Answer:
$990 per unit.
Step-by-step explanation:
The Unit Cost (C) and Unit Revenue R from the production and sale of x units are related by the function:
[tex]C=\dfrac{R^2}{220000} +3221[/tex]
We are required to find the rate of change of revenue per unit when the cost per unit is changing by $9 and the revenue is $1,000.
Rate of Change of C,
[tex]\dfrac{dC}{dt}=\dfrac{R}{110000} \dfrac{dR}{dt} \\\dfrac{dC}{dt}=\$9, R=\$1000\\9=\dfrac{1000}{110000} \dfrac{dR}{dt}\\\dfrac{dR}{dt}=9 \div \dfrac{1000}{110000}\\=9 X \dfrac{110000}{1000}\\\dfrac{dR}{dt}=\$990 $ per unit$[/tex]
The Revenue is changing at a rate of $990 per unit.
The problem is solved by first finding the derivative of the given equation to determine the rate of change. Given that the cost per unit is changing by $9, we substitute this in the derivative equation to get the revenue. Real-world applications of such problems help understand the concepts of marginal revenue and marginal cost.
Explanation:As per the equation C = R2/220000 + 3221, we first need to find the derivative to determine the rate of change. So, C'(R) = 2R/220000 where C' represents the derivative of the cost with respect to revenue.
Given that the cost per unit is changing by $9, we can represent this as C' = 9 and solve for R using the derivative equation. Hence, R = sqrt(220000 * 9 / 2) = $1000. Therefore, the rate of change of revenue per unit when the cost per unit is changing by $9 and the revenue is $1,000 is found by substituting the revenue value into derivative equation.
These types of problems demonstrate how rates of change can be evaluated using calculus concepts in real-world applications such as understanding marginal revenue and marginal cost in economics and business studies.
Learn more about Rate of Change here:https://brainly.com/question/31226174
#SPJ3
Volume with cubes with fraction lengths
How many cubes with side lengths of
cm does it take to fill the prism?
Answer:
You could fit 48 cubes with side lengths of 1/3 cm inside a rectangular prism with dimensions of 1 cm X 2 2/3 cm X 2/3 cm.
An ice cream cone has a height of 6 inches and a radius of 2 inches. A scoop of ice cream sits on the top of the cone. The scoop is a sphere with a diameter of 4 inches. If the entire scoop of frozen yogurt melts into the cone, will the cone overflow? Show all your work and explain your reasoning.
Answer:
Yes, it will overflow, because the volume of the scoop of ice cream is higher than the volume of the cone.
Step-by-step explanation:
To know if the cone will overflow when the entire scoop of frozen yogurt melts, we need to compare the volume of the scoop and the volume of the cone: if the volume of the scoop is higher, it will overflow.
The volume of the cone is:
V_cone = (1/3)*pi*r^2*h
Where V_cone is the volume, r is the radius and h is the height. So:
V_cone = (1/3)*pi*2^2*6 = 25.1327 in3
The volume of a sphere is:
V_sphere = (4/3)*pi*r^3
Where V_sphere is the volume and r is the radius. If the diameter is 4, the radius is 4/2 = 2. So:
V_sphere = (4/3)*pi*2^3 = 33.5103 in3
The volume of the sphere is higher, so the cone will overflow.
The volume of the melted ice cream scoop[tex](\( 33.51032 \, \text{cubic inches} \))[/tex] is greater than the volume of the cone [tex](\( 25.13272 \, \text{cubic inches} \))[/tex] the cone will overflow if the entire scoop of ice cream melts into it.
Step 1: Volume of the Cone
The formula for the volume of a cone is:
[tex]\[V_{\text{cone}} = \frac{1}{3} \pi r^2 h\][/tex]
where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height.
