Answer:
y= -2x²+4x.
Step-by-step explanation:
the common equation of the parabola is y=ax²+bx+c, where a, b, c - numbers.
1) the coordinates of the vertex are:
[tex]x_0=-\frac{b}{2a} \ and \ y_0=\frac{4ac-b^2}{4a}.[/tex]
2) if according to the condition x₀=1, then b= -2a.
If according to the condition y₀=2, then [tex]2=\frac{4ac-b^2}{4a}=\frac{4ac-4a^2}{4a}=c-a;[/tex]
it means that c=a+2.
3) if b= -2a; c=a+2 and the point (3;-6) belongs to the given parabola, then it is possible to substitute them into the common equation of the parabola:
-6=3²*a-6a+a+2; ⇔ a= -2.
4) if a= -2, then b=-2a=4, and c=a+2=0.
5) if a=-2, b=4 and c=0, then the required equation of the parabola is:
y= -2x²+4x.
Two containers designed to hold water are side by side, both in the shape of a
cylinder. Container A has a diameter of 10 feet and a height of 8 feet. Container B has
a diameter of 12 feet and a height of 6 feet. Container A is full of water and the water
is pumped into Container B until Container A is empty.
To the nearest tenth, what is the percent of Container B that is empty after the
pumping is complete?
Container A
play
Container B
10
d12
8
h6
O
Answer: Volume of Cylinder A is pi times the area of the base times the height
π r2 h = (3.1416)(4)(4)(15) = 753.98 ft3
Volume of Cylinder B is likewise pi times the area of the base times the height
π r2 h = (3.1416)(6)(6)(7) = 791.68 ft3
After pumping all of Cyl A into Cyl B
there will remain empty space in B 791.68 – 753.98 = 37.7 ft3
The percentage this empty space is
of the entire volume is 37.7 / 791.68 = 0.0476 which is 4.8% when rounded to the nearest tenth
.
Step-by-step explanation: I hope that help you.
Note: you may not need to type in the percent sign.
===========================================================
Explanation:
Let's find the volume of water in container A.
Use the cylinder volume formula to get
V = pi*r^2*h
V = pi*5^2*8
V = 200pi
The full capacity of tank A is 200pi cubic feet, and this is the amount of water in the tank since it's completely full.
We have 200pi cubic feet of water transfer to tank B. We'll keep this value in mind for later.
-----------------------
Now find the volume of cylinder B
V = pi*r^2*h
V = pi*6^2*6
V = 216pi
Despite being shorter, tank B can hold more water (since it's more wider).
-----------------------
Now divide the results of each section
(200pi)/(216pi) = 200/216 = 25/27 = 0.9259 = 92.59%
This shows us that 92.59% of tank B is 200pi cubic feet of water.
In other words, when all of tank A goes into tank B, we'll have tank B roughly 92.59% full.
This means the percentage of empty space (aka air) in tank B at this point is approximately 100% - 92.59% = 7.41%
Then finally, this value rounds to 7.4% when rounding to the nearest tenth of a percent.
A subcommittee of six is to be selected from a committee containing 10 democrats and 12 republicans. In how many ways can at least 1 democracy be selected for the subcommittee?
