The sides of the triangle shown increase in such a way that
dz/dt=1, and dx/dt=3 dy/dt At the instant when x = 12 and y= 5, what is the value of dx/dt?
Answers
Therefore , the solution of pythgoras theorem is the value of is dx/dt = 0.95, when x = 12 and y =5.
What is Pythagoras theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
Here,
It is given that -
dz/dt = 1,
dx/dt = 3(dy/dt)
⇒dy/dt = 1/3 (dx/dt)
As shown in the diagram x = base, y = perpendicular and z = hypotenuse.
According to the Pythagoras theorem -
z² = x² + y²
Differentiating both sides -
d/dt (z²) = d/dt (x² + y²)
2z dz/dt = 2x dx/dt + 2y dy/dt
z dz/dt = x dx/dt + y dy/dt
Substituting the value of dy/dt -
z dz/dt = x dx/dt + y/3 (dx/dt)
z dz/dt = dx/dt (x + y/3)
dx/dt = (z dz/dt)/(x + y/3)....equation 1
So, when x = 12 and y = 5, the value of z -
z = √[(12)² + (5)²]
z = √(144+25)
z = √169
z = 13
Substituting the value of x, y, z and dz/dt in equation 1 -
dx/dt = (13 × 1)/(12 + 5/3)
dx/dt = 13 / 41/3
dx/dt = (13 × 3)/41
dx/dt = 39/41
dx/dt = 0.95
Therefore, the value of dx/dt = 0.95.
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Therefore , the solution of pythgoras theorem is the value of is dx/dt = 0.95, when x = 12 and y =5.
What is Pythagoras theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
Here,
It is given that -
dz/dt = 1,
dx/dt = 3(dy/dt)
⇒dy/dt = 1/3 (dx/dt)
As shown in the diagram x = base, y = perpendicular and z = hypotenuse.
According to the Pythagoras theorem -
z² = x² + y²
Differentiating both sides -
d/dt (z²) = d/dt (x² + y²)
2z dz/dt = 2x dx/dt + 2y dy/dt
z dz/dt = x dx/dt + y dy/dt
Substituting the value of dy/dt -
z dz/dt = x dx/dt + y/3 (dx/dt)
z dz/dt = dx/dt (x + y/3)
dx/dt = (z dz/dt)/(x + y/3)....equation 1
So, when x = 12 and y = 5, the value of z -
z = √[(12)² + (5)²]
z = √(144+25)
z = √169
z = 13
Substituting the value of x, y, z and dz/dt in equation 1 -
dx/dt = (13 × 1)/(12 + 5/3)
dx/dt = 13 / 41/3
dx/dt = (13 × 3)/41
dx/dt = 39/41
dx/dt = 0.95
Therefore, the value of dx/dt = 0.95.
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Related Questions
Sureh ha 4 coupon book, each with 6 coupon. He keep 13 of the coupon and give the ret away. Fifty percent of thoe he keep are for the movie theater
Answers
So, the final expression that represents the number of movie theater coupons Suresh has is 4.
Suresh has 4 coupon books, each containing 6 coupons, for a total of 4*6 = 24 coupons.
He wants to keep 1/3 of these coupons, so we can write an expression to represent this as: (1/3) * 24 = 8
So he keeps 8 coupons and gives away 24-8 = 16 coupons.
Out of the 8 coupons he keeps, 50% of them are for the movie theater, so we can write an expression to represent this as: 8 * 0.50 = 4
Therefore, the final expression that represents the number of movie theater coupons Suresh has is: 8 * 0.50 = 4
In this question, we have used the basic arithmetic operations like multiplication and subtraction to find the number of coupons Suresh keeps and gives away. And then we have used the percentage to find out how many movie theater coupons he has out of the total number of coupons he kept.
Complete Question: Suresh has 4 coupon books, each with 6 coupons. He keeps 1/3 of the coupons and gives the rest away. Fifty percent of those he keeps are for the movie theater. Write and evaluate an expression to show how many movie theater coupons he has.
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11. A cattle ranch has 1,400 acres of grazing land. The ranch has 140 cows. How many acres of grazing land does the ranch have per cow?
Answers
Step-by-step explanation:
1400-140 this is answer of this question
if theta is an angle in standard position and it’s terminal side passes through the point (3, -4) find the exact value of csc theta in simplest radical form
Answers
The exact value of tanθ is -4/3 that is -1.33 in the simplest radical form.
What is Tanx in terms of sinx and cosx ?
The value of Tanx can be the ratio of sinx and cosx or it can be defined by the ratio of its opposite side and adjacent side.
