Answer:
v = 24
Step-by-step explanation:
Ft + mu = mv
v = (Ft + mu)/m = (55*3 + 5*(-9))/5 = 24
Find the area of the triangle
A
47°
b
32 ft
C
19 ft
Answer:
222 [ft²].
Step-by-step explanation:
1. the required area can be calculated according to the formula:
A=0.5*b*c*sin(A);
2. after substitution of b=32; c=19 and sin(A)≈0.7313537:
A=0.5*32*19*0.7313537=222.3315248 [ft²].
Resuelve los siguientes ejercicios:
Hallar la ecuación de la circunferencia:
a) Centro (2,-1) y radio 4
b) Centro C (1,3) y que pasa por el punto P (4, 6)
3. Hallar la ecuación de la parábola, las coordenadas de su foco y la longitud de su lado recto, si el vértice es el origen y pasa por el punto P:
a) Eje focal coincidente con el eje coordenado en x, P(2,4)
b) Eje focal coincidente con el eje coordenado en, P (6,3)
4. Hallar el foco, la ecuación de la directriz y la longitud del lado recto de las siguientes parábolas.
a) 4 x2 = 32y
b) 2y2 = -3x
5. Dadas las ecuaciones de las elipses, hallar las longitudes del semieje mayor y semieje menor, las coordenadas de los focos, los vértices y la longitud del lado recto.
a) 81 x2 + 144 y2 = 11664
b) 36x2+25y2 = 3600
Por restricciones de longitud no es posible resumir las respuestas asociadas a esta pregunta, invitamos cordialmente a leer la explicación para mayores detalles sobre el análisis de secciones cónicas.
¿Cómo analizar ecuaciones de secciones cónicas?
Según la geometría analítica, existen cinco tipos de secciones cónicas: (i) Circunferencia, (ii) Parábola, (iii) Elipse, (iv) Hipérbola, (v) Recta. 2) a) La ecuación estándar de la circunferencia se caracteriza con el centro (h, k) y la longitud del radio (r):
(x - h)² + (y - k)² = r²
(x - 2)² + (y + 1)² = 4²
b) La longitud del radio de la circunferencia se obtiene por el teorema de Pitágoras sobre la longitud del segmento CP:
r = √[(4 - 1)² + (6 - 3)²]
r = √(3² + 3²)
r = 3√2
(x - 1)² + (y - 3)² = 18
3) a) El eje focal forma parte del eje de simetría de la parábola. La ecuación estándar de la parábola es:
4 · p · x = y²
Donde p es la distancia entre el foco y el vértice.
Si tenemos que (x, y) = (2, 4), entonces la ecuación de la parábola es:
4 · p · 2 = 4²
p = 2
8 · x = y²
Las coordenadas del foco de la parábola son de la forma (x, y) = (h + p, k):
F(x, y) = (2, 0)
Ahora se determinan los extremos del lado recto: (x = 2)
8 · 2 = y²
y = ± 4
Los extremos del lado recto son (2, 4) y (2, - 4), cuya longitud de segmento es 8 unidades.
b) El eje focal forma parte del eje de simetría de la parábola. La ecuación estándar de la parábola es:
4 · p · x = y²
Si tenemos que (x, y) = (6, 3), entonces la ecuación de la parábola es:
4 · p · 6 = 3²
p = 8 / 3
(32 / 3) · x = y²
Las coordenadas del foco son F(x, y) = (8 / 3, 0).
Ahora se determinan los extremos del lado recto: (x = 6)
(32 / 3) · 6 = y²
y = ± 8
Los extremos del lado recto son (6, 8) y (- 6, - 8), cuya longitud de segmento es 16 unidades.
4) a) Tenemos una ecuación estándar de la forma 4 · p · y = x². A continuación, hallamos todas las variables requeridas:
x² = 8 · y
p = 2
Directriz: y = - 2, Foco: F(x, y) = (0, 2), Longitud del lado recto: 4
b) Tenemos una ecuación estándar de la forma 4 · p · x = y². A continuación, hallamos todas las variables requeridas:
y² = - (3 / 2) · x
p = - 3 / 8
Directriz: x = 3 / 2, Foco: F(x, y) = (- 3 / 2, 0), Longitud del lado recto: 3.
