Answer:
a=2
Step-by-step explanation:
[tex]area=2\int\limits^a_b {y} \, dx =2\int\limits^a_b {\sqrt{4ax} } \, dx \\=2 \times 2\sqrt{a} \frac{x^{\frac{3}{2} } }{\frac{3}{2} } ~from~~b~to~a\\=\frac{8}{3}\sqrt{a} (a^{\frac{3}{2} } -b^{\frac{3}{2} } )\\=\frac{8}{3} \sqrt{a}( (4a)^{\frac{3}{2} } -0)\\=\frac{8}{3} \sqrt{a} ((4a)\sqrt{4a} -0)\\=\frac{32 a}{3} \times 2a\\=\frac{64}{3} a^2[/tex]
[tex]\frac{64}{3} a^2=\frac{256}{3} \\a^2=\frac{256}{3} \times \frac{3}{64} =4\\a=2 (a > 0)[/tex]
the curve is a right parabola.
here b=0,and a=4a for x
we are finding the area between x-axis and x from 0 t0 4a.
curve is symmetrical about x-axis so we multiply by 2.
If the area of the region bounded by the curve [tex]y^2 =4ax[/tex] and the line [tex]x= 4a[/tex] is [tex]\frac{256}{3}[/tex] Sq units, then the value of [tex]a[/tex] will be [tex]2[/tex] .
What is area of the region bounded by the curve ?An area bounded by two curves is the area under the smaller curve subtracted from the area under the larger curve. This will get you the difference, or the area between the two curves.
Area bounded by the curve [tex]=\int\limits^a_b {x} \, dx[/tex]
We have,
[tex]y^2 =4ax[/tex]
⇒ [tex]y=\sqrt{4ax}[/tex]
[tex]x= 4a[/tex],
Area of the region [tex]=\frac{256}{3}[/tex] Sq units
Now comparing both given equation to get the intersection between points;
[tex]y^2=16a^2[/tex]
[tex]y=4a[/tex]
So,
Area bounded by the curve [tex]= \[ \int_{0}^{4a} y \,dx \][/tex]
[tex]\frac{256}{3} =\[ \int_{0}^{4a} \sqrt{4ax} \,dx \][/tex]
[tex]\frac{256}{3}= \[\sqrt{4a} \int_{0}^{4a} \sqrt{x} \,dx \][/tex]
[tex]\frac{256}{3}= \[2\sqrt{a} \int_{0}^{4a} x^{\frac{1}{2} } \,dx \][/tex]
[tex]\frac{256}{3}= 2\sqrt{a} \left[\begin{array}{ccc}\frac{(x)^{\frac{1}{2}+1 } }{\frac{1}{2}+1 }\end{array}\right] _{0}^{4a}[/tex]
[tex]\frac{256}{3}= 2\sqrt{a} \left[\begin{array}{ccc}\frac{(x)^{\frac{3}{2} } }{\frac{3}{2} }\end{array}\right] _{0}^{4a}[/tex]
[tex]\frac{256}{3}= 2\sqrt{a} *\frac{2}{3} \left[\begin{array}{ccc}(x)^{\frac{3}{2}\end{array}\right] _{0}^{4a}[/tex]
On applying the limits we get;
[tex]\frac{256}{3}= \frac{4}{3} \sqrt{a} \left[\begin{array}{ccc}(4a)^{\frac{3}{2} \end{array}\right][/tex]
[tex]\frac{256}{3}= \frac{4}{3} \sqrt{a} *\sqrt{(4a)^{3} }[/tex]
[tex]\frac{256}{3}= \frac{4}{3} \sqrt{a} * 8 *a^{2} \sqrt{a}[/tex]
[tex]\frac{256}{3}= \frac{4}{3} * 8 *a^{3}[/tex]
⇒ [tex]a^{3} =8[/tex]
[tex]a=2[/tex]
Hence, we can say that if the area of the region bounded by the curve [tex]y^2 =4ax[/tex] and the line [tex]x= 4a[/tex] is [tex]\frac{256}{3}[/tex] Sq units, then the value of [tex]a[/tex] will be [tex]2[/tex] .
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The data below represent a demand schedule.
Product Price: $30, $25, $20, $15, $10
Quantity Demanded: 5, 15, 25, 35, 45
Using the midpoint approach, determine the price elasticity of demand between each of the following prices:
A. Between P1 = $30 & P2 = $25, Ed=?
B. Between P1 = $25 & P2 = $20, Ed=?
C. Between P1 = $20 & P2 = $15, Ed=?
D. Between P1 = $15 & P2 = $10, Ed=?
Round your answers to two decimal places. Enter your answers as a positive value (absolute value).
