I am thinking the answer is 225. Sorry if I'm wrong!
Identify the equation of the translated graph in general form (Picture provided)
Answer:
The equation after translation is x² + y² + 16x - 8y + 73 = 0 ⇒ answer (a)
Step-by-step explanation:
* Lets study the type of the equation:
∵ Ax² + Bxy + Cy² + Dx + Ey + F = 0 ⇒ general form of conic equation
- If D and E = zero
∴ The center of the graph is the origin point (0 , 0)
- If B = 0
∴ The equation is that of a circle
* Lets study our equation:
x² + y² = 7 ⇒ x² + y² - 7 =0
∵ B = 0 , D = 0 , E = 0
∴ It is the equation of a circle with center origin
- The equation of the circle with center origin in standard form is:
x² + y² = r²
∴ x² + y² = 7 is the equation of a circle withe center (0 , 0)
and its radius = √7
* We have two translation one horizontally and the other vertically
- Horizontal: x-coordinate moves right (+ve value) or left (-ve value)
- Vertical: y-coordinate moves up (+ve value) down (-ve value)
∵ The point of translation is (-8 , 4)
∵ x = -8 (-ve value) , y = 4 (+ve value)
∴ The circle moves 8 units to the left and 4 units up
* now lets change the x- coordinate and the y-coordinate
of the center (0 , 0)
∴ x-coordinate of the center will be -8
∵ y-coordinate of the center will be 4
* That means the center of the circle will be at point (-8 , 4)
- the standard form of the equation of the circle with center (h , k) is
(x - h)² + (y - k)² = r²
∵ h = -8 and y = 4
∴ The equation is: (x - -8)² + (y - 4)² = 7
∴ (x + 8)² + (y - 4)² = 7
* lets change the equation to the general form by open the brackets
∴ x² + 16x + 64 + y² - 8y + 16 - 7 = 0
* Lets collect the like terms
∴ x² + y² + 16x - 8y + 73 = 0
∴ The equation after translation is x² + y² + 16x - 8y + 73 = 0
* Look at the graph the blue circle is after translation
Two catalysts may be used in a batch chemical process. Twelve batches were prepared using catalyst 1, resulting in an average yield of 85 and a sample standard deviation of 3. Fifteen batches were prepared using catalyst 2, and they resulted in an average yield of 89 with a standard deviation of 2. Assume that yield measurements are approximately normally distributed with the same standard deviation. (a) Is there evidence to support the claim that catalyst 2 produces higher mean yield than catalyst 1? Use (b) Find a 99% confidence interval on the difference in mean yields that can be used to test the claim in part (a). Round your answer to two decimal places (e.g. 98.76).
To test whether there is evidence to support the claim that catalyst 2 produces a higher mean yield than catalyst 1, a two-sample t-test can be performed. To find a 99% confidence interval on the difference in mean yields, a formula can be used.
Explanation:To test whether there is evidence to support the claim that catalyst 2 produces a higher mean yield than catalyst 1, we can perform a two-sample t-test.
Null Hypothesis: There is no difference in mean yields between catalyst 2 and catalyst 1.Alternative Hypothesis: The mean yield of catalyst 2 is higher than that of catalyst 1.Calculate the pooled standard deviation:Calculate the t-value using the formula: t = ((mean1 - mean2) - 0) / (pooled standard deviation * sqrt(1/n1 + 1/n2))Compare the t-value with the critical t-value from the t-distribution table to determine if there is enough evidence to reject the null hypothesis.(b) To find a 99% confidence interval on the difference in mean yields, we can use the formula: CI = (mean1 - mean2) ± (critical t-value * standard error), where standard error = sqrt((standard deviation1^2/n1) + (standard deviation2^2/n2)).
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(a) Yes, there is evidence to support the claim that catalyst 2 produces a higher mean yield than catalyst 1.
(b) The 99% confidence interval on the difference in mean yields is approximately (-6.52, -1.48).
(a) To test whether there is evidence to support the claim that catalyst 2 produces a higher mean yield than catalyst 1, we can conduct a hypothesis test.
- Null Hypothesis [tex](\(H_0\))[/tex]:
The mean yield produced by catalyst 2 is not higher than the mean yield produced by catalyst 1. [tex]\( \mu_1 \geq \mu_2 \)[/tex]
- Alternative Hypothesis [tex](\(H_1\))[/tex]:
The mean yield produced by catalyst 2 is higher than the mean yield produced by catalyst 1. [tex]\( \mu_1 < \mu_2 \)[/tex]
We'll use a two-sample t-test for independent samples since we are comparing the means of two independent groups.