Given,
if theta is an angle in standard position and
it’s terminal side passes through the point (3, -4)
So, the given point is (3,-4)
By the definition we can say that ,
If the terminal side passes through the point (a,b)
than tanθ = b/a .
so, similarly
tanθ = -4/ 3
Hence, The exact value of tanθ is -4/3 that is -1.33 in the simplest radical form.
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What is the best interpretation of P(3) =12
Answers
The best interpretation of P(3) = 12 is that the probability of 3 is 12
What is probability?Probability is simply described as an important branch of mathematics that concerns numerical descriptions of the likelihood of the occurance of an event the proposition of how true it is.
The probability of an event is a number that must be between 0 and 1.
Given that;
0 indicates impossibility of the occurance of the event 1 represents certaintyNote that the analysis of events that is being governed by probability is known as statistics.
The types of probability are;
Theoretical ProbabilityExperimental ProbabilityAxiomatic ProbabilityHence, P(3) = 12 is the probability of 3 is 12
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amanda used a total of 13 gallons of gas while driving her car each hour she was driving she used 3/10 gallons of gas what was the total number of hours she was driving
Answers
The fraction 10/10 would be equal to one gallon, so just 1. So that would mean 3/10 of a gallon would equal 0.3
Divide 13 by 0.3 and you get 43.3 hours. So you’d just put 43 hours as your answer.
What is 2 ordered pair?
Answers
If the given ordered pair [tex](2,3) = (3x-4,3)[/tex] are equal , then on simplifying we get that the value of x is 2 .
The Ordered Pair is given as [tex](2,3) = (3x-4,3)[/tex] , and the ordered pair are equal ,
We know that the two ordered pairs [tex](a_{1} ,b_{1} )[/tex] and [tex](a_{2} ,b_{2} )[/tex] , are said to be equal if and only if the elements , [tex]a_{1} =a_{2}[/tex] and [tex]b_{1} =b_{2}[/tex] .
So , By the above definition ,
we get that , [tex]3x-4=2[/tex] ;
adding 4 to both the sides of equation ,
we get ; [tex]3x=6[/tex]
Dividing both sides by 3 ,
we get ;
⇒ [tex]x=\frac{6}{3}[/tex] ;
On simplifying further ,
we have ;
⇒ [tex]x=2[/tex] .
Therefor , the value of x is 2 .
The given question is incomplete , the complete question is
What is the value of x if the 2 ordered pair (2 , 3) = (3x-4 , 3) are equal ?
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A fair quarter is flipped three times. For
each of the following probabilities, use the formula for the binomial distribution and a calculator to compute the requested probability.
(a) Find the probability of getting exactly three heads.
(b) Find the probability of getting exactly two heads.
(c) Find the probability of getting two or more heads.
(d) Find the probability of getting exactly three tails.
Answers
Answer:
(a) P(exactly 3 heads) = P(X = 3) = (3!/3^3)(1/4)^3 = 0.21875
(b) P(exactly 2 heads) = P(X = 2) = (2!/2^2)(1/4)^2 = 0.375
(c) P(2 or more heads) = P(X ≥ 2) = 1 - P(X ≤ 1) = 1 - (1!/1^1)(1/4) - (0!/0^0)(1/4)^0 = 0.9375
(d) P(exactly 3 tails) = P(X = 3) = (3!/3^3)(1/4)^3 = 0.21875
3
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
The table shows the mode of transportation to school for families with a specific number of children.
Mode of Transportation
Car
Number of
Children
0.284
1-2
63
38
3+
25
49
Total
88
87
A family from the survey is selected at random. Match the probability to each event.
0.662
Bus
0.203
0.249
101
74
175
0.624
P (3+ Children Bus)
Total
P(1-2 Children Car) - P (3+ Children Car)
Reset
P (Car 1-2 Children)
0.563
P (Bus 1-2 Children) - P (Bus 3+ Children)
▸
Next
Answers
The probability of number of 1-2 Children in car and 3 plus children in car is 0.203.
What is probability?The possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur.
The probability of P(1-2 children| car). P (3 plus children| car) is given by:
P = 63/88 × 25/88
P=0.203
The probability of P(Bus| 1-2 children). P (Bus | 3 plus children) is given by:
P = 38/101 × 49/74
P=0.249
The probability of P(Car |1-2 Children) is given by:
P= 63/101
P=0.624
The probability of P(3 plus children | Bus)is given by:
P=49/87
P=0.563
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Answer: The picture below
Step-by-step explanation: Correct on Edmentum, if you give me a low rating than you are mean :(
Order these numbers from these two greatest?
