Using the Pythagorean Theorem and implicit differentiation, it is found that the distance between them is increasing at a rate of 2050 km/h when they are 0.5 hours away from the harbor.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
For this problem, we have that since the ships are moving west and north, the distance between them as a function of the time will be given by the hypotenuse of a right triangle, as follows:
d² = x² + y².
In which;
x is the position of Ship A(moving horizontally).y is the position of Ship B(moving vertically).Applying implicit differentiation, the rate of change of the position is given as follows:
[tex]2\frac{dd}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]
[tex]\frac{dd}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]
From the velocities, we have that:
[tex]\frac{dx}{dt} = 40, \frac{dy}{dt} = 50[/tex]
From the velocities, and the time of half an hour, the positions are given as follows:
x = 0.5 x 40 = 20, y = 0.5 x 50 = 25.
Hence:
[tex]\frac{dd}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]
[tex]\frac{dd}{dt} = 20(40) + 25(50)[/tex]
dd/dt = 2050.
The distance between them is increasing at a rate of 2050 km/h when they are 0.5 hours away from the harbor.
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1st sweater
2nd sweater
3rd sweater
4th sweater
50
35
30
Save
Suppose the price of a sweater is $10. Jaylen's marginal benefit for purchasing each additional sweater is given in the table below. He
gets the most benefit from the first sweater and less benefit from each additional sweater. If Jaylen is behaving rationally, how many
sweaters will he purchase?
She should buy five sweaters.
She should buy five sweaters?A rational consumer would purchase a good as long as marginal benefit is equal or greater than marginal cost.
Marginal cost is the additional cost generated by producing an additional unit of output. Marginal benefit is the benefit derived from consuming one extra unit of a good.
The marginal benefit of the first five sweaters is greater than the marginal cost. Thus, she should buy five sweaters.
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help would be so so appreciated!! thank you <3333
Answer: 21 degrees
Step-by-step explanation:
Since (2x + 9) + 129 = 180, we can get that 2x = 42 and x = 21. Hope this helped!
Dan's has a current credit card statement of $785. His credit card APR is 24.42%. What would be his finance charge if he does not pay the balance in full?
The $785 balance on Dan's credit card is currently due. The APR on his credit card is 24.42%. He has to pay the full balance that is $785.2442.
Given that,
The $785 balance on Dan's credit card is currently due.
The APR on his credit card is 24.42%.
We have to find what finance fee would he pay if he didn't pay the balance in full.
To find the balance full he has to pay.
We have to add the balance of current due and APR .
We get,
=$785+24.42%
=$785+0.2442
=$785.2442
Therefore, he has to pay the full balance that is $785.2442.
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the price of a candy bar in a vending machine increased from 1.35 to 2.75. what is the percent increase? give your answer to the nearest tenth of a percent
The percentage increase is 103.7%.
Answer:
103.7%
Step-by-step explanation:
Given the following question:
Original price = $1.35
New price = $2.75
Find the percent change. To find the percent change we will use the formula to calculate the percent change of course rounding if needed.
[tex]\frac{np\times op}{op} \times100[/tex]
[tex]\frac{2.75\times1.35}{1.35} \times100[/tex]
[tex]2.75 - 1.35\div1.35\times 100% =[/tex]
[tex]=103.7037037037[/tex]
Round to the nearest tenth:
[tex]103.7037037037[/tex]
[tex]0 < 5[/tex]
[tex]103.7[/tex]
1.35 to 2.75 is a "103.7%" increase.
Hope this helps.
find values for x so that the perimeter of the figure is less than 100 meters
Answer:
x=21
Step-by-step explanation:
21*2+25*2=92
Answer:
x < 23
Explanation:
perimeter of a rectangle = 2(length + width)
Here given:
Length = x + 4Width = xSetting equation:
[tex]\sf \rightarrow 2(x + 4 + x) < 100[/tex]
[tex]\sf \rightarrow 2(2x + 4) < 100[/tex]
[tex]\sf \rightarrow 4x + 8 < 100[/tex]
[tex]\rightarrow \sf 4x < 100 - 8[/tex]
[tex]\sf \rightarrow4x < 92[/tex]
[tex]\sf \rightarrow x < 23[/tex]
PLEASE ANSWERING THIS QUESTION QUICKLY!
When f(x)=9x^2-x-2, evaluate f(-3)
f(-3)= (blank)
Explain your answer!
Show your work!
Do not spam answers!
No nonsense answers!
No incorrect answers!