Given:
[tex]\[r = 2 \, \text{inches}, \quad h = 6 \, \text{inches}\][/tex]
Substitute these values into the formula:
[tex]\[V_{\text{cone}} = \frac{1}{3} \pi (2)^2 (6)\][/tex]
[tex]\[V_{\text{cone}} = \frac{1}{3} \pi (4) (6)\][/tex]
[tex]\[V_{\text{cone}} = \frac{1}{3} \pi (24)\][/tex]
[tex]\[V_{\text{cone}} = 8 \pi \, \text{cubic inches}\][/tex]
Step 2: Volume of the Ice Cream Scoop
The formula for the volume of a sphere is:
[tex]\[V_{\text{sphere}} = \frac{4}{3} \pi r^3\][/tex]
where [tex]\( r \)[/tex] is the radius of the sphere.
Given that the diameter of the sphere is [tex]4\ inches[/tex], the radius [tex]\( r \)[/tex] is:
[tex]\[r = \frac{4}{2} = 2 \, \text{inches}\][/tex]
Substitute this value into the formula:
[tex]\[V_{\text{sphere}} = \frac{4}{3} \pi (2)^3\][/tex]
[tex]\[V_{\text{sphere}} = \frac{4}{3} \pi (8)\][/tex]
[tex]\[V_{\text{sphere}} = \frac{32}{3} \pi \, \text{cubic inches}\][/tex]
Step 3: Compare the Volumes
The volume of the cone:
[tex]\[V_{\text{cone}} = 8 \pi \, \text{cubic inches}\][/tex]
The volume of the ice cream scoop:
[tex]\[V_{\text{sphere}} = \frac{32}{3} \pi \, \text{cubic inches}\][/tex]
Let's convert them to decimal form for easier comparison:
[tex]\[V_{\text{cone}} = 8 \pi = 8 \times 3.14159 = 25.13272 \, \text{cubic inches}\][/tex]
[tex]\[V_{\text{sphere}} = \frac{32}{3} \pi = \frac{32}{3} \times 3.14159 = 33.51032 \, \text{cubic inches}\][/tex]
Write the equation in slope-intercept form of a line that has a slope of One-third and passes through the point (-6, 0).
y = one-third x
y = one-third x minus 6
y = one-third x minus 2
y = one-third x + 2
Slope-intercept form: y = mx + b
(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)
You know:
m = [tex]\frac{1}{3}[/tex] So substitute/plug it into the equation
y = mx + b
[tex]y=\frac{1}{3} x+b[/tex] To find b, plug in the point (-6, 0) into the equation, the isolate/get the variable "b" by itself
[tex]0=\frac{1}{3} (-6)+b[/tex]
0 = -2 + b Add 2 on both sides to get "b" by itself
0 + 2 = -2 + 2 + b
2 = b
[tex]y=\frac{1}{3} x+2[/tex] Your answer is the 4th option
The equation in slope-intercept form is y = 1/3x + 2
Equation of a lineThe equation of the line in point slope form is expressed as:
y-y1 = m(x-x1)where:
m is the slope = 1/3(x1, y1) is the point on the line = (-6, 0)Substitute:
y - 0 = 1/3(x+6)
Write in slope-intercept form
y = 1/3(x+6)
3y = x + 6
y = 1/3x + 6/3
y = 1/3x + 2
Hence the equation in slope-intercept form is y = 1/3x + 2
Learn more on slope-intercept here: https://brainly.com/question/19440459
s) An e-mail lter is planned to separate valid e-mails from spam. The word free occurs in 50% of the spam messages and only 3% of the valid messages. Also, 20% of the messages are spam. Determine the following probabilities: (a) The message contains the word free. (b) The message is spam given that it contains free. (c) The message is valid given that it does not contain free.