Given:
- Sample mean [tex](\( \bar{x}_1 \))[/tex] for catalyst 1 = 85
- Sample mean [tex](\( \bar{x}_2 \))[/tex] for catalyst 2 = 89
- Sample standard deviation [tex](\( s_1 \))[/tex] for catalyst 1 = 3
- Sample standard deviation ([tex]\( s_2 \)[/tex]) for catalyst 2 = 2
- Sample size [tex](\( n_1 \))[/tex] for catalyst 1 = 12
- Sample size [tex](\( n_2 \))[/tex] for catalyst 2 = 15
- Degrees of freedom [tex](\( df \)) = \( n_1 + n_2 - 2 \)[/tex]
Let's calculate the t-statistic:
[tex]\[ t = \frac{(\bar{x}_1 - \bar{x}_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \][/tex]
[tex]\[ t = \frac{(85 - 89)}{\sqrt{\frac{3^2}{12} + \frac{2^2}{15}}} \][/tex]
[tex]\[ t \approx \frac{-4}{\sqrt{\frac{9}{12} + \frac{4}{15}}} \][/tex]
[tex]\[ t \approx \frac{-4}{\sqrt{0.75 + 0.2667}} \][/tex]
[tex]\[ t \approx \frac{-4}{\sqrt{1.0167}} \][/tex]
[tex]\[ t \approx \frac{-4}{1.0083} \][/tex]
[tex]\[ t \approx -3.97 \][/tex]
Now, we'll find the critical value for the t-distribution with the given degrees of freedom and a one-tailed test at a 99% confidence level.
Since it's a one-tailed test, we're interested in the critical value to the right of the distribution.
Using a t-table or a statistical software, the critical value for a one-tailed test with [tex]\( df = 12 + 15 - 2 = 25 \)[/tex] and [tex]\( \alpha = 0.01 \)[/tex] is approximately [tex]\( t_{\text{critical}} \approx 2.492 \)[/tex].
Since [tex]\( t = -3.97 < t_{\text{critical}} = 2.492 \)[/tex]we reject the null hypothesis.
Therefore, there is evidence to support the claim that catalyst 2 produces a higher mean yield than catalyst 1.
(b) To find a 99% confidence interval on the difference in mean yields, we'll use the formula:
[tex]\[ \text{Confidence Interval} = (\bar{x}_1 - \bar{x}_2) \pm t_{\alpha/2} \times \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} \][/tex]
Substituting the given values:
[tex]\[ \text{Confidence Interval} = (85 - 89) \pm 2.492 \times \sqrt{\frac{3^2}{12} + \frac{2^2}{15}} \][/tex]
[tex]\[ \text{Confidence Interval} = -4 \pm 2.492 \times \sqrt{0.75 + 0.2667} \][/tex]
[tex]\[ \text{Confidence Interval} = -4 \pm 2.492 \times \sqrt{1.0167} \][/tex]
[tex]\[ \text{Confidence Interval} = -4 \pm 2.492 \times 1.0083 \][/tex]
[tex]\[ \text{Confidence Interval} = -4 \pm 2.5161 \][/tex]
[tex]\[ \text{Confidence Interval} = (-6.5161, -1.4839) \][/tex]
Rounded to two decimal places, the 99% confidence interval on the difference in mean yields is approximately (-6.52, -1.48).
Your grade point average is 3.48.How can you write the point average as a fraction
your fraction would be 3 12/15
The expression 60+25x represents the cost of the bracelet for x charms added to the purchase. What does the 25 represent in the expression?
Answer:
the cost of each charm
Step-by-step explanation:
Since x is the number of charms and it is multiplied by 25, 25 is the cost of each charm
Which equation is equivalent to 5√X+8=35? A. 3√x+8=175 B. X+8=343 C. X+8=21 D. X=351
Answer with explanation:
The equation whose equivalent equation we have to find is:
5 √X +8=35
Two equations are said to be equivalent,if they have same solution .
There is another definition of equivalent equation.Two equation are said to be equivalent ,also, if their solution are not same, but these equations appear Identical that is congruent but not Similar.