Answer:
the number of ways to select at least 1 democrat in the subcommittee is 69,486 ways
Step-by-step explanation:
Given;
number of the subcommittee, = 6
number of democrats = 10
number of republicans, = 12
The number of ways to select at least 1 democrat in the subcommittee is calculated as follows;
Let D represent Democrats
let R represent Republicans
= (1D & 5R) or (2D & 4R) or (3D & 3R) or (4D & 2R) or (5D & 1R) or (6D)
= 10C₁ x 12C₅ + 10C₂ x 12C₄ + 10C₃ x 12C₃ + 10C₄ x 12C₂ + 10C₅ x 12C₁ + 10C₆
[tex]=( \frac{10!}{9!1!} \times \frac{12!}{7!5!} )+ (\frac{10!}{8!2!} \times \frac{12!}{8!4!})+ (\frac{10!}{7!3!} \times \frac{12!}{9!3!})+ (\frac{10!}{6!4!} \times \frac{12!}{10!2!})+ (\frac{10!}{5!5!} \times \frac{12!}{11!1!}) \\\\ +(\frac{10!}{4!6!})\\\\= (7,920) + (17,820) + (26,400) + (13,860)+ (3,276) + (210)\\\\= 69,486 \ ways[/tex]
Therefore, the number of ways to select at least 1 democrat in the subcommittee is 69,486 ways
the bath tap was left dripping at 18 :00. The water dripped out at a rate of 3 drops per minute. each drop contains 2ml of water. how much water had been lost by 06 :00 the next morning
Find z such that 6% of the standard normal curve lies to the right of z.
P(Z ≥ z) = 1 - P(Z ≤ z) = 0.06
==> P(Z ≤ z) = 0.94
==> z ≈ 1.7507
What is the range of the function f(x) = 3x2 + 6x – 8?
O {yly > -1}
O {yly < -1}
O {yly > -11}
O {yly < -11}
Answer:
Range → {y| y ≥ -11}
Step-by-step explanation:
Range of a function is the set of of y-values.
Given function is,
f(x) = 2x² + 6x - 8
By converting this equation into vertex form,
f(x) = [tex]3(x^2+2x-\frac{8}{3})[/tex]
= [tex]3(x^2+2x+1-1-\frac{8}{3})[/tex]
= [tex]3[(x+1)^2-\frac{11}{3}][/tex]
= [tex]3(x+1)^2-11[/tex]
Vertex of the parabola → (-1, -11)
Therefore, range of the function will be → y ≥ -11
The range of the function f(x) = 3x² + 6x - 8 is {y|y ≥ -11}
What is the range of a function?The range of a function is the set of output values of the function
Since f(x) = 3x² + 6x - 8, we differentiate f(x) = y with respect to x to find the value of x that makes y minimum.
So, df(x)/dx = d(3x² + 6x - 8)/dx
= d(3x²)/dx + d6x/dx - d8/dx
= 6x + 6 + 0
= 6x + 6
Equating the experssion to zero, we have
df(x)/dx = 0
6x + 6 = 0
6x = -6
x = -6/6
x = -1
From the graph, we see that this is a minimum point.
So, the value of y = f(x) at the minimum point is that is a t x = - 1 is
y = f(x) = 3x² + 6x - 8
y = f(-1) = 3(-1)² + 6(-1) - 8
y = 3 - 6 - 8
y = -3 - 8
y = -11
Since this is a minimum point for the graph, we have that y ≥ -11.
So, the range of the function is {y|y ≥ -11}
So, the range of the function f(x) = 3x² + 6x - 8 is {y|y ≥ -11}
Learn more about range of a function here:
https://brainly.com/question/25915612
SAQ 5.1
1. Find the first four terms of the sequence whose general term is given by
i.
ii.
7 x 3"
n-2 5 x
2. Say what the pattern of is for each of the following sequences and give the next three
terms
i.
ii.
2, 6, 12, 20
8, 0.8, 0.08, 0.008
1 1 1 '2'3'4
Answer:
1. (i) 7, 21, 63, 189
(ii) 20, 10, 5, 2.5
2. (i) n²+n (where n = 1, 2, 3, ..)
(ii) 8/(10^n) (where n = 1, 2, 3, ..)
(iii) 1/(n+1) (where n = 1, 2, 3, ..)
Which expression is equivalent to the area of square A, in square inches?
1. 1/2(10)(24)
2. 10(24)
3. (10+24)^2
4. 10^2 + 24^2
Answer:
4.) 10^2 + 24^2
Step-by-step explanation:
From the attached diagram, the area of a square A is given by the measure of the square of its hypotenus :
The hypotenus is given by :
Hypotenus² = opposite² + Adjacent²
Hypotenus² = 10² + 24²
The square of hypotenus = 10^2 + 24^2
if √3CosA = sin A , find the acute angle A
Answer:
Here is your answer.....