Thanks!
Answer:
f(-3)= 9(-3)^2+3-2= 9(9)+3-2= 81+1 = 82
At the sewing store, Gina bought a bag of mixed buttons. The bag included 30 buttons, of which 70% were large. How many large buttons did Gina get?
let f (x) = 4x-9. write a function g whose graph is a translation 1 unit right of the graph of f
Function g(x) = 4x -13 after the graph is translated 1 unit right of the graph of f(x) = 4x - 9.
As given in the question,
Function f(x) = 4x -9
Graph g(x) get translated 1 unit right of the graph of function f(x)
It means change in the value of x equals to x-1
g(x) = 4(x-1) -9
⇒ g(x) = 4x -4 -9
⇒ g(x) = 4x-13
Therefore, function g(x) = 4x -13 after the graph is translated 1 unit right of the graph of f(x) = 4x - 9.
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IF YOUR GOOD AT MATH PLEASE HELP ME PLEASE!
Here are the inequalities:
x ≥ 8
x < 3
x ≤ 3
x ≤ 8
x < 8
x ≥ 3
What are the inequalities?Here are inequality signs and what they mean:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
for example :
2 < 3 means 2 is less than 3
3 >2 means 3 is greater than 2
Steps to interpret an inequality graph :
If the circle above the number is colored, the inequality sign to use is either ≥ or ≤.
If the circle above the number is not colored, the inequality sign to use is either < or >.
If the arrow is pointing to the left, the inequality sign would either be ≤. or <.
If the arrow is pointing to the right, the inequality sign would either be ≥ or >.
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write the equation of the line through the points (-6,-9) and (2,5)
Answer: y2-y1 and x2-x1
Step-by-step explanation:
5-9=-4
2--6=8
-4,8
pls help me
Drag the tiles to the boxes to form correct pairs.
Consider functions f and g.
(a) The answer of (g.f)(2) is [tex]\sqrt{23}[/tex] .
(b)The answer of (g + f) (2) is [tex]\sqrt{3}[/tex] - 3 .
(c)The answer of (g - f) (-1) is [tex]\sqrt{15}[/tex] .
(d)The answer of [tex]\frac{f}{g}(-1)[/tex] is 0 .
The composition of functions f(x) and g(x) on which g(x) acts first is denoted by f(g(x)) or (f ∘ g)(x). It combines two or more functions to provide another function. In function composition, the output of the function inside the parentheses becomes the input of the outer function.We have given two functions f(x) = [tex]1-x^2[/tex] and g(x) = [tex]\sqrt{11-4x}[/tex]
(a) Put x = 2 in f(x) we get f(2) = 1 - 4 = -3
(g.f)(2) = g(f(2))
= g(-3)
[tex]=\sqrt{11-4(-3)}\\=\sqrt{11+12} \\=\sqrt{23}[/tex]
which is option (c) .
(b) Put x = 2 in f(x) we get f(2) = 1 - 4 = -3 and g(2) = [tex]\sqrt{11-8} =\sqrt{3}[/tex]
(g + f) (2) = g(2) + f(2)
= [tex]\sqrt{3}[/tex] + (-3)
= [tex]\sqrt{3}[/tex] - 3
which is option (a)
(c) Put x = -1 in f(x) we get f(-1) = 1 - 1 = 0 and g(-1) = [tex]\sqrt{11+4} =\sqrt{15}[/tex]
(g - f) (-1) = g(-1) - f(-1)
= [tex]\sqrt{15}[/tex] + 0
= [tex]\sqrt{15}[/tex]
which is option (b)
(d) Put x = -1 in f(x) we get f(-1) = 1 - 1 = 0 and g(-1) = [tex]\sqrt{11+4} =\sqrt{15}[/tex]
[tex]\frac{f}{g}(-1)[/tex] = f(-1) / g(-1)
= 0 / [tex]\sqrt{15}[/tex]
= 0
which is option (d)
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What is the slope of y = -19
Answer: 0
Step-by-step explanation: the slope intercept form is y= mx +b. The equation here is y = -19. It means that the slope, m, is 0. You can also think about it this way. y= -19 graph will show you that for every x value, the y is at -19 since there is no rise over run. it is just a straight line at y= -19
How can you write and evaluate an nth root of a number?
Let's say you wanted to find the cube root of 8
You write it on your paper like this: [tex]\sqrt[3]{8}[/tex]
In your calculator, you'd type this in: 8^(1/3)
The exponent of 1/3 corresponds to a cube root.
