caculate the following multiplication
[tex]67 \times 12[/tex]
Answer:
804
Step-by-step explanation:
Just use a calculator.
Product -72 and sum -6
The ordered pair that respect the given conditions are: (6,-12) and (-12,6).
System of Equations
A system of equations is the given term of math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.
You can solve a system of equations by substitution or adding methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.
You should convert the text of the question into equations. See below.
Product = -7 -> xy= -72 (1)Sum= -6 -> x+y=-6 (2)From equation 1, you have x=-72/y. Thus, applying the substitution method, you can solve this question by following the steps below:
1) Replace x=-72/y into equation 2. Then, you have:
[tex]\frac{-72}{y} +y=-6\\ \\[/tex]
-72+y²=-6y
y²+6y-72=0
2) Solving the quadratic equation y²+6y-72=0 for finding y:
Δ=b²-4ac
Δ=6²-4*1*(-72)
Δ=36+288
Δ=324
[tex]y=\frac{-b\pm \sqrt{\Delta} }{2a} =\frac{-6\pm \sqrt{324} }{2*1}=\frac{-6\pm18 }{2}[/tex]. Therefore,
y1=(-6-18)/2=-12
or
y2=(-6+18)/2=12/2=6
3) Finding x
If x=-72/y and y=-12 or y=6. You have
For y=-12, x=-72/-12, thus x=6
For y=6, x=-72/6, thus x=-12
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Use the Chain Rule to find dz/dt. z = cos(x + 8y), x = 7t^5, y = 5/t
Answer:
We need to find dz/dt given:
z = cos(x + 8y), x = 7t^5, y = 5/t
Using the chain rule, we can find dz/dt by taking the derivative of z with respect to x and y, and then multiplying by the derivatives of x and y with respect to t:
dz/dt = dz/dx * dx/dt + dz/dy * dy/dt
First, let's find dz/dx and dz/dy:
dz/dx = -sin(x + 8y)
dz/dy = -8sin(x + 8y)
Now, let's find dx/dt and dy/dt:
dx/dt = 35t^4
dy/dt = -5/t^2
Substituting these values, we get:
dz/dt = (-sin(x + 8y)) * (35t^4) + (-8sin(x + 8y)) * (-5/t^2)
Simplifying this expression, we get:
dz/dt = -35t^4sin(x + 8y) + 40sin(x + 8y)/t^2
Substituting x and y, we get:
dz/dt = -35t^4sin(7t^5 + 40/t) + 40sin(7t^5 + 40/t)/t^2
Therefore, dz/dt is given by -35t^4sin(7t^5 + 40/t) + 40sin(7t^5 + 40/t)/t^2.
Which of the following statements is equivalent to saying that there is a 50% increase in the cost of a movie? Circle all that apply. a. The new cost of the movie is twice the old cost. b. The new cost of the movie is one and a half times the old cost. C. The increase in the cost of the movie is half the original cost. d. The increase in the cost of the movie is half the new cost. e. The cost of the movie doubled.
All of the statements are equivalent to saying that there is a 50% increase in the cost of a movie.
The formula for calculating a percentage increase is:
Percentage increase = (New Value - Original Value) ÷ Original Value x 100
In this case, we can say that the original value is the cost of the movie before the increase, and the new value is the cost of the movie after the increase. Let's say the original cost of the movie is $10. Then the percentage increase is 50%.
We can calculate the new cost of the movie as follows:
New Cost = Original Cost + (Original Cost x Percentage Increase)
New Cost = 10 + (10 x 0.50)
New Cost = 10 + 5
New Cost = 15
Therefore, we can say that the new cost of the movie is 15, which is one and a half times the original cost of $10. The increase in the cost of the movie is 5, which is half the original cost of $10. The cost of the movie did double, from the original cost of $10 to the new cost of 15.
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When two unequal forces act on an object, it causes the object to move.
These forces are called:
Answer:
resultant force
Step-by-step explanation:
the body will move to the direction where greater force is applied
what are the coordinates of point p on the directed line segment from a to b such that p is the length of the line segment from a to b?
the coordinates of point P are ((Ax + Bx) / 2, (Ay + By) / 2).