Hope it helps you....
Consider a set of data in which the sample mean is 26.826.8 and the sample standard deviation is 7.97.9. Calculate the z-score given that x.
Answer:
The answer is "0.59".
Step-by-step explanation:
Please find the whole question in the attached file.
Given:
[tex]\mu=26.8\\\\\sigma=6.4\\\\X=30.6[/tex]
Using formula:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
[tex]=\frac{30.6-26.8}{6.4}\\\\=\frac{3.8}{6.4}\\\\=\frac{380}{640}\\\\=\frac{38}{64}\\\\=\frac{19}{32}\\\\=0.59375\approx 0.59[/tex]
In order for the parallelogram to be a
rectangle, x = [?]
Diagonal AC = 7x - 35
Diagonal BD = 3x + 45
A
B.
D
C С
Explanation:
For any rectangle, the diagonals are the same length.
AC = BD
7x-35 = 3x+45
7x-3x = 45+35
4x = 80
x = 80/4
x = 20
Sam is making a table of values and a graph for the equation 16x + y = −48. He says that when x = 3, y = 0. Is Sam correct?
Answer:
No
Step-by-step explanation:
16x + y = −48
Substitute the point into the equation and see if it is true
16(3) +0 = -48
48 = -48
This is not true so the point is not a solution
2 squared plus b squared equal 256
Answer:
[tex]2^2+b=256[/tex]
b=252
Step-by-step explanation:
[tex]2^2+b=256[/tex]
4+b=256
b=252
I wasn't very sure about what you are asking, but I hope this helps!
Midpoint for
(-2,3) and (4,-1)
Midpiont=(_2+3\2), (4+_1/2)
=2/2,6/2
=1,3
Evaluating functions (pic attached)
f(x) = 2x³ - 3x² + 7
f(-1) = 2(-1)³ - 3(-1)² + 7
=> f(-1) = 2(-1) - 3(1) + 7
=> f(-1) = -2 -3 + 7
=> f(-1) = 2
f(1) = 2(1)³ - 3(1)² + 7
=> f(1) = 2(1) - 3(1) + 7
=> f(1) = 2 -3 + 7
=> f(1) = 6
f(2) = 2(2)³ - 3(2)² + 7
=> f(2) = 2(8) - 3(4) + 7
=> f(2) = 16 - 12 + 7
=> f(2) = 11
simplify -2/5(sqrt(75))
Answer:
= - 2√3/75
Step-by-step explanation:
Remove parentheses: (a) = a
= -2/5√75
Apply the fraction rule: -a/b = -a/b
= -2/5√75
= - 2/5 . 5√3
Multiply the numbers: 5 . 5 = 25
= - 2/25√3
= - 2√3/75
Which is an x-intercept of the graph of the function?
Answer:
D
Step-by-step explanation:
X intercept=y=0. 0=tan(x-5pi/6). x-5pi/6=0, x=5pi/6
A insurance office keeps track of the number of car insurance claims filed each day. Based on the data collected, it determines that the following probability distribution applies: Number of Claims Probability 0 .25 1 .15 2 .25 3 .25 4 .10 a. What is the expected number of new claims filed each day
Answer:
The expected number of new claims filed each day is 1.8.
Step-by-step explanation:
We are given the following probability distribution:
[tex]P(X = 0) = 0.25[/tex]
[tex]P(X = 1) = 0.15[/tex]
[tex]P(X = 2) = 0.25[/tex]
[tex]P(X = 3) = 0.25[/tex]
[tex]P(X = 4) = 0.1[/tex]
a. What is the expected number of new claims filed each day
Multiplication of each outcome by its probability, so:
[tex]E(X) = 0*0.25 + 1*0.15 + 2*0.25 + 3*0.25 + 4*0.1 = 1.8[/tex]
The expected number of new claims filed each day is 1.8.
a) __m=10km 25m =___km
b) __m=__km__m=1.5 km
Answer:
0.01m=10km
25m=25000km
1m=1000km
0.0015m=1.5km
If this is incorrect forgive me plz
I hope this will help you
The length of a rectangle is 4 in longer than its width.