Answer:
A) P(F) = 0.124
B) P(S|F) = 0.8065
C) P(V|F^(c)) = 0.886
Step-by-step explanation:
Let us denote as follows;
F = Message contains word free
S = message is spam
V = message is valid
From the question, we are given that;
The probability that word free occurs in spam messages;P(F|S) = 50% = 0.5
The probability of the valid messages that contain free; P(F|V) = 3% = 0.03
Spam messages; P(S) = 20% = 0.2
Valid messages; P(V) = 1 - 0.2 = 0.8
A) From rule of total probability ;
probability that the message contains the word free is given as;
P(F) = P(F|S)•P(S) + P(F|V)•P(V)
P(F) = (0.5 x 0.2) + (0.03 x 0.8)
P(F) = 0.124
B) From Baye's theorem;
probability that the message is spam given that it contains free is given as;
P(S|F) = P(F|S)•P(S)/P(F)
P(S|F) = (0.5 x 0.2)/0.124
P(S|F) = 0.8065
C) From combination of complement rule and Baye's theorem;
probability that the message is valid given that it does not contain free is given as;
P(V|F^(c)) = P(F^(c)|V)•P(V)/P(F^(c))
Thus,
P(V|F^(c)) = [(1 - P(F|V))•P(V)]/(1 - P(F))
P(V|F^(c)) = ((1 - 0.03)•0.8)/(1 - 0.124)
P(V|F^(c)) = 0.776/0.876
P(V|F^(c)) = 0.886
What is the area of the following figure?
Answer:
16.56
Step-by-step explanation:
The area of the square is 2 × 2
The area of the circle is-
A=πr²
A=3.14 × 2²
A=3.14 × 4
A=12.56
You don't need to divide it by half because there are two half circles so it would be a whole circle
12.56 + 4 = 16.56
Sorry if it is wrong
Answer:
Area of square =side( square)
(2) square
4
diameter= 2
radius=2/2
= 1
Area of circle=πrsquare
22/7×1×1
3.14
Area of figure= Area of square+area of circle
4+3.14
7.14
What is the surface area of the cube shown?
6.5 lenthe 6.5 hieght
Answer:A=253.5
Step-by-step explanation:
In words, the surface area of a cube is the area of the six squares that cover it. The area of one of them is a*a, or a 2 . Since these are all the same, you can multiply one of them by six, so the surface area of a cube is 6 times one of the sides squared.
Answer:
253.5
Step-by-step explanation:
if the side lengths of the cube is 6.5 then the surface area of one side is 42.25. Since the 6 sides of the cube are all the same you can multiply this by 6 to get 253.5
The length of a rectangle is 14 centimeters and the width is 5 centimeters.
A similar rectangle has a width of 2.5 centimeters.
What is the length of the second rectangle in centimeters?
Answer:
7
Step-by-step explanation:
One side is half of the other (5/2.5=2)
So 14/2=7
original price? percent of discount: 80% sales price: $90
Answer:
18.00 dollars
Step-by-step explanation:
message me if you need help. Or this was not the answer you were looking for.
how many swimmers are holding exaclty 3 toy whales?
Answer:
3 swimmers
Step-by-step explanation:
The archway to the entrance of an art gallery can be model by y= -1/3(x-5)(x+5) where x and y are measured in feet. The x-axis represents the floor. Find the width of the arch at floor level.
Answer:
x=5 feet
Step-by-step explanation:
At floor level y=0
If the expression is:
[tex]0=1/3(x-5)(x+5)\\0=1/3(x^2-25)\\0=1/3x^2-25/3\\25/3=1/3x^2\\25=x^2\\x=5[/tex]
But, with the negative sign, the answer is x= 5i (where i is imaginary)
Final answer:
The width of the arch at floor level is found by determining the points where the parabola intersects the x-axis, which are at x = 5 and x = -5. The width is the distance between these points, which is 10 feet.
Explanation:
To find the width of the arch at floor level, we need to determine the distance between the two points where the parabola represented by the equation y = -1/3(x-5)(x+5) intersects the x-axis. The x-axis represents the floor, and the points of intersection occur where y is equal to 0.
Setting the equation to 0 gives:
0 = -1/3(x-5)(x+5)
By solving for x, we get x = 5 and x = -5, which are the points where the parabola intersects the x-axis. The distance between -5 and 5 on the x-axis is 10 feet, so the width of the arch at floor level is 10 feet.
The green turtle, Monique, traveled 250 centimeters in 8.7 minutes. The calculation that will give you the speed as a unit rate is The green turtle’s speed as a unit rate is centimeters per minute if the answer is rounded to the nearest tenth
Answer:
About 28.74 centimeters per minute
Step-by-step explanation:
250 centimeters / 8.7 minutes = ~28.74 centimeters per minute
Answer:
the correct answer for the first question is: 250 divided by 8.7
The second one is: 28.7 cm/min
Step-by-step explanation:
I did edgenuity
Carrie is finding the set of even numbers within the set of prime numbers.
