This means that the coordinates of P are (a, b), where a is the value for which f'(a) = 0, and b = f(a).
What is coordinate?The term "coordinate" generally refers to a value or set of values that describe the position or location of a point or object in a particular system or space. In mathematics, coordinates are typically used to describe the position of a point on a graph or in a geometric plane, and they usually consist of a set of numerical values that indicate the distance or direction of the point from a specified origin or reference point. In geographic or cartographic contexts, coordinates might refer to latitude and longitude values that indicate a specific location on the Earth's surface. Other systems may use different types of coordinates, but the underlying idea is usually the same: a set of values that describe the position of an object or point in a given space or system.
if the graph of f has a horizontal tangent at point P, this means that the slope of the tangent line at P is zero.
Let (a, b) be the coordinates of P. Then the equation of the tangent line at P is:
[tex]y - b = f'(a)(x - a)[/tex]
Since the slope of the tangent line at P is zero, we have:
f'(a) = 0
This means that the derivative of f at x = a is zero. So, we need to find the value of a for which f'(a) = 0.
Once we find the value of a, we can substitute it into the equation of the tangent line to find the value of b.
So, let's find f'(x) first:
f(x) = ... (the function is not given, so we cannot find f'(x) explicitly)
We know that f'(a) = 0, so we have:
[tex]f'(a) = lim h- > 0 [f(a+h) - f(a)]/h = 0[/tex]
This means that:
[tex]lim h- > 0 [f(a+h) - f(a)]/h = 0[/tex]
Multiplying both sides by h, we get:
[tex]lim h- > 0 [f(a+h) - f(a)] = 0[/tex]
Taking the limit as h approaches 0, we get:
[tex]f(a) - f(a) = 0[/tex]
So, we have:
[tex]f(a) = b[/tex]
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A soccer goal is 8 yards wide. Suppose a goalie is standing on her line in
the center of her goal as a striker from the opposing team moves the ball
towards her. The near post angle, a, is formed by rays extending from the
ball to the near post and the goalie. Similarly, the far post angle, ß, is
formed by rays extending from the ball to the far post and the goalie. See
the figure.
a) Determine the near post angle and the far post angle when the striker is
24 yards from the near post and 28 yards from the far post.
b) How far is the goalie from the ball?
c) To cover the near post, the goalie moves toward the near post in order
to make the near post angle and the far post angle equal. How far
toward her near post does the goalie need to move?
Where the following triangle problem is given, note that:
A) α [tex]\approx[/tex] 11.0
β β [tex]\approx[/tex] 9.4
B) 25.59 yrds
C) 0.38 yrds
What is the explanation for the above?A) To determine the near post angle and the far post angle when the striker is 24 yards from the near post
1/2 (24²) + 1/2 (28²) - 1/4(10²) = 655 (central line length formula)
Cos α = (24² + 655 - 5²)/ (2 x 24 x √655)
= 0.98171498561
α = Cos ⁻¹ 0.98171498561
α = 10.973603643623608717848651724941
α [tex]\approx[/tex] 11.0° (Cosine Law)
For 28 yards from the far post.
Cos β = (28² + 655 - 5²)/ (2 x 28 x √655)
= 0.98659913977
β = Cos ⁻¹ 0.98659913977
β = 9.3905311636838307510867912796592
β [tex]\approx[/tex] 9.4°
B) Distance between the goalie from the ball is
√655 = 25.592967784139454896443137575823
Distance [tex]\approx[/tex] 25.59 yrds
C) 5-10 * ((24)/(24+28)) = 0.38 yrds (Angular Bisector Theorem)
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The polygon below is a regular polygon. Find the answer rounded to the nearest tenth.
HELP GIVING BRAINLIST HW DUE SOOON
Answer:
In a 30°-60°-90° right triangle, the length of the longer leg is √3 times the length of the shorter leg.
A = (1/2)Pa
= (1/2)(2)(8/√3)(6)(8)
= (384√3)/3 = 128√3 = 221.7 units^2
what is the answer to this problem
Calculate the MAY raw materials purchases in dollars. (SEE IMAGE FOR DETAILS) financial accounting
Rensing Ltd estimates sales for the second quarter of 2020 will be as follows. April: 2,520 May: 2,440 June: 2,390
target ending inventory finished products. March 31: 2,010 April 30: 2,280 May 31: 2,170 June 30: 2,330
The May raw materials purchases for May in Rensing Ltd., in dollars terms, is $32,620.
