Answer:
The answer is approximately equal to 14.14214
find the cartesian equation of r=3i+paremeter (i+2j)
The Cartesian equation will be;
⇒ (x - 3) / 1 = (y - 0)/2
What is Equation of line?
The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The equation is,
⇒ r = 3i + λ (i + 2j)
Where, 'λ' is a parameter.
Now,
Since, The equation is,
⇒ r = 3i + λ (i + 2j)
Where, 'λ' is a parameter.
Hence, The Cartesian equation is find as;
⇒ xi + yj = 3i + λi + 2λj
By compare, we get;
⇒ x = 3 + λ
⇒ y = 2λ
Thus, The Cartesian equation is;
⇒ (x - 3) / 1 = (y - 0)/2 = λ
Therefore, The Cartesian equation will be;
⇒ (x - 3) / 1 = (y - 0)/2
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Michael averages 12 points in each basketball game. His team plays 2 games each week. About how many points will he score in 12 weeks? Explain your reasoning.
Michael will score about 288 points in 12 weeks. This is because he scores 12 points in each game and there are 2 games each week, so he will score 24 points in each week. Multiplying 24 points by 12 weeks, Michael will score 288 points.
What is x+y=-15 converted to slope intercept form
Answer: y = -x - 15
Step-by-step explanation:
Slope intercept form is written as y = mx + b where m is the slope and b is the y-intercept. In other words, we need to isolate the y-variable.
Given:
x + y = - 15
Subtract x from both sides of the equation:
y = -x - 15
Suppose that you roll a fair, six-sided die 10 times. What’s the probability that you get at least one 6?
Answer:
0.8385, turned into a percentage is 83.9%
Step-by-step explanation:
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 5 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Answer:210
Step-by-step explanation:
What is the x-coordinate of the midpoint of the segment between (4 , -5) and (8 , 2)?
Answer:
(6, -1.5) or (6, -1 1/2)
The function f(x) = –x3 – 7x2 – 7x + 15 has zeros located at –5, –3, 1. Verify the zeros of f(x) and explain how you verified them. Describe the end behavior of the function.
The zeros of the function f(x) = -x³ - 7x² - 7x + 15 are -5, -3 and 1
Zeros of a FunctionThe zeros of a function are defined as the values of the variable of the function such that the function equals 0. Graphically, the zeros of a function are the points on the x-axis where the graph cuts the x-axis. In other words, we can say that the zeros of a function are the x-intercepts of its graph. The number of zeros of a polynomial function is equal to the degree of the polynomial.
To verify if the zeros are for the function, we simply need to plug the values in for x and solve.
f(x) = -x³ - 7x² - 7x + 15
f(-5) = -5³ - 7(-5)² - 7(-5) + 15
f(-5) = 0
When x = - 3
f(-3) = -3³ - 7(-3)² -7(-3) + 15
f(-3) = 0
when x = 1
f(1) = 1³ -7(1) - 7(1) + 15
f(1) = 0
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Graph the function (fx) = 2√ + 3 on the coordinate plane
The graph of the function y = 2√x + 6 is plotted and attached.
What is the general equation of a Straight line? What are the points of intersection of the graph of y = x and y = √x? Which curve is more diverged?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
The points of intersection of the graph of y = x and y = √x are (0, 0) and (1, 1). The curve y = √x diverges more.
We have the following equation -
y = 2√x + 6
Given is the following equation as -
y = 2√x + 6
Refer to the graph of the function attached.
Therefore, the graph of the function y = 2√x + 6 is plotted and attached.
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An investor needs $18000 in 10 years.
(a) What amount should be deposited in a fund at the end of each quarter at 9% compounded quarterly so that there will be enough money in the fund?
(b) Find the investor's quarterly deposit if the money is deposited at 4.5% compounded quarterly.
(a) Let P be the amount deposited at the end of each quarter. Then, the future value F after n quarters is given by
F = P(1 + 0.09)^n
Given that there must be enough money in the fund, we can set F = A, the amount required. Therefore,
A = P(1 + 0.09)^n
Solving for P,
P = A(1 + 0.09)^-n
(b) Let P be the amount deposited at the end of each quarter. Then, the future value F after n quarters is given by
F = P(1 + 0.045)^n
Given that there must be enough money in the fund, we can set F = A, the amount required. Therefore,
A = P(1 + 0.045)^n
Solving for P,
P = A(1 + 0.045)^-n
Malik deposited $2,439 in an account earning 7% interest compounded annually.
To the nearest cent, how much interest will he earn in 3 years?
Answer: $548.00
Step-by-step explanation: In order to find out how much interest Malik will earn in 3 years, we need to first calculate the amount of interest earned each year. We can do this by multiplying the initial amount he deposited by the interest rate, which is 7%. So, the amount of interest earned each year is $2,439 * 7% = $169.73.
Since the interest is compounded annually, this means that the amount of interest earned in the first year is added to the initial deposit to form the new balance. This new balance will then earn interest in the second year, and so on.
Therefore, the amount of interest earned in the second year is 7% of the new balance, which is $2,439 + $169.73 = $2,608.73. So, the interest earned in the second year is $2,608.73 * 7% = $182.61.
