a plane flying horizontally at an altitude of 1 mile and a speed of 430 mi/h passes directly over a radar station. find the rate at which the distance from the plane to the station is increasing when it has a total distance of 5 miles away from the station. (round your answer to the nearest whole number.) 430 incorrect: your answer is incorrect. mi/h
Answers
The rate at which the distance from the plane to the station is increasing when it is 5 mi away from the station is 421 mi/h.
Given information:
A plane flying horizontally at an altitude of "1" mi and a speed of "430" mi/h passes directly over a radar station.
z = 1
\(\frac{dx}{dt} = 430\)
We need to find the rate at which the distance from the plane to the station is increasing when it is 5 mi away from the station.
y = 5
According to Pythagoras
\(hypotenuse^2 = base^2 + perpendicular^2\\\\y^2 = x^2 + 1^2\\\\y^2 = x^2 + 1\).... (1)
Put z=1 and y=5, to find the value of x.
\(5^2 = x^2 + 1^2\\\\25 = x^2 + 1\\\\25 - 1 = x^2\\\\24 = x^2\)
Taking square root both sides.
\(\sqrt{24} = x\)
Differentiate equation (1) with respect to t.
\(2y\frac{dy}{dt} = 2x\frac{dx}{dt} + 0\)
Divide both sides by 2.
\(y\frac{dy}{dt} = x\frac{dx}{dt}\)
Put \(x = \sqrt{24}\), y=5, \(\frac{dx}{dt} = 430\) in the above equation.
\(2\frac{dy}{dt} = \sqrt{24}(430)\)
Divide both sides by 2.
\(\frac{dy}{dt} = \frac{\sqrt{24}(430) }{5} \\\\\frac{dy}{dt} = 421.312\\\\\frac{dy}{dt} = 421\)
Hence the answer is the rate at which the distance from the plane to the station is increasing when it is 5 mi away from the station is 421 mi/h.
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Related Questions
1/5 divied by 2 as a fraction
Answers
The simplified form of the expression 1/5 divied by 2 as a fraction is 1/10.
What is 1/5 divied by 2 ?Given the expression in the question;
1/5 divied by 2
1/5 ÷ 2
To simplify, multiply 1/2 by the reciprocal of 2
1/5 ÷ 2
1/5 × 1/2
Simplify
( 1 × 1 ) / ( 5 × 2 )
( 1 ) / ( 5 × 2 )
Multiply 5 and 2
( 1 ) / ( 10 )
1/10
Therefore, the simplified form is 1/10.
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q5 ANSWER FOR 20 POINTS!
Answers
The absolute value model |x - 30| = 10 represents the time required for Jack to fold his laundry. (Correct choice: D)
How to represent variability by means of absolute values
Absolute values are functions used in mathematics that represents the magnitude of a number, whose definition is summarized below:
For x - a ≥ 0, |x - a| = x - a.For x - a < 0, |x - a| = - x + aIn this case, we must determine an absolute value model that contains the maximum and minimum times required by Jack to fold his laundry, This is represented by the following model:
|x - a| = b
Where:
x - Real time, in minutes.a - Mean time, in minutes.b - Time variance, in minutes.If we know that a = 30 min and b = 10 min, then the absolute value model is:
|x - 30| = 10
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What is the least common denominator (lcd) of 1/2 2/3
Answers
Answer:
6
Step-by-step explanation:
Find the least common multiple (LCM) of the denominators in order to find the least common denominator (LCD).
i need this done pls :)
Answers
Answer:
300....?
Step-by-step explanation:
2. Which of the following is parallel to the line y= 3/4x + 7
Answers
Answer:
the answer would be C. y = 3/4 x - 9
this line has the same slope => ¾
(n^(4))/(n^(4)) what does that equal?
Answers
Answer:
the answer would be 1 happy to help ya :)
Step-by-step explanation:
Which of the following is logically equivalent to “I wear a jacket if it is cold outside." ?
If I wear a jacket, then it is cold outside.
If I do not wear a jacket, then it is not cold outside.
I wear a jacket if and only if it is cold outside.
If it is not cold outside, then I do not wear a jacket.
Answers
The option from the following that is logically equivalent to the statement is that: If it is not cold outside, then I do not wear a jacket.
What is Logical equivalence?Two statements are regarded to be logically equivalent if, and only if, their resultant forms are logically equivalent during the time at which identical statement variables are utilized to illustrate their component statements.
Similarly; two statement forms are noted to be logically equivalent if, and only if, their resultant truth tables show an identical form per variation of statement variables.Therefore, we can conclude that the correct option that is logically equivalent to the statement being made is that: If it is not cold outside, then I do not wear a jacket.
