10=90, and thus x=40.
So, the acute angles measure 40° and 50°.
Therefore, the three angles are 40°, 50°, and 90°.
Sahil has a fish tank in the shape of a cuboid, as The tank is 3 cm shown in the diagram. water 55 cm 33 cm 28 cm Diagram M accurately 55 cm long 28 cm wide 33 cm high The surface of the water in the tank is 3 cm below the top of the tank. Sahil is going to put some neon tetra fish in his tank. He must allow 4 litres of water for each of the neon tetra fish he puts in the ta What is the greatest number of neon tetra fish Sahil can put in his tank?
Answer:
9 Sahil has a fish tank in the shape of a cuboid, as shown in the diagram-- Diagram is NOT accurately drawn The tank is
55 cm long
28cm wide
cm 33 high The surface of the water in the tank is 3 cm below the top of the tank. Sahil is going to put some neon tetra fish in his tank. He must allow 4 litres of water for each of the neon tetra fish he puts in the tank. What is the greatest number of neon tetra fish Sahil can put in his tank?
Step-by-step explanation:
Find the height (in meters) of a storage tank in the shape of a right circular cylinder that has a circumference measuring 4 m and a volume measuring 36 m3.
Answer:
[tex]h = \bf 28.3 \space\ m[/tex]
Step-by-step explanation:
• We are given:
○ Volume = 36 m³,
○ Circumference = 4 m
• Let's find the radius of the cylinder first:
[tex]\mathrm{Circumference} = 2 \pi r[/tex]
Solving for [tex]r[/tex] :
⇒ [tex]4 = 2 \pi r[/tex]
⇒ [tex]r = \frac{4}{2\pi}[/tex]
⇒ [tex]r = \bf \frac{2}{\pi}[/tex]
• Now we can calculate the height using the formula for volume of a cylinder:
[tex]\mathrm{Volume} = \boxed{\pi r^2 h}[/tex]
Solving for [tex]h[/tex] :
⇒ [tex]36 = \pi \cdot (\frac{2}{\pi}) ^2 \cdot h[/tex]
⇒ [tex]h = \frac{36 \pi^2}{4 \pi}[/tex]
⇒ [tex]h = 9 \pi[/tex]
⇒ [tex]h = \bf 28.3 \space\ m[/tex]
Answer:
9π m ≈ 28.27m
Step-by-step explanation:
The volume of a right cylinder is given by the formula
πr²h where r is the radius of the base of the cylinder(which is a circle), h is the height of the cylinder
Circumference of base of cylinder is given by the formula 2πr
Given,
2πr = 4m
r = 2/π m
Volume given as 36 m³
So πr²h = 36
π (2/π)² h = 36
π x 4/π² h = 36
(4/π) h = 36
h = 36π/4 = 9π ≈ 28.27m
Which of the following equations has a minimum value of (3,-10)? y = 2x2 + 40x + 203 y = x2 + 6x + 19 y = 2x2 − 12x + 8 y = -2x2 + 12x − 8
Answer:
y = 2x² − 12x + 8
Step-by-step explanation:
FIRST METHOD :
y = 2x² − 12x + 8
= (2x² − 12x) + 8
= 2 (x² − 6x) + 8
= 2 (x² − 6x + 9 − 9 ) + 8
= 2 (x² − 6x + 9) − 2×9 + 8
= 2 (x² − 6x + 9) − 18 + 8
= 2 (x² − 6x + 9) − 10
= 2 (x − 3)² − 10
Then ,the equation has a extremum value of (3,-10)
Since the number 2 in the equation y = = 2 (x − 3)² − 10 is greater than 0
(2 > 0) , the graph (parabola) opens upward
Therefore ,the extremum (3,-10) is a minimum.
SECOND METHOD :
the graph of a function of the form f(x) = ax² + bx + c
has an extremum at the point :
[tex]\left( -\frac{b}{2a} ,f\left( -\frac{b}{2a} \right) \right)[/tex]
in the equation : f(x) = 2x² − 12x + 8
a = 2 ; b = -12 ; c = 8
Then
[tex]-\frac{b}{2a} = -\frac{-12}{2 \times 2} = 3[/tex]
Then
[tex]f\left( -\frac{b}{2a} \right) = f(3) = 2(3)^2- 12(3) + 8 = 18 - 36 + 8 = -18 + 8 = -10[/tex]
the graph of a function f(x) = 2x² − 12x + 8
has an extremum at the point (3 , -10)
Since the parabola opens up ,then the extremum (3,-10) is a minimum.
For a certain company, the cost function for producing x items is C(x)=40x+200 and the revenue function for selling x items is R(x)=−0.5(x−80)2+3,200 . The maximum capacity of the company is 100 items.
Based on the cost and revenue functions to the company for selling x items, the domain of C(x) is [0, 100].
The range of C(x) is (200, 4,200).
What is the domain and range of C(x)?The domain would be the lowest capacity and the maximum capacity. As these are physical units to sell, the lowest unit would be 0 units as units can't be negative.
The maximum capacity is given as 100 items so the domain is:
= [0, 100]
The range is:
When x is 0, the function gives C(x) as:
= 40(0) + 200
= 200
When x is the maximum of 100, the C(x) is:
= 40(100) + 200
= 4,200
Range is:
(200, 4,200)
Full question is:
What is the domain and range of C(x)?
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A chord AB divides a circle of radius 5 cm into
two segments. If AB subtends a central angle of
30, find the area of the minor segment.
the area of the minor segment is 0. 29 cm^2
How to determine the areaFrom the information given, we have the following parameters;
radius, r = 5cmThe angle is 30 degreesAB subtends the angleIt is important to note the formula for area of a sector is given as;
Area = πr² + θ/360° - 1/ 2 r² sin θ
The value for π = 3.142
θ = 30°
Now, let's substitute the values
Area = 3. 142 × 5² × 30/ 360 - 1/ 2 × 5² × sin 30
Find the difference
Area = 3. 142 × 25 × 1/ 12 - 1/ 2 × 25 × 1/2
Multiply through
Area = 6. 54 - 6. 25
Area = 0. 29 cm^2
The area of the minor segment is given as 0. 29 cm^2
Thus, the area of the minor segment is 0. 29 cm^2
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Attached as an image. Please help.
The general solution of the logistic equation is y = 14 / [1 - C · tⁿ], where a = - 14² / 3 and C is an integration constant. The particular solution for y(0) = 10 is y = 14 / [1 - (4 / 10) · tⁿ], where n = - 14² / 3.
How to find the solution of an ordinary differential equation with separable variablesHerein we have a kind of ordinary differential equation with separable variables, that is, that variables t and y can be separated at each side of the expression prior solving the expression:
dy / dt = 3 · y · (1 - y / 14)
dy / [3 · y · (1 - y / 14)] = dt
dy / [- (3 / 14) · y · (y - 14)] = dt
By partial fractions we find the following expression:
- (1 / 14) ∫ dy / y + (1 / 14) ∫ dy / (y - 14) = - (14 / 3) ∫ dt
- (1 / 14) · ln |y| + (1 / 14) · ln |y - 14| = - (14 / 3) · ln |t| + C, where C is the integration constant.
y = 14 / [1 - C · tⁿ], where n = - 14² / 3.
If y(0) = 10, then the particular solution is:
y = 14 / [1 - (4 / 10) · tⁿ], where n = - 14² / 3.
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