In the third year, the interest is again compounded, so the new balance is $2,608.73 + $182.61 = $2,791.34. The interest earned in the third year is 7% of this new balance, which is $2,791.34 * 7% = $196.48.
In total, Malik will earn $169.73 + $182.61 + $196.48 = $548.82 in interest over 3 years. To the nearest cent, this is $548.00.
Consider a function f(x) = |x|. A second function g(x) is the result of translating f(x) by 5 units in
the negative y-direction (downward), and 3 units in the positive x-direction (to the right). Write the equation of g(x)
Please Help!!!
The translated function g(x) = | x - 3 | - 5 shifted 3 units along the positive x-axis and 5 units along the negative y-axis.
What are some transformations of functions?Suppose we have a function f(x).
f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).
f(x ± c) = Horizontal left/right shift by c units (x - + c, y).
(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).
f(-x) = Reflection over y axis, (-x, y).
-f(x) = Reflection over x-axis, (x, -y).
Given, A parent function f(x) = | x |.
Now the result of translating f(x) by 5 units in the negative y-direction and 3 units in the positive x-direction g(x) = | x - 3 | - 5.
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the diamter of a circle is 14 yards what is the area of this cirlce
The area of a circle with diameter of 14 yards is 153.86 yards².
How to find area of a circle?The diameter of the circle is 14 yards . The area of the circle can be found as follows;
area of a circle = πr²
where
r = radius of a circleThe radius of a circle is half of its diameter.
Therefore,
r = 14 / 2 = 7 yards
Hence,
area of a circle = πr²
area of a circle = 3.14 × 7²
area of a circle = 3.14 × 49
area of a circle = 153.86 yards²
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Let y be differentiable with respect to x. For the relation x³ + y³ = 9xy, find dy/dx by
implicit differentiation
Answer: (3y² * dy/dx + 3x² * dy/dx - 9y) / 9.
Step-by-step explanation: To find dy/dx for the relation x³ + y³ = 9xy, we can use the chain rule. The chain rule states that if y is a function of x and x is a function of t, then the derivative of y with respect to t is equal to the derivative of y with respect to x times the derivative of x with respect to t.
In this case, we are given that y is a function of x and we want to find the derivative of y with respect to x. To do this, we can rewrite the given equation as follows:
x³ + y³ = 9xy
y³ = 9xy - x³
We can then take the derivative of both sides of the equation with respect to x to find dy/dx as follows:
3y² * dy/dx = 9y + 9x * dy/dx - 3x² * dy/dx
3y² * dy/dx = (9y + 9x * dy/dx) - 3x² * dy/dx
0 = (9y + 9x * dy/dx) - (3y² * dy/dx + 3x² * dy/dx)
0 = 9y + 9x * dy/dx - 3y² * dy/dx - 3x² * dy/dx
We can then solve this equation for dy/dx as follows:
0 = 9y + 9x * dy/dx - 3y² * dy/dx - 3x² * dy/dx
9x * dy/dx = 3y² * dy/dx + 3x² * dy/dx - 9y
9x * dy/dx = 3y² * dy/dx + 3x² * dy/dx - 9y
dy/dx = (3y² * dy/dx + 3x² * dy/dx - 9y) / 9x
dy/dx = (3y² * dy/dx + 3x² * dy/dx - 9y) / 9x
Therefore, the derivative of y with respect to x for the given equation is equal to (3y² * dy/dx + 3x² * dy/dx - 9y) / 9.
Answer
[tex]\frac{dy}{dx}[/tex]
Step-by-step explanation:
Your welcome ;)
The volume of a cubical tank is 8,000 m³. Find the length of that tank.
Answer:
20m
Step-by-step explanation:
Volume of Cube: s³ = 8000m³
∛s³ = ∛8000m³
s = 20m
Answer:
20
Step-by-step explanation:
We know that,
volume of cube = l*l*l
8000 = l*l*l
l = 3√8000
l= 20
Answer
Suppose you go to work for a company that pays one penny on the first day, 2 cents on the second day, 4 cents on the third day and so on.
Hint: use an= a1 (r)^n-1 and Sn= a1 (1-r^n) / 1 - r
A. If the daily wage keeps doubling, what would your income be on day 31? Give your answer in dollars NOT pennies.
Income on day 31 = $ __________
B. If the daily wage keeps doubling, what will your total income be for working 31 days? Give your answer in dollars NOT pennies.
Total Income for working 31 days = $ _________
The income on day 31 would be $21,1474,836.48 and the total income for working 31 days would be $42,949,672.94.
The company pays one penny on the first day, 2 cents on the second day, 4 cents on the third day, and so on.
This situation represents the geometry sequence below as
0.02, 0.04, 0.08,..
Here first-term a₁ = 0.02
And common ratio r = 0.04/0.02 = 2
The income on day 31 would be:
⇒ a₁ (r)ⁿ⁻¹
⇒ 0.02 (2)³¹⁻¹
⇒ 0.02 (2)³⁰
⇒ 21,1474,836.48
Total income for working 31 days would be:
⇒ a₁ (1-rⁿ) / 1 - r
⇒ 0.02 (1-2³¹) / (1 - 2)
⇒ 42,949,672.94
Thus, the income on day 31 would be $21,1474,836.48 and the total income for working 31 days would be $42,949,672.94.
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stop charging me immediately
Answer:
what do you mean
Step-by-step explanation:
Last week, a dairy farm produced p kg of cheese. The dairy farm also produced 24 kg more yoghurt than cheese and 3 times as much ice cream as cheese. The dairy farm produced more kilograms of ice cream than yoghurt last week. Write and solve an inequality to work out the possible values of p.
Answer:
4w>39+w
3w>39
w>13
Step-by-step explanation:
The coldest temperature ever recorded in Mathville was - 16 deg * F This happened on January 30th, 1978. The normal low for that day is 19 deg * F How much colder was the record temperature than the normal ow temperature?
It was recorded 35°F colder temperature than the normal ow temperature that year in January 30th, 1978.
Explain the term temperature change?Diabatic temperature change is the term used to describe a temperature shift brought on by a heat exchange between two bodies. The term "adiabatic temperature change" refers to another highly significant method of altering the temperature of air. Air undergoes adiabatic temperature change without the addition or subtraction of energy.For the stated data-
Coldest temperature : -16°F
Normal low: 19°F
Thus, the difference in the temperature-
Difference = Normal low - Coldest temperature
Difference = 19°F - (-16°F)
Difference = 35°F
Thus, it was recorded 35°F colder temperature than the normal ow temperature that year in January 30th, 1978.
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How do you line up 14.72 ×36.8=
The first Christmas bell rings every six minutes. The second Christmas bell rings every seven minutes. The third Christmas bell rings every hour. If all the bells ring at 12 noon, at what time will they next all ring together?
Answer:7 PM is whenthey all ring together
Step-by-step explanation:
4. Ms. Wagner painted the outside of the patio
door to her house, as shown below. She did
not paint the window or the doorknob.
Answer: 18 ft ^2
Step-by-step explanation:
can sum1 help i got no teachers near
Answer:
Option C : x-6
Step-by-step explanation:
since tina’s brother height is X we start there
x
And tine is 6 less than her bother so we subtract 6
x-6
and that’s it
Hopes this helps please mark brainliest
Please help asap! thank you
Find the quotient. Round to the hundredths' place when necessary.
Answer:
17: 0.65
18: 0.05
19: 0.27
20: 1840
Step-by-step explanation:
A ball is thrown from a height of 3 meters with an initial downward velocity of 5 m/s The ball's height h (in meters) after t seconds is given by the following. how long after the ball is thrown does it hit the ground
The ball hits the ground at a time of 1.433 seconds.
How to calculate the time until the ball hits the ground
In this problem we have the case of a ball that experiments a free fall, that is, an uniform accelerated motion due to gravity. The position of the ball in time is described by a quadratic equation:
y = y' + v' · t + 0.5 · g · t²
Where:
y' - Initial position, in meters.v' - Initial speed, in meters per second. t - Time, in seconds. g - Gravitational acceleration, in meters per square second.y - Final position, in meters.If we know that y' = 3 m, v' = 5 m / s, g = - 9.807 m / s², y = 0 m, then the time of the ball until it hits the ground is:
0 = 3 + 5 · t - 4.904 · t²
Then, by the quadratic formula:
t = - v' / g ± (1 / g) · √[v'² - 2 · g · y']
t = - 5 / (- 9.807) ± [1 / (- 9.807)] · [5² - 2 · (- 9.807) · 3]
t₁ = 1.433 s. or t₂ = - 0.424 s.
The hitting time of the ball is 1.433 seconds.
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Which of the following sentences uses homophones incorrectly?
a
The baker is required to knead the dough every hour.
b
The celebrity thought it would be best to have a plain plane
c
The artist erased the whole drawing and made a large hole.
d
The principle of the school makes decisions based on principals.
Help plss
Answer:
Answer: D. The principle of the school makes decisions based on principals.
Serena estimates that she can paint 60 square feet of wall space every half-hour.write an equation for the relationship with time in hours as the independent variable.can Serena paint 400 square feet of wall space in 3.5 hours?why or why not?
Answer:x=3.5 x 60
the answer is yes because when she's doing 3.5 hour, and she can do 420 square feet
Explain why the equation cos(x) = x has at least 1 solution
There exists a point c ∈ [0, 2π], therefore, f(c) =0, Hence cos x = x has at least one solution.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equation is,
cos(x) = x (1)
For the given interval [0, 2π],
By intermediate theorem, for c ∈ [0, 2π], for which f(c) =0
Or we can say that, at x = 0, f(0) = 0
Therefore, cos(x) has at least one solution, in the interval [0, 2π]
So, given equation cos(x) = x has one solution.
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Can you please help me with this question
Answer: I can’t read it
Step-by-step explanation:
What is the slope of the line with equation 2x + 3y = 10?
Answer:
Step-by-step explanation:
-2/3
What is x when x=2-4+5
3. Find the length of the bridge.
20 ft
160 ft
32.5 ft