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a medical devices company wants to know the number of hours its mri machines are used per day. a previous study found a standard deviation of four hours. how many mri machines must the company find data for in order to have a margin of error of at most 0.20 hour when calculating a 98% confidence interval?
Answers
The medical devices company must find data for at least 543 MRI machines.
How to calculate the number MRI machines?To calculate the number of MRI machines needed for a 98% confidence interval with a margin of error of 0.20 hour, we need to use the formula:
n = [(z*σ)/E]²
where:
n is the sample sizez is the z-score for the desired confidence level (98% = 2.33)σ is the standard deviation (4 hours)E is the margin of error (0.20 hour)Substituting the values:
n = [(2.33*4)/0.20]²
n = 542.89
Rounding up to the nearest whole number, the medical devices company must find data for at least 543 MRI machines to have a margin of error of at most 0.20 hour when calculating a 98% confidence interval.
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FIND BC
round to the nearest HUNDREDTH
Answers
Answer:
CB = 30.15
Step-by-step explanation:
180-58-93 = 29 degrees for angle B
draw a line perpendicular to BC down to point A, lets call the perpendicular point D.
now you've got 2 similar, smaller triangles
angle A is split into two angles, 29 degrees above and 58 degrees below.
sin 29 =CD/16
CD = 7.75
cos 29 = AD/16
AD = 14
tan 58 =DB/AD = DB/14
DB = 22.40
CD + DB = 7.75 + 22.40 = 30.15
anyone have any idea on how to solve this
Answers
Answer:
Option 1 : y = ( x+5 ) ( x+3 )
Step-by-step explanation:
HELP urgently please please❤️❤️❤️Please
Answers
Answer:
Step-by-step explanation:
From the graph we can notice that :
g(2)=5g(-2)=2g(3)=0g(5)=1Again we can deduce from the graph that :
g(x)=0 when x= -3g(x)=6 when x= 0Blake Hamilton has money in a savings account that earns an annual interest rate of 3%, compounded monthly. What is the APY (in percent) on Blake's account? (Round your answer the nearest hundredth of a percent.)
Answers
The Annual Percentage Yield (APY) on Blake Hamilton's savings account, which earns an annual interest rate of 3% compounded monthly, is approximately 3.04%.
The APY represents the total annualized rate of return, taking into account compounding. To calculate the APY, we need to consider the effect of compounding on the stated annual interest rate.
In this case, the annual interest rate is 3%. However, the interest is compounded monthly, which means that the interest is added to the account balance every month, and subsequent interest calculations are based on the new balance.
To calculate the APY, we can use the formula: APY = (1 + r/n)^n - 1, where r is the annual interest rate and n is the number of compounding periods per year.
For Blake Hamilton's account, r = 3% = 0.03 and n = 12 (since compounding is done monthly). Substituting these values into the APY formula, we get APY = (1 + 0.03/12)^12 - 1.
Evaluating this expression, the APY is approximately 0.0304, or 3.04% when rounded to the nearest hundredth of a percent.
Therefore, the APY on Blake Hamilton's account is approximately 3.04%. This reflects the total rate of return taking into account compounding over the course of one year.
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If f(x) = 3x + 2, then find the value of x such that f(x) = -4.
Answers
Answer:
See Below
Step-by-step explanation:
Solve by substituting
-4 = 3x + 2
-2 -2
-6 = 3x
3x/3 = -6/3
x = -2
Answer:
x = -2
Step-by-step explanation:
So we are given the function f(x) = 3x + 2 and we are asked to find the value of x that makes f(x) = -4. To do this, we can replace f(x) with -4 in the given function and solve for x.
-4 = 3x + 2
Swap sides.
3x + 2 = -4
Subtract 2 from both sides.
3x = -6
Divide both sides by 3.
x = -2
So we have found that x = -2 when f(x) = -4. This means that when x = -2, f(x) = -4.
I hope you find my answer and explanation to be helpful. Happy studying.
Compare \(\sqrt{130}\) and \(\frac{111}{8}\) using <, >, or =
CHOICES :
\(\sqrt{130} \geq \frac{111}{8}
\\\sqrt{130} = \frac{111}{8}
frac{111}{8} \geq \sqrt{130}
\(\frac{111}{8} \leq \sqrt{130}\)
Answers
The result of comparing √130 and 111/8 is √130 < 111/8
How to compare the numbers?The expressions that represent the numbers are given as:
√130 and 111/8
The expression √130 is a radical expression.
Start by evaluating the radical expression, this is shown as follows
√130 = 11.4018
The expression 111/8 is a rational expression.
Next, we evaluate the rational expression, this is shown as follows
111/8 = 13.875
Next, we compare the results of evaluating each expression
i.e. 13.875 and 11.4018
By comparison, we have:
11.4018 < 13.875
Substitute the known values in the above equation
√130 < 111/8
Hence, the result of comparing √130 and 111/8 is √130 < 111/8
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Austin needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 4.5 hours and charged him $126 for parts. The total was $553.50. Which equation could be used to determine xx, the cost of labor per hour?
Answers
The cost of labour per hour is $90.56
The total amount paid by Austin is the sum of the total cost of labour and the cost of the parts
Total amount paid = total cost of labour + cost of parts
$553.50 = total cost of labour + $126
total cost of labour = $533.50 - $126
= $407.50
The total cost of labour = cost of labour per hour x total time worked
$407.50 = xx × 4.5
xx = $407.50 / 4.5
xx = $90.56
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i need the answer as soon a possible
Answers
Answer:
\(x = 0 \\ 7y = 28 \\ y = 28 \div 7 = 4 \\ \\ \\ y = 0 \\ - 4x = 28 \\ x = 28 \div ( - 4) = - 7\)
let f(x) = 1 3x . compute lim h→0 f(5 + h) − f(5) h .
Answers
For a function, f(x) = 1 + 3x , the computed value of lim h→0 [f(5 + h) − f(5)]/h is equals to the three.
In Mathematics, the limit of a function is a value of the function as the input of the function tries approaches some number. Function limits are used to define continuity, integrals, and derivatives. Mathematically, let f(x) be a function and L be limit of function, f(x) at x a exist if and only if lim f(x) = lim f(x) = L
x→a⁻ x→a⁺
We have, f(x) = 1+3x and will compute lim h→0 [f(5 + h) − f(5)]/h . Firstly, determine the value of function at x = 5 , x = 5+h.
So, f(5) = 1+ 3×5 = 16 and f(5+ h) = 1+3(5+h)
= 16+ 3h
Now, lim [ f(5 + h) − f(5)]/ h
h→0
= lim [(16 + 3h) − (16) ]/ h
h→0
= lim [ 16 + 3h - 16 ]/ h
h→0
= lim [ 3h/ h ] = lim [ 3h¹h⁻¹ ]
h→0 h→0
= lim [ 3h¹⁻¹ ] = lim [ 3h⁰ ]
h→0 h→0
= lim 3 (1) = 3 ( since, x⁰ = 1 )
h→0
Hence, the required limit value is 3.
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Find the value of x.
Answers
The value of x in the trapezoid is 117°.
What is trapezoid ?A trapezoid is a quadrilateral a four-sided polygon with two parallel sides and two non-parallel sides. The parallel sides are most call the bases of the trapezoid, and the non-parallel sides are called the legs.
In a trapezoid, the opposite angles are supplementary. Therefore, we can set up an equation:
x + 63° = 180°
Solving for x, we get:
x = 180° - 63°
x = 117°
Therefore, the value of x in the trapezoid is 117°.
Full question "Find the value of x in the trapezoid below.
X
63°
X = = [?]°"
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please help me with this
Answers
Answer:
a. range: 4
b. 5 students
c. mean: 8
Step-by-step explanation:
range: subtract the smallest number from the largest number in the data.
10 - 6 = 4
students amount was counted by the number of marks given.
mean: add the data together. (40) divide the sum by the number of marks provided. (5)
40 divided by 5 equals 8
Answer:
4 244 8
Step-by-step explanation:
10 - 6 = 4 is the range
6x5 = 30 7x4 = 28 8x7 = 56 9x10 = 90 10x4 = 40 244 students
mean = 6+7+8+9+10 = 40/5 = 8
Plz help fast will mark brainliest!!!
Answers
I think it is 457.333333 π m3
Hope this helped :T
Answer:
1436.76
Step-by-step explanation.
\(\frac{4}{3}\pi r^{3}\)
that is the formula, with r being the radius.
then if you replace r with 7 that would be the answer.
pi, also equals 3.14159265359, or shortened 3.14.
so it would look like:
\(\frac{4}{3}*3.14*7^{3}\)
helpp plzzzzzzzzzzzzzzzzzzzzzzzzz
Answers
Answer:
jhgydghv f yf
Step-by-step explanation:
Fill in the blank. When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the mean, we call the new value a _____ . When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the mean, we call the new value a ____.
Answers
When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the mean, we call the new value a Z-Score.
In statistics, each mathematical formula and each element has an internationally recognised name. This is to ensure that everyone in the world understands what every researcher has to say in every letter. A statistic that tells the number of standard deviations a data value is above or below the mean is called a z-score. And its formula is, Z = (X − μ)/σ
where, μ--> population mean,
σ --> population standard deviation and
x --> the raw-score.
Hence, when a data value is converted to a standardized scale, new value, Z-Score is representing the number of standard deviations the data value lies from the mean.