7,404, 7.44, 7.2, 7.2041
Answers
Answer:Greatest to Smallest > 7.44, 7.404, 7.2041, 7.2 and Smallest To Largest > 7.2, 7.2041, 7.404, 7.44
Step-by-step explanation:
Sample Response: The diagram should have five columns, one for each 25% and one for the total, because 25% is 1 4 of 100%. It should have 2 rows, 1 for percents and 1 for dollar amounts. What key phrases did you include in your response? 4 columns, because 25% is One-fourth of 100% 1 column for total amount 2 rows for percents and dollar amounts
Answers
The correct option regarding the number of columns representing a percentage of 25% is given as follows:
4 columns, because 25% is One-fourth of 100%.
How to obtain the number of columns of the diagram?The percentage that represents the total of the diagram is given as follows:
100%.
The ratio between the total percentage of 100% and the percentage of 25% is given as follows:
100/25 = 4.
The ratio represents the number of columns, which is of 4, and is the justification for the correct option.
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Justin opens a savings account with $8. He saves $4 each week. The table represents his account balance. Decide whether the table represents a linear function or a nonlinear function.
Answers
The required relationship formed as of the given information is a linear function.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Justin opens a savings account with $8. He saves $4 each week.
Let the x be the number of weeks and y be the number of money saved after x weeks.
According to the question,
y = 8 + 4x
Since the above function is a linear function, so table representing the data followed the above expression shows the linear function
Thus, the required relationship formed as of the given information is a linear function.
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What is a 1/2 scale factor?
Answers
Every coordinate point of the original triangle has its scale factor doubled by one-half if the scale factor is one. multiply by half after dilation with a scale factor of two.
What is a 1/2 scale factor?A fractional scale factor will result in a smaller form. Reduction describes this. A scaling factor of 1/2 therefore indicates that the new shape is half of the old shape.1:2 is the half scale. One useful way to conceptualise this is as follows: one unit on the picture equals two units on the item. A little object can be drawn in 2:1 scale after being enlarged on paper. In other words, the object's drawing is twice as big as the actual object.Find the two equivalent sides on each figure, one on each, to determine the scale factor. To determine the scale factor from one figure to the next, write the ratio of one length to the next.To learn more about scale refer to:
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What is the area of triangle if sides are 9cm 12cm and 15cm *?
Answers
The area of triangle if sides are 9cm 12cm and 15cm is 54 square cm.
In the given question we have to find the area of triangle if sides are 9 cm 12 cm and 15 cm.
The entire area bounded by a triangle's three sides is referred to as the triangle's area. In essence, it equals half of the base times height, or A = 1/2bh. So, in order to calculate the area of a triangular polygon, we need to know its base (b) and height (h).
Area of Triangle = 1/2 bh
Area of Triangle = 1/2 9*12
Area of Triangle = 9*6
Area of Triangle = 54 square cm
Hence, the area of triangle if sides are 9cm 12cm and 15cm is 54 square cm.
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helpppppp i love math :))
You are beautiful. Don't let anyone tell you different<3
Answers
There are √131 lies between the two whole numbers 11 and 12.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.
The square root of 131 is approximately 11.445 It lies between the two numbers 11 and 12, specifically, it is greater than 11 and less than 12.
We know that the square root of a number is the value that, when multiplied by itself, gives that number.
For example, the square root of 121 (which is 11) is 11 because 11 x 11 = 121.
In the same way, the square root of 131 is the number that, when multiplied by itself, will give 131.
Since 131 is a prime number and it is not a perfect square, the square root of 131 cannot be a whole number, it should be decimal and it lies between 11 and 12.
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what is x < 3 as a solution or not a solution
Answers
x < 3 is a solution of the inequality x - 3 < 0 and x < 3 is not the solution of the inequality x + 3 < 0.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Suppose that the inequality is x - 3 < 0.
x - 3 < 0
Adding 3 on both sides of the equation,
x - 3 + 3 < 0 + 3
x < 3
x< 3 is the solution of the expression x - 3 < 0.
Consider the inequality x + 3 < 0.
x + 3 < 0
Subtracting 3 from both sides,
x + 3 - 3 < 0 - 3
x < -3
x < 3 is not the solution of the expression x + 3 < 0
Hence the expression with x < 3 as a solution is x - 3 < 0 and not as a solution is x + 3 < 0.
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What is the y-intercept (initial value) for the function shown in the graph?
Answers
Answer:
5 is the y-intercept
Step-by-step explanation:
write an expression for x fewer than 62
Answers
The expression for x fewer than 62 can be written as 62 - x
What is a mathematical expression?An expression can be evaluated to a single value by substituting specific values for the variables and performing the operations in the correct order. Mathematical expressions can be used to model real-world phenomena, make predictions, and solve problems. Expressions are used in various branches of mathematics such as Algebra, Calculus and Geometry.
