The value of tan 30° after using trigonometric ratio is [tex]\frac{1}{\sqrt{3} }[/tex] .
What is trigonometric ratio?
There are six trigonometric ratios used in trigonometry: sine, cosine, tangent, secant, and cotangent. The abbreviations for these ratios are sin, cos, tan, sec, cosec(or csc), and cot. Look at the below-displayed right-angled triangle. Any two of the three sides of a right-angled triangle can be compared in terms of their relative angles using trigonometric ratios.
Here the given
=> tan30°
Now ,Tan 30 degrees in radians is written as
=>tan (30° × π/180°)
=> [tex]\frac{1}{\sqrt{3} }[/tex]
Therefore the value of tan30° is [tex]\frac{1}{\sqrt{3} }[/tex] .
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Find g(x), where g(x) is the translation 10 units up of f(x) = 8x - 10.
Write your answer in the form mx + b, where m and b are integers.
The translated function is g(x)= 8x+0
What is Function?
A relation between a collection of inputs and outputs is known as a function. A function is an association between inputs in which each input is connected to precisely one output. A domain, range exists for every function.
An example of a rule is a function, which produces one output for a single input.
Given:
f(x)= 8x - 10
Now, translation 10 units up
Thus, g(x)= f(x) + 10
g(x)= 8x - 10+ 10
Hence, g(x)= 8x+0
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need help with geometry
According to the concept of polynomial division, the equivalent expression is option (a). x+7 + 26/(x-3)
Polynomial division
Polynomial division refers the process of dividing one polynomial with another.
Given,
Here we have the expression (x² + 4x + 5) / x - 3.
Now, we have to find the equivalent polynomial expression when x - 3 is not equal to 3.
In order to find the equivalent expression, we have to do the following steps:
1. Divide the first term of the dividend by the first term of the divisor
2. Write down the calculated result x in the upper part of the table.
3. Multiply it by the divisor
4. Subtract this result from the dividend
Repeat this 4 steps until no further division.
This process is illustrated below.
According to this process, the equivalent fraction for the given fraction is
x + 7 + 26/(x - 3)
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help plsssss
Function f is an exponential function.
x 2 3 4 5 6
f(x) 9 27 81 243 729
What is the ratio of outputs for any two inputs that are 2 units apart? Divide the output for the larger x-value by the output for the smaller x-value.
Answer: 9
Step-by-step explanation:
The ratio of two outputs for any two input values that are 2 units apart is
27
What is a ratio?Ratio refers to fractions of two numbers say a and b written in the form
a / b
How to find the required expressionThe problem involves dividing the output for the larger x-value by the output or the smaller x-value
choosing output for x = 3 and x = 6, the two values are 2 units apart
the outputs are y = 27 and y = 729 respectively
taking the ratios
= 729 / 27
dividing gives the lowest term of the fraction
= 27 / 1
= 27
Hence dividing the output values for x = 3 and x = 6 is 27
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Graph the equation 4x−5y=1 by plotting points.
y=4/5x-2/5 is the equation used to plot the graph.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The given equation is 4x−5y=1
Four times of x minus five times of y equal to one
4x−5y=1
Let us write this equation in slope intercept form
-5y=1-4x
5y=-2+4x
y=-2/5+4/5x
y=4/5x-2/5
x 0 1 2 3
y -2/5 2/5 6/5 10/5
y -0.4 0.4 1.2 2
by using these points we plot the graph.
Hence y=4/5x-2/5 is the equation used to plot the graph.
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a track coach creates an obstacle course for his team. the coach plots the locations of the three obstacles on the coordinate plane shown to the right. each unit on the coordinate plane represents three yards. a student starts at Obstacle A. Then runs south to obstacle b, and then runs west to obstacle c. what is the total distance, in yards, the student runs to get from obstacle a to obstacle c?
The Total Distance is 51 yards.
What are Coordinates?Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x axis (horizontal) and y axis are the two axes that make up a coordinate plane (vertical).
