Answers
Ok, so
We want to find the equation of an ellipse centered at the origin with a horizontal major axis of 8 units and a minor axis of 6 units.
For this, let's remember the form of the equation of an ellipse:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]Where the center of the ellipse is located at the point (h,k).
If the ellipse is centered at the origin, then, h=0 and k=0, so the form of our equation will be:
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]Now, we're given that our ellipse has a horizontal major axis of 8 units and a minor axis of 6 units. Since the major and minor axis are given by the parameters 2a and 2b, then, a=4 and b=3. the greater number will divide the x² term and a>b.
So, the equation of this ellipse is:
[tex]\frac{x^2}{16}+\frac{y^2}{9}=1[/tex]The graph of this ellipse will be something like:
Related Questions
Content attribution QUESTION 11.1 POINT Find the perimeter of the figure.
Answers
Let us assume that the dimension of each square is 1 unit by 1 unit
The figure is a rectangle. The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(length + width)
By counting the squares,
length = 7 * 1 = 7 units
width = 2 * 1 = 2 units
Perimeter = 2(7 + 2)
Perimeter = 18 units
The price of the item has risen to $133 today. Yesterday it was $95. Find the percentage increase.
Answers
Answer:
40%
Step-by-step explanation:
133-95=
38/95=
40%
Find the 12thterm of the following geometric sequence.5, 10, 20, 40,
Answers
5, 10, 20, 40, . . .
SolutionStep1 Find the common ratio(r)[tex]r=\frac{a_2}{a_1}=\frac{10}{5}=2[/tex]Step 2The geometric sequence formula
[tex]a_n=a_1\times r^{n-1}[/tex]Step 3[tex]\begin{gathered} r=2,\text{ } \\ a_1=5 \\ n=12 \end{gathered}[/tex]Step 4[tex]\begin{gathered} a_{12}=5\times2^{12-1} \\ a_{12}=5\times2^{11} \\ a_{12}=10240 \end{gathered}[/tex]The final answer The 12th term of the geometric sequence is 10240PLEASE HELP! ITS DUE SOON AND I LOST MY CALULATER I HAVE 7 QUESTIONS I NEED HELP WITH!!!!! WILL ONLY LET ME UPLOAD 5! BUT ILL ADD THAT IN AN OTHER QUESTIO I HAVE 35 MINTUTES LEFT TO GET THIS DONE! PLEASE HELP!! WILL GET 100 POINTS! MANY THANKS!!!!
Answers
Answer:
Step-by-step explanation:
d
c
a
b i think
a
work for question #4:
Side a = 30.27382
Side b = 30
Side c = 27.83241
Angle ∠A = 63° = 1.09956 rad = 7/20π
Angle ∠B = 62° = 1.0821 rad
Angle ∠C = 55° = 0.95993 rad
Odalis invierte $1200 en una cuenta y gana 7% anual ¿ su inversión crecerá a Qué cantidad en 5 años
Answers
$1683.06
1) Desde que Odalis invierte $1200 podemos escribir
$1200
7% anualmente ( 0.07)
Tiempo: 5 anos
2) Vamos aplicar esta formula:
[tex]\begin{gathered} A=P(1+\frac{0.07}{1})^{1\cdot5} \\ A=1200(1+\frac{0.07}{1})^{1\cdot5} \\ A=1200(1.07)^5 \\ A=\text{ }1683.06 \end{gathered}[/tex]Considerando una capitalización anual, tenemos al termino un valor de $1683.06
PACKAGING A juice manufacturer is creating new cylindrical packaging. The height of the cylinder is to be 3 inches longer than the radius of the can. The cylinder is to have a volume of 628 cubic inches. Use 3.14 for π.
Answers
The radius and height of a cylinder with volume 628 cubic inches are 5 inches and 8 inches respectively.
Volume of a CylinderThe volume of a given cylinder with radius r and height h can be calculated using the formula πr^2h.
In this question, we have the volume of the cylinder given as 628 cubic inches. The height of the cylinder is 3 inches longer than the radius of the can.
Lets assume the radius of the cylinder is equal to r
Substituting the values into the equation;
[tex]v = \pi r^2 h\\628 = \pi r^2 (r + 3)\\628 = 3.14* r^2(r+3)\\r = 5[/tex]
The radius of the equation is 5 inches and the height of the equation is 8 inches.