Fewer than tells us that x is less than 62, the solution is to tell us by what number that it is less than.
Hence 62 - x is the expression for x fewer than 62
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On the second grid, create a graph of y = 3 – 4t for -2 ≤ t ≤ 7 with y on the vertical axis and t on the horizontal axis.
Answers
The graph of y = 3 - 4x is given above.
The coordinates on the graph are:
(-2, 11) and (7, -25).
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
y = 3 - 4t
Where -2 ≤ t ≤ 7
Now,
Find the coordinates on the graph.
y = 3 - 4t
For t = -2
y = 3 - 4 x (-2) = 3 + 8 = 11
i.e
(-2, 11)
For t = 7
y = 3 - 4 x 7 = 3 - 28 = -25
i.e
(7, -25)
Thus,
The coordinates on the graph are:
(-2, 11) and (7, -25).
The graph is given below.
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How would you classify the polynomial equation with a degree of 2?
Answers
A quadratic equation with real or complex coefficients has two roots.
What is quadratic equation?A quadratic equation with real or complex coefficients has two roots. A quadratic equation is any algebraic equation that can be expressed in standard form as where x is an unknown value and a, b, and c are known values, with a 0. A second-degree equation is a quadratic equation.This signifies that it has at least one (1) squared phrase. 'ax2 + bx + c = 0' is a typical formula for solving quadratic equations, where a, b, and c are constants or numerical coefficients.
Here,
A quadratic equation with real or complex coefficients has two solutions, known as roots.
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The answer is:
⇨ belowWork/explanation:
You would classify a polynomial with a degree of 2 based on the number of terms. The degree is second.
So you would say "this is a second-degree polynomial".
An example of a second-degree polynomial would be [tex]\bf{y^2+7}[/tex].
Hence, this is the answer.The cost of a stereo cable was $14 yesterday. Today, the cost rose to $16 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answers
100 was 14 and what was 16
You need to multiply 100 and 16 then divide to 14
The function f(x)=x√ is translated 4 units right to form function g(x).
What is the equation of g(x)?
Enter your answer in the box.
g(x) =
Answers
The equation of g(x), after the translation of [tex]f(x) = \sqrt{x}[/tex] 4 units to the right is given as follows:
[tex]g(x) = \sqrt{x - 4}[/tex]
What is a translation?Among the many transformations that a function or a figure can undergo is a translation, along with reflections, rotations and dilation.
In a translation, only the position of the figure changes, either left, right, up or down, keeping the inclination, orientation and congruence.
The translations are defined as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.The parent function for this problem is given as follows:
[tex]f(x) = \sqrt{x}[/tex]
After the translation 4 units right, the function g(x) is defined as follows:
[tex]g(x) = f(x - 4) = \sqrt{x - 4}[/tex]
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Is it possible to have a triangle with the sides 3cm 6cm 7cm?
Answers
Answer:
yes
Step-by-step explanation:
for the sides to form a triangle.
the sum of any 2 sides must be greater than the third.
As a check
3 + 6 = 9 > 7
3 + 7 = 10 > 6
6 + 7 = 13 >3
this meets the condition for a triangle to be made.
What point on the number line is three fourths of the way from the point −3 to point 4? 5.25 2.25 −1.25 −2.25
Answers
(B) 2.25 is three-fourths of the way between -3 and 4 on the number line.
What is a number line?A number line is basically a straight line that illustrates real numbers.
It has all the integers marked out evenly and each point corresponds to a certain real number.
We can usually see numbers from -3 up to 3, but it includes all real numbers and even the ones in between the integers.
It's a great tool to help teach basic addition and subtraction, especially when you're dealing with negative numbers.
So, according to the number line, we have to count from -3 to 4.
If we count as 3/4 from -3 to 4.
Then, we will land on 2.25 on the number line.
Therefore, (B) 2.25 is three-fourths of the way between -3 and 4 on the number line.
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Complete question:
What point on the number line is three-fourths of the way from point −3 to point 4?
(A) 5.25
(B) 2.25
(C) −1.25
(D) −2.25
Answer:
2.25
Step-by-step explanation:
In parallelogram MLKJ, find mZMLK
and mZLKJ.
18°
M
K
12°
L
Answers
So on solving the provided question, we can say that here in the quadrilateral; angle MJL = angle JLK = 60
what is quadrilateral?A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
here in the quadrilateral
angle MJL = 60
angle MJL = angle JLK = 60
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what is the fractional part that make up 7/3?