5) En esta parte debemos manipular algebraicamente las ecuaciones hasta su forma estándar para determinar los datos requeridos de cada caso. La ecuación estándar de la elipse tiene el siguiente problema:
(x - h)² / a² + (y - k)² / b² = 1
Donde:
(h, k) - Centro de la elipse.a, b - Longitudes de los semiejes.a) 81 · x² + 144 · y² = 11664
x² / 144 + y² / 81 = 1
x² / 12² + y² / 9² = 1
Longitud del semieje mayor: 12
Longitud del semieje menor: 9
c = √(12² - 9²)
c ≈ 7.937
Coordenadas de los focos: F₁ (x, y) = (- 7.937, 0), F₂ (x, y) = (7.937, 0)
Vértices: V₁ (x, y) = (- 12, 0), V₂ (x, y) = (12, 0)
Longitud del lado recto
144 · y² = 11664 - 81 · x²
y² = (11664 - 81 · x²) / 144
y = ± (1 / 12) · √(11664 - 81 · x²)
y = ± (1 / 12) · √(11664 - 81 · 7.937²)
y = ± 6.750
La longitud del lado recto es 13.5.
b) 36 · x² + 25 · y² = 3600
x² / 10² + y² / 12² = 1
Longitud del semieje mayor: 12
Longitud del semieje menor: 10
c = √(12² - 10²)
c ≈ 6.633
Coordenadas de los focos: F₁ (x, y) = (0, - 6.637), F₂ (x, y) = (0, 6.637)
Vértices: V₁ (x, y) = (0, - 12), V₂ (x, y) = (0, 12)
Longitud del lado recto
36 · x² = 3600 - 25 · y²
x² = 100 - (25 / 36) · y²
x = √[100 - (25 / 36) · y²]
x = √[100 - (25 / 36) · 6.637²]
x = ± 8.331
La longitud del lado recto es 16.662.
Para aprender más sobre secciones cónicas: https://brainly.com/question/16156916
#SPJ1
solve (6b^2+5)+(8b-20)
The sum of the given expression is 6b^2+8b-15
Sum of expressionGiven the following expression
(6b^2+5)+(8b-20)
We are to take the sum. On expansion;
6b^2+5 + 8b-20
Collect the like terms
6b^2+8b +5 - 20
6b^2+8b-15
Hence the sum of the given expression is 6b^2+8b-15
Learn more on sum of expression here: https://brainly.com/question/723406
#SPJ1
A game has an expected value to you of $. It costs $ to play, but if you win, you receive $100,000 (including your $ bet) for a net gain of $. What is the probability of winning? Would you play this game? Discuss the factors that would influence your decision.
The probability of winning this game is 0.003
How to solve for the probability of winningLet us name p to be the probability of winning the game.
We have the expected value to be 100
100 = probability of winning + 1-p x loss
win = 100000 - 200
We then input in the formula
100 = p*99800 +(1-p) x -200
100 = 99800p - 200 + 200p
Collect like terms
100 + 200 = 99800 + 200p
300 = 100000p
Divide through by 100000
This give the
Probability of winning = 0.003
The probability of winning the game is very low hence I would not play.
The factors that would influence the decision are:
The cost of playingThe expected valueComplete questionA game has an expected value to you of ?$100. It costs ?$200 to? play, but if you win you receive? $100,000 (including your ?$200 ?bet), for a net gain of ?$99,800. What is the probability of? winning
Read more on probability here:
https://brainly.com/question/24756209
#SPJ1
Intelligence test.
If you get it right ,you are a critical thinker.
You were in the garden, there are 34 people in the yard. You killed 30 .How many people are in the garden.
I
Answer: 5
Step-by-step explanation:
Because there are 35 when you add yourself so u subtract 30 to get 5
There would be 4 people left in the garden.
34 - 30 = 4.
Subtraction of NumbersSubtraction is a mathematical operation that involves taking away one number from another to find the difference between them. For the question, At first, there were 34 people in the garden and later 30 people were no longer alive in the garden, so the difference between 30 people and 34 people is 4.
Subtraction is the opposite of addition, and it is used to measure the distance between two values on the number line.
Subtraction is represented by minus Sign (-). For example, subtracting 5 from 10 gives you a difference of 5 (10 - 5 = 5).
Learn more about subtraction of Numbers here
https://brainly.com/question/28467694
#SPJ3
What are the solutions of the equation 9x4 - 2x2 - 7 = 0? Use u substitution to solve.
Money savers bank offers a savings account that earns 6% interest compounded continuously. If Manuel deposits $2200, how much will he have in the account after three years?
Answer:
2633.88
Step-by-step explanation:
Pe^rt
2200*e^.06*3
What type of motion transforms the letter “p” into a “b”?
The type of motion which transforms the letter “p” into a “b” is; Reflection.