In general, the exponent of 1/n is for the nth root
The connection is [tex]\sqrt[n]{\text{x}} = \text{x}^{1/n}[/tex]
Find the other endpoint of the segment with a midpoint of (-6, 4) and endpoint of (4, 8).
Show your own work
Answer:
(-16, 0)
Step-by-step explanation:
The midpoint can be found using the formula below, where [tex](x_1,y_1)[/tex] is the first endpoint and [tex](x_2, y_2)[/tex] is the other endpoint.
[tex]\boxed{\text{Midpoint}=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )}[/tex]
Let the other endpoint be (x, y).
Substitute the given midpoint and one endpoint into the formula above:
(-6, 4)= [tex](\frac{x+4}{2},\frac{y+8}{2} )[/tex]
Comparing the x-coordinate:
[tex]-6=\frac{x+4}{2}[/tex]
Multiply both sides by 2:
x +4= -12
Subtract 4 from both sides:
x= -12 -4
x= -16
Comparing the y-coordinate:
[tex]4=\frac{y+8}{2}[/tex]
Multiply both sides by 2:
y +8= 8
Subtract 8 from both sides:
y= 8 -8
y= 0
Thus, the other endpoint is (-16, 0).
Supplementary:
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A large jar contains an unknown number of red gumballs and 145 green gumballs. As part of a seventh-grade class project the teacher asks Carlos to estimate the total number of gumballs in the jar using a sample. Carlos draws a sample of 55 gumballs, of which 11 are red and 44 are green. Use Carlos' sample to estimate the number of gumballs in the jar.
The total number of gumballs in the jar calculated using probability is about 181.
Probability is the study of chance. The likelihood of an event to occur given as a fraction is probability.
For a sure event the probability is 1 and for an impossible event the probability is 0.
Carlos draws a sample of 55 gumballs. Out of which the number of green gumballs is 44.
Probability of a green gumball= number of green gumballs ÷ total number of gumballs
P(green) = 44 ÷ 55 = 4/5
Now in the sample the number of green gumballs is 4/5 , and in the jar the number of green gumballs is 145 .
Let us consider there are x gumballs in total in the jar.
P(green)=145 ÷ x
We know that P(green)= 4/5
∴4/5 = 145 ÷ x
or, x = 145 × 5 ÷ 4
or, x = 181.25 gumballs.
or, x ≈ 181 gumballs(As the number of gumballs cannot be a fraction)
Therefore there are about 181 gumballs in total .
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The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 53 minutes of calls is $12.03 and the monthly cost for 65 minutes is $13.59. What is the monthly cost for 57 minutes of calls?
The monthly cost of 57 minutes calls is $12.55.
The monthly cost is $12.03 for 53 minutes and $ 13.59 for 65 minutes call
Therefore we have two points (53, 12.03) and ( 65, 13.59)
slope = (13.59 - 12.03)/ ( 65 - 53)
= 1.56/ 12
= 0.13
The intercept is
y = mx + c
12.03 = 0.13×53 + c
12.03 = 6.89 + c
c = 5.14
Equation:
cost = 0.13(minutes) + 5.14
= 0.13×57 + 5.14
= 7.41 + 5.14
= 12.55
Therefore the monthly cost for 57 minutes is $12.55.
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There are hard sweets and soft sweets in a bowl in the ratio 3:5 The hard sweets are blue and red in the ratio 1:4 The soft sweets are blue and red in the ratio 2:3 What fraction of the sweets are blue?
The fraction of the sweets that are blue given the ratios is 13/40.
What is the fraction of blue sweets?A fraction is a non-integer that is made up of a numerator and a denominator. An example is 2/3. 2 is the numerator and 3 is the denominator.
Ratio shows the relationship between two or more numbers. It is the number of times that one value is contained in other value(s). Ratios are used to compare two or more numbers.
We would be assuming the numbers of sweet based on the given ratios.
The number of hard sweets = 30
The number of soft sweets = 50
Number of hard sweets that are blue = (1/5) x 30 = 6
Number of soft sweets that are blue = (2/5) x 50 = 20
Total number of blue sweets =20 + 6 = 26
Total number of sweets = 30 + 50 = 80
Fraction of blue sweets = 26/80 = 13 /40
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Express 60 as the product of its prime factors
Write the factors in as ascending order and give your answer in index form
Answer:
2^2 × 3 × 5
Step-by-step explanation:
hope this works :)
You get hired for a job through ACME Employment Agency. You signed a contract that requires you to pay 20% of your first 6 weeks pay. The job pays you $42,700 per year. How much must you pay ACME for their services?