Option A: Equation ,3√X +8=175 is equivalent to 5√X+8=35.
Answer:
A
Step-by-step explanation
WHAT ARE THE SPECIFIC RULES FOR PROVING SIMILARITY IN TRIANGLES? EXPLAIN.
Answer:
AAA (Or even just two angles work too, since the last has to be the same no matter what) ASA and SSS
Step-by-step explanation:
I believe this is the same as before? As far as I know these are the main rules for proving similarity. (AAS and A** do not exist (Brainly won't let me say the two Ss), make sure no trick questions get you ;p)
I'm not sure if what you needed earlier was the relationships between angles to find them? Like to find Exterior Angles subtract <C from 180 = <EA?
identify the horizontal and vertical intercepts of the limacon represented by the equation r=7+3cos theta
Answer:
vertical intercepts: (7, pi/2) and (-7, pi/2)
horizontal intercepts: (10,0) and (-4,0)
Step-by-step explanation:
The horizontal and vertical intercepts are respectively; [(10,0) and (-4,0)] and [(7, π/2) and (-7, π/2)]
What are the horizontal and vertical intercepts?We are given the parametric equation;
r = 7 + 3 cos θ
Now, the vertical intercept will be when cos θ = 0 and that is at θ = π/2
Thus;
At θ = π/2, we have;
r = 7 + (3 * 0)
r = 7
But this will also give the same value of θ when r = -7
Thus; vertical intercepts are; (7, π/2) and (-7, π/2)
Horizontal intercept will occur when cos θ = 1. Thus;
At θ = 0, we have;
r = 7 + (3 * 1)
r = 10
Also, the lower interval will be when cos θ = -1. Which is 0 on the negative side. Thus
r = 7 + (3 * -1)
r = 4
Thus; horizontal intercepts are; (10,0) and (-4,0)
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The difference of two numbers is 20 and their product is 125, what is the answer?
find prime factors to get the inbetween numbers for product, and choose the one that has a difference of 20, and it should be 5 and 25, both requirements are met.
Answer:
Solution 1: The numbers are 25 and 5
Solution 2: The numbers are -5 and -25
Step-by-step explanation:
We have 2 unknown numbers, then we can define them as:
x: Unknown number 1
y: Unknown number 2
The problem states that "the difference of two numbers is 20". We can translate this to x - y = 20
We also know that "their product is 125". We can translate this to x . y = 125
Putting both equations together, we get the following system of equations
[tex]\left \{ {{x - y = 20} \atop {x y=125}} \right.[/tex]
Now, to solve this system of equations we can use the Substitution Method.
We can solve 1st equation for x, by adding y to both sides
x - y + y = 20 + y
x = 20 + y
We can substitute x by 20 + y on the 2nd equation
(20 + y) . y = 125
Applying distributive property on the left side
20y + y² = 125
Substracting 125 to both sides and rearranging the terms, we get
20y + y² - 125 = 125 -125
y² + 20y - 125 = 0
We can apply the quadratic equation attached to solve this (with a = 1, b = 20, c = -125).
( -20 ± √(20² - 4 . 1 . -125) ) / ( 2. 1 ) =
( -20 ± √(400 + 500) ) / ( 2) =
( -20 ± √900 ) / ( 2) =
( -20 ± 30 ) / ( 2) =
We get 2 results:
y1 = (-20 + 30) / 2 = 5y2 = (-20 - 30) / 2 = -25For each of these values of y, we can find the corresponding value of x:
x1 = 20 + y1 = 20 + 5 = 25 x2 = 20 + y2 = 20 + (-25) = -5
Find the circumferences of both circles to the nearest hundredth.
Answer:
28.27 inches for inner and 36.12 inches for outer
Step-by-step explanation:
2[tex]\pi[/tex]r
and 2 pi r with 4.5 +2.5 inches as the radius.
You're done :-)
A road bike has a wheel diameter of 622 mm. What is the circumference of the wheel? Use 3.14
The formula for finding the circumference of a circle is [tex]c=\pi *d[/tex] (where d is the diameter). So, simply plugging in 622 mm for d and 3.14 for pi, we find that c = 622 * 3.14 = 1953.08 mm.
Angle AOB and angle AOC are complementary angles. What is the measure of angle AOB if the measure of angle AOC is 37°?