How to find?
If we want to find the coordinates of point P on the directed line segment from A to B such that P is the length of the line segment from A to B, we can use the following formula:
P = (1 - t)A + tB
where A and B are the coordinates of the two endpoints of the line segment, t is a scalar between 0 and 1, and P is the coordinates of the point we are trying to find.
When t = 1, we get the coordinates of point B, and when t = 0, we get the coordinates of point A. When t is between 0 and 1, we get a point on the line segment from A to B.
To find the point P that is the length of the line segment from A to B, we set t = 1/2, which gives us:
P = (1 - 1/2)A + (1/2)B
= (1/2)A + (1/2)B
So the coordinates of point P are the average of the coordinates of A and B:
Px = (Ax + Bx) / 2
Py = (Ay + By) / 2
where (Ax, Ay) and (Bx, By) are the coordinates of points A and B, respectively.
Therefore, the coordinates of point P are ((Ax + Bx) / 2, (Ay + By) / 2).
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Complete Question:
What are the Cartesian coordinates of point P on the directed line segment from point A to point B such that point P is located at a distance equal to the length of the line segment from point A to point B?
Is the function represented by the following table linear, quadratic or exponential?
The function represented by the table is symmetric, and the values of y vary with the square of the corresponding values of x. Therefore, the function is exponential.
What is function?In mathematics, a function is a rule that assigns a unique output value for every input value. It is a mathematical object that takes an input and produces an output. A function is often represented symbolically as f(x), where f is the name of the function and x is the input. The output value of the function depends on the input value, and the relationship between the input and output is determined by the rule of the function. Functions can be linear, quadratic, exponential, trigonometric, or many other types. They are used to model real-world phenomena and solve mathematical problems.
Here,
To determine if the function represented by the table is linear, quadratic, or exponential, we can plot the points on a graph and look at the pattern of the data.
x y
-2 12
-1 3
0 0
1 3
2 12
|
12 * * 12
| \ /
6 * *
| |
0 --*--*--*--*--*--*--*--*--
| |
* *
/ \ /
-6 * * *
|
-2 -1 0 1 2
Looking at the graph, we can see that the points do not fall on a straight line, so the function is not linear. Additionally, the curve of the points does not resemble a parabola, so the function is not quadratic. However, the points are symmetric around the y-axis, suggesting that the function may be exponential.
To confirm this, we can calculate the ratio of consecutive y-values:
12/3 = 4
3/0 = undefined
0/3 = 0
3/12 = 1/4
We can see that the ratio is not constant except for the first and last points, which have a ratio of 4. This suggests that the function is not purely exponential, but may have some other component.
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The distribution of pitches thrown in all the at-bats in a baseball game is as follows
The probability of a pitcher throwing exactly 5 pitches in an at-bat is 0.1 or 10%.
What is probability and how is it calculated?
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain. The probability of an event A is calculated as the ratio of the number of outcomes that correspond to event A to the total number of possible outcomes.
Calculating probability of a pitcher throwing exactly 5 pitches :
To calculate the probability of a pitcher throwing exactly 5 pitches in an at-bat, we need to add up the frequencies of all the at-bats that have exactly 5 pitches. From the given table, we see that there are 8 at-bats that have exactly 5 pitches.
The total number of at-bats is the sum of the frequencies of all pitch counts.
Total number of at-bats = 12+16+32+12+8 = 80
Therefore, the probability of a pitcher throwing exactly 5 pitches in an at-bat is:
P(5) = Frequency of 5-pitch at-bats / Total number of at-bats
P(5)= 8/80 = 0.1 or 10%
Hence, the probability that a pitcher will throw exactly 5 pitches in an at-bat is 10%.
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Consider a Poisson probability distribution with λ = 2.8. Determine the following probabilities.
a) P(x = 5)
b) P(x > 6)
c) P(x ≤3)
Answer:
a) Using the Poisson probability formula:P(x = 5) = (e^(-λ) * λ^x) / x!
P(x = 5) = (e^(-2.8) * 2.8^5) / 5!