Of the sets described, which is the universal set?
Group of answer choices
all real numbers
even numbers
prime numbers
all integers
Answer:
Universal set ( U ) = Set of prime numbers
Step-by-step explanation:
Solution:-
- All even numbers are numbers that are divisible by 2 or have at-least an LCM of 2 associated with that number.
- All prime numbers are divisible by 1 and the number itself. Which 2 which is divisible by 1 and itself is a prime number and an even number.
- Considering only positive integers.
- Carrie is looking for a set of even numbers within the set of prime number.
- As stated above, the only integer, 2, is common to both prime number set and even number set.
- Hence, universal set ( U ) should be prime numbers.
- Universal set ( U ) = Set of prime numbers.
Answer:
c. prime numbers
Step-by-step explanation:
edg 2020
Is 7, 20, 25 a right triangle?
Answer:
The answer to your question is below
Step-by-step explanation:
Process
To answer if they are right triangles or not use the Pythagorean theorem which states that the square of the hypotenuse equals the sum of the square of the legs.
a) 25² = 20² + 7²
625 = 400 + 49
625 ≠ 449 It is not a right triangle
b) 26² = 24² + 10²
676 = 576 + 100
676 = 676 it is a right triangle
c) 13² = 8² + (√10)²
169 = 64 + 10
169 ≠ 74 it is not a right triangle
d) 52² = 48² + 20²
2704 = 2304 + 400
2704 = 2704 it is a right triangle
The electronic sign that showed the speed of motorists was installed on a road.the line plots below show the speeds of some motorists before and after the sign was installed. based on these data which statement is true about the speeds of motorists after the sign was installed?
Answer:
The correct option is;
A. The mean speed and the range of the speeds of the motorists decreased
Step-by-step explanation:
Here we have the speeds given as
Before Sign Installation
Speed Frequency
20 1
24 1
25 4
30 2
35 2
38 1
40 1
∑ 212 12
Mean = 17.67
Median (25 + 30)/2 = 27.5
Range = 40 - 20 = 20
After Sign Installation
Speed Frequency
20 1
22 1
25 4
28 1
30 3
35 2
∑ 160 12
Mean = 160/12 = 13.33
Median = (25+28)/2 = 26.5
Range = 35 - 20 = 15.
Therefore, the mean speed and the range of the speeds of the motorists decreased
PLEASE HELP IT IS VERY URGENT!!
Please help to find (b) (c) (d)
(b) is in the picture
(c) Given that the ratio of PL to LF is 2 : 3, find the ratio of the area of triangle PLM to the area of triangle PFG.
(d) A circle is drawn by using FG as the diameter. Explain if the point M lies on the circumference of this circle.
Step-by-step explanation:
(c)
[tex] In\: \triangle PLM \: \&\: \triangle PLM\\
\angle PLM \cong\triangle PFG.. (corresponding \:\angle s) \\
\angle LPM \cong \angle FPG.. (common \: \angle s) \\
\therefore \triangle PLM\sim\triangle PFG.. (by\: AA\:Postulate) \\
PF = PL + LF = 2 + 3 = 5[/tex]
By area of similar triangle theorem:
[tex] \frac {A(\triangle PLM)}{A(\triangle PFG)}= \frac{PL^2}{PF^2}\\
\therefore \frac {A(\triangle PLM)}{A(\triangle PFG)}= \frac{2^2}{5^2}\\
\therefore \frac {A(\triangle PLM)}{A(\triangle PFG)}= \frac{4}{25}\\
A(\triangle PLM)\: :\: A(\triangle PFG) = 4 \: :\: 25
[/tex]
Marta bought a paperweight in the shape of a cone. The radius was 10 centimeters and the height 9 centimeters. Find the volume. Round to the nearest tenth.
Answer:
The volume of the paper weight is 942.8 cubic cm.
Step-by-step explanation:
We are given the following in the question:
Dimensions of paperweight :
Radius, r = 10 cm
Height,h = 9 cm
Volume of paper weight = Volume of cone
[tex]V= \dfrac{1}{3}\pi r^2 h[/tex]
where r is the radius and h is the height of the cone.
Putting values, we get,
[tex]V = \dfrac{1}{3}\times \dfrac{22}{7}\times (10)^2\times 9\\\\V = 942.8\text{ cubic cm}[/tex]
Thus, the volume of the paper weight is 942.8 cubic cm.
The volume is 942.5 [tex]cm^{3}[/tex].
To calculate the volume of a cone, you can use the formula:
V = (1/3)πr²h
where:
V is the volumer is the radius of the baseh is the height of the cone1. For Marta's paperweight with a radius of 10 centimeters and a height of 9 centimeters, you substitute the values into the formula as follows:
V = (1/3)π(10 cm)²(9 cm)
2. First, calculate the base area:
(10 cm)² = 100 cm²
3. Then, multiply by the height:
100 cm² × 9 cm = 900 cm³
4. Finally, multiply by (1/3)π:
V = (1/3)π × 900 cm³ ≈ 942.5 cm³
Therefore, the volume of the cone is approximately 942.5 [tex]cm^{3}[/tex], rounded to the nearest tenth.
8. The mean of the winning scores of a bowling tournament over the last 10 years was 279, with a standard deviation of 3. Considering that the scores were in a normal
distribution, how many scores were below 282?
For a normal distribution with a mean of 279 and a standard deviation of 3, 50% of the scores are below 282, given that 282 is one standard deviation above the mean.
Explanation:In a normal distribution, 68.2% of values fall within one standard deviation of the mean,
95.4% fall within two standard deviations, and 99.7% fall within three standard deviations. Given that the bowling scores have a mean of 279 and a standard deviation of 3, a score of 282 will fall one standard deviation above the mean.
Since 68.2% of scores fall within one standard deviation around the mean, half the scores will fall below the mean and the other half will fall above it. Thus, 50% of the scores will fall below 282. In case of a normal distribution that has no skew, the mean, median, and mode are equal, which implies that half the values fall below the mean and half the values fall above it.
Learn more about normal distribution here:https://brainly.com/question/34741155
#SPJ12
Landons car used 10 gallons of gas to drive 220miles. At what rate does his car use gas in gallons per mile
Answer:
1/22 gallons per mile
Step-by-step explanation:
We want to find gallons per mile, so we take the gallons and divide by the mile
10gallon/ 220 mile
1/22 gallons per mile
Answer:
1/22 gallons per mile
Step-by-step explanation:
50 pts if correct and will mark brainliest
Answer:
see below
Step-by-step explanation:
Tally question
There are 6 marks for A out of 30 total
6/30 = 1/5
Sample space question
{run 50 run 100 run 150, swim 50 swim 100 swim 150}
We have to list all the possible choices that the spinners can land
run 50
swim 100
150
There are 2*3 = 6 choices
Tomas Game
1/36
The normal die has 1,2,3,4,5,6
P(5) = Number of 5's / total number of numbers = 1/6
Then roll another 5
P(5) = Number of 5's / total number of numbers = 1/6
P(5,5) = 1/6*1/6 = 1/36
Joe game
1/4
1,2,3,4,5,6 triangle, square
P(0dd) = {1,3,5}/ 6 numbers = 3/6 = 1/2
P (square) = square/ total = 1/2
Coin
1/2
HT HH TH TT
We want one heads and one tails
2 of the four
2/4 = 1/2
P (odd,square) = P(odd) * P(square) = 1/2*1/2 = 1/4
Answer:
1) ⅕
2) sample space: D
3) 1/36
4) P(odd & square) = ¼
5) ½
Step-by-step explanation:
1) P(A) = 6/30 = 1/5
2) sample space is the collection of all possible outcomes
{activity & distance}
3) P(5 & 5) = 1/6 × 1/6
1/36
4) odd: 1,3,5
P(odd) = 3/6 = 1/2
P(square) = 1/2
1/2 × 1/2 = 1/4
5) P(H & T) = 1/2 × 1/2 = 1/4
2 × 1/4 = 1/2
7n=30 what is the n
Answer:
n=4.28571429
Step-by-step explanation:
Solve for n by isolating it
7n=30
Divide both sides by 7 to "reverse" the multiplication being done to n
n=4.28571429
Answer "n" is 4 and 2 sevenths
Step-by-step explanation:
7n = 30 get "n" alone
7n / 7 = 30 / 7
n = 4 and 2/7
Write an equation to find the amount of money in Pertro’s account if the total of all their accounts is $148.
Answer:
P = 2(21 + 3)
= 2(24)
=$48
Step-by-step explanation:
Add them all up.
s + 2(s+3) + 4s-5 = 148
s + 2s + 6 + 4s - 5 = 148
Group all s together and all numbers together 7s + 1 = 148
7s = 147
Divide by 7
s = 21
Plug s=21 back in for Petro
To find the amount of money in Pertro's account, use the equation x = 148 - (y + z), where y and z represent the amounts in the other two accounts.
Explanation:The equation to find the amount of money in Pertro's account can be written as:
x + y + z = 148
where x, y, and z represent the amounts in different accounts. To find the amount in Pertro's account, we need to set up another equation using the information given. If we know that the total of all accounts is $148 and we want to find the amount in Pertro's account (x), we can write:
x = 148 - (y + z)
where y and z represent the amounts in the other two accounts.
Learn more about Equation to find amount of money in Pertro's account:https://brainly.com/question/17595716
#SPJ2
Troy says that 0.9>0.90 because tenths are greater than hundredths.Keith says that 0.9<0.90 bra side 90 is greater than 9. Is either Troy or Keith correct?Explain
Answer:
Neither Troy nor Keith is correct.
Step-by-step explanation:
Neither Troy nor Keith is correct.
The value 0.9 is the same as the value 0.90.
The zeros after a decimal point are always insignificant unless they are followed by a number different from zero.
0.90 = 0.900 = 0.9000 = 0.90000 = ... = 0.9000000000
and all these can be easily written as 0.9, as the zeros after the decimal point do not change the value.
But 0.901, 0.9000004, 0.90002, and so on are all different, and the zeros are relevant, as they are followed by numbers different from zero.
Answer:
None of them is correct
0.9=0.90
Step-by-step explanation:
0.9>0.90 (not valid)
0.9<0.90 (not valid)
1. when dealing with decimals, the digits on the left hand side of the decimal point is a whole number.
The digits at the right hand side are considered individually.
2. the place value of the first digit is tenth, next is hundredth
3. if the last digits at the right hand side of the decimal point are zeros, then they are insignificant having no place value.
Hence, 0.9 is not greater 0.90
0.9 is not also less than 0.90,
because, the '0' at the right hand side of the decimal point, immediately after 9 is insignificant.
Therefore, 0.9=0.90
A rectangle has an area of 0.24 square meter what is one possibility for the length and width of the rectangle?
S=wl
0.24=wl
it can be w=0,6 and l=0,4 or w=0,4 and l=0,6
Hi guys!
Im having trouble on the working out for this question could you please explain how to work it out?
Two-thirds of the jelly beans in a jar are black. There are 96 jelly beans in the jar. How many of them are black?
Thanks! Have an awesome day!
Answer:
64
Step-by-step explanation:
The first thing I would do is break down the question and put it into number form. 2/3 of the jelly beans are black. You want to find out the number of jelly beans out of 96 are black. I can try my best to explain how to do this.
Divide the number of jelly beans (96) by the denominator (3) to find out how many jelly beans would be 1/3. This is 32. To find out how many are 2/3 you would multiply the 1/3 (32) by 2 to find that it is 64.
To check your work simplify this. 64/96 and it should equal 1/3. Or put it in your calculator to find that it equals .667 which is the decimal form of 2/3.
what are the 5 perfect prime numbers between 50 and 140
Answer:
61 67 71 73 79
There you go:)
Answer:
53, 59, 61, 67, 71.
Step-by-step explanation:
It goes on....
53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109
, 113, 127, 131, 137, 139
I hope this helps :)
use the protractor to measure this angle
To measure an angle using a protractor, follow these steps: Place the center point of the protractor at the vertex, align the base line with one side, and read the measure where the other side intersects the scale.
Explanation:To measure an angle using a protractor, follow these steps:
Place the center point of the protractor at the vertex of the angle.Align the base line of the protractor with one of the sides of the angle.Read the measure on the protractor where the other side of the angle intersects the measure scale.For example, if the measure reads 45 degrees, then the angle is 45 degrees.
Learn more about Protractor measurement here:https://brainly.com/question/29898085
#SPJ12
Find the center, vertices, and foci for the ellipse 25x^2 + 64y^2 = 1600
Answer:
The answer to your question is below
Step-by-step explanation:
Data
Equation 25x² + 64y² = 1600
Process
1.- Divide all the equation by 1600
25x²/1600 + 64y²/ 1600 = 1600/1600
-Simplify
x²/64 + y²/ 25 = 1
2.- Equation of a horizontal ellipse
[tex]\frac{x^{2} }{a^{2}} + \frac{y^{2}}{b^{2}} = 1[/tex]
3.- Find a, b and c
a² = 64 a = 8
b² = 25 b = 5
-Calculate c with the Pythagorean theorem
a² = b² + c²
-Solve for c
c² = a² - b²
-Substitution
c² = 8² - 5²
-Simplification
c² = 64 - 25
c² = 39
-Result
c = √13
4.- Find the center
C = (0, 0)
5.- Find the vertices
V1 = (-8, 0) V2 = (8, 0)
6.- Find the foci
F1 = (-√13, 0) F2 = (√13, 0)
The center of the ellipse is (0,0), the vertices are (5.657, 0) and (-5.657, 0), and the foci are (3.317, 0) and (-3.317, 0).
Explanation:The given equation of the ellipse is 25x^2 + 64y^2 = 1600.
To find the center of the ellipse, we can rewrite the equation in standard form: x^2/32 + y^2/25 = 1. The center is (0,0) since the x and y terms are squared and have the same coefficients.
To find the vertices of the ellipse, we can calculate the distance from the center to the major axis. The length of the major axis is 2*a, where a is the square root of the denominator of the x term. In this case, a = sqrt(32) ≈ 5.657. So the vertices are (5.657, 0) and (-5.657, 0).
To find the foci of the ellipse, we can calculate the distance from the center to the foci. The length of the foci is 2*c, where c is the square root of the difference between the squares of a and b (sqrt(32-25) ≈ 3.317). So the foci are (3.317, 0) and (-3.317, 0).
Learn more about ellipse here:https://brainly.com/question/33868440
#SPJ3
The graph of which function has an axis of symmetry at x = 3?
f(x) = x2 + 3x + 1 On a coordinate plane, a parabola opens up. It goes through (negative 4, 5), has a vertex at (negative 1.75, 6.75), and goes through (1, 5).
f(x) = x2 – 3x – 3 On a coordinate plane, a parabola opens up. It goes through (negative 2, 7), has a vertex at (1.75, 5), and goes through (5, 7).
f(x) = x2 + 6x + 3 On a coordinate plane, a parabola opens up. It goes through (negative 6, 3), has a vertex at (negative 3, negative 6), and goes through (0, 3).
f(x) = x2 – 6x – 1 On a coordinate plane, a parabola opens up. It goes through (0, negative 1), has a vertex at (3, negative 10), and goes through (6, 0).
Answer: fax 2 F (y axis) +4.5 =23x2=46
Step-by-step explanation:
Answer:
its D
Step-by-step explanation:
Simplify:
7a² + ab - 4a² + 2a + 8ba + 4a
Group terms
= (7a² - ?a²) + (ab + 8ba) + ( ? + 4a)
Answer:
simplify question is 3a^2 +6a+9ab
Step-by-step explanation:
(5 x 5) + (6 × 7) - 50 =?
Answer:
17
Step-by-step explanation:
5 x 5 is 25
6 x 7 42
25 + 42 is 67
67 - 50 = 17
17 is your answer :)