If the perimeter of the rectangle is 32 in, find its area.
Answer:
60 sq in
Step-by-step explanation:
Perimeter = 2l + 2w
If l = w+4
Perimeter = 2(w+4) + 2w
Perimeter = 4w+8
32 = 4w + 8
24 = 4w
6 = w
If w = 6, l = 6+4 = 10
Area = l * w
Area = 10 * 6
Area = 60
Which statement is true about the slope of the graphed line?
Answer: positive
Step-by-step explanation: because it is going up from the left to the right
"when reading a cd-rom disk 2.8 cm from its center the rotational speed is 726 rpm what is the rpm at 5.2cm
9514 1404 393
Answer:
726 rpm
Step-by-step explanation:
The angular speed is not dependent upon the radius. The rotational speed is 726 rpm at any radius.
establish this identity
Answer:
see explanation
Step-by-step explanation:
Using the identities
tan x = [tex]\frac{sinx}{cosx}[/tex] , sin²x = 1 - cos²x
sin2x = 2sinxcosx
Consider left side
cosθ × sin2θ
= [tex]\frac{sin0}{cos0}[/tex] × 2sinθcosθ ( cancel cosθ )
= 2sin²θ
= 2(1 - cos²θ)
= 2 - 2cos²θ
= right side , then established
Nick buys a bag of cookies that contains 9 chocolate chip cookies, 8 peanut butter cookies, 4 sugar cookies and 5 oatmeal cookies. What is the probability that Nick reaches in the bag and randomly selects a chocolate chip cookie from the bag, eats it, then reaches back in the bag and randomly selects an oatmeal cookie
Answer:
7/26
Step-by-step explanation:
Add all of it up.
9 + 8 + 4 +5 = 26
26 cookies, but done twice so,
26 × 2 = 52
14/52 = 7/26
Which of the following choices is the correct range for the function
h(x) =-3x^2if the domain is (0.-2. 1)?
(0, -6, -3)
(0,6, -3)
None of the choices are correct.
(0, 12, 3)
(0, -12,3)
9514 1404 393
Answer:
None of the choices are correct
Step-by-step explanation:
The squared term (x²) is never negative, so all non-zero range values will be negative. For the given domain values, the range is {0, -12, -3}.
None of the choices are correct.
PLEASE HELPPPP
The cost function in a computer manufacturing plant is C(x) = 0.28x^2-0.7x+1, where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands. Determine the minimum production cost.
Given:
The cost function is:
[tex]C(x)=0.28x^2-0.7x+1[/tex]
where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands.
To find:
The minimum production cost.
Solution:
We have,
[tex]C(x)=0.28x^2-0.7x+1[/tex]
It is a quadratic function with positive leading efficient. It means it is an upward parabola and its vertex is the point of minima.
If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex], then the vertex of the parabola is:
[tex]\text{Vertex}=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex]
In the given function, [tex]a=0.28, b=-0.7, c=1[/tex]. So,
[tex]-\dfrac{b}{2a}=-\dfrac{-0.7}{2(0.28)}[/tex]
[tex]-\dfrac{b}{2a}=1.25[/tex]
Putting [tex]x=1.25[/tex] in the given function to find the minimum production cost.
[tex]C(x)=0.28(1.25)^2-0.7(1.25)+1[/tex]
[tex]C(x)=0.28(1.5625)-0.875+1[/tex]
[tex]C(x)=0.4375+0.125[/tex]
[tex]C(x)=0.5625[/tex]
Therefore, the minimum production cost is 0.5625 million dollars.
Answer:
The minimum cost is 0.5625.
Step-by-step explanation:
The cost function is
C(x) = 0.28x^2 - 0.7 x + 1
Differentiate with respect to x.
[tex]C = 0.28x^2 - 0.7 x + 1\\\\\frac{dC}{dt} = 0.56 x - 0.7\\\\\frac{dC}{dt} = 0\\\\0.56 x - 0.7 = 0\\\\x = 1.25[/tex]
The minimum value is
c = 0.28 x 1.25 x 1.25 - 0.7 x 1.25 + 1
C = 0.4375 - 0.875 + 1
C = 0.5625
Help plz help needed i need the answer
Answer:
x = ±sqrt(26)
Step-by-step explanation:
ln ( x^2 -25) = 0
Raise each side to base e
e^ln ( x^2 -25) = e^0
x^2 -25 = 1
Add 25 to each side
x^2 -25 +25 = 1+25
x^2 = 26
Take the square root of each side
sqrt(x^2) = ±sqrt(26)
x = ±sqrt(26)
Answer:
The third option
Step-by-step explanation:
If we rewrite this in log form, we get
[tex]e {}^{0} = {x}^{2} - 25[/tex]
Remeber anything to the 0 power is 1, so simplifying the equation first
[tex]1 = {x}^{2} - 25[/tex]
Add 25 to both sides
[tex]26 = {x}^{2} [/tex]
Take the square root of both sides
[tex]x = \sqrt{26} [/tex]
Square root are both so
[tex]x = - \sqrt{26} [/tex]
Is also a answer.
The third option is the answer
10v-6v=28
Simplify your answer as much as possible
Step-by-step explanation:
10v-6v=28
4v=28
v=28/4
v=7
Answer:
10v-6v=28
or, 4v = 28
or, v = 28/4
or, v = 7
hence 7 is the required value of v
t^2 +11t+30/t^2+5t-24 ÷ t^2+4t-21/t^2+10t+25
Answer:
t^2 + 30t - 15/t^2 + 25
Step-by-step explanation:
What is this fraction converted by a decimal?
Answer:
2
Step-by-step explanation:
The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, produced by Phonola Media, is related to the price per compact disc. The equation
p = −0.00051x + 5 (0 ≤ x ≤ 12,000)
where p denotes the unit price in dollars and x is the number of discs demanded, relates the demand to the price. The total monthly cost (in dollars) for pressing and packaging x copies of this classical recording is given by
C(x) = 600 + 2x − 0.00002x2 (0 ≤ x ≤ 20,000).
Hint: The revenue is
R(x) = px,
and the profit is
P(x) = R(x) − C(x).
Find the revenue function,
R(x) = px.
R(x) =
Answer:
[tex]R(x) = -0.00051x^2 + 5x[/tex]
[tex]P(x) = -0.00049x^2 + 3x-600[/tex]
Step-by-step explanation:
Given
[tex]p = -0.00051x + 5[/tex] [tex]\to[/tex] [tex](0 \le x \le 12,000)[/tex]
[tex]C(x) = 600 + 2x - 0.00002x^2[/tex] [tex]\to[/tex] [tex](0 \le x \le 20,000)[/tex]
Solving (a): The revenue function
We have:
[tex]R(x) = x * p[/tex]
Substitute [tex]p = -0.00051x + 5[/tex]
[tex]R(x) = x * (-0.00051x + 5)[/tex]
Open bracket
[tex]R(x) = -0.00051x^2 + 5x[/tex]
Solving (b): The profit function
This is calculated as:
We have:
[tex]P(x) = R(x) - C(x)[/tex]
So, we have:
[tex]P(x) =-0.00051x^2 + 5x - (600 + 2x - 0.00002x^2)[/tex]
Open bracket
[tex]P(x) =-0.00051x^2 + 5x -600 - 2x +0.00002x^2[/tex]
Collect like terms
[tex]P(x) = 0.00002x^2-0.00051x^2 + 5x - 2x-600[/tex]
[tex]P(x) = -0.00049x^2 + 3x-600[/tex]