How the raw materials purchases are determined:The cost of raw materials purchased in May is determined by computing the required production units and multiplying the result by 2 units and the unit raw material cost.
Purchase Budget:April May June
Sales 2,520 2,440 2,390
Ending inventory 2,280 2,170 2,330
Goods available for
sale 4,800 4,610 4,720
Beginning inventory 2,280 2,170
Production units 2,330
Raw materials purchases 4,660 (2,330 x 2)
Raw materials price per unit = $7
Total purchases of Raw Materials for May = $32,620 (4,660 x $7)
Thus, we can conclude that in May Rensing Ltd. purchased raw materials worth $32,620.
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Find the range for the set numbers
Answer:
25
Step-by-step explanation:
range = largest number - smallest number
38-13=25
view the photo below. This is timed.
The other angle that is congruent to ∠DFA is: ∠BFC
How to identify Congruent angles?Congruent angles are defined as two or more angles that are said to be identical to each other. This means that the measure of these angles is equal to each other. These type of angles do not make any difference in the congruence of angles, which tells us that they can be acute, obtuse, exterior, or interior angles.
Now, we want to find the angle that is congruent to ∠DFA.
By inspection, we can see that ∠BFC is an opposite angle to ∠DFA.
We know that Opposite angles are the two angles opposite each other when two lines cross. They can also be called vertical angles due to sharing a vertex, which is the point where the two lines connect. Opposite angles always have the same measurement, making them congruent.
Thus, ∠BFC is congruent to ∠DFA.
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a cuboid with length of 21 cm and height of 16 cm has a volume of 6384 cm3. find its breadth ik
Answer:18
Step-by-step explanation:18
Minimise : 3x+2y
Subject to: 5x+y=10
X+y=6
X+4y= 12
Find this question?
This is a linear programming problem with three constraints and two variables, where the objective is to minimize the expression 3x + 2y subject to the following constraints:
5x + y = 10
x + y = 6
x + 4y = 12
The first constraint represents a straight line in the x-y plane, the second constraint represents another straight line, and the third constraint represents yet another straight line. The feasible region is the region where all three constraints are satisfied simultaneously, which is the intersection of the three lines.
To solve this problem, you can use the method of substitution or elimination to solve for one variable in terms of the other in two of the equations, and then substitute this expression into the third equation to obtain a single equation in one variable. You can then solve for that variable, and use back-substitution to find the values of the other variable.
For example, using the first and second equations, you can solve for x in terms of y as follows:
x = 6 - y (from the second equation)
y = 10 - 5x (from the first equation)
Substituting y = 10 - 5x into the third equation, you get:
x + 4(10 - 5x) = 12
Simplifying this equation, you get:
-19x + 40 = 0
Solving for x, you get:
x = 40/19
Using x = 40/19 and the equation x + y = 6, you can solve for y as:
y = 6 - x = 6 - 40/19 = 94/19
Therefore, the minimum value of 3x + 2y subject to the given constraints is:
3(40/19) + 2(94/19) = 222/19
And the values of x and y that minimize this expression are:
x = 40/19 and y = 94/19.
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This is a linear programming problem with three constraints and two variables, where the objective is to minimize the expression 3x + 2y subject to the following constraints:
5x + y = 10
x + y = 6
x + 4y = 12
The first constraint represents a straight line in the x-y plane, the second constraint represents another straight line, and the third constraint represents yet another straight line. The feasible region is the region where all three constraints are satisfied simultaneously, which is the intersection of the three lines.
To solve this problem, you can use the method of substitution or elimination to solve for one variable in terms of the other in two of the equations, and then substitute this expression into the third equation to obtain a single equation in one variable. You can then solve for that variable, and use back-substitution to find the values of the other variable.
For example, using the first and second equations, you can solve for x in terms of y as follows:
x = 6 - y (from the second equation)
y = 10 - 5x (from the first equation)
Substituting y = 10 - 5x into the third equation, you get:
x + 4(10 - 5x) = 12
Simplifying this equation, you get:
-19x + 40 = 0
Solving for x, you get:
x = 40/19
Using x = 40/19 and the equation x + y = 6, you can solve for y as:
y = 6 - x = 6 - 40/19 = 94/19
Therefore, the minimum value of 3x + 2y subject to the given constraints is:
3(40/19) + 2(94/19) = 222/19
And the values of x and y that minimize this expression are:
x = 40/19 and y = 94/19.