PLEASE ANSWER NOW
What is the distance between -22 and 12 on a number line? Write an expression using subtraction and absolute value to show the distance.
Answer:
34
Step-by-step explanation:
Solve the following compound inequality. −x−4≤x−12≤−x+2 Submit your answer by dragging the movable blue points on the number line.
Solution:
Inequality Form: [tex]4\leq x\leq 7[/tex]
Interval Notation: [tex][4,7][/tex]
_________________________________________________________
As for plotting on your line graph, one point should be a closed circle on 4, then the next should be a closed circle on 7.
__________________________________________________________
Hope this helps! If so, lmk! Thanks and good luck!
Solve for x.
3x+2
70°
Answer:
it 21
Step-by-step explanation:
rr
The pentagons ABCDE and PQRST are similar.
Find the length x of PQ .
The measure of the length PQ is 7.2
Similar shapesFigures are known to be similar if the ratio of the sides is equal to a constant "k".
In order to determine the value of k, we will use the following ratio as shown:
AB/BC = PQ/QR
Substitute the given parameters
6/2 = x/2.4
Cross multiply
2x = 2.4(6)
2x = 14.4
x = 14.4/2
x = 7.2
Hence the measure of the length PQ is 7.2
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can I get help with this Problem
Which equation has no solution?
O 14x-21 = -6
O 1-2-x1=9
O 13x + 61 = 6
O 1-2x + 81 = 0
Equation has no solution is |4x-2|=-6
checking option A
|4x-2|=-6 . . . .1
if 4x-2≥0
4x≥2
x≥1/2
then |4x-2| = 4x-2
So , .. . . 1 becomes
4x-2=-6
4x=-4
x=-1
But x≥1/2
So x=-1 is not a solution.
if 4x-2≤0
4x≤2
x≤1/2
then |4x-2| = -(4x-2)
So , .. . . 1 becomes
-4x+2=-6
4x=8
x=2
but x≤1/2
So x=2 is not a solution.
checking option B
|-2-x| = 9 . . . 2
if -2-x ≥ 0
x≤-2
then
|-2-x| = -2-x
So, . . .. . 2 becomes
-2-x=9
x=-11
so it has a solution .
checking option C
|3x+61| = 6 . . . . . 3
if 3x+61≥0
x≥-61/3
then
|3x+61| = 3x+61
So, . . .3 becomes
3x+61=6
x=-55/3
So it has a solution.
checking option D
|-2x+8|=0 . . . . .4
if -2x+8≥0
x≤4
then |-2x+8| = -2x+8
So , .. . . . .4 becomes
-2x+8=0
x=4
So it has a solution.
Hence option A |4x-2|=-6
has not a solution.
Sometimes equations have no solution. This means that no matter what value is plugged in for the variable, you will ALWAYS get a contradiction.
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A 75% antifreeze solution is to be mixed with a 90% antifreeze solution to get 360 liters of a 85% solution. How many liters
of the 75% and how many liters of the 90% solutions will be used?
In linear equation , 240 liters of 90% solutions will be used.
What are a definition and an example of a linear equation?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.Let x be the quantity of 75% antifreeze solution and y be the quantity of 90% antifreeze solution,
Since, the total quantity of the mixture = 360,
⇒ x + y = 360 ----- (1),
Also, the resultant solution is of 85% antifreeze solution,
⇒ 75 % of x + 90% of y = 85% of 360
0.75x + 0.90y = 0.85 × 360
0.75x + 0.90y = 306
75x + 90y = 30600 -----(2),
Equation (2) - 75 × equation (1),
We get,
15y = 3600
⇒ y = 240
Hence, 240 liters of 90% solutions will be used.
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Convert 121 lb to kg and round to the nearest tenth
Answer: 54.9
Step-by-step explanation:
121 lb converted to kk is 54.885
54.885 rounded to the nearest tenth is 54.9
{x€N | 25 ≤ x² < 50}
Answer:
x = { 5; 6; 7}
Step-by-step explanation:
25 ≤ 25 < 36 < 49 < 50
=> x² = {25; 36; 49}
Because x€N => x = {5; 6; 7}
Which number is closest to √58?
Answer:
8
Step-by-step explanation:
sqrt 58 =7.62 closer to 8 than 7
help me out please!!!!
Answer:
I believe the Answer is C.
Step-by-step explanation: