Answer:
Step-by-step explanation:
The Chief Secretary's total monthly salary, including basic salary, dearness allowance, and festival allowance, is Rs 1,50,000.
We have,
The monthly basic salary of the married Chief Secretary of Nepal Government is given as Rs 74,000.
This is the fixed amount he receives as his base salary every month, before any additional allowances or deductions are considered.
Now,
In this case, the dearness allowance of Rs 2,000 is added to the basic salary.
This allowance is provided to compensate for the rising cost of living and is a fixed amount added to the basic salary.
Additionally, he receives 1 month's basic salary as a festival allowance. Since his monthly basic salary is Rs 74,000, his festival allowance would also be Rs 74,000.
Therefore, his total monthly salary can be calculated as follows:
Basic salary + Dearness allowance + Festival allowance
= Rs 74,000 + Rs 2,000 + Rs 74,000
= Rs 1,50,000
Thus,
The Chief Secretary's total monthly salary, including basic salary, dearness allowance, and festival allowance, is Rs 1,50,000.
4 litres of paint has a mass of 7.88 kg. Calculate the density of the paint, in kg/litre. Give your answer to 2 d.p.
The density of the paint is 1.97 kg/liter.
To calculate the density of a substance, we use the formula:
Density = Mass / Volume
In this case, we are given that 4 liters of paint has a mass of 7.88 kg.
To find the density of the paint, we divide the mass by the volume.
Density = 7.88 kg / 4 liters
Performing the calculation:
Density = 1.97 kg/liter
Therefore, the density of the paint is 1.97 kg/liter.
Density is a measure of how much mass is contained in a given volume. In this case, the density tells us that for every liter of paint, there is an average mass of 1.97 kilograms.
This value is rounded to two decimal places as per the instructions.
Understanding the density of a substance is important in various fields such as physics, chemistry, and engineering.
It provides valuable information about the compactness and weight of a material.
For example, knowing the density of a liquid like paint is essential in determining how it will behave when poured, how much space it will occupy, and how much it will weigh.
Additionally, density plays a role in calculations involving buoyancy and fluid dynamics.
In conclusion, the density of the paint is calculated to be 1.97 kg/liter. This information helps us understand the relationship between the mass and volume of the paint and provides insights into its physical properties.
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I just need help with the range domain is [-2,3)
Answer:
We don't need to worry about the displaystyle- {3} −3 anyway, because we dcided in the first step that displaystyle {x}ge- {2} x ≥ −2. So the domain for this case is displaystyle {x}ge- {2}, {x}ne {3} x≥ −2,x≠ 3, which we can write as displaystyle {left [- {2}, {3}right)}cup {left ({3},inftyright)} [−2,3)∪(3,∞).
Step-by-step explanation:
One of the graphs represents the statement, "y is greater than two less than the product of x and three." Which graph is it?
Based on the analysis, the graph that represents the statement "y is greater than two less than the product of x and three" is Option C.
To determine which graph represents the statement "y is greater than two less than the product of x and three," we need to analyze the given options and match them with the statement.
The statement "y is greater than two less than the product of x and three" can be represented mathematically as:
y > 2 - 3x
Now let's examine the given graphs and compare them to the equation:
Option A: This graph shows a horizontal line at y = 2. It does not involve any product of x and three, so it does not match the given statement.
Option B: This graph shows a line with a positive slope passing through the point (0, 2). While it includes the product of x and three, it does not satisfy the condition of "y is greater than two less than the product of x and three." Therefore, it does not represent the given statement.
Option C: This graph shows a line with a positive slope passing through the point (0, 2) and includes the region above the line y = 3x - 2. This region satisfies the condition of "y is greater than two less than the product of x and three." Therefore, Option C represents the given statement.
Option D: This graph shows a horizontal line at y = -2. It does not match the given statement.
Option C is correct.
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Note: This is the final question on search engine
Un objeto que se hace girar, se desplaza 25 radianes en 0.8 segundos. ¿cuál es la velocidad angular de dicho objeto?
The angular velocity of the object is 31.25 radians/second.
Angular velocity is defined as the change in angular displacement per unit of time. In this case, the object rotates a total of 25 radians in 0.8 seconds. Therefore, the angular velocity can be calculated by dividing the total angular displacement by the time taken.
Angular velocity (ω) = Total angular displacement / Time taken
Given that the object rotates 25 radians and the time taken is 0.8 seconds, we can substitute these values into the formula:
ω = 25 radians / 0.8 seconds
Simplifying the equation gives:
ω = 31.25 radians/second
So, the angular velocity of the object is 31.25 radians/second.
Angular velocity measures how fast an object is rotating and is typically expressed in radians per second. It represents the rate at which the object's angular position changes with respect to time.
In this case, the object completes a rotation of 25 radians in 0.8 seconds, resulting in an angular velocity of 31.25 radians per second. This means that the object rotates at a rate of 31.25 radians for every second of time.
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Note the translated question is:
An object that is rotated moves 25 radians in 0.8 seconds. what is the angular velocity of said object?
Five years older than Mukhari. Find the value of the expression if Mukhari is 43 years old.
Find the length of side a. 13, 5 B on a right triangle
In a right triangle, the length of side "a" is 12.
The Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, can be used to find the length of side "a" in a right triangle with sides of 13 and 5 units.
Let's assign "a" as the unknown side. According to the Pythagorean theorem, we have the equation: [tex]a^{2}[/tex] = [tex]13^{2}[/tex] - [tex]5^{2}[/tex].
Simplifying the equation, we get [tex]a^{2}[/tex] = 169 - 25, which becomes [tex]a^{2}[/tex] = 144.
To solve for "a," we take the square root of both sides: a = √144.
The square root of 144 is 12. Therefore, side "a" has a length of 12 units.
In summary, using the Pythagorean theorem, we determined that side "a" in the right triangle with side lengths 13 and 5 units has a length of 12 units.
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raul enlarges a photo 6 times and then reduces it 2 times. Jen enlarges a photo 5 times. If they start with the same photo, how much wider is Jen's photo than Rauls?
Step-by-step explanation:
x = width
Raul x then 6x then finally 3x
Jen x then 5 x
5x versus 3x
5x/3x = 1 2/3 wider
Quadrilateral EFGH is an isosceles trapezoid with bases EH and FG. The measure of angle HGF is (9y + 3)°, and the measure of angle EFG is (By + 5)°.
What is the measure of angle HGF?
The correct Option is A. The measure of angle HGF is 20°.
Quadrilateral EFGH is an isosceles trapezoid with bases EH and FG.
The measure of angle HGF is (9y + 3)°, and the measure of angle EFG is (By + 5)°.
To find the measure of angle HGF, we need to solve for the value of y.
Since EFGH is an isosceles trapezoid, the opposite angles are congruent.
Therefore, the measure of angle EFG is also (9y + 3)°.
To find the value of y, we can set the two expressions equal to each other: (9y + 3)° = (By + 5)°.
Next, we can solve for y by isolating it.
We subtract 3° from both sides: 9y = By + 2.
To get y by itself, we subtract By from both sides: 9y - By = 2.
Finally, we can factor out y: y(9 - B) = 2.
To solve for y, we divide both sides by (9 - B): y = 2 / (9 - B).
Now that we have the value of y, we can substitute it back into the expression for angle HGF: (9y + 3)°.
Thus, the measure of angle HGF is (9(2 / (9 - B)) + 3)°.
Therefore, The correct Option is A.
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Read the following statements.
Statement 1: "If she is stuck in traffic, then she is late."
Statement 2: "If she is late, then she is stuck in traffic."
Statement 3: "If she is not late, then she is not stuck in traffic."
Meg writes, "Statement 3 is the inverse of statement 2 and contrapositive of statement 1."
Cassandra writes, "Statement 2 is the converse of statement 1 and inverse of statement 3."
Who is correct?
Both Meg and Cassandra are incorrect.
Only Meg is correct.
Both Meg and Cassandra are correct.
Only Cassandra is correct.
`Both Meg and Cassandra are incorrect in their assessments (option a).
Meg and Cassandra have both misunderstood the logical relationships between the statements. Let's analyze each statement and compare their claims:
Statement 1: "If she is stuck in traffic, then she is late."
Statement 2: "If she is late, then she is stuck in traffic."
Statement 3: "If she is not late, then she is not stuck in traffic."
Meg's claims: Meg states that Statement 3 is the inverse of Statement 2 and the contrapositive of Statement 1. However, this is incorrect. The inverse of Statement 2 would be "If she is not stuck in traffic, then she is not late," and the contrapositive of Statement 1 would be "If she is not late, then she is not stuck in traffic." So Meg's analysis is incorrect.
Cassandra's claims: Cassandra states that Statement 2 is the converse of Statement 1 and the inverse of Statement 3. However, this is also incorrect. The converse of Statement 1 would be "If she is late, then she is stuck in traffic," and the inverse of Statement 3 would be "If she is late, then she is stuck in traffic." So Cassandra's analysis is incorrect as well.
Therefore, both Meg and Cassandra are wrong in their assessments. The correct logical relationships are as follows:
- The contrapositive of Statement 1 is Statement 3.
- The converse of Statement 1 is Statement 2.
Hence, the correct answer is that both Meg and Cassandra are incorrect.
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find the critical numbers of the function.
f(x)=x^2(x-3)^2
√7
7. Given that the sin(E)= 4 and TE = 4, determine the
remaining sides of A THE. Give exact answers.
E
Answer:
Step-by-step explanation:
To determine the remaining sides of triangle THE given that sin(E) = 4 and TE = 4, we can use the sine ratio.
The sine ratio is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.
In this case, sin(E) = 4/TE, which means the side opposite angle E is 4 and the hypotenuse TE is 4.
Using the Pythagorean theorem, we can find the length of the remaining side TH:
TH^2 = TE^2 - HE^2
TH^2 = 4^2 - 4^2
TH^2 = 16 - 16
TH^2 = 0
TH = 0
Therefore, the length of side TH is 0.
The base of a triangle is 3 inches more than two times the height. If the area of the triangle is 7 in.² find the base and height.
Answer:
Let's denote the height of the triangle as "h" inches.
According to the given information, the base of the triangle is 3 inches more than two times the height. Therefore, the base can be expressed as (2h + 3) inches.
The formula to calculate the area of a triangle is:
Area = (1/2) * base * height
Substituting the given values, we have:
7 = (1/2) * (2h + 3) * h
To simplify the equation, let's remove the fraction by multiplying both sides by 2:
14 = (2h + 3) * h
Expanding the right side of the equation:
14 = 2h^2 + 3h
Rearranging the equation to bring all terms to one side:
2h^2 + 3h - 14 = 0
Now, we can solve this quadratic equation. We can either factor it or use the quadratic formula. In this case, let's use the quadratic formula:
h = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, the values are:
a = 2
b = 3
c = -14
Substituting these values into the quadratic formula:
h = (-3 ± √(3^2 - 4 * 2 * -14)) / (2 * 2)
Simplifying:
h = (-3 ± √(9 + 112)) / 4
h = (-3 ± √121) / 4
Taking the square root:
h = (-3 ± 11) / 4
This gives us two possible solutions for the height: h = 2 or h = -14/4 = -3.5.
Since a negative height doesn't make sense in this context, we discard the negative solution.
Therefore, the height of the triangle is h = 2 inches.
To find the base, we substitute this value back into the expression for the base:
base = 2h + 3
base = 2(2) + 3
base = 4 + 3
base = 7 inches
Hence, the base of the triangle is 7 inches and the height is 2 inches.
Step-by-step explanation:
-The answer for the height is 5.5 units.
-The base of the triangle is aproximately 2.5454 units.
To answer this problem, you have to set an equation with the information you're given. If you do it correctly, it should look like this:
7=1/2(3+2h)
-Now, you have to solve for h:
7=1.5+h
7-1.5=h
5.5=h
-Now that you have the height, you plug it in into the triangle area formula to solve for the base:
7=1/2(b)5.5
7=2.75b
7/2.75=b
b≈2.5454
-To make sure that the corresponding values for the base and height are correct, we plug the values in and this time we are going to solve for a(AREA):
A(triangle)=1/2(2.5454)(5.5)
A=1/2(13.9997)
A=6.99985 square units
-We round the result to the nearest whole number and we get our 7, which is the given value they gave us.
Last year, Ali biked b miles. This year, he biked 358 miles. Using b, write an expression for the total number of miles he biked
Let f(x) = 4x² - 2x +11
The slope of the tangent line to the graph of f(x) at the point (3, 41)
Slope =
M=
B=
Answer:
f(x) = 4x² - 2x + 11
f'(x) = 8x - 2
m = f'(3) = 8(3) - 2 = 24 - 2 = 22
41 = 22(3) + b
41 = 66 + b
b = -25
y = 22x - 25
An electric utility company determines the monthly bill for a residential customer by adding an energy charge of 9.32 cents per kilowatt-hour to its base charge of $18.32 per month. Write an equation for the monthly charge y in terms of x, the number of kilowatt-hours used.
Answer: y = 18.32 + 0.0932x
Step-by-step explanation:
Given that the base charge per month is $18.32 and the charge per kilowatt-hour is 9.32 cents, which is assigned to the variable x, we can write an equation to find the total monthly charge based on kilowatt-hours.
total = monthly charge + kilowatt-hour x the amount of kilowatts
y = 18.32 + 0.0932x
here we see that y is the total cost per month, our base monthly charge is $18.32, our kilowatt hour charge is 9.32 cents, which we write in terms of dollar amounts for the sake of the equation (just divide by 100), and our variable x represents the number of kilowatts.
nt- Maths ACSF Level 3
Your mum has saved $12,000 and has agreed to give you a share.
Would you rather have
1/5 or 1/10
HELP ANSWER THIS AND GET 65 POINTS
Amelie is asked to draw a rhombus. Raj is asked to draw a rectangle. They both drew this shape.
(a)What shape did they draw? Explain how you know.
(b)Was Amelie correct drawing this shape? Was Raj correct drawing this
shape? Explain.
Step-by-step explanation:
They both drew a square
a rhombus has four sides of equal length === so a square is a rhombus
a rectangle has four 90 degree angles....so a square is a rectangle too
Sooooo...they are both correct
Answer:
Are there any dimensions given?
Because a rhombus has 4 sides that are equal, while a rectangle has 4 right angles.
⦁ The construction of copying is started below. The next step is to set the width of the compass to the length of . How does this step ensure that the new angle will be congruent to the original angle?
Answer:
i believe by creating radii of equal lengths.
Step-by-step explanation:
it gives a path to create an angle congruent to angle APB. The angle APB would have the same radii (BP and AP) and the same width as the congruent angle that would be created.
Wish you good luck.
university theater sold 527 tickets for a play. Tickets cost $22 per adult and $13 per senior citizen if total receipts were 8579 how many senior citizens tickets were shown?? A.282 B.192 C.335 D. 245
Answer:
C. 335
Step-by-step explanation:
We will need a system of equations to determine how many senior citizen tickets were sold, where
A represents the quantity of adult tickets sold,and S represents the quantity of senior citizen tickets sold.First equation:
The sum of the revenues earned from the adult and senior citizen tickets equals $8579.00:
(price of adult tickets * quantity) + (price of senior citizen tickets * quantity) = total revenue earned
Since adult tickets cost $22/adult, senior citizen tickets cost $13/senior citizen, and the total revenue earned is $8579.00, our first equation is given by:
22A + 13S = 8579
Second Equation:
The sum of the quantities of adult and senior citizen tickets equals the total number of ticket sold:
quantity of adult tickets + quantity of senior citizen tickets = total quantity of tickets sold
Since the theater sold 527 tickets in total, our second equation is given by:
A + S = 527
Method to Solve: Elimination:
We can solve for S by first eliminating. To eliminate A, we'll first need to multiply the second equation by -22:
Multiplying -22 by A + S = 527
-22(A + S = 527)
-22A - 22S = -11594
Now we can add this equation to the first equation to find S, the number of senior citizen tickets:
Adding 22A + 13S = 8579 to -22A - 22S = -11594:
22A + 13S = 8579
+
-22A - 22S = -11594
----------------------------------------------------------------------------------------------------------
(22A - 22A) + (13S - 22S) = (8579 - 11594)
(-9S = -3015) / -9
S = 335
Thus, 335 senior citizen tickets (answer C.)
Optional: Find A (the number of adult tickets sold) to check the validity of our answers:
We can find A by plugging 335 for S in any of the two equations in our system. Let's use the second one:
Plugging in 335 for S in A + S = 527:
(A + 335 = 527) - 335
A = 192
Thus, 192 adult tickets were sold.
Checking the validity of our answers:
Now we can check that our two answers for S and A are correct by plugging in 335 for S and 192 for A in both of the equations in our system and seeing if we get the same answer on both sides:
Plugging in 335 for S and 192 for A in 22A + 13S = 8579:
22(192) + 13(335) = 8579
4224 + 4355 = 8579
8579 = 8579
Plugging in 335 for S and 192 for A in A + S = 527:
192 + 335 = 527
527 = 527
Thus, our answers for S and A are correct.
4. In triangle PQR, Q = 90°, cos R = 0.6 and PQ = 8 cm. Find PR and RQ. (May draw the own diagram by above info provided)
Answer:
PR = 10
RQ = 6
Step-by-step explanation:
We have cos R = 0.6
also, cos R = adjacent/ hypotenuse
= RQ/PR
⇒ RQ/PR = 0.6
⇒ RQ = 0.6 PR -eq(1)
By pythagoras theorem,
PQ² + RQ² = PR²
given PQ = 8 and sub the value of RQ from eq(1):
8² + (0.6 PR)² = PR²
⇒ 64 + 0.36PR² = PR²
⇒ (1-0.36)PR² = 64
⇒ 0.64 PR² = 64
⇒ PR² = 64/0.64
⇒ PR² = 100
⇒ PR = 10
sub PR in eq(1):
RQ = 0.6*10
⇒ RQ = 6
Question 2 (1 point)
Which one of the following is true of the mean?
1) one of the less common averages
2) equals some whole number
observations must be ordered from least to most before calculating the
3)
mean
4) equals the sum of all observations divided by the number of observations
The correct statement about the mean is:
The mean equals the sum of all observations divided by the number of observations.
The mean is a commonly used measure of central tendency. It is calculated by summing up all the observations and then dividing the sum by the total number of observations. It provides an average value that represents the typical value of the data set.
To calculate the mean, it is not necessary to order the observations from least to most. The order of the observations does not affect the mean calculation.
The mean is not necessarily a whole number. It can be a decimal or a fraction, depending on the data set and the values of the observations. The mean represents the balance point of the data set and can take on any real number value.
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Which linear function has the greatest y-intercept?
y = 6 x + 1
On a coordinate plane, a line goes through points (0, 2) and (5, 0).
On a coordinate plane, a line goes through points (1, 2) and (0, negative 3).
y = 3 x + 4
The linear function that has the greatest y-intercept is [tex]y = 3x + 4[/tex].
In a linear equation, the y-intercept is where the line crosses the y-axis.
It is represented by the constant term in the equation.
So, to determine which linear function has the greatest y-intercept, we need to look at the constant term of each equation.
Let's consider each equation: [tex]y = 6x + 1[/tex]
The constant term in this equation is 1.
So, the y-intercept is 1.
On a coordinate plane, a line goes through points (0, 2) and (5, 0).
To find the equation of this line, we can use the point-slope form:
[tex]y - y1 = m(x - x1)[/tex]
where m is the slope and (x1, y1) is a point on the line.
Using the points (0, 2) and (5, 0), we get:
[tex]m = \frac{(0 - 2)}{(5 - 0)} =-\frac{2}{5}[/tex]
So, the equation of the line is:
[tex]y - 2 = (\frac{-2}{5} )(x - 0)[/tex]
[tex]y = (\frac{-2}{5} )x + 2[/tex]
The constant term in this equation is 2.
So, the y-intercept is 2.
On a coordinate plane, a line goes through points (1, 2) and (0, -3).
To find the equation of this line, we can use the point-slope form:
[tex]y - y1 = m(x - x1)[/tex]
where m is the slope and (x1, y1) is a point on the line.
Using the points (1, 2) and (0, -3), we get:
[tex]m = \frac{ (-3 - 2) }{(0 - 1)} = -5[/tex]
So, the equation of the line is:
[tex]y - 2 = (-5)(x - 1)y = -5x + 7[/tex]
The constant term in this equation is 7.
So, the y-intercept is 7.
[tex]y = 3x + 4[/tex]
The constant term in this equation is 4.
So, the y-intercept is 4.
Therefore, we can see that the linear function that has the greatest y-intercept is [tex]y = 3x + 4[/tex].
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Q.14 In the figure given below, let the lines 1, and 1, be parallel and t is transversal. Find
the value of x.
Answer:
The consecutive interior angles are supplementary, so we have:
3x + 20 + 2x = 180
5x + 20 = 180
5x = 160, so x = 32
After long study, tree scientists conclude that a eucalyptus tree will
3
grow at the rate of +
ft. per years, where t is time in years. Find the
5 (t+1)³
number of feet the tree will grow in the first year. Be sure to use the proper
units of measure.
After a long study, tree scientists conclude that a eucalyptus tree will grow at the rate of 3ft per year, where t is time in years. So, the tree will grow 5 feet in the first year.
We have to find the number of feet the tree will grow in the first year, given that 5(t + 1)³. The rate of growth of a tree is given as 3ft/year. Therefore, in the first year, the tree will grow 3 feet.
To find the number of feet the tree will grow in the first year, we substitute t = 0 in the given expression.
5(t + 1)³ = 5(0 + 1)³= 5(1)³= 5(1)= 5. Therefore, the tree will grow 5 feet in the first year.
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GEOMETRY 100 POINTS
TY
Answer:
A.
Step-by-step explanation:
In this case, we have to use tan ([tex]\frac{opposite}{adjacent}[/tex] because we are asked for the opposite side (x) given the adjacent side (20 m).
So tan(75)=[tex]\frac{x}{20}[/tex]
Solve for x
x = 20 * tan(75)
x = 74.641...
x = 74.64 m
Answer:
The height is 74.64 meters
Step-by-step explanation:
We have a ΔABC with ∠B = 75°, hypotenuse = AB
[tex]cos\; 75\textdegree = \frac{\sqrt{3} -1}{2\sqrt{2} }\\\\\frac{1}{cos\; 75\textdegree} = \frac{2\sqrt{2} }{\sqrt{3} -1}[/tex]
cos B = adjacent/hyppotenuse
⇒ hypotenuse (AB) = adjacent/cosB = 20/cosB
[tex]= 20 \frac{2\sqrt{2} }{\sqrt{3} -1}\\\\= \frac{40\sqrt{2} }{\sqrt{3} -1}\\\\= 77.27[/tex]
⇒ AB = 77.27
By pythagoras theorem,
AB² = AC² + BC²
⇒ AC² = AB² - BC²
= 77.27² - 20²
AC² = 5570.65
⇒ AC = √5570.65
AC = 74.64
What is the perimeter of a rectangle with workings
Answer:
See below
Step-by-step explanation:
The perimeter of a rectangle is [tex]P=2L+2W[/tex] where L is the length and W is the width.
Find the focus of the parabola defined by the equation 100 points.
Answer : Focus is (0,3)
To find the focus of the parabola defined by the equation (y - 3)² = -8(x - 2), we can compare it with the standard form of a parabolic equation: (y - k)² = 4a(x - h).
In the given equation, we have:
(y - 3)² = -8(x - 2)
Comparing it with the standard form, we can determine the values of h, k, and a:
h = 2
k = 3
4a = -8
Solving for a, we get:
4a = -8
a = -8/4
a = -2
Therefore, the vertex of the parabola is (h, k) = (2, 3), and the value of 'a' is -2.
The focus of the parabola can be found using the formula:
F = (h + a, k)
Substituting the values, we get:
F = (2 + (-2), 3)
F = (0, 3)
Therefore, the focus of the parabola defined by the equation (y - 3)² = -8(x - 2) is at the point (0, 3).
Answer:
Focus = (0, 3)
Step-by-step explanation:
The focus is a fixed point located inside the curve of the parabola.
To find the focus of the given parabola, we first need to find the vertex (h, k) and the focal length "p".
The standard equation for a sideways parabola is:
[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]
where:
Vertex = (h, k)Focus = (h+p, k)If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left.
Given equation:
[tex](y-3)^2=-8(x-2)[/tex]
Compare the given equation to the standard equation to determine the values of h, k and p:
h = 2k = 34p = -8 ⇒ p = -2The formula for the focus is (h+p, k).
Substituting the values of h, p and k into the formula, we get:
[tex]\begin{aligned}\textsf{Focus}&=(h+p,k)\\&=(2-2,3)\\&=(0,3)\end{aligned}[/tex]
Therefore, the focus of the parabola is (0, 3).
3. Your family is planning a road trip stretching from coast to coast for this summer. The route and the time frame are nearly set; now you need to plan out the finances. Your parents have decided that rental of an RV will be cheaper than staying in hotels, but they would like an estimate on the total cost. Can you help them?
a. To rent an RV, the following costs apply: $125 per day, plus 32 cents per mile. Additionally, to drop off the RV on the other side of the country, there is an extra fee of $2,500. Write an equation to describe the total cost of RV rental.
b. Your parents have two options for their road trip plans. The first option stretches over 3500 miles and includes fewer stops but more beautiful scenery. It will take about a week and a half (11 days). The second option stretches over just 3000 miles, but it includes more overnight stops and will therefore take two weeks (14 days). Which of these two options is cheaper?
c. Your little sister really wants to take the two-week trip, but your parents really want to keep the RV rental cost under $5,000. You can compromise by either taking a more direct route (lessening the miles) or by stopping for less overnight stays (lessening the days of the rental). What would the domains be for these two compromises? Justify why you think your domains are correct.
d. Write and solve equations to find how many miles or how many days you would have to eliminate in order to stay under the $5,000 budget. Explain each step as you solve your equations. Finally, make a recommendation to your parents about which compromise you think is best.
Answer:
Step-by-step explanation:
a. To write an equation describing the total cost of RV rental, we can use the given information:
Let x be the number of days of rental.
Let y be the number of miles driven.
The total cost of RV rental can be calculated as follows:
Total cost = (125 * x) + (0.32 * y) + 2500
b. To compare the cost of the two options, we need to calculate the total cost for each option.
Option 1:
x = 11 days
y = 3500 miles
Total cost = (125 * 11) + (0.32 * 3500) + 2500
Option 2:
x = 14 days
y = 3000 miles
Total cost = (125 * 14) + (0.32 * 3000) + 2500
Compare the total costs of both options to determine which one is cheaper.
c. To compromise and keep the rental cost under $5,000, we can adjust either the number of miles driven or the number of days of rental.
For the first compromise (lessening the miles), let's assume the new number of miles driven is y1.
The domain for the compromise in miles would be 0 ≤ y1 ≤ 3500, as you cannot drive more miles than the original option or negative miles.
For the second compromise (lessening the days of rental), let's assume the new number of days of rental is x1.
The domain for the compromise in days would be 0 ≤ x1 ≤ 14, as you cannot have more days of rental than the original option or negative days.
The justification for these domains is that they restrict the values within the range of the original options while allowing for adjustments in the desired direction.
d. To find out how many miles or how many days need to be eliminated to stay under the $5,000 budget, we can set up and solve equations.
For the compromise in miles (y1):
(125 * x) + (0.32 * y1) + 2500 ≤ 5000
For the compromise in days (x1):
(125 * x1) + (0.32 * y) + 2500 ≤ 5000
Solve each equation by isolating the variable to determine the maximum allowed value for y1 or x1, respectively.
Finally, after solving the equations, compare the maximum allowed values for y1 and x1 and consider other factors like practicality, time constraints, and preferences to make a recommendation to your parents about which compromise is best.
James wants to have earned $6,180 amount of interest in 28 years. Currently he finds
that his annual interest rate is 6.12%. Calculate how much money James needs to invest
as his principal in order to achieve this goal.
Answer:
$3606.44
Step-by-step explanation:
The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.
To do this, we need to use the formula for simple interest:
[tex]\boxed{I = \frac{P \times R \times T}{100}}[/tex],
where:
I = interest earned
P = principal invested
R = annual interest rate
T = time
By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:
[tex]6180 = \frac{P \times 6.12 \times 28}{100}[/tex]
⇒ [tex]6180 \times 100 = P \times 171.36[/tex] [Multiplying both sides by 100]
⇒ [tex]P = \frac{6180 \times 100}{171.36}[/tex] [Dividing both sides of the equation by 171.36]
⇒ [tex]P = \bf 3606.44[/tex]
Therefore, James needs to invest $3606.44.
please answer ASAP I will brainlist
Step-by-step explanation:
a) 23.6 (1.08)^x for 2016 x = 26 ('x' is the number of years past 1990)
23.6 (1.08)^(26) = 174.6 billion
b) 109 = 23.6 ( 1.08)^x
4.6186 = 1.08^x
x = log 4.6186 / log1.08 = 19.88 yrs
means 1990 + 19.88 yrs = year 2010