By using the midpoint approach, the price elasticity of demand between each of the given prices are:
5.502.251.170.63What is the price elasticity of demand?The price elasticity of demand measures the responsiveness of the quantity demanded by a consumer with respect to a specific change in price of the product, all things being equal (ceteris paribus).
By using the midpoint approach, the price elasticity of demand between each of the given prices is given by:
Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]
Price elasticity of demand = (15 - 5)/[(15 + 5)/2]/(25 - 30)/[(25 + 30)/2]
Price elasticity of demand = 1/-0.1818
Price elasticity of demand = 5.50.
Part B.Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]
Price elasticity of demand = (25 - 15)/[(25 + 15)/2]/(20 - 25)/[(20 + 25)/2]
Price elasticity of demand = 0.5/-0.2222
Price elasticity of demand = 2.25.
Part C.Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]
Price elasticity of demand = (35 - 25)/[(35 + 25)/2]/(15 - 20)/[(15 + 20)/2]
Price elasticity of demand = 0.33/-0.2857
Price elasticity of demand = 1.17.
Part D.Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]
Price elasticity of demand = (45 - 35)/[(45 + 35)/2]/(10 - 15)/[(10 + 15)/2]
Price elasticity of demand = 0.25/-0.4
Price elasticity of demand = 0.63.
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When -3v = -18 is solved, the result is:
Answer:
When -3v = -18 is solved, the result is:
21v
The result of this mathematical sentence is v=6
First degree equationFirst degree equation is a mathematical sentence - having at least one unknown. Its representation is given by ax + b = 0. To calculate an equation, as it is in the expression in the statement, simply: isolate x and divide the second to the first member.
*Note: Equal signs, the result will be equated as positive.
-3v = -18
v = -18/-3
v = 6
Therefore, the correct value of this equation is v = 6.
I need help please
A family purchases a light sphere to be used out on their patio. The diameter of the sphere is 20 in.
What is the volume of the light sphere?
Use 3.14 for pi.
Enter your answer, as a decimal, and round only your final answer to the nearest hundredth.
I have seen two different answers with 5 stars so I am confused on which person solved it correctly
Answer:
4,186.67 in³
Step-by-step explanation:
V = (4/3)πr³
V = (4/3)(3.14)(10 in)³
V = (4/3)(3.14)(1,000 in³)
V = 4,186.666667 in³
Une fonction polynomiale du second degré possède les caractéristiques
suivantes :
• La fonction est croissante sur l'intervalle [0, 8].
• La fonction est décroissante sur l'intervalle ]-10, 0].
• La courbe passe par le point (-8, 4).
PSST
↓
Voici les symboles dont tu pourrais avoir besoin dans ta réponse. N'hésite pas à
les copier-coller à partir d'ici si tu ne les trouves pas sur ton clavier.
[]%
SAVOIR-FAIRE
INDICE
Représente graphiquement la fonction, puis détermine son codomaine. Utilise la
notation décimale au besoin.
Le codomaine est.
Je n’arrive pas à trouver le co domaine si quelqu’un peut m’aider svp?
A second-degree polynomial takes the form
[tex]f(x) = ax^2 + bx + c[/tex]
for some constants a, b, and c. Such a function is continuous and differentiable everywhere in its domain.
Differentiating f(x) with respect to x gives
[tex]\dfrac{df}{dx} = 2ax + b[/tex]
We're told that
• f(x) is increasing on [0, 8]
• f(x) is decreasing on ]-10, 0]
and since df/dx is continuous, this tells us that df/dx = 0 when x = 0. It follows that b = 0, and we can write
[tex]f(x) = ax^2 + c[/tex]
We're also given that the curve passes through the point (-8, 4), which gives rise to the constraint
[tex]f(-8) = 64a - 8b + c = 4 \implies 64a + c = 4[/tex]
Since f(x) is decreasing on ]-10, 0], we have df/dx < 0 when x = -8, so
[tex]2ax+b < 0 \implies -16a < 0 \implies a > 0[/tex]
This means f(x) is minimized when x = 0, with min{f(x)} = c, so the co-domain of f(x) is the set {f(x) ∈ ℝ : f(x) ≥ c}.
Without another condition, that's all we can say about the co-domain. There are infinitely many choices for the constants a and c that satisfy the given conditions. For example,
a = 1, c = -60 ⇒ f(x) = x² - 60 ⇒ f(-8) = 4
⇒ co-domain = {f(x) ∈ ℝ : f(x) ≥ -60}
a = 2, c = -124 ⇒ f(x) = 2x² - 124 ⇒ f(-8) = 4
⇒ co-domain = {f(x) ∈ ℝ : f(x) ≥ -124}
etc.
EASY POINTS
Which answer represents the following conditional statement in shorthand?
Answer:
B
Step-by-step explanation:
if it is warm the Megan is swimming
(A+1)/a = y make a the subject of this equation
Given the side measurements. classify the triangle as acute, right, obtuse, or not a triangle. 11, 4, 16
Answer: not a triangle
Step-by-step explanation:
If this were to be a triangle, the shorter sides would be 11 and 4 and the longest side would be 16.
First, we should determine if it is a triangle.
Sum of shorter sides = 15 This is less than the longest side, 16, so therefore, it is not a triangle.El parámetro a de una distribución exponencial cumple que
Pregunta 7 opciones:
a = 0
a < 0
a ≥ 0
a > 0
The parameters of an Exponential Distribution is D. a > 0
What is an Exponential Distribution?This refers to the distribution of probability with respects to time taken in a Poisson point process.
Hence, we can see that from the previous knowledge of exponential distributions, it is stated that λ > 0 is the parameter of the distribution, and is supported on the interval [0, ∞).
Therefore, option D is correct.
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5 divided by 4/9
i need the answer in a fraction form please.
Find the value of x.
55
X
44
X = [?]
Enter the number that belongs in
the green box.
Answer:
Step-by-step explanation:
x^2 + 44^2 = 55^2
x^2 + 1936 = 3025
3025-1936 = 1089
sqrt(1089) = 33
x = 33
Answer:
X=33
Step-by-step explanation:
this is a right traingle so you can use pythagorean theorem
A^2 +B^2 =C^2
A^2 +44^2= 55^2
A^2 + 1936= 3025 subtract 1936 from both sides
A^2= 1089 now square root both sides
A=33
Pls help meeeeeeeeeeeee
Answer:
24%
Step-by-step explanation:
there are 50 numbers total
number of 4's: 7
number of 7's: 5
it's asking for the odds of a 4 or a 7 meaning that they're fine with either one. that means you can ADD the number of them up!
7 + 5 = 12
to get the odds, we need to divide!
12/50 = ?.24convert that into a percent!
24%
let me know if you're still confused :))
Which combined inequality has the same solution set shown in the graph of x?
Number line ranging from negative four to four, with a line beginning with an open point at negative three and ending with a closed point at negative one
–3 > x ≥ –1
–3 < x ≤ –1
–3 ≤ x < –1
–3 ≤ x > –1
Step-by-step explanation:
an open (empty) point means the point itself is not included.
a closed (filled) point means the point itself is included.
the x values going from -3 (not included) to -1 (included) means
-3 < x <= -1
so, the second answer is correct.
What is the value of
(1/8)^-1/3
PLEASE I NEED THE AWNSER QUICK PLEASE AND TY
Answer:
2.66666666667
Step-by-step explanation:
(1/8)^-1/3 means 1/8 to the -1/3 power, which equals 2.66666666667. So the answer is 2.66666666667.
What is P(greater than 8)?
Answer:
Yes
Step-by-step explanation:
The sum must be greater than 8 it can't be 7 anyway. Sums can be 9, 10 or 12. P = (4+3+1)/36 = 3/36
93/100
Natalie needs 3 1/2 cups of flour to make 4 dozen cookies. How many.cups will she
need to make 2 dozen cookies?
7 cups
1 cup
13/4 cups
11/2 cups
Answer:
3/4 cups
Step-by-step explanation:
3 1/2 divided by 2
Which is the equation of the parabola with focus (6, 2) and vertex (6, –4)?
Based on the calculations, the equation of this parabola is equal to (x - 6)² = 16(y + 4).
How to determine the equation of this parabola?Mathematically, the standard equation with the vertex for a parabola is given by:
(y - k)² = 4a(x - h) for horizontal parabola.
(x - h)² = 4a(y - k) for vertical parabola.
where:
h and k are the vertex.a is a point.By critically observing the points, we can deduce that both the focus and vertex lie on the same vertical line x = 6.
Given the following data:
Focus with points = (6, 2).
Vertex (h, k) = (6, –4).
Note: a = 2 - (-4) = 2 + 4 = 6.
Substituting the given parameters into the formula, we have;
(x - 6)² = 4 × 4(y - (-4))
(x - 6)² = 16(y + 4).
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Find the volume of the
triangular prism.