What type of motion transforms the letter “p” into a “b”?It follows that the task content demands that the type of motion which maps p to b be identified. On this note, it follows that the type of motion in discuss is Reflection. More particularly, a reflection over the horizontal axis most definitely causes this transformation.
Therefore, the motion which transforms the letter “p” into a “b” is; Reflection.
Read more on reflection;
https://brainly.com/question/1908648
#SPJ1
Express v=
(2,1,5) as a linear combination of (1,2,1), (1,0,2) and (1,1,0)
The expression of v = (2,1,5) as a linear combination of (1,2,1), (1,0,2) and (1,1,0) is [tex](2,1,5)=1(1,2,1)+2(1,0,2)+-1(1,1,0)[/tex]
Linear CombinationsTo express v= (2,1,5) as a linear combination of (1,2,1), (1,0,2) and (1,1,0), it will be written as:
[tex](2,1,5)=x(1,2,1)+y(1,0,2)+z(1,1,0)[/tex]
This will yield the following equations:
x + y + z = 2........(1)
2x + z = 1..........(2)
x + 2y = 5........(3)
The solution to the system of equations above is:
x = 1, y = 2, z = -1
Therefore, the linear combination is:
[tex](2,1,5)=1(1,2,1)+2(1,0,2)+-1(1,1,0)[/tex]
Learn more on linear combinations here:https://brainly.com/question/17407318
#SPJ1
If sin(theta)=0.7 what is tan(theta)?
The value of tan theta from the given. expression is 7/√51
Trigonometry identityTrigonometry identity are expressions written in terms of sine, cosine and tangents.
Given the following trigonometry values as shown:
sin(theta)=0.7
Convert the decimal to fractions
sin(theta)= 7/10
According to SOH CAH TOA;
sin theta = opp/hyp
Determine the adjacent
adj = √hyp²-opp²
Substitute the values;
adj = √10²-7²
adj = √100-49
adj = √51
Determine the value of tan theta
tan(theta) = opp/adj
Substitute
tan(theta) = 7/√51
Hence the value of tan theta from the given. expression is 7/√51
Learn more on trig identity here: https://brainly.com/question/20094605
#SPJ1
Continue preparing to analyze the data (step 3): Choose an appropriate numerical summary.
An appropriate numerical summary is descriptive statistics.
What is a numerical summary?It should be noted that a numerical summary means a number used to describe specific characteristics of a data set.
In this case, descriptive statistics can be used. This is used to describe the data set.
Learn more about numerical summary on:
brainly.com/question/13846750
#SPJ1
What is
3/2^2 equal to
Answer: SQUARE ROOT OF 8
Step-by-step explanation: 2^3^1/2 is SQUARE ROOT OF 8. GOD BLESS
- FRIEND TO DINO
Sarah had three times as many quarters as nickels. She had $3.20 in all. How many quarters did she have?
A. 12
B. 15
C. 4
Answer:
A. 12
Step-by-step explanation:
If she had 12 quarters, then she would have to have 4 nickels according to the problem.
12 * .25 = $3 (money in quarters)
4 * .05 = $.2 ( money in nickels)
Adding those 2 together, we get $3.2.
She have 12 quarters
what is unitary method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
There are two situation in Unitary method:
There are 5 ice-creams. 5 ice-creams cost $125.
Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.
Given:
If she had 12 quarters, then
12 * .25 = $3 ( quarters)
4 * .05 = $.2 ( in nickels)
Hence, she have 12 quarters.
Learn more about unitary method here:
https://brainly.com/question/22056199
#SPJ2
Explain how to draw a line segments that measures 2 7/16 inches. d
Answer: draw the line using a ruler on which you have identified points 2 7/16 inches apart
Step-by-step explanation: On your ruler graduated in inches with marks at 1/16-inch intervals, locate the 0 mark and the mark 1/16 inch before the half-inch mark between 2 and 3 inches.Draw your line along the edge of the ruler between the two marks you have identified: 0 and 2 7/16. The line will be 2 7/16 inches
13)
Medical officials want to determine if birth weights are lower than usual in Southeast Asia. They randomly weigh 100 babies, and they determine that the average birth weight is 6 pounds 8 ounces.
State the variable.
What are the units for the variable?
State the population.
State the sample.
POINTS Out OF
7
What is the individual.
What is the Parameter.
What is the statistic.
See below for the response to each question
The variableThis is the item that is being surveyed.
The surveyed item is birth weights
Hence, the variable is birth weights
The units of the variableFrom the question, we have:
Average birth weight is 6 pounds 8 ounces.
Hence, the units of the variable are pounds and ounces
The populationThis is the total number of babies in Southeast Asia
Hence, the population of interest is the babies in Southeast Asia
The individualThis is the people in the survey
Hence, the individual in the study is the 100 babies that were randomly surveyed
The parameter of interestThis is the value that gives the required information.
Hence, the parameter of interest is the average birth weight
What is the statistic involvedThe statistic is the average
Read more about random surveys at:
https://brainly.com/question/15105321
#SPJ1
Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1700 fish. Absent constraints, the population would grow by 170% per year.
Answer: 2890
Step-by-step explanation:
a = b x p%
= 1700 x 170%
= 1700 x 1.7
= 2890
the population would be 2890 fish after one year
How much will you have saved after 6 years by contributing $1,200 at the end of each year if you expect to earn 11% on the investment?
Savings after 6 years would be $ 1992.
What are savings?Savings is the money that remains after expenses and other commitments have been subtracted from income.
Savings are the sum of money that would otherwise be lying about, not being risked on investments or used for consumption.
Savings and investing can be compared because the latter includes putting money at risk in an effort to try to increase wealth.
Indicators of household debt or a negative net worth include negative savings.
According to the question,
Amount contributed(P)= $1200
Rate(R)= 11%
Time(T)= 6 years
Interest(SI)=P*R*T/100
= 1200*11*6/100
= 792
Savings after 6 years = P+ SI
= 1200 + 792
= $ 1992
Learn more about savings here:
https://brainly.com/question/738615
#SPJ1
write an equation in slope -intercept form for the line that passes through the points (8,-3) and has a slope of 3 over 2
Answer:
y = 3/2x -15
Step-by-step explanation:
y = mx + b this is the slope intercept form. We need the slope and the y intercept. The slope (m) has been given (3/2), we just need the b (y-intercept). We will use the point given to find b. The point given is (8,-3). 8 is the x term and -3 is the y term. We will plug them into y = 3/2x + b to solve for b.
y = mx + b
y = (3/2) x + b The slope was given
-3 = (3/2)(8) + b Plugged in the given x and y from the point (8, -3)
-3 = 12 + b I can make 8 into a fraction by putting a 1 under it.
(3/2)(8/1). I can cross cancel to make the number easier to
2 and 8 both share the factor 2 so I will divide both numbers
by 2 and I will now have (3/1)(4/1). 3x4 is 12 and 1x1 is 1, so
12/1 is the same as 12.
-15 = b Subtract both sides by 12. -3-12 is -15
Now that I have the m and the b, I can write the equation in the slope intercept form. y = 3/2 + (-15) or y = 3/2 -15
Carlos spent 1\dfrac141
4
1
1, start fraction, 1, divided by, 4, end fraction hours doing his math homework. He spent 1\dfrac141
4
1
1, start fraction, 1, divided by, 4, end fraction as much time practicing piano.
How many hours did Carlos spend practicing piano?
write as a fraction
The time Carlos spend practicing his multiplication facts in fraction is 5/16 hours.
FractionA fraction is a value which has a numerator (upper or top value) divided by a denominator (lower or bottom value).
Time Carlos spent doing his math homework = 1 1/4 hoursTime spent practicing his multiplication facts = 1/4 of 1 1/4 hours
= 1/4 × 1 1/4
= 1/4 × 5/4
= (1 × 5) / (4 × 4)
= 5/16 hours
Therefore, the time Carlos spend practicing his multiplication facts is 5/16 hours.
Complete question:
Carlos spent 1 1/4 hours doing his math home work. He spent 1/4 of this time practicing his multiplication facts.
How many hours did Carlos spend practicing his multiplication facts?
Learn more about fraction:
https://brainly.com/question/11562149
#SPJ1
which integer is closest to the third root of -23
Answer:
The number 23 is prime. Therefore, the cube root of 23 = ∛23 = 2.8439.
Step-by-step explanation:
convert this into a standard number
[tex]10^{12}[/tex]
10^12 in standard number is 1000000000000
How to convert the number?The number is given as:
[tex]10^{12[/tex]
Expand the expression
[tex]10^{12} = 10 * 10 * 10 * 10 *10 * 10 * 10 * 10*10 * 10 * 10 * 10[/tex]
Evaluate the product
[tex]10^{12} = 1000000000000[/tex]
Hence, 10^12 in standard number is 1000000000000
Read more about standard number at:
https://brainly.com/question/5756316
#SPJ1
At full price, Melvin would pay 1.679 dollars per liter of gasoline. Using his loyalty card, Melvin only pays 1.439 dollars per liter
He pays $0.24 less when using his loyalty card.