P(x = 5) ≈ 0.1008
b) P(x > 6) = 1 - P(x ≤ 6)
We can find P(x ≤ 6) using the cumulative Poisson probability formula:
P(x ≤ 6) = Σ (e^(-λ) * λ^x) / x!
P(x ≤ 6) = (e^(-2.8) * 2.8^0) / 0! + (e^(-2.8) * 2.8^1) / 1! + (e^(-2.8) * 2.8^2) / 2! + (e^(-2.8) * 2.8^3) / 3! + (e^(-2.8) * 2.8^4) / 4! + (e^(-2.8) * 2.8^5) / 5! + (e^(-2.8) * 2.8^6) / 6!
P(x ≤ 6) ≈ 0.8581
Therefore,
P(x > 6) = 1 - P(x ≤ 6)
P(x > 6) ≈ 0.1419
c) P(x ≤ 3) = Σ (e^(-λ) * λ^x) / x!
P(x ≤ 3) = (e^(-2.8) * 2.8^0) / 0! + (e^(-2.8) * 2.8^1) / 1! + (e^(-2.8) * 2.8^2) / 2! + (e^(-2.8) * 2.8^3) / 3!
P(x ≤ 3) ≈ 0.4232
Mr. Brown's Thrift Shop
Quarter of 2012 Profit (in dollars)
1 $9,841.28
2 $8,957.67
3 $7,429.84
4 $11,095.67
How much total profit did Mr. Brown's store earn in the third and fourth quarters?
A.
$17,298.45
B.
$17,548.65
C.
$18,124.78
D.
$18,525.51
The correct option is D. $18,525.51. is the total profit made in the third as well as fourth quarters by Mr. Brown's store.
Explain about addition?In math, addition is the process of adding two or more integers together. The numbers having added are known as addends, while the outcome of the addition process, or the final response, is known as the sum. It is among the most fundamental mathematical operations we employ on a daily basis.
Quarterly profit for Mr. Brown's Goodwill Store in 2012 (in dollars)
1 $9,841.28
2 $8,957.67
3 $7,429.84
4 $11,095.67
Total profit = profit of 3rd quarter + profit of 4th quarter
Total profit = $7,429.84 + $11,095.67
Total profit = $18,525.51.
Thus, $18,525.51. is the total profit made in the third as well as fourth quarters by Mr. Brown's store.
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HELP ME ITS DUE TODAY!!!
Answer:
see step by step
Step-by-step explanation:
He can spin a lot of times the wheel, Notice IF THE SPINNER IS FAIR the probability must be equally, since the spinner have 4 options it must have 0.25 (25%) probability in each of the colors. Of course, since the probability is random the theoretically probability need to be closer to 0.25 for each one, to evade the randomness Klevon can spin the spinner a lot of times.
(for example, if he spins 100 times, he can get 28, 31, 25 and 20 and the spinner can still be fair, he can spin another 100 times to see the results, but if he have 5,5,80, 5 in the results, the probability is really low of this happening, so its probability unfair, but still, posible)
help I’ll give brainliest ^•^ just question (7) thanks!!
Answer:
To shift the graph of f(x) = |x| to have a domain of [-3, 6], we need to move the left endpoint from -6 to -3 and the right endpoint from 3 to 6.
A translation to the right by 3 units will move the left endpoint of the graph of f(x) to -3, but it will also shift the right endpoint to 6 + 3 = 9, which is outside the desired domain.
A translation to the left by 3 units will move the right endpoint of the graph of f(x) to 3 - 3 = 0, which is outside the desired domain.
A translation upward or downward will not change the domain of the graph, so options B and D can be eliminated.
Therefore, the correct answer is C g(x) = x - 3. This translation will move the left endpoint to -3 and the right endpoint to 6, which is exactly the desired domain.
A shopkeeper pays a total of $570 to buy 300 identical items. The shopkeeper sells 200 of these items. The selling price of each of these items is such that the shopkeeper makes a profit of 20% on what he paid for each item.The shopkeeper then reduces this selling price by 25% and he sells the remaining 100 items at this reduced price.Calculate the total profit made by the shopkeeper in selling all 300 items.