3.6 cm
5.4 cm
9 cm
Answer:
174.96cm2
Step-by-step explanation:
V=lbh
=3.6×5.4×9
=174.96cm2
I don't knowif you want it in milliliters or litres so here are both of them
milliliters = 174.96
litres = 0.17496
Triangle ABC is defined by the points A(2,9), B(8,4), and ((-3,-2).
Complete the following equation for a line passing through point C and perpendicular AB.
The equation of the line is 5y = 6x + 8 which passes through point C and perpendicular AB.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have a triangle ABC is defined by the points A(2,9), B(8,4), and C(-3,-2).
The slope of the segment AB:
[tex]\rm m =\dfrac{4-9}{8-2}[/tex]
m = -5/6
The slope of the line perpendicular to AB:
Let M is the slope of the line:
mM = -1
(-5/6)M = -1
M = 6/5
The line:
y = Mx + c
y = (6/5)x + c
The line passing through the point C(-3, -2)
-2 = (6/5)(-3) + c
c = 8/5
y = (6/5)x + 8/5
5y = 6x + 8
Thus, the equation of the line is 5y = 6x + 8 which passes through point C and perpendicular AB.
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what is -23/6 - 7/3
A -37/6
B -30/9
C -16/6
D 37/6
Answer:A
Step-by-step explanation:
-23/6 - 7/3 =-6.16666666667
-37/6 = -6.16666666667
Answer:
[tex] \frac{ - 37}{6} [/tex]
Step-by-step explanation:
[tex] \frac{23}{6} - \frac{7}{3} \\ lcm = 6 \\ \frac{ - 23 - 14} {6} = - \frac{ - 37}{6} \\ final \: answer \\ = \frac{ - 37}{6} [/tex]
Which criterion, if any, could prove the triangles are congruent?
Answer: None
Step-by-step explanation:
There is only one pair of angles and one pair of sides, which is not sufficient to prove triangle congruence.
An icicle drips at a rate that can be represented by the function f(x) = −x2 + 8x − 7, where 0 ≤ x ≤ 10 and x is the number of hours after the sun has risen. When f(x) is a negative number, the icicle is not dripping. Determine the values when the icicle starts and stops dripping.
Find when f(x) = 0. By factorizing, we have
-x² + 8x - 7 = - (x - 7) (x - 1) = 0
so either x - 7 = 0 or x - 1 = 0, or simply x = 1 or x = 7.
Split the domain into three intervals, and check the sign of f(x) over each interval at some test point in the interval. The sign will tell you when the icicle is dripping (positive) or not (negative).
• [0, 1) : at x = 0, we have f(0) = -7 < 0
• (1, 7) : at x = 2, we have f(2) = 5 > 0
• (7, 10] : at x = 8, we have f(8) = -7 < 0
This tells us that the icicle is not dripping when 0 ≤ x < 1, begins to drip when x = 1, drips for the duration of 1 < x < 7, stops dripping when x = 7, and keeps on not dripping when 7 < x ≤ 10.
The seventh-grade students at Charleston Middle School are choosing one girl and one boy for student council. Their choices for girls are Michaela (M), Candice (C), and Raven (R), and for boys, Neil (N), Barney (B), and Ted (T). The sample space for the combined selection is represented in the table. Complete the table and the sentence beneath it.
Boys
Neil Barney Ted
Girls Michaela N-M
T-M
Candice N-C
T-C
Raven N-R
T-R
The new sample size based on the information will be B-M, B-C, B-R, 8.
What is a sample size?Sample size is the number of participants or observations that are included in a study. This is usually represented by n.
When the boys and girls are to be chosen, the new sample size based on the information will be B-M, B-C, B-R, 8.
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Answer:
Step-by-step explanation:
B-M, B-C, B-R, 8.
Estimate the product.