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Ada drank 5/8 of a glass of water. What percentage of a glassof water did Ada drink?%Pls help
Answers
Answer:
[tex]\begin{gathered} \frac{5}{8}=\frac{x}{100} \\ \therefore\rightarrow \\ x=\frac{100\cdot5}{8}=\frac{500}{8}=62.5\text{ percent} \end{gathered}[/tex]Therefore he drank 62.5% of the glass. a little bit above half.
Answer:62.5 percentage of water
Step-by-step explanation: divide 5 by 8 the whole, then multiply by 100 to get the percentage
I need help with Algebra 2 Simplify(9x+8)-(x+4)
Answers
Given the expression:
[tex]\mleft(9x+8\mright)-(x+4)[/tex]Remove brackets
[tex]9x+8-x-4[/tex]Collect like terms and evaluate
[tex]\begin{gathered} 9x-x+8-4 \\ =8x+4 \end{gathered}[/tex]please help me I DONT REMEMBER HOW TO DO THIS
Answers
Answer:
The answer is 6.72 x 10⁷
Step-by-step explanation:
The answer is 6.72 x 10⁷ because I solved it and I got this answer.
Kim bought an outfit that cost $24.50. She had to pay 6.55% sales tax.What was the total amount of her purchase?a. $1.60b. $26.10c. $28.24d. $31.05
Answers
Given
Cost = $24.50
Tax = 6.55%
Procedure
The total cost of the product would be the cost plus the value of taxes.
[tex]\begin{gathered} P=C+C\cdot T \\ P=24.50+24.50\cdot6.55\text{ \%} \\ P=26.10 \end{gathered}[/tex]The total amount would be $26.10
If xy + 7ey = 7e, find the value of y'' at the point where x = 0.
Answers
Answer:
Please read my updated answer.
I am wasn't sure what you were asking so here and 2 answers.
1st answer [tex]y=\frac{1}{e}[/tex]
2nd answer [tex]\frac{dy}{dx}=-\frac{y}{x+7e}[/tex]
Step-by-step explanation:
[tex]xy+7ey=7[/tex]
[tex]when \\ x=0[/tex]
Substitute [tex]0[/tex] for [tex]x[/tex] then simplify.
[tex](0*y)+7ey=7\\ 0+7ey=7\\ 7ey=7[/tex]
Divide each term in [tex]7ey=7[/tex] by [tex]7e[/tex] and simplify.
[tex]\frac{7ey}{7e}=\frac{7}{7e}[/tex]
Cancel the common factor of [tex]7[/tex] on the left side.
Rewrite the expression.
[tex]\frac{ey}{e}=\frac{7}{7e}[/tex]
Cancel the common factor of [tex]e[/tex] on the left side.
[tex]y=\frac{7}{7e}[/tex]
Cancel the common factor of 7 on the right side.
Rewrite the expression.
[tex]y=\frac{1}{e}[/tex]
2nd Answer
Step-by-step explanation:
[tex]xy+7ey=7[/tex]
Differentiate both sides of the equation.
[tex]\frac{d}{dx} (xy+7ey)=\frac{d}{dx}(7e)[/tex]
Differentiate the left side of the equation.
By the Sum Rule, the derivative of [tex]xy+7ey[/tex] with respect to x is [tex]\frac{d}{dx} [xy]+\frac{d}{dx}[7ey][/tex]
Evaluate [tex]\frac{d}{dx} [xy][/tex]
Differentiate using the Product Rule
Rewrite [tex]\frac{d}{dx} [xy][/tex] as [tex]y'[/tex].
[tex]xy'+y+\frac{d}{dx} [7ey][/tex]
Evaluate [tex]\frac{d}{dx} [7ey][/tex]
Since [tex]7e[/tex] is constant with respect to [tex]x[/tex], the derivative of [tex]7e[/tex] with respect to [tex]x[/tex] is [tex]0[/tex].
Reform the equation by setting the left side equal to the right side.
[tex]xy'+7ey'+y=0[/tex]
Solve for [tex]y'[/tex].
Subtract [tex]y[/tex] from both sides of the equation.
[tex]xy'+7ey'=-y[/tex]
Factor [tex]y'[/tex] out of [tex]xy'[/tex].
[tex]y'x+7ey'=-y[/tex]
Factor [tex]y'[/tex] out of [tex]7ey'[/tex].
[tex]y'(x)+y'(7e)=-y[/tex]
Factor out [tex]y'[/tex] out of [tex]y'(x)+y'(7e)[/tex]
[tex]y'(x+7e)=-y[/tex]
Divide each term in [tex]y'(x+7e)=-y[/tex] by [tex]x+7e[/tex] and simplify.