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Americans are stressed out!
A psychologist would like to estimate the proportion of Americans that say "the future of the nation is a
significant source of stress for me." To help form an estimate, the psychologist randomly selected 664
Americans and found that 69.6% of the sample agreed with the statement "the future of the nation is a
significant source of stress for me."
Using a 99% confidence level, determine the margin of error, E, and a confidence interval for the true
proportion of all Americans that say the "the future of the nation is a significant source of stress for me."
Report the confidence interval using interval notation. Round solutions to four decimal places, if necessary.
The margin of error is given by E:
A 99% confidence interval is given by:
To find the margin of error, we can use the formula: E = z√((p(1-p))/n)
How is margin of error determined?where z is the z-score for a 99% confidence level, p is the sample proportion, and n is the sample size.
From the table of standard normal distribution, the z-score for a 99% confidence level is 2.576.
Plugging in the values, we get:
E = 2.576√((0.696(1-0.696))/664) ≈ 0.0385
So the margin of error is 0.0385.
To find the confidence interval, we can use the formula:
p ± E
where p is the sample proportion and E is the margin of error.
Plugging in the values, we get:
0.696 ± 0.0385
So the 99% confidence interval for the true proportion of all Americans that say "the future of the nation is a significant source of stress for me" is (0.6575, 0.7345). In interval notation, this can be written as [0.6575, 0.7345].
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4. An opportunity cost that a business might face is
a. forgoing the interest that the owners could have earned on their savings if they had not
invested their savings in the business
Ob. forgoing rental income to be earned if the business rented out its building
forgoing the salaries the owners would have received at other jobs
OC.
c.
Od.
d. all of the above
5. The difference between macroeconomics and microeconomics is that
a. microeconomics studies inflation while macroeconomics studies taxes
Economics
b. macroeconomics looks at the economy as a whole while microeconomics looks at single
units in the economy
Oc. macroeconomics measures the price of a good and quantity demanded while
microeconomics looks
at things like unemployment or GDP
Od.
d. macroeconomics looks at single units in the economy while microeconomics looks at the
economy as a whole
It’s probability and I need your help pls
The theoretical probabilities are: 0.15, 0.15, and 0.05 respectively
What is probability?Probability is a branch of mathematics concerned with the analysis of random phenomena
The given parameters that will help us to get the probabilities are
25% are stakeholders
20% have dark hair
The probability of being stakeholders 20%/25%
= 0.20/0.25 = 0.
b) 1-0.8 * 1.0.25
0.2 * 0.75 = 0.15
c. 0.2 * 0.75 = 0.15
d. Has light hair and is a stakeholder
0.20 * 0.25
= 0.05
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Two different rectangles are joined together to make a compound shape. Shape A has a length of (x + 3) and a width of (x + 2). Shape B has a length of (x + 6) and a width of (x-2). All measurements are in centimetres. (x+3) Shape A Shape B (x+6) (x + 2) NOT TO SCALE (x-2) Find an expression for the area of the compound shape in cm². Give your answer in the form ax² + bx + c.
The expression for the area of the compound shape in cm² is 2x^2 + 11x - 6.
What is the expression for the area?To find the expression for the area of the compound shape, we need to first calculate the individual areas of Shape A and Shape B, and then add them together.
The area of Shape A is given by multiplying its length and width:
Area of Shape A = (x + 3) * (x + 2)
The area of Shape B is given by multiplying its length and width:
Area of Shape B = (x + 6) * (x - 2)
Now, we can add the two areas together to get the expression for the area of the compound shape:
Area of compound shape = Area of Shape A + Area of Shape B
= (x + 3) * (x + 2) + (x + 6) * (x - 2)
Expanding the above expression, we get:
= x^2 + 2x + 3x + 6 + x^2 + 6x - 12
= 2x^2 + 11x - 6
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IF YOU CAN ANSWER THIS CORRECT WITH A Good explanation I'll give 5 stars, a thanks and brainly (also your very smart)
Rebecca is x years old.Mary is 8 years older than rebecca. Jill is three times older than mary. The sum of their ages is 67.