14×212
Which of the following could be the value of x in the equation x^2 - 21 = 100 Choose all the correct answers
How to solve your problem
x^{2}-21=100
Quadratic formula
Factor
1
Move terms to the left side
x^{2}-21=100
x^{2}-21-100=0
2
Subtract the numbers
x^{2}\textcolor{#C58AF9}{-21}\textcolor{#C58AF9}{-100}=0
x^{2}\textcolor{#C58AF9}{-121}=0
3
Use the quadratic formula
x=\frac{-\textcolor{#F28B82}{b}\pm \sqrt{\textcolor{#F28B82}{b}^{2}-4\textcolor{#C58AF9}{a}\textcolor{#8AB4F8}{c}}}{2\textcolor{#C58AF9}{a}}
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
x^{2}-121=0
a=\textcolor{#C58AF9}{1}
b=\textcolor{#F28B82}{0}
c=\textcolor{#8AB4F8}{-121}
x=\frac{-\textcolor{#F28B82}{0}\pm \sqrt{\textcolor{#F28B82}{0}^{2}-4\cdot \textcolor{#C58AF9}{1}(\textcolor{#8AB4F8}{-121})}}{2\cdot \textcolor{#C58AF9}{1}}
4
Simplify
Evaluate the exponent
Multiply the numbers
Add the numbers
Evaluate the square root
Add zero
Multiply the numbers
x=\frac{\pm 22}{2}
5
Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
x=\frac{22}{2}
x=\frac{-22}{2}
6
Solve
Rearrange and isolate the variable to find each solution
x=11
x=-11
Find the inverse
[tex]f(x)={e}^{3x - 1} [/tex]
Tank you for your support
Answer:
[tex]f^{-1}(x)=\dfrac{1}{3}(\ln x +1)[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=e^{3x-1}[/tex]
Replace f(x) with y:
[tex]\implies y=e^{3x-1}[/tex]
Take natural logs of both sides:
[tex]\implies \ln y = \ln e^{3x-1}[/tex]
Apply the Power Log Law [tex]\ln x^n=n\ln x[/tex] :
[tex]\implies \ln y = (3x-1)\ln e[/tex]
As [tex]\ln e=1[/tex] then:
[tex]\implies \ln y = 3x-1[/tex]
Rearrange to make x the subject:
[tex]\implies 3x=\ln y +1[/tex]
[tex]\implies x=\dfrac{1}{3}(\ln y +1)[/tex]
Swap x for [tex]f^{-1}(x)[/tex] and y for x:
[tex]\implies f^{-1}(x)=\dfrac{1}{3}(\ln x +1)[/tex]
Which could be the entire interval over which the function, f(x), is positive?
Why?
Notice that f(x) is positive when -2 < x < 1. In other words, f(x) is positive when x = -1 and when x = 1.
This interval of -2 < x < 1 translates directly to the interval notation of (-2, 1)
Unfortunately this interval notation looks identical to ordered pair notation. Be sure not to mix the two concepts up.
The parenthesis in interval notation tell the reader "do not include the endpoints". We cannot include x = -2 nor x = 1 because these values make f(x) zero, but we want f(x) > 0.
Something like choice D is a non-answer because the value x = 2 is in the interval (1,4), but f(2) = -8 which isn't positive. We can rule choice D out because of it. Choices A and C are similar situations.
HELP PLSSSSSSSSS WIL GIVE BRAINLEST Nathan needs 10 ounces of lemonade.
He needs to know how much liters that is.
A 16
B 5
C 943
D 0.295735
The volume of 10 ounces of lemonade in litres is 0.295735 litres.
How to convert from ounces to litres?
He needs 10 ounces of lemonade.
To know the volume in litres, we have to convert from ounces to litres.
Therefore,
1 ounces = 0.0295735 litres
10 ounces = ?
cross multiply
volume in litres = 0.0295735 × 10
volume in litres = 0.295735
Therefore, the volume of the lemonade in litres is 0.295735 litres.
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What is the probability that student A choses yellow and student b choses yellow from their skittles at the same time
Which algebraic expression is equivalent to the expression below?
3(5x + 7)-6(4- 2x)
3(5x+7)-6(4-2x) - given
15x+21-24+12x - distributive property
27x-3 - combine like terms
There is a circular pool in the backyard with an approximate area of 113 square inches. What was the diameter?
A.12 inches
B.36 inches
C.48 inches
D.144 inches
A circle is a curve sketched out by a point moving in a plane. The diameter of the circular poll is 12 inches. Thus, the correct option is A.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
The area of a circle is given as πR², where r is the radius of the circle. Since the area of the pool is 113 sq. inches, therefore, the radius of the circle will be,
Area of pool = πR²
113 sq. inches. = πR²
113/π = R²
R = √35.9690
R = 5.9974 ≈ 6 inches
Now, since the diameter of a circle is twice the radius of the circle, therefore, the diameter of the circle will be,
Diameter of the circle = 2 × 6 inches = 12 inches
Hence, the diameter of the circular poll is 12 inches. Thus, the correct option is A.
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Answer:
a. 12 inches
Step-by-step explanation:
113 ÷ 3.14 = 35.98726114649682
2√35.98726114649682 = 5.998938334947011
5.998938334947011 x 2 = 11.99787666989402
keyword approximate ;)