Given:
As, A and B have same x- coordinate
AB = | (y- coordinate of A) - (y- coordinate of B)|
= |5 - (-2)|
= 7
and, B and C have same y- coordinate
AB = | (x- coordinate of B) - (x- coordinate of A)|
= |3 - (-7)|
= 10
Then, Total distance= 7+ 10= 17
and, Total distance in yards = 17 x 3= 51 yards
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What is the slope of the line 8x + 3y = 8 – 2x?
The slope of the line, 8x + 3y = 8 – 2x, is -10/3
Determining the slope of the equation of a lineFrom the question, we are to determine the slope of the given equation.
The given equation is
8x + 3y = 8 – 2x
To determine the slope of the line, we will express the equation in the general form of the slope-intercept form of the equation a line.
The general form of the slope-intercept form of a line is
y = mx + b
Where m is the slope
and b is the y-intercept
Expressing the equation in the slope-intercept form of a line
8x + 3y = 8 - 2x
Subtract 8x from both sides of the equation
8x - 8x + 3y = 8 - 2x - 8x
3y = 8 - 10x
3y = -10x + 8
Divide through by 3
3y/3 = -10x/3 + 8/3
Y = -10/3 x + 8/3
By comparison,
m = -10/3
Hence, the slope is -10/3
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A jewelry store buys a necklace for $75. They decide to mark the necklace up 55% and put it in their store. The store is running a promotion that everything purchased during the month of February will be 15% off. A customer comes in with a coupon that gives them an additional 10% off the sale price (after all other discounts were applied). After all discounts customers will be changed an 8% sales tax. Determine the final cost of the necklace if the customer bought the necklace February 28th and March 1st.
The final cost of the necklace if the customer bought it on February 28th or March 1st is $96.05 or $113, respectively.
How is the final cost determined?The final cost of the necklace purchased on February 28th includes the markup and excludes the promotional and coupon discounts, before adding the sales tax.
Similarly, the final cost of the necklace purchased on March 1st includes the markup and excludes the coupon discount, before adding the sales tax.
February 28 Purchase:Cost price to the store = $75
Markup =55%
Marked-up selling price = $116.25 ($75 x 1.55)
February sales discount = 15%
Promotional price during February = $98.81 ($116.25 x 1 - 15%)
Discount coupon rate = 10%
Discounted price = $88.93 ($98.81 x 1 - 10%)
Sales tax = 8%
Final selling price = $96.05 ($88.93 x 1.08)
March 1 Purchase:Cost price to the store = $75
Markup =55%
Marked-up selling price = $116.25 ($75 x 1.55)
Discount coupon rate = 10%
Discounted price = $104.63 ($116.25 x 1 - 10%)
Sales tax = 8%
Final selling price = $113 ($104.63 x 1.08)
Thus, the customer pays an additional $16.95 if they purchase the necklace on March 1st without the promotional discount, instead of February 28th.
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15.75 + .5x = 16.53 - .13x
Ms. High brought each class a shout-out box. The
length of the box was 2.6 inches and the width was
0.8 inches. What is the area of the shout-out box?
A standard die is rolled. Find the probability that the number rolled is less than 3. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answer:
When a die is rolled, here it's Total possible outcome is= 6
and sample space is = 2 ( i.e. 1 & 2)
So. Probability of getting less than 3 = 26
=13
That's it.
Step-by-step explanation:
x^x=4
Find the solution
Answer: 2
x = 2
[tex]x^{2}[/tex] = 4
[tex]2^{2}[/tex] = 4
4 = 4
You have 100 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area.
Note: The length of the sum of three sides is 100. Let w be the width, find the length in terms of w, setup an equation for the area, then find the vertex (maximum) of your equation. Area of rectangle is length * width.
The length and width of the rectangular plot that will maximize the area are 50 feet and 25 feet respectively.
The vertex (maximum) of this equation is equal to 1,250 square feet.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = lw
Where:
A represents the area of a rectangle.w represents the width of a rectangle.l represents the length of a rectangle.Since one side of this rectangular plot along the river does not require fencing, the perimeter equation is given by:
P = 2(l + w)
100 = 2w + l
Making length the subject of formula, we have:
l = 100 - 2w
Therefore, the area of this rectangular plot would now be:
A = (100 - 2w)w
A = 100w - 2w²
Next, we would take the first derivative and equate to zero in order to obtain the maximum area:
dA/dw = 100 - 4w
0 = 100 - 4w
4w = 100
Width, w = 25 feet.