[tex]\frac{y'(x+7e)}{x+7e} =\frac{-y}{x+7e}[/tex]
Cancel the common factor of [tex]x+7e[/tex].
[tex]y'=-\frac{-y}{x+7e}[/tex]
Replace [tex]y'[/tex] with [tex]\frac{dy}{dx}=-\frac{y}{x+7e}[/tex]
[tex]\frac{dy}{dx}=-\frac{y}{x+7e}[/tex]
The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 49 minutes of calls is$13.08 and the monthly cost for 86 minutes is $16.41. What is the monthly cost for 72 minutes of calls?Monthly costin dollars)
Answers
Answer
The monthly cost for 72 minues of calls = $15.15
Explanation
Let the monthly cost in dollars of the long distance phone plan be represented by y.
Let the total calling time in minutes be represented by x.
We are told that montly cost in dollars of the long distance phone plan, y, is a linear function of the total calling time in minute, x. In mathematical terms and using the equation of a straight line model,
y = a + bx
where
a = fixed amount paid monthly
b = dollar per unit time rate charged on the calls
when x = 49 minutes, y = 13.08 dollars
13.08 = a + 49b ........... equation 1
when x = 86 minutes, y = 16.41 dollars
16.41 = a + 86b ........... equation 2
Combining these simultaneous equations
a + 49b = 13.08 .............. equation 1
a + 86b = 16.41 .............. equation 2
Subtract equation 1 from equation 2
a - a + 86b - 49b = 16.41 - 13.08
37b = 3.33
Divide both sides by 37
(37b/37) = (3.33/37)
b = 0.09 dollars per minute.
We can now solve for a
when b = 0.09
a + 49b = 13.08
a + 49(0.09) = 13.08
a + 4.41 = 13.08
a = 13.08 - 4.41
a = 8.67 dollars
So, the linear function that relates the montly cost in dollars of the long distance phone plan, y, to the total calling time in minute, x is
y = a + bx
a = $8.67 and b = $0.09 per minute
y = 8.67 + 0.09x
When total calling time in minutes, x = 72 minutes, we can now calculate the monthly cost, y.
y = 8.67 + 0.09x
y = 8.67 + 0.09(72)
y = 8.67 + 6.48
y = $15.15
Hope this Helps!!!
Jackson goes to the gym 1, 2, or 3 days in a week, depending on work demands at the office. The probability that he goes 1 day is 0.1, the probability that he goes 2 days is 0.65, and the probability that he goes 3 days is 0.25. What is the expected value of the number of days per week for which Jackson goes to the gym?Do not round your answer.
Answers
We have the following values and their probabilities:
1 day = 0.1
2 days = 0.65
3 days = 0.25
Expected value = 1 (0.1) + 2 (0.65) + 3(0.25) = 0.1 + 1.3+ 0.75 = 2.15
Which expression will have a positive value?
Responses
the product of a negative number and a positive number
the product of a negative number and a positive number
the sum of a negative number and a negative number
the sum of a negative number and a negative number
the quotient of a positive number and a negative number
the quotient of a positive number and a negative number
the quotient of a negative number and a negative number
Answers
Answer:negative
Step-by-step explanation: the product of a negative number and a positive number
If the dividend is 415 and the quotient is 83 what is the divisor
Answers
the divisor = 5
Explanation:
let the divisor be = x
dividend = number to be divided = 415
quotient = result of the division = 83
dividend/divisor = quotient
415/x = 83
cross multiply:
415 = 83x
Divide both sides by 83:
83x/83 = 415/83
x = 5
Hence, the divisor = 5
The amount y (inThe cups) of flour is proportional to the number x of eggs in a recipe.The recipe calls for 5 cups of flour for every 3 eggs.Interpret the slope
Answers
The amount y (inThe cups) of flour is proportional to the number x of eggs in a recipe.The recipe calls for 5 cups of flour for every 3 eggs.Interpret the slope
we have
y -----> cups of flour
x ----> number of eggs
so
slope=y/x
slope=5/3 cups of flour per egg
therefore
slope means 5/3 cups of flour per eggIn this problem the slope is equal to the unit rate
to find out the slope divide the total cups of flour by the total number of eggs
so
we have
5/3=1.67
that means
1.67 cups of flour per one eggor 5/3 cups of flour per one eggI'm trying to solve for x by rounding to the nearest hundredth ? can anyone help me please ?
Answers
Notice that you are asked to find side "x" in a right angle triangle. and that side "x" is adjecent to the given acute angle of 47 degrees.
Since in this triangle you know the values of the adjacent angle (47 degrees) and that of the hypotenuse (3), you can use the trigonometric function that uses those, that is the "cosine" function of the angle:
Recall that :
[tex]\cos (\theta)=\frac{adjacent}{\text{hypotenuse}}[/tex]so, we can solve for the unknown "adjacent" side (x) multiplying both sides by the hypotenuse value (3), and get:
[tex]\begin{gathered} \text{adjacent}=\text{hypotenuse}\cdot\cos (47) \\ x\text{ = 3 }\cdot\text{ cos(47}^{\circ})=2.04599 \end{gathered}[/tex]Therefor, rounding this to two decimals we get:
x = 2.05
which agrees with answer "D" in your list.
(ignore the answer i selected i accidentally clicked it) Pleez help
Answers
Okay, here we have this:
We need to find the inverse of the following function:
[tex]f\mleft(x\mright)=\mleft(\frac{x^5}{7}\mright)^{\frac{1}{7}}-1[/tex]First we will replace x with y:
[tex]x=\mleft(\frac{y^5}{7}\mright)^{\frac{1}{7}}-1[/tex]Now, let's clear y:
[tex]\begin{gathered} \mleft(\frac{y^5}{7}\mright)^{\frac{1}{7}}-1=x \\ \mleft(\frac{y^5}{7}\mright)^{\frac{1}{7}}=x+1 \\ \frac{y^5}{7}=(x+1)^7 \\ y^5=7(x+1)^7 \\ y=\sqrt[5]{7(x+1)^7} \end{gathered}[/tex]Finally we obtain that the correct answer is the second option.
The price of a technology stock has risen to $9.74 today. Yesterday's price was 9.65. Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answers
Answer:-0.924025
Step-by-step explanation:
[(9.65 - 9.74) / 9.74] × 100%
= -0.0092402464066 × 100%
= -0.92402464066%
If the angle of elevation of the sun is 61.7° when a building casts a shadow of 56.5 feet, what is the height of the building rounded to the nearest tenth of a foot?
Answers
SOLUTION
Let us use a simple diagram to interprete the question
In the diagram above, the dark stuff below represents the shadow and the rectangular bar represents the building. I have labelled the height of the building as h.
So we will use the right-angled triangle formed to find h
As we can see h represents the opposite side and 56.5 feet represents the adjacent side of the right-angle triangle. So we will use TOA
[tex]\text{TOA tan }\theta=\frac{opposite}{\text{adjacent}}[/tex]So we have
[tex]\begin{gathered} \text{ tan }\theta=\frac{opposite}{\text{adjacent}} \\ \text{ tan }61.7\degree=\frac{h}{56.5} \\ 1.8572015=\frac{h}{56.5} \\ \text{cross multiplying, we have } \\ h=1.8572015\times56.5 \\ h=104.931887 \end{gathered}[/tex]Hence the answer is 104.9 feet to the nearest tenth
Type in the answer to each problem, be sure to include the correct sign with your final answer.
Answers
Remember that when adding positive and negative numbers,there are a couple of rules to follow. For example, in this case:
[tex]-8+6[/tex]first, notice that since 8 is greater than 6, then the result will be a negative number.
Then, we substract 6 from 8 to get 2, so the final result would be:
[tex]-8+6=-2[/tex]Next, if we want to add two negative numbers, then we add the numbers and keep the negative sign, for example:
[tex]-2-3[/tex]Notice that 2 plus 3 is 5, and since both 2 and 3 are negative,we have that:
[tex]-2-3=-5[/tex]If we want to substract a negative number from another negative number, like in thiscase:
[tex]-9-(-4)[/tex]just remember that anything that is inside of a parenthesis with a negative sign will change its sign, then, we have the following:
[tex]-9-(-4)=-9+4[/tex]applying the same rules as before we have:
[tex]-9+4=-5[/tex]On the remaining cases, we have the following results:
[tex]\begin{gathered} 5-7=-2 \\ +4+3=7 \end{gathered}[/tex]I need help with this question:
Find the value of y that satisfies the given conditions.
The line is containing (−4, 9) and (4, 3) which is parallel to the line containing (−8, 1) and (4, y).
y= ?
Answers
The value of "y" that satisfies the given conditions is -8.
The first straight line passes through two points. The coordinates of the two points are (−4, 9) and (4, 3). The second straight line passes through two points. The coordinates of the two points are (−8, 1) and (4, y).
We know that the first line is parallel to the second line. Hence, the slope of both the lines must be equal.