Answers
Answer:
1/3
Step-by-step explanation:
7/3 = 6/3 + 1/3 = 2 + 1/3 = 2 1/3
The fractional part is 1/3.
Determine whether S is a basis for P3.
S = {4t − t2, 5 + t3, 5 + 3t, −3t2 + 2t3}
Answers
No, S is not a basis for P³. In order for a set of vectors to be a basis for a vector space, the vectors must be linearly independent and span the space.
In this case, the set of vectors does not span P³ because the highest order of the polynomials in S is t³, which does not span all of P³ which contains polynomials of order up to and including t³.
Additionally, the set of vectors is not linearly independent. For instance, 4t−t²= 5+3t−2t³, which means that the two vectors are linearly dependent. Therefore, S is not a basis for P³.
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In a geometric series, the sum of the first three terms is 14. 25 and the sum of the first four terms is 24. 375. Find the first term and the common ratio.
Answers
The first term and the common ratio in the geometric series are 3 and 3/2.
What is a geometric series?A geometric series is described as the sum of the sequence of numbers. The sum of the nth term of a geometric sequence is expressed as:
Sₙ = a (r^n – 1) / r – 1
In this case, if the sum of the first three terms is 14.25, it means:
n = 3
S₃ = 14.25
Now, substitute the value into the formula:
Sn = a (r^n – 1) / r – 1
S₃ = a (r^3 – 1) / r – 1
14.25 = a (r^3 – 1) / r – 1
And, if the sum of the first four terms is 24.375, it means:
n = 4
S₄ = 24.375
Substitute the value into the formula:
Sₙ = a (r^n – 1) / r – 1
S₄ = a (r^4 – 1) / r – 1
24.375 = a (r^4 – 1) / r – 1
Then, we now can divide both above equations:
14.25 / 24.375 = r^3 – 1 / r^4 – 1
14.25r^4 – 14.25 = 24.375r^3 – 24.375
14.25r^4 – 24.375r^3 = –24.375 + 14.25
14.25r^4 – 24.375r^3 = –10.125
14.25r^4 – 24.375r^3 + 10.125 = 0
After factorizing we get:
r = 3/2
This is the common ratio.
Now, substitute the value of r into the equation
14.25 = a (r^3 – 1) / r – 1
14.25 = a ((3/2)^3 – 1) / (3/2) – 1
14.25 = a (19/8) / 0.5
19a / 8 = 14.25 * 0.5
19a / 8 = 7.125
19a = 57
a = 57 / 19
a = 3
Thus, the first term is 3.
Hence, the first term in the geometric series is 3 and the common ratio is 3/2.
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what is the answer for this math question -q/7>-1 im stuck on it
Answers
All possible solutions for inequality are (-∞,-7)U(-7, ∞).
What is inequality?
In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.
The inequality q/7 > -1 is a mathematical statement that compares the value of q/7 to -1.
To solve the inequality, we can start by isolating q on one side of the inequality.
To do this, we need to multiply both sides of the inequality by 7:
q/7 * 7 > -1 * 7
q > -7
Now we have the inequality q > -7, this inequality states that q is greater than -7.
To find all possible solutions for the inequality, we can use interval notation. The interval notation for the solution of this inequality is (-infinity,-7)U(-7, infinity)
It means all real numbers except -7, the solution set is an open interval.
Alternatively, we can also graph the solution set of the inequality on a number line, shading the region that represents the solution. The shaded region will be all the points to the right of -7 on the number line.
Hence, all possible solutions for inequality are (-∞,-7)U(-7, ∞).
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What is the y-intercept of a line that passes through the points (3, -3.8) and (5, -3)? (1 point)
Enter the solution in the box below.
Answers
Answer:
Step-by-step explanation:
We can solve this by either identifying the equation or by graphing. We'll try both.
Find the Equation
The slope of the line can be determined from the Rise/Run of the 2 given points:
Going from ((3,-3.8) to (5,-3):
Rise = (-3 - (-3.8) = 0.8
Run = (5 - 3) = 2
Slope = 0.8/2 or 0.4
The equation for this line is y = 0.4x + b, where b is the y-intercept.
Enter either point to find b:
y = 0.4x + b
-3 = 0.4*(5) + b for point (5,-3)
-3 = 2+b
b = -5
The equation is y = 0.4x - 5
The y=intercept is -5 (the value of b)
Graphing
See the attached graph. Mark the two points and then draw a straight line between them. The point at which the line crosses the y axis is the y-intercept (0,
y’all I just need help with the vertex.
Answers
Answer:
Step-by-step explanation:
Since it is a rectangle, the vertex is easily found.
It has a width of 10, and a length of 4.
Using this, the missing vertex can be found.
Missing vertex: (6,-3)