For the length of this rectangular plot, we have:
Length, l = 100 - 2w
Length, l = 100 - 2(50)
Length, l = 50 feet.
Now, we can find the vertex (maximum) of this equation is given by:
Maximum area = 50 × 25
Maximum area = 1,250 square feet.
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Find the sum using (+) and (-) chips: -5+1
Answer: The answer is -4
If you use the chips to help illustrate your point, here's a good way to explain it:
Let's say that there are five -1 chips and one +1 chip. In order to use chips, you would have to subtract the chips from each other. Put a -1 chip and a +1 chip together and then take them away (as to subtract them). This would leave you with four -1 chips, thus giving you your answer.
Hope this helps!
Answer:
when two different signs are in numbers if +or_ you I'll substruct or +or+ you I'll added ok
Square of 10^4 is ?
Multiply.
0.01 x 4066.61
OA. 4066.61
OB. 406.661
OC. 40.6661
OD. 4.06661
The solution after the multiplication of 0.01 x 4066.61 is 40.6661
Multiplication
Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. And the word multiply means the repeated addition of groups of equal sizes.
Given,
Here we have the operation 0.01 x 4066.61
Now we have to perform the multiplication operation in it.
While we looking into the given operation, we have identified that there are 4 total decimal places in both numbers.
First, we have to ignore the decimal places and complete the multiplication as if operating on two integers.
The the calculation for the multiplication is shown in the following image.
Now, we have to rewrite the product with 4 total decimal places.
Then we get the answer is 40.6661
Therefore, 0.01 × 4066.61 = 40.6661
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If I have a pack of cards and 20 are red, 20 yellow, 20 green and 10 blue, how many cards are needed to be drawn (at random) to ensure that I have 12 cards of the same color?
The number of cards that are needed to ensure that you have 12 cards of the same color is of:
43 cards.
How to guarantee that there are at least one color has 12 cards?The highest number of cards for which at least one color having 12 cards is not guaranteed is obtained as follows:
11 red. (there are 20 red cards, so it is possible to take 11).11 yellow. (there are 20 yellow cards, so it is possible to take 11).11 green. (there are 20 green cards, so it is possible to take 11).10 blue, as there are only 10 blue cards.Hence the number is:
11 + 11 + 11 + 10 = 3 x 11 + 10 = 33 + 10 = 43 cards.
With the next card, that is, the 44th card, it will be ensured that at least one color will have 12 cards.
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Select the correct answer. Identify the end behavior and the zeros of function h. h ( x ) = - x 3 − 9 x 2 + 4 x + 96 Based on these key features, which statement is true about the graph representing function h? A. The graph is negative on the intervals ( - 3 , 4 ) and ( 8 , ∞ ) . B. The graph is positive on the intervals ( - 8 , - 4 ) and ( 3 , ∞ ) . C. The graph is negative on the intervals ( - ∞ , - 8 ) and ( - 4 , 3 ) . D. The graph is positive on the intervals ( - ∞ , - 8 ) and ( - 4 , 3 ) .
The statement which is true about the graph representing function h is the graph is positive on the intervals (- ∞, - 8) and (- 4, 3). Option D is correct.
We are given;
h(x) = -x^3 - 9x^2 + 4x + 96
The function is a cubic function.
Since the leading coefficient is negative the graph start from second quadrant.
So, the graph must be positive in the second quadrant.
Let us check the option D;
The graph is positive on the intervals (- ∞ , - 8) and (- 4, 3).
The graph is positive in the second quadrant. So, (- ∞ , - 8) satisfy.
Let's choose any point between -4 to 3 and substitute in the given equation.
Put x = -1 in the given equation;
h(x) = -(-1)^3 - 9(-1)^2 + 4(-1) + 96 = 1 - 9 - 4 + 96 = 84
So, h(x) is positive.