The slope of the first line is :
m1 = (3-9)/[4-(-4)]
m1 = -6/8
m1 = -3/4
The slope of the second line is :
m2 = (y-1)/[4-(-8)]
m2 = (y-1)/12
We know that m1 = m2.
-3/4 = (y-1)/12
y = -8
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What is the slope of the line that passes through the points (7, -4) and (11. -4)?
Write your answer in simplest form.
Answers
The slope of the line for the given coordinate point is: slope = 0
What is slope of the line?
In mathematics, the slope of the line is the ratio of the change in the y-axis and x-axis. Basically, it tells the steepness of the line. Depending upon the slope value, the line is categorized as parallel or perpendicular or constant line.
According to the question, the given coordinate points for the calculation of the slope of the line are as follows:
Points: (7, -4) and (11, -4) ⇒ x1 = 7; y1 = -4; x2 = 11; y2 = -4
The formula for the slope of the line is as follows:
Slope = (y2 - y1)/(x2 - x1)
Slope = (-4 - (-4))/(11 - 7) = 0
Hence, the slope of the line for the given coordinate point is: slope = 0
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what is the 6th value in the sequence with the explicit formula a n equals -2 and -14?
Answers
Since the explicit formula of the sequence is
[tex]a_n=-2n-14[/tex]Where n is the position of any term
We need to find the sixth term, which means
n = 6
Substitute n by 6 in the formula above
[tex]\begin{gathered} a_6=-2(6)-14 \\ a_6=-12-14 \\ a_6=-26 \end{gathered}[/tex]The sixth term is -26
The answer is B (2nd answer)
65% of the people at the party were females. The rest were males. How many
were males were there at the school party? There are 1,600 people
Answers
Answer:
560
Step-by-step explanation:
If 65% were females, 35% were males.
1600(35%) = 1600(0.35) = 560
the highest temperature ever recorded for today's date in a certain town was 15 Celsius
Answers
To find out the difference, subtract the minimum value from the maximum value
so
15-(-23)=15+23=38 degrees
answer is 38 degrees
expression is 15-(-23)
90 marbles in a bag represent three colors of the US flag there are three times as many red marbles as white marbles there are twice as many blue marbles as white marbles find the number of marbles for each color you select one marble at random from the bag find the probability you picked a red or blue marble
Answers
For the given question.
US flag has to be made by total 90 marbles.
Let the number of white marbles be 'x'.
Red marbles are three times the white marble = '3x'.
Blue marbles be twice of white marble = '2x'.
Total marbles = white marble + red marble + blue marble
90 = x + 2x + 3x
6x = 90
x = 15
White marble = 15.
Blue marble 2x = 2×15 = 30.
Red marble 3x = 3×15 = 45.
Probability = favourable outcomes /total outcome
The probability for picking red marble = 45/90 = 1/2.
The probability for picking blue marble = 30/90 = 1/3.
Probability (red or blue) = 1/2 × 1/3
Probability (red or blue) = 1/6
Thus, the probability for picking red or blue marble is 1/6.
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4≤9x-10≤3
Help please school test tomorrow
Answers
Answer:
[tex]\frac{14}{9}[/tex] ≤[tex]\frac{13}{9}[/tex]
Step-by-step explanation:
4 ≤ 9x - 10 ≤ 3 add 10 from the far left, the middle and the far right.
+10 +10 =10
14 ≤ 9 x ≤13 Divide all the way through by 9
[tex]\frac{14}{9}[/tex]≤x≤
Write a multiplication expression with a product of x^20
Answers
Answer:
x¹¹ • x⁹
Step-by-step explanation:
so hope it help
have a nice day
find:when does the motion of the object change direction given:
Answers
The object change direction when the first derivative change its sign,. So we need to find the first derivative and equate this result to zero.
The first derivative is given by
[tex]s(t)=7\frac{5}{2}t^{\frac{3}{2}}-\frac{7}{2}t^{\frac{5}{2}}[/tex]By equating this result to zero ,we have
[tex]7\frac{5}{2}t^{\frac{3}{2}}-\frac{7}{2}t^{\frac{5}{2}}=0[/tex]This implies that
[tex]\frac{7}{2}t^{\frac{3}{2}}(5-t^)=0[/tex]so, the first derivative change its sign when
[tex]\begin{gathered} t=0 \\ and \\ t=5 \end{gathered}[/tex]as we can note in the following graph:
because the graphs falls when t= 5seconds.
This means that the motion objects change direction at t=5 seconds.