Answer:
I HOPE ITS HELPFUL
Step-by-step explanation:
Cost price of 300 articles = ₹1500Hence cost of each item = 1500/300 = ₹5With 20% profit, selling price of each item = 5 * 120/100 = ₹6Hence, total selling price of 260 items = 260 * 6 = ₹1560Selling price of balance items = 6/2 = ₹3Total selling price for balance items = 40 * 3 = ₹120Total selling price = 1560 + 120 = ₹1680Profit gained = 1680 - 1500 = ₹180Profit percentage = 180/1500 * 100 = 12
Figure ABCD is a parallelogram.Parallelogram A B C D is shown. The length of A D is 5 x + 3 and the length of B C is 38.What is the value of x?6789
ABCD is a parallelogram, the value of x is 7
A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus.
The opposing sides of a parallelogram are equal and parallel.
AD = BC
5x + 3 = 38
Take 3 away from both sides.
5x + 3 - 3 = 38 - 3
5x = 35
Subtract 5 from both sides.
5x/5 = 35/5
x = 7
A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral. Convex and concave are the two main forms. Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.
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For your monthly budget: for each $15 earned, only $4 can be spent on fast food. If your paycheck is $1850 and you spent $400 on fast food, which sentence correctly describes your spending compared to your budget?
You have 78% of money left to spend on fast food in your budget ratio.
Yes, that is correct. Here's a step by step explanation of how to figure that out:
1. Calculate the total amount of fast food that can be spent in a month: $15 x 4 = $60.
2. Calculate the total amount of money left in the budget for fast food: $1850 - $60 = $1790.
3. Calculate the percentage of money left in the budget for fast food: ($1790/$1850) x 100 = 78%.
A random sample of 10 subjects have weights with a standard deviation of 12.3194
kg. What is the variance of their weights?
Answer: The variance of a sample of size n can be calculated using the formula:
variance = (sum of squared deviations from the mean) / (n - 1)
where the deviation from the mean is the difference between each individual value and the sample mean, and the sum of squared deviations is the sum of the squares of these differences.
However, we don't have the individual weights or the sample mean, only the standard deviation. We can use a related formula that expresses the standard deviation in terms of the variance:
standard deviation = sqrt(variance)
Solving for variance, we get:
variance = (standard deviation)^2
Plugging in the given standard deviation of 12.3194 kg, we get:
variance = (12.3194 kg)^2 = 151.8992 kg^2
Therefore, the variance of the weights of the 10 subjects is 151.8992 kg^2.
Step-by-step explanation:
complete the table below.
4775 g968r648 747474874 483892874 23773259635y84b2375789325 7437594365825 4378574937587 49388959365n 98437858746587 32o4iy548569
Answer:
?
Step-by-step explanation:
1.The volume of a toaster is 100 in . If the toaster is 2.5 inches wide and 4 inches high, how long is the toaster, in inches?
2. Find the volume of a cylinder with a diameter of 9 ft and a height of 1 ft.
Use 3.14 or the calculator value for pi and provide an answer accurate to the nearest tenth.
Answer:
10 in.
Step-by-step explanation:
V = LWH
100 = L × 2.5 × 4
L = 10
rewrite 0,26 as a proper fraction, show all steps
The fraction form of 0.26 is 13/50.
What is a fraction that is improper or proper?
When a fraction's numerator is less than its denominator and it doesn't contain any whole numbers, the fraction is said to be appropriate. When a fraction represents a number bigger than one, it is said to have an inappropriate fraction since the numerator is larger than the denominator.
When the numerator value is less than the denominator, the fraction is said to be appropriate. 23, 6/7, 8/9, and other correct fractions are examples.
The decimal is 0.26
= 26/100
= 13/50
Hence, The answer is 13/50
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Which set of numbers could represent the lengths of the sides of a right triangle?
Responses
9, 10, 11
8, 12, 16
3, 4, 5
16, 32, 36
Answer:
3, 4, 5
Step-by-step explanation:
Take any odd number and square it.
3²=9
Divide that number by 2.