So, option D is correct.
Thus, the statement which is true about the graph representing function h is the graph is positive on the intervals (- ∞, - 8) and (- 4, 3). Option D is correct.
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How many 2/5 can go into 1/2?
Use the digits -9 to 9 to complete the puzzle below. Try all the combinations. But as you begin doing that, you will realize that in some cases you are looking for factor combinations with a particular sum or difference. You will see that some numbers have to be greater than a particular value in order to produce the product you are looking for. Show your work to confirm your solution.
According to the concept of complex numbers, the solution function is (5 - 6i) (2 + 4i) = (34 + 8i)
Complex numbers:
Complex numbers means a combination of a real number and an imaginary number.
The standard form of complex number is,
a + ib
Where a complex number, where a,b are real numbers and i = √-1.
Given,
Here we have the following complex number expression
(_ + _i) (_ + _i) = 34 + 8i
Here we need find the value of the dashes and the number must lies between -9 to +9.
Let us consider a, b, c and d as the number presented in the dashes then it can be written as,
=> (a + bi) (c + di)
Now, we have to expand this expression then we get,
=> ac + adi + bci + bdi²
Combine the like terms,
=> (ac − bd) + (ad + bc)i
Now, we have to match the coefficients as,
30 < ac − bd < 80
We also know that,
=> ad + bc = 0
Now, we need to pick four integers between -9 and 9 such that these two equations are satisfied.
We also know that
=> ac − bd = 34
=> ad + bc = 8
Therefore, it makes sense to assume b is negative.
After some trial and error, one possible answer is a = 5, b = -6, c = 2, d = 4
Therefore, the expression is written as,
=> (5 - 6i) (2 + 4i) = (34 + 8i)
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can someone simplify 2\sqrt(6 and 3\sqrt(54))ft
Will mark brainliest
Answer:
2/sqrt6 = sqrt6/3
3/sqrt54 = sqrt6/6
2/sqrt6 + 3/sqrt54
= sqrt6/2
Step-by-step explanation:
Simplifying when there are radicals involved usually means "rationalizing".
Rationalizing means getting rid of the square root on the bottom of a fraction.
See image.
Sophie put $3330 in a savings account at a simple interest rate of 7.4% per year. Adam put $2795 in a savings account at a simple interest rate of 8.1% per year.
Who will have earned more interest after 5 years? How much more?
Adam earned $100.12 more interest than the Sophie
Consider Sophie
The principal amount = $3330
The interest rate = 7.4%
The time period = 5 years
Simple interest = PRT
Where P is the principal amount
R is the interest rate
T is the time period
Substitute the values in the equation
Simple interest = 3330× (7.4/100) × 5
= $1232.1
Consider Adam
The principal amount = $2795
The interest rate = 8.1%
The time period = 5 years
Simple interest = 2795 × (8.1/100) × 5
= $1131.98
The difference = 1232.1 - 1131.98
= $100.12
Hence, the Adam earned $100.12 more interest than the Sophie
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Match the equations with the value of x that makes them true. 2(2x − 3) = 6 5x − 2x − 4 = 5 x + 2x + 3 = 9 5(x + 3) = 25 4x − (2x + 1) = 3 5x − (3x − 1) = 7
Each of the equations should be matched with the value of x that makes them true as follows:
x = 2; x + 2x + 3 = 9, 5(x + 3) = 25, and 4x − (2x + 1) = 3.
x = 3; 2(2x − 3) = 6, 5x - 2x - 4 = 5, and 5x − (3x − 1) = 7.
How to determine the true equations?In order to determine which x-values are true solutions based on the given equations, we would have to test each of the values of x by substituting them into the equations as follows;
When x = 2, we have:
2(2x − 3) = 6
4x − 6 = 6
4(2) - 6 = 6
8 - 6 = 6
2 = 6 (False).
When x = 3, we have:
2(2x − 3) = 6
4x − 6 = 6
4(3) - 6 = 6
12 - 6 = 6
6 = 6 (True).
When x = 2, we have:
5x - 2x - 4 = 5
3x - 4 = 5
3(2) - 4 = 5
6 - 4 = 5
1 = 5 (False).
When x = 3, we have:
5x - 2x - 4 = 5
3x - 4 = 5
3(3) - 4 = 5
9 - 4 = 5
5 = 5 (True).
When x = 2, we have:
x + 2x + 3 = 9
3x + 3 = 9
3(2) + 3 = 12
9 = 12 (False).
When x = 3, we have:
x + 2x + 3 = 9
3x + 3 = 9
3(3) + 3 = 12
12 = 12 (True).
5(x + 3) = 25
5x + 15 = 25
5x = 25 - 15
5x = 10
x = 2 (True).
4x − (2x + 1) = 3
4x - 2x - 1 = 3
2x = 3 + 1
2x = 4
x = 2 (True).
5x − (3x − 1) = 7
5x - 3x + 1 = 7
2x = 7 - 1
2x = 6
x = 3 (True).
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Kakashi is filling his new bookshelf. The shelf holds 40 books. If he fills the bookshelf 4/5 of the way, how many books will Kakashi need?
Answer: 8 books
Step-by-step explanation:
First, she has 40 books.
1) Then she fills 4/5 of it. 4/5 of 40 is 32.
2) (4/5) x (40) = 32.
3) 40 - 32 = 8
4) So she needs to add 8 books.
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What is the answer to c?
Answer:
The answer is 6.5
Step-by-step explanation:
The equation is y=3x-1. Plug in 2.5 as the value for x and solve.
3×2.5=7.5
7.5-1=6.5
A recording studio charges musicians an additional fee of $50 to record an album studio time cost in additional fee of $75 per hour
write a lean your model that represents the cost C of recording an album as a function of studio time in hours.
use the variable T to represent the number of hours recording studio is used.
Is less expensive to purchase 12 hours of recording time at the studio or a 750 music software program that you can use to record on your own computer
The equation that will be used to illustrate the information regarding the total cost is C = 50 + 75h.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Initial fee = 50
Amount charged by hour = 75
Number of hours = h
The total cost will be:
= Initial fee + Amount for each hour
= 50 + 75(h)
= 50 + 75h
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A football team ran four plays. The first play lost 5 yards. The second play lost 9 yards. The third play gained 12 yards. The last play lost 8 yards. Find the total gain or loss of yards. Select the correct integer.A football team ran four plays. The first play lost 5 yards. The second play lost 9 yards. The third play gained 12 yards. The last play lost 8 yards. Find the total gain or loss of yards. Select the correct integer.
The total loss of yards is 10yards(-10yards)
What is addition of negative and positive integers?An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.
There are positive integers e g 1,2,3,5,7,8,11,16 and negative integers -1,-2,-4, -22 e t c
The addition of a negative and positive integers of the same number will give 0 .i.e -5+(+5)=0
similarly -6+(+6)= 0
if the lost yards are represented by negative and the gained yards by positive then,
-5yards-9yards-8yards = -22yards
+12 yards is gained
therefore the total yards lost or gained is
-22+12= -10yards
since it is -10yards then the yards are lost yards.
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There are three consecutive odd integers.Three times the largest is seven times the smallest. What are the integers?
The three consecutive odd intergers are 3,5 and 7
What do you mean by algebraic expression ?
An algebraic expression is the idea of using letters or alphabets to represent numbers without specifying the actual values. Algebra Basics taught us how to use letters like x, y, and z to represent unknown values. These characters are called variables here.
An algebraic expression can be a combination of variables and constants. Any multiplied value that is prefixed to a variable is a factor.
Let the three consecutive odd integers are x, x+2 and x+ 4
Here x is the smallest odd integer and x+4 is the largest odd integer
According to the question:
3(x +4) = 7x
3x + 12 = 7x
7x - 3x = 12
4x = 12
x = 12/4
x = 3
Three consecutive odd integers become:
x = 3
x + 2 = 3 +2 = 5
x + 4 = 3 + 4 = 7
Hence, the three consecutive odd intergers are 3,5 and 7
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Find a so that the point (-1,5) is on the graph of f(x)=ax^2+2
Answer:
a=3
Step-by-step explanation:
To find a, you plug the known numbers into the given equation (coordinates). f(x) is the same as the y-coordinate.
With that, you get:
5=a(-1)^2+2
Then you solve for a
3=a(-1)^2
3=a(1)
3=a
Food and clothing are shipped to victims of a natural disaster. Each carton of food will feed 11 people, while each carton
of clothing will help 4 people. Each 20-cubic-foot box of food weighs 40 pounds and each 5-cubic-foot box of clothing
weighs 20 pounds. The commercial carriers transporting food and clothing are bound by the following constraints:
The total weight per carrier cannot exceed 23,000 pounds.
- The total volume must be no more than 9000 cubic feet.
Use this information to answer the following questions.
...
Through linear programming, we find out that the number of cartons of food is 360 cartons and the number of cartons of clothing is 550 cartons.
It is given to us that -
Each carton of food will feed 11 people
Each carton of clothing will help 4 people
Each 20-cubic-foot box of food weighs 40 pounds
Each 5-cubic-foot box of clothing weighs 20 pounds
The total weight per carrier cannot exceed 23,000 pounds
The total volume must be no more than 9000 cubic feet
We have to find out the number of cartons of food and clothing should be sent with each plane shipment to maximize the number of people who can be helped.
Let us say that -
The number of cartons of food = x
The number of cartons of clothing = y
According to the given information, the constraints on weight and size can be represented as -
Constraints on weight:
[tex]40x+20y\leq 23000\\= > 20y\leq 23000-40x\\= > 20y\leq -40x+23000\\= > y\leq -2x+1150[/tex]------ (1)
Constraints on size:
[tex]20x+5y\leq 9000\\= > 5y\leq 9000-20x\\= > 5y\leq -20x+9000\\= > y\leq -4x+1800[/tex]----- (2)
We also know that
[tex]x\geq 0[/tex] and [tex]y\geq 0[/tex]
The equation for the help that will be provided with each carton of food and clothing can be represented as -
[tex]11x+4y[/tex] ---- (3)
From equation (1), for weight graph, we have
[tex]y\leq -2x+1150[/tex]
For [tex]x=0[/tex], [tex]y\leq 1150[/tex]
For [tex]y=0, x\leq 575[/tex]
From equation (2), for size graph, we have
[tex]y\leq -4x+1800[/tex]
For [tex]x=0, y\leq 1800[/tex]
For [tex]y=0, x\leq 450[/tex]
For (0,1150), the equation (3) becomes
[tex]11x+4y[/tex]
[tex]= 11*0+4*1150\\= 4600[/tex]
For (360, 550), the equation (3) becomes
[tex]11x+4y\\= 11*360 + 4*550\\= 6160[/tex]
For (450,0), the equation (3) becomes
[tex]11x+4y\\= 11*450 + 4*0\\= 4950[/tex]
Thus, through linear programming, we find out that the number of cartons of food is 360 cartons and the number of cartons of clothing is 550 cartons.
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Five hours and 20 minutes after a raft left a dock, a patrol boat left the dock and traveled in the same direction as the raft. The boat caught up to the raft 20 km away from their starting point. What was the speed of the raft if the speed of the patrol boat was 12km/hr ?
The speed of the raft was 2.86 km/hr.
What is speed?Speed is defined as the rate of change of position of an object in any direction.
Given that, a patrol boat with speed of 12 km/hr caught a raft after travelling for 20 km and patrol boat left the dock after 5 hours and 20 minutes the raft left,
The time taken by the patrol boat to catch the raft is;
t = 20/15 = 5/3 hours
5/3 hours = 1 hour 40 minutes
Thus, it took 1 hour 40 minutes for the patrol boat to catch the raft
Thus, the raft was travelling for 5 hours 20 minutes plus 1 hour 40 minutes which 7 hours,
The speed of raft = 20/7 = 2.86 km/hr
Hence, The speed of the raft was 2.86 km/hr.
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