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wich inequality does the graph sow HURRY
Answers
Answer: The correct answer is A)
Calculate the slope of the given line
Answers
The slope of the given line is, m = 2.
What is slope of the line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively. where "m" represents a line's slope. So, the slope of a line is tanθ.
The given line passes through the points, (2, 1) and (0, -3).
Since, the line's slope is calculated as,
\(m = \frac{y_2-y_1}{x_2-x_1}\)
Here,
\((x_1, y_1) =(2, 1)\\(x_2, y_2)=(0, -3)\)
So,
\(m = \frac{-3-1}{0-2}\\ m=\frac{-4}{-2}\\ m = 2\)
Hence, the slope of the line is 2.
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find an interval of t-values such that c(t)=(cost,sint) traces the upper half of the unit circle (in the counter-clockwise direction).
Answers
The interval of t-values such that c(t)=(cost,sint) traces the upper half of the unit circle (in the counter-clockwise direction) is [π/2, 3π/2].
To trace the upper half of the unit circle in the counter-clockwise direction, we need the y-coordinate (sint) of the curve to be positive. Since sin is positive in the first and second quadrants of the unit circle, we need to find the interval of t-values such that cos(t) is within the b [-1, 1] of the x-coordinate in the first and second quadrants. This interval will correspond to the portion of the unit circle in which the curve c(t) lies on the upper half.
The interval of t-values that satisfies this condition is [π/2, 3π/2]. To see why, note that at t = π/2, c(t) = (0, 1), which is the point on the upper half of the unit circle with y-coordinate 1. As t increases from π/2 to 3π/2, the curve c(t) moves counter-clockwise along the upper half of the unit circle until it reaches the point (0, -1) at t = 3π/2. At t > 3π/2, the y-coordinate of c(t) becomes negative and the curve moves to the lower half of the unit circle. Therefore, the interval [π/2, 3π/2] corresponds to the portion of the unit circle in which c(t) lies on the upper half.
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You want to survey twenty of the 150 ninth graders to get their opinion on the school's
new schedule. Which of the following methods is most likely to lead to a sample that is
the most representative of the 150 ninth graders
Answers
Answer: Simple random sample
Step-by-step explanation: This will be the most representative of the 150 ninth graders.
The sample that is the most representative of the 150 ninth graders is
Simple random space
What is sample space?It is the total number of possible outcomes from a given set.
We have,
Number of 9th grader students = 150
Number of students to survey = 20
Sample that is the most representative of the 150 ninth graders.
= Simple random space
This means,
The 20 students will be selected randomly.
Thus,
Sample random space is the most representative of the 150 ninth graders.
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A line passes through the points (7, 10) and (7, 20). Which statement is true about the line? It has a slope of zero because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the numerator of a fraction cannot be zero. It has a slope of zero because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the denominator of a fraction cannot be zero. It has no slope because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the numerator of a fraction cannot be zero. It has no slope because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the denominator of a fraction cannot be zero.
Answers
Answer:
It has no slope because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the denominator of a fraction cannot be zero.
Step-by-step explanation:
Points:
(7, 10) and (7, 20)Slope-intercept form:
y= mx+bslope is:
m= (y2-y1)/(x2-x1)= (20-10)/(7-7)= 10/0,denominator of the fraction is zero, we can't divide by zero, so this line has no slope
----------
It has a slope of zero because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the numerator of a fraction cannot be zero.
no, numerator is not zeroIt has a slope of zero because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the denominator of a fraction cannot be zero.
no, it has no slopeIt has no slope because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the numerator of a fraction cannot be zero.
no, numerator is not zeroIt has no slope because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the denominator of a fraction cannot be zero.
yesAnswer:
D;
Step-by-step explanation:
It has no slope because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the denominator of a fraction cannot be zero.
a ton of recycled paper will save 17 trees. if one bag weighs 2 oz, how many bags are needed to save 68 trees?
Answers
Answer:8
Step-by-step explanation:divide 136 with 17 to see how many tons needed
Determine the values of x and y.
Answers
Answer:
answer is d please follow me I hope it will help you
Select all the correct answers.
Which expressions are equivalent to log4 (²) ?
Answers
Answer:
A: -1 + 2 log4^x
C: log4 (1/4) + log4 x^2
Step-by-step explanation:
Apply logarithm properties:
log4 (1/4x^2) = log4 (1/4) + log4 x^2
Evaluate: log4 (1/4)
log4 (1/4) = -1
Substitute the value back:
-1 + lg4 x^2
Apply logarithm properties:
-1 + 2 log4 ^x
Draw a conclusion:
The expressions equivalent to: log4 (1/4x^2) are:
Answer Choices: A, and C
A= -1 + 2 log4^x
C= log4 (1/4) + log4 x^2
Hope this helps!