A) form an expression in terms of x
Answer:
A) 5x+32=67
Rebecca is 7, Mary is 15, and Jill is 45
Step-by-step explanation:
Rebecca is x years old.
If Mary is 8 years older than Rebecca, Mary's age is 8 more than x.
We can write Mary's age as:
x+8
Jill is three times older than Mary.
This means that Jill's age is equal to three times x+8.
We can write Jill's age as:
3(x+8)
Use the distributive property.
3(x+8)=
3x+24
So, Jill's age (in terms of x) is 3x+24.
The sum of their ages is 67, so if we add all of their ages, we will get 67.
x+(x+8)+(3x+24)=67=
5x+32=67
Not sure if you want this solved, but here it is:
5x+32=67=
5x=35=
x=7
Let's find Mary's age.
x+8=
7+8=
15.
Now, let's find Jill's age.
3x+24=
3(7)+24=
21+24=
45.
So, Rebecca is 7, Mary is 15, and Jill is 45.
Select the statement that shows equivalent measurements.
4.5 meters = 0.0045 kilometers
4.5 meters = 0.045 centimeters
4.5 meters = 0.45 decimeters
4.5 meters = 45 decameters
The statement that shows equivalent measurements is "4.5 meters = 0.0045 kilometers".
How to solve the problem?
To convert meters to kilometers, we need to divide by 1000, since there are 1000 meters in a kilometer. Therefore, 4.5 meters is equal to 4.5/1000 = 0.0045 kilometers.
The other statements are incorrect:
4.5 meters is not equal to 0.045 centimeters, since there are 100 centimeters in a meter, so 4.5 meters is equal to 450 centimeters.
4.5 meters is not equal to 0.45 decimeters, since there are 10 decimeters in a meter, so 4.5 meters is equal to 45 decimeters.
4.5 meters is not equal to 45 decameters, since there are 10 meters in a decameter, so 4.5 meters is equal to 0.45 decameters.
It is important to be able to convert between different units of measurement in order to make accurate comparisons and calculations. In this case, the correct conversion factor was used to convert meters to kilometers, resulting in an equivalent measurement.
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Find a rational number halfway in between the two numbers.
8/10 and 1/8
A rational number between 8/10 and 1/8 is 37/80.
We know that a rational number between two rational numbers can be given by finding the average of the two given numbers:
The numbers are 8/10 and 1/8.
Let's simplify the fractions first:
8/10 = 4/5 (dividing both numerator and denominator by 2)
1/8 = 1/8 (already in simplest form)
Average = [tex](\frac{4}{5} + \frac{1}{8})/2[/tex]
= [tex](\frac{(4*8) + (5*1)}{40} )/2[/tex]
= [tex](\frac{37}{40}) /2[/tex]
= [tex]\frac{37}{80}[/tex]
So, the rational number halfway between 8/10 and 1/8 is 37/80.
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help me in 8th grade mathhh
Answer:
C
Step-by-step explanation:
input y=x+3 into the second equation and solve for x
-2x+y=1
so -2x +x+3 =1
solve for x
x = 2
y= 5
Can somebody please help me find poetic elements in this poem fast!!!
Poem: citizenship by Javier Zamora
There’s also an image of the poem
Some poetic elements found in the poem are:
IronyRepetitionPersonificationMetaphorImageryWhat are poetic elements?Poetic elements are described as the devices used that characterize a piece of writing as a poem and are integral to categorise a piece of writing as poetry, such as poetic meter and rhyme scheme.
In the poem, the author uses Imagery which is described as use of sensory details to create vivid mental images in the reader's mind.
The author made use of metaphor as a comparison between two things that are not alike, in order to create an image or deepen understanding.
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Find the area of the shapes below. Make sure to label your answers with units.
You must show all of your work to receive credit.
Find the area for a
a) The area of the triangle is 13.3 square units.
b) The area of the rectangle is 57.4 square units.
Let's start with the triangle. The area of a triangle can be calculated by multiplying its base and height and then dividing the result by 2. In your case, the base of the triangle is 7 units and the height is 3.8 units. Therefore, the area of the triangle can be calculated as:
Area of triangle = (Base × Height) ÷ 2
= (7 × 3.8) ÷ 2
= 13.3 square units
Now, let's move on to the rectangle. The area of a rectangle can be calculated by multiplying its length and width. In your case, the width of the rectangle is 7 units and the height is 8.2 units. Therefore, the area of the rectangle can be calculated as:
Area of rectangle = Length × Width
= 8.2 × 7
= 57.4 square units
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HELPP Billie solved the equation below by completing the square, but she got the incorrect solution. In which step did Billie first make an error?
Step 1 : x 2 + 6 x = 16
Step 2 : x 2 + 6 x + 9 = 16
Step 3 : ( x + 3 ) 2 = 16
Step 4 : x + 3 = ± 4 Step 5 : x = 1 , x = − 7
Billie made the error in the second step of the equation
How to solve the equationBillie made an error in Step 2. She added 9 to one sides of the equation, but she should have added 9 to the left side only. The correct steps are as follows:
Step 1: x^2 + 6x = 16
Step 2: x^2 + 6x + 9 = 16 + 9
Step 3: (x + 3)^2 = 25
Step 4: x + 3 = ±√25
Step 5: x = -3 + 5, x = -3 - 5
Step 6: x = 2, x = -8
So, the correct solutions are x = 2 and x = -8.
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Evaluate the function as indicated
[tex]g(x) = {5.9}^{x} [/tex]
(a) x = -1 G(-1) =
(b) G(-2) = x = -2
(c) x = √5 G(√5) =
what is the answer for a, b, and c?
Calculate how far the village is north of O
Step-by-step explanation:
See image
The scale drawing car length is 3cm. If the scale is 1cm:4ft, what is the actual car length?
Answer: The actual car length is 12ft.
Step-by-step explanation:
Actual car length = 3cm x 4ft/cm = 12ft
What is the equation of the line that represents the horizontal asymptote of the function
f(x) = 3000 (1 +0.09)^x-2 +4?
Answer: y=4
Step-by-step explanation:
The Parent function [tex]y=a^{x}[/tex] has a horizontal asymtote at y=0
because the function approaches 0 but never touches it no matter how small the number you input. See image. Asymtotes are like a boundary that is not passed
Your curve has been shifted up 4 so y=4
See image
Extra info: y-intercept = 3000
shifted right 2
In circle O, chords AB and CD intersect at E, AE = 3 inches, BE = 8 inches, and CE is 2 inches longer than DE. What is the length of DE, expressed in inches?
Okay, let's break this down step-by-step:
* Circle O has chords AB and CD that intersect at E
* AE = 3 inches
* BE = 8 inches
* CE is 2 inches longer than DE
So we know:
AE = 3 inches
BE = 8 inches
CE = DE + 2 inches
To find DE, we can use the Pythagorean theorem for any right triangle:
a^2 + b^2 = c^2
In this case:
3^2 + 8^2 = c^2
9 + 64 = 73
c = 8 inches
So the hypotenuse AE forms a right triangle with leg BE of length 8 inches.
Now we have the length of one leg (BE = 8 inches) and the hypotenuse (AE = 8 inches).
We can use the relation between leg, hypotenuse and sine to calculate the other leg (DE):
sin(A) = DE / 8
DE = 8 * sin(A)
Without knowing the angle A, we can make an estimate:
sin(A) ≈ A (for small A)
So DE ≈ 8A inches
Now we know:
CE = DE + 2 inches
And DE ≈ 8A inches
So: 8A + 2 = DE
=> DE = 10A
And since A is small, we can say: DE ≈ 10 * A inches
To summary, if AE = 3 inches and BE = 8 inches,
then DE ≈ 10 * A inches
DE is approximately 10 times some small angle A.
Does this make sense? Let me know if you have any other questions!
A drawer is filled with 2 white shirts, 5 black shirts, and 3 gray shirts. One shirt is
chosen at random from the drawer. Find the probability that it is not a white shirt.
Okay, let's break this down step-by-step:
* There are 2 white shirts, 5 black shirts, and 3 gray shirts in the drawer.
* That's a total of 2 + 5 + 3 = 10 shirts.
* We want to find the probability that the chosen shirt is NOT white.
* So there are 5 + 3 = 8 shirts that are NOT white.
* Probability = (Number of favorable outcomes) / (Total possible outcomes)
* So in this case, Probability = 8/10 = 4/5
Therefore, the probability that the chosen shirt is NOT white is 4/5.
Cylinder 1 contains a 1.25 M stock solution of Cu(NO3)2. What volume of stock is needed to prepare 20.0 mL of 0.0750 M Cu(NO3)2 solution shown in Cylinder 2?
The Volume of stock solution needed = 1 mL
How to solveMolarity of stock solution (M1) = 1.50 M
The volume of stock solution needed (V1) = to be calculated
Molarity of diluted solution (M2) = 0.0750 M
The volume of diluted solution (V2) = 20 mL
M1V1 = M2V2
Volume of stock solution (V1) = M2V2 / M1 = (0.075 M x 20 mL) / (1.5 M) = 1 mL
So; the Volume of stock solution needed = 1 mL
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HELP ASAP (I chose 34 as random number) (please good explanation because I want to know how to do this well)
The table shows the grading scale for Ms. Gray's social studies class.
A 90%–100%
B 80%–89%
C 70%–79%
Part A: Pick a number between 28 and 39. This number will represent how many points you earned. If you have a pop quiz worth a total of 40 points, using the number you selected, calculate the percentage you earned on the test. Show each step of your work. (8 points)
Part B: Based on the percentage found in Part A, would you earn a grade of A, B, or C using the grading scale provided? Explain your answer. (4 points)
Your percentage score would be 85% if you completed the quiz and received 34 out of a possible 40 points.
What is a percentage?A percentage is a means to represent a piece of 100 as a ratio or percentage. The sign for it is % (percent), which stands for "per hundred." If you state, for instance, that 50 out of 100 people like chocolate, then means that 50 out of 100 people, or 0.5 (50/100), like chocolate overall. In several disciplines, including finance, business, mathematics, and statistics, percentages are frequently used.
Part A:
Say we decide to set the number of points gained on the quiz at 40. The following formula is used to determine your percentage score if the quiz was worth a total of 40 points and you received 34 of them:
(Points earned / Total Points) x 100% is the percentage score.
Score in percentage: (34 / 40) x 100%
Score in percentages: 85%
Your percentage score would be 85% if you completed the quiz and received 34 out of a possible 40.
Part B:
You would receive a B on the specified grading scale based on the percentage score of 85%. The percentage score gained in section A falls within the range required for a B grade on the grading scale, which is awarded for percentage scores between 80% and 89%.
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Which two values are located at the same point on a number line? 4/1 and 4 , 1/3 and 3 , 8/8 and 8 , 6/2 and 4
The two values which are located at the same point on a number line as required to be determined are; 4/1 and 4.
Which answer choice represents equivalent points on the number line?It follows from the task content that the answer choice which represents two values located at the same point on the number line be determined.
On this note, such two values must be equivalent.
Hence, by observation; the answer choice which represents two equivalent values is; 4/1 and 4 and they represent values located at the same point on the number line.
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Gary and Ann have a joint checking account their bounce at the beginning of October was 9145.87 during the month they made deposits totalling 2,783.71 wrote checks totaling 4,871.90 paid a maintenance fee of $12 earned 11.15 at interest on the account what was the balance at the end of the month?
The balance at the end of the month was $7046.93.
What is balance at the end of the month?To determine the balance at the end of the month, we need to:
add the initial balance to the deposits and interest earnedsubtract the checks written and fees paid.Data
Starting balance = $9145.87
Deposits = $2783.71
Interest earned = $11.15
Checks written = $4871.90
Maintenance fee = $12
Balance at the end of the month will be:
= Starting balance + Deposits + Interest earned - Checks written - Maintenance fee
= $9145.87 + $2783.71 + $11.15 - $4871.90 - $12
= $7046.93.
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A boat needs to travel North at 30km/h, a constant current of 4km/h is flowing in a north-west direction - What is the equivalent speed in still water for the boat to achieve actual speed of 30km/h ?
The equivalent speed in still water for the boat is 30.26 km/h.
What is the equivalent speed of the boat?
The equivalent speed of the boat in still water is calculated as follows;
The boat needs to travel North at 30 km/h,
The speed of the wave = 4 km/h
The equivalent speed of the boat in still water is calculated by applying Pythagoras theorem;
v² = (4 km/h)² + (30 km/h)²
v = √ [(4 km/h)² + (30 km/h)²]
v = 30.26 km/h
Thus, the equivalent speed of the boat is calculated by applying vector addition principle.
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