9/2=4.5
The original number (3 in this case), as well as the numbers 0.5 above and below the new number (4.5 in this case), are your set of numbers.
3, 4, 5
Hope that helps :)
Use the partial quotients method to find 1032/32 division Upload a photo of your work
By using the partial quotients method 1032/32 = 32 R8.
What is expression?In mathematics, an expression is a combination of numbers, symbols, and operators that represents a mathematical quantity or relationship. It can be a single number, a variable, or a combination of both, and can also include mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. Expressions can be evaluated or simplified using mathematical rules and formulas.
According to the given information:Step 1: Estimate how many times 32 goes into 1032. It's helpful to find a multiple of 32 that is close to 1032. In this case, 32 x 30 = 960, which is less than 1032, and 32 x 31 = 992, which is greater than 1032. So we can estimate that 32 goes into 1032 around 30 to 31 times.
Step 2: Write 30 on top of a division symbol, and multiply 30 by 32. Write the result, 960, under 1032, and subtract.
30
-------
32|1032
960
------
72
Step 3: Write 72 next to the 30 on top of the division symbol. Then, add 72 to the partial quotient (30) to get 102. Write 102 under the partial difference (72) and bring down the next digit, which is 2.
30 72
-------
32|1032
960
------
72
64
------
8
step 4: Estimate again how many times 32 goes into the new partial difference, 82. Since 32 x 2 = 64 is less than 82 and 32 x 3 = 96 is greater than 82, we estimate 32 goes into 82 two to three times.
Step 5: Write 2 on top of the division symbol, and multiply 32 by 2. Write the result, 64, under 82, and subtract.
30 72 2
------------
32|1032
960
------
72
64
------
8
tep 6: Write 2 next to the 30 and 72 on top of the division symbol, and add 2 to the partial quotient to get 32. Write 32 under the partial difference and bring down the next digit, which is 0.
30 72 2
------------
32|1032
960
------
72
64
------
8
0
Step 7: Since there are no more digits to bring down, we have the final answer. The quotient is 32 with a remainder of 8. Therefore, 1032 divided by 32 is equal to 32 with a remainder of 8.
Therefore, by using the partial quotients method 1032/32 = 32 R8 .
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given natural numbers a and b not both equal to 0, we know that there exist integers k and l with ak bl
The equation can be rearranged to the form y = -qx + r. This is the equation of a straight line, which can be graphed. The point of intersection of the two lines, ak + bl = 0 and y = -qx + r, is the solution for the two variables (k and l).
The equation ak + bl = 0 is a linear equation in two variables and is solved using the method of elimination. The equation can be written in the form ax + by = c, where a, b, c are constants. To solve this equation, both sides of the equation should be divided by the coefficient of one of the variables (a or b). This will result in a equation of the form x + qy = r, where q and r are constants. Then, the equation can be rearranged to the form y = -qx + r. This is the equation of a straight line, which can be graphed. The point of intersection of the two lines, ak + bl = 0 and y = -qx + r, is the solution for the two variables (k and l). The two variables can then be calculated using the point of intersection by substituting the x and y values into the two equations. In this way, the two variables k and l can be found such that ak + bl = 0.
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What are the integers k and l such that ak + bl = 0?
If y= cos x - sin x /cos x + sin x then dy /dx is :
Answer:
Step-by-step explanation:
We can find dy/dx by differentiating y with respect to x using the quotient rule.
First, we need to rewrite y using the trigonometric identity for the tangent of the difference of two angles:
y = (cos x - sin x)/(cos x + sin x) = [(cos x - sin x)/(cos x + sin x)] * [(cos x - sin x)/(cos x - sin x)]
y = (cos^2 x - 2cos x sin x + sin^2 x)/(cos^2 x - 2sin x cos x + sin^2 x)
y = (cos 2x - sin 2x)/(cos 2x + sin 2x)
Now we can apply the quotient rule:
dy/dx = [(-sin 2x - cos 2x)(cos 2x + sin 2x) - (cos 2x - sin 2x)(-sin 2x + cos 2x)]/(cos 2x + sin 2x)^2
dy/dx = (-sin^2 2x - cos^2 2x - 2