How much less does Melvin pay per liter when using his credit card?
We know that, without the card, he would pay $1.679 dollars per liter of gasoline.
With his card, he would pay $1.439
To find the relation between the two prices, we just need to take the difference between the two values (a difference is a subtraction).
d = $1.679 - $1.439 = $0.24
He pays $0.24 less when using his loyalty card.
If you want to learn more about subtractions:
https://brainly.com/question/4721701
#SPJ1
F(x) = | sin 3x | -3 find the maximum and minimum value
Answer:
-2 and -3
Step-by-step explanation:
The minimum of |sin 3x| is 0 and the max is 1 (since the sine function ranges from -1 to 1)
Therefore, the maximum is 1 - 3 = -2 and the minimum is 0 - 3 = -3.
Create a problem with a quadratic equation that you would solve graphically and solve it.
The solutions to the quadratic problem are x = -1 and x= 4
Solving Quadratic equations graphicallyFrom the question, we are to create a problem with a quadratic equation and solve graphically
Consider the quadratic equation
x² -3x -4 = 0
The graph of the quadratic equation is shown below
We can observe that the graph cuts the x-axis at the point x = -1 and x = 4
Hence, the solutions to the quadratic problem are x = -1 and x= 4
Learn more on Quadratic Equations here: https://brainly.com/question/13724583
#SPJ1
The length of the major axis of the ellipse below is 14, and the length of the
red line segment is 3. How long is the blue line segment?
Answer:
11
Step-by-step explanation:
The focal length is 14, and thus the sum of the lengths of the blue and red segments is also 14.
HELP !! anyone please i need this done in less than in hour JUST ANSWERS WILL DO
Answer:
Step-by-step explanation:
Aperson invest 10,000 shillings for 40 months compounded monthly. Find the accumulated amount If the rate is 5% per annum.
hi
monthly interest rate is : [tex]\sqrt[12]{1.05}[/tex]
So in forty month there will be : 10 000 * ( [tex]\sqrt[12]{1.05}[/tex] )^40 ≈11 776,06
NO LINKS!!! Please help me with this problem
Answer:
length: 8end points: (-8, 1), (0, 1)Step-by-step explanation:
In the quadratic form ...
(x -h)² = 4p(y -k)
The value 4p is the length of the latus rectum. It also tells the distance between the vertex (h, k) and the focus (h, k+p).
ApplicationThe value of 4p is given as 8. This means p = 8/4 = 2.
The length of the latus rectum is 8.
The end points of the latus rectum have the same y-value as the focus:
y = k +p = -1 +2 = 1
The end points of the latus rectum have x-values that are h±2p.
x = h ± 2p = -4 ± 2·2 = {-8, 0}
The end points of the latus rectum are (-8, 1) and (0, 1).
What is the complete factorization of the polynomial below?
x³ + 2x² + 4x+8
A. (x-2)(x+ 2i)(x+2i)
B. (x-2)(x+2i)(x-2i)
C. (x+2)(x + 2i)(x+2i)
D. (x+2)(x+2i)(x-2i)
The complete factorisation of the polynomial given; x³ + 2x² + 4x + 8 as in the task content can be factorised and determined as; Choice D; (x+2)(x+2i)(x-2i).
What is the complete factorisation of the given polynomial; x³ + 2x² + 4x+8?It follows from the given task content that the polynomial whose factors are to be determined by means of factorisation is; x³ + 2x² + 4x+8.
It follows from observation that one of the zeros of the polynomial expression is at; x = -2.
Consequently, one of the factors of the polynomial in discuss is; (x+2).
x³ + 2x² + 4x+8 = (x+2) (x² - 4i²)
= (x+2)(x+2i)(x-2i)
Consequently, it follows that the complete factorisation of the polynomial is; (x+2)(x+2i)(x-2i).
Read more on polynomial factorisation;
https://brainly.com/question/11434122
#SPJ1
In a one tail hypothesis where you only in the lower tail, what is the p-value if
P-Value becomes 0.8599 when (z < 1.08).
According to the statement
We have given that the Z-stat value is 1.08 and we have to find the P value with the help of Z-stat value.
So,
A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.
and we know that
The P-Value is calculated by converting your statistic (such as mean / average) into a Z-Score.
So, If the z-stat is 1.08, the p-value for a left-tail test is the probability that (z < 1.08), which is 0.8599.
So, P-Value becomes 0.8599 when (z < 1.08).
Learn more about P-VALUE here https://brainly.com/question/4621112
#SPJ1