A. 53°
B. 63°
C. 323°
D. 143°
90-37=53 complementary angles are 90 degrees
Answer:
Option A, 53°
Step-by-step explanation:
If the two angles are complimentary to each other then sum of these angles is equal to 90°.
∠AOB + ∠AOC = 90°
If ∠AOC = 37°
Then ∠AOB = 90° - ∠AOC
= 90° - 37°
= 53°
Option A 53° is the answer.
Use the x-intercept method to find all real solutions of the equation.
x^3-8x^2+9x+18=0
Answer:
a. [tex]x=-1,3,\:or\:6[/tex]
Step-by-step explanation:
The given equation is;
[tex]x^3-8x^2+9x+18=0[/tex]
To solve by the x-intercept method we need to graph the corresponding function using a graphing calculator or software.
The corresponding function is
[tex]f(x)=x^3-8x^2+9x+18[/tex]
The solution to [tex]x^3-8x^2+9x+18=0[/tex] is where the graph touches the x-axis.
We can see from the graph that; the x-intercepts are;
(-1,0),(3,0) and (6,0).
Therefore the real solutions are:
[tex]x=-1,3,\:or\:6[/tex]
Answer:
Use a graphing utility or a graphing calculator.
x = -1, 3, 6. (3 real solutions).
Step-by-step explanation:
The points of intersection on the x axis are the 3 solutions to the equation.
Jay ate 2/3 of a pizza. Dan ate 4 times the amount of jay ate . How much did dan eat
Answer:
Dan eat [tex]2\frac{2}{3}[/tex] pizzas
Step-by-step explanation:
Let
x-----> amount of pizza Jay ate
y-----> amount of pizza Dan ate
we know that
[tex]x=\frac{2}{3}[/tex] ----> equation A
[tex]y=4x[/tex] -----> equation B
substitute equation A in the equation B and solve for y
[tex]y=4(\frac{2}{3})=\frac{8}{3}[/tex]
Convert to mixed number
[tex]\frac{8}{3}=\frac{6}{3}+\frac{2}{3}=2\frac{2}{3}[/tex]
To find the amount Dan ate, we multiply the amount Jay ate (2/3) by 4, giving us 8/3, which is also known as 2 2/3 pizzas.
Jay ate 2/3 of a pizza. Dan ate 4 times the amount that Jay ate. To find out how much Dan ate, we need to multiply the fraction of the pizza that Jay ate by 4.
So, Dan ate 4 x (2/3) = 8/3 pizzas. Since 8/3 is greater than the whole, it can also be represented as 2 2/3 pizzas.
A shirt's sale price is marked $14.40, which is 60% off the original price. How many dollars was the original price of the shirt?
Answer:
The original price of the shirt is $36.
Step-by-step explanation:
Let us call p_o the original price of the shirt, then we know that $14.40 is 60% off [tex]p_o[/tex]; or $14.40 is 100% - 60% = 40% of [tex]p_o[/tex]. In other words,
[tex]\dfrac{40\%}{100\%}*p_o= \$ 14.40.[/tex]
This equation simplifies to
[tex]0.4p_o= \$14.40[/tex] (we evaluated 40/100 )
We divide both sides by 0.4 and get:
[tex]p_o= \dfrac{\$14.40}{0.4}[/tex]
[tex]\boxed{p_o = \$36.}[/tex]
The original rice of the shirt is $36.
Answer:
$36
Step-by-step explanation:
If the shirt is 60% off, it is currently .4 of the original price. Thus the original price was: $36
Hope this helped! :)
if y varies directly with x, find the constant of variation with x = 4 and y = - 24
A: -6
B: 4
C: -96
D: 6
Answer:
A: -6
Step-by-step explanation:
A direct variation is y =kx
We know x =4 and y = -24
Substituting in
-24 = 4k
Dividing by 4
-24/4 = 4k/4
-6 =k
The constant of variation is -6
Solve each exponential equation by using properties of common logarithms. Do not round the expression until the final answer. When necessary, round answers to the nearest hundredth.
17x = 89
x ≈ 1.58
x ≈ 5.24
x ≈ 63
Answer:
Option 1 - [tex]x\approx 1.58[/tex]
Step-by-step explanation:
Given : Exponential equation [tex]17^x=89[/tex]
To find : Solve exponential equation by using properties of common logarithms?
Solution :
Step 1 - Write the exponential equation,
[tex]17^x=89[/tex]
Step 2 - Take logarithm both side,
[tex]\log 17^x=\log 89[/tex]
Step 3 - Apply logarithmic property, [tex]\log a^x=x\log a[/tex]
[tex]x\log 17=\log 89[/tex]
Step 4 - Divide both side by log 17,
[tex]x=\frac{\log 89}{\log 17}[/tex]
Step 5 - Solve,
[tex]x=1.584[/tex]
[tex]x\approx 1.58[/tex]
Therefore, Option 1 is correct.
Hadley has a 1/2 kilogram of popcorn. She divides the popcorn into 3 equal bags. How many kilograms of popcorn are in each bag?
Answer:
1/6
Or in decimal form,
0.16
Let’s say the area of the map is 21 square inches. You want to make an enlarged map of Central Park to take with you on your journey. Describe how you can determine the area of the enlarged map. plzzzzzzz answer quickly I have 20 minutes.
Answer:
find the perimeter and multiply it to a decent size to see what you would need to do to enlarge the map
Step-by-step explanation:
can i get brainliest i need 5
The area of the enlarged map is gotten by multiplying the square of the scale factor by 21 in²
What is scaling?Scaling is the increase or decrease in the size of a figure by a scale factor so as to create an image.
If a map is enlarged by a scale factor. To determine the area of the enlarged map, if the original map has an area of 21 in²:
Area of enlarged map = scale factor² * 21 in²
The area of the enlarged map is gotten by multiplying the square of the scale factor by 21 in²
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What's the length of the hypotenuse of right ΔDEF shown?
A. 15
B. √87
C. √117
D. 12
Answer:
C
Step-by-step explanation:
a^2 + b^2 = c^2 so 6^2 + 9^2 = 36 + 81 = square root of 117
The length of the hypotenuse of right triangle ΔDEF is 10.82 units
What is Pythagorean theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
Here we have ,
to find hypotenuse of a right triangle:
The hypotenuse side can be found using Pythagoras theorem,
Therefore,
c² = a² + b²
where
c = hypotenuse
a and b are the other legs.
Therefore,
a^2 + b^2 = c^2
so 6^2 + 9^2
= 36 + 81
= square root of 117
=10.82
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How much would it cost to ship a package weighing 3.2 lbs at a cost of $2.69 per pound. Explain how you arrived at your answer.
Answer:
$8.608
Step-by-step explanation:
We are given that it costs $2.69 per pound to ship a package and we are to find how much would it cost to ship a package weighing 3.2 lbs.
To find this, we simply need to multiply the unit cost per pound with the weight of the package that is to be shipped.
Total cost to ship 3.2 lbs package = [tex] 3.2 \times 2.69 [/tex] = $8.608
(1 point) Suppose F⃗ (x,y)=−yi⃗ +xj⃗ F→(x,y)=−yi→+xj→ and CC is the line segment from point P=(4,0)P=(4,0) to Q=(0,5)Q=(0,5). (a) Find a vector parametric equation r⃗ (t)r→(t) for the line segment CC so that points PP and QQ correspond to t=0t=0 and t=1t=1, respectively. r⃗ (t)=r→(t)= <4,0>+t<-4,5> (b) Using the parametrization in part (a), the line integral of F⃗ F→ along CC is ∫CF⃗ ⋅dr⃗ =∫baF⃗ (r⃗ (t))⋅r⃗ ′(t)dt=∫ba∫CF→⋅dr→=∫abF→(r→(t))⋅r→′(t)dt=∫ab 20 dtdt with limits of integration a=a= 0 and b=b= 1 (c) Evaluate the line integral in part (b). 20 (d) What is the line integral of F⃗ F→ around the clockwise-oriented triangle with corners at the origin, PP, and QQ
The vector parametric equation for the line segment CC is <4,0> + t<-4,5>. The line integral of F⃗ along CC is 20. The line integral of F⃗ around the clockwise-oriented triangle with corners at the origin, P, and Q cannot be determined without additional information.
Explanation:(a) To find a vector parametric equation for the line segment CC, we can use the points P=(4,0) and Q=(0,5). We can represent the line segment CC as r(t) = <4,0> + t<-4,5>, where t is the parameter. This equation represents the line segment from P to Q, with t=0 corresponding to P and t=1 corresponding to Q.
(b) Using the parametrization in part (a), we can evaluate the line integral of F⃗ along CC. The line integral is given by ∫CF⃗ ⋅ dr⃗ = ∫baF⃗ (r⃗ (t))⋅r⃗ ′(t)dt. In this case, the line integral is ∫01-5yi⃗ +4xj⃗⋅-4i⃗ +5j⃗ dt
(c) Evaluating the line integral from part (b), we get 20.
(d) The line integral of F⃗ around the clockwise-oriented triangle with corners at the origin, P, and Q can be found using the Green's theorem. We can calculate it by subtracting the line integral along CP from the line integral along CQ. However, we would need more information to determine the path from C to the origin.
The swimming pool is open when the high temperature is higher than 20^\circ\text{C}20 ? C20, degree, C. Lainey tried to swim on Monday and Thursday (which was 333 days later). The pool was open on Monday, but it was closed on Thursday. The high temperature was 30^\circ\text{C}30 ? C30, degree, C on Monday, but decreased at a constant rate in the next 333 days.
Answer:
[tex]30-3d\leq 20[/tex]
Step by step explanation:
Let d represent the rate of temperature decrease in degrees Celsius per day from Monday to Thursday.
As temperature decreased at a constant rate in the next 3 days, so the rate of temperature will decrease 3d degree Celsius in 3 days.
We are told that the pool was open on Monday. The high temperature was [tex]30^{\circ}{\text{C}[/tex] on Monday. So the decrease in temperature from Monday to Thursday will be [tex]30-3d[/tex].
We have been given that the swimming pool is open when the high temperature is higher than [tex]20^{\circ}{\text{C}[/tex].
As the pool was closed on Thursday. This means that temperature on Thursday was less than or equal to 20 degree Celsius. We can represent this information in an inequality as:
[tex]30-3d\leq 20[/tex]
Therefore, the inequality [tex]30-3d\leq 20[/tex] can be used to determine the rate of temperature decrease in degrees Celsius per day, d, from Monday to Thursday.
Answer:
30-3d=20
Step-by-step explanation:
Trust me i got it correct
The quadrilateral is inscribed in a circle with opposite angles measuring 3x + 2 and 3x – 32. Find the value of x.
Question 5 options:
35
22
25
30
Answer:
[tex]x=35\°[/tex]
Step-by-step explanation:
we know that
In a quadrilateral inscribed in a circle , the opposite angles are supplementary
so
In this problem
[tex](3x+2)\°+(3x-32)\°=180\°[/tex]
Solve for x
[tex]6x-30\°=180\°[/tex]
[tex]6x=210\°[/tex]
[tex]x=210\°/6=35\°[/tex]
Answer:
A. 35
Step-by-step explanation:
I did this question earlier and A. 35 was the answer that was right for me. Hope this helps!
can i have some help please uwu?
use the iterative rule to find the 8th term in the sequence
an= 25-3n
a8=___
thankyou! ~bangtanboys7
hope im right but i think it 1 sorry if im wrong
Plug in 1, 2, 3, ... up to 8 into our sequence an.
You really just need to plug in 8, but plug in lower numbers to see the sequence emerge.
For example:
a1 means n equals 1, so a1 = 25 - (3 * 1) = 25 - 3 = 22
a2 means n equals 2, so a2 = 25 - (3 * 2) = 25 - 6 = 19
...
a8 means n equals 8, so a8 = 25 - (3 * 8) = 25 - 24 = 1
I hope this helps you understand the problem.
EDIT: You can also graph your iterative rule an on a graph. The values on the x axis correspond to the value of n and the y-axis would then correspond to the value of the sequence. Notice that a8 = 1, as shown in the attached picture.
Consider the equation below. f(x) = 4x3 + 18x2 − 216x + 3 (a) Find the intervals on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) (b) Find the local minimum and maximum values of f. local minimum value local maximum value (c) Find the inflection point. (x, y) = Find the interval on which f is concave up. (Enter your answer using interval notation.) Find the interval on which f is concave down. (Enter your answer using interval notation.)
Answer:
a) The increasing intervals would be from negative infinity to -6 and 3 to infinity. The decreasing interval would just be from -6 to 3
b) The local maximum comes at x = -6. The local minimum would be x = 3
c) The inflection point is x= -3/2
Step-by-step explanation:
To find the intervals of increasing and decreasing, we can start by finding the answers to part b, which is to find the local maximums and minimums. We do this by taking the derivatives of the equation.
f(x) = 4x^3 + 18x^2 - 216x + 3
f'(x) = 12x^2 + 36x -216
Now we take the derivative and solve for zero to find the local max and mins.
f'(x) = 12x^2 + 36x - 216
0 = 12(x^2 + 3x - 18)
0 = 12(x + 6)(x - 3)
x = -6 OR x = 3
Given the shape of a positive quartic function, we know that the first would be a maximum and the second would be a minimum.
As for the increasing, we know that a third power, positive function starts down and increases to the local maximum. It also increases after the local min. The rest of the time it would be decreasing.
In order to find the inflection point, we take a derivative of the derivative and then solve for zero.
f'(x) = 12(x^2 + 3x - 18)
f''(x) = 2x + 3
0 = 2x + 3
-3 = 2x
-3/2 = x
For analyzing the given function, find the first and second derivatives, and solve for critical points. Use these points to determine your intervals where the function is increasing, decreasing, concave up, or concave down. Also, find local minima, maxima, and inflection points.
Explanation:The subject of this question is Calculus, a branch of mathematics. We are asked to analyze the function f(x) = 4x3 + 18x2 − 216x + 3. To determine intervals where this function is increasing or decreasing, we'd differentiate the function to find its derivative, f'(x). We then set f'(x) equal to zero and solve for x. These solutions define the intervals. Similarly, for finding local minima, maxima and inflection points, we'd need to determine f''(x), the second derivative.
Given the nature of this question, specific calculations have been omitted. However, carrying out the steps of finding the first and second derivatives of the function, solving for critical points, and then using these points to define your intervals, will yield your final results.
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33/8 x 12/5 = ? Jdnnhdwjebcbraoq
Answer:
9.9
Step-by-step explanation:
First, you divide the 33 by 8 because that's the first part that goes together.
33/8=4.125
Second, divide 12 by 5.
12/5=2.4
Then, you multiply the 4.125 and the 2.4 together.
4.125 x 2.4 = 9.9
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➷To multiply a fraction, you can just multiply the top and multiply the bottom.
Top: 33 * 12 = 396
Bottom: 8 * 5 = 40
Fraction: 396/40
Simplify: 28 2/7
Or in decimal form: 9.9
Final answer:
33/8 * 12/5 = 28 2/7
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TROLLER
Choose the slope-intercept form of y 3 = 4(x – 5). Y = 4x – 8 y = 4x 2 y = 4x 17 y = 4x – 23
Answer:
y = 4x - 23
Step-by-step explanation:
To write the slope intercept form, convert the point slope form using the distributive property and inverse operations.
y + 3 = 4(x - 5) Distributive Property
y + 3 = 4x - 20 Subtract 3 from both sides
y = 4x - 23
Answer:
y=4x-23
Step-by-step explanation:
its correct i just did the assignment on linear functions.
manufacturer tests 1200 computers and finds that 9 of them have defects. Find the probability that a computer chosen at random has a defect. Round your answer to the nearest hundredth. Predict the number of computers with defects in a shipment of 15,000 computers. Round your answer to the nearest whole number.
Answer:
0.01.
113.
Step-by-step explanation:
Probability of a defect = 9/1200
= 0.0075
= 0.01 to the nearest hundredth.
Prediction of number of defects in 15,000 computers
= 15,000 * 0.0075
= 113.
The probability of choosing defective computers is 0.01 and the number of predictions is 113.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of samples
Given that manufacturer tests 1200 computers and finds that 9 of them have defects. Find the probability that a computer chosen at random has a defect.
The probability will be calculated as,
Probability of a defect = 9/1200
= 0.0075
= 0.01 to the nearest hundredth.
Prediction of the number of defects in 15,000 computers
= 15,000 * 0.0075
= 113.
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At lunch, 8 friends share 6 sandwiches equally what fraction of a sandwich does each friend get?
Please help me asap!!!
Answer:
C x=17
Step-by-step explanation:
The top and bottom sides have to be equal for the quadrilateral to be a parallelogram
2x-9 = x+8
Subtract x from each side
2x-9-x = x+8-x
x-9 = 8
Add 9 to each side
x-9+9=8+9
x=17
➷ Opposite lengths in a parallelogram are equal
Therefore:
2x - 9 = x + 8
Add 9 to both sides:
2x = x + 17
Subtract x from both sides:
x = 17
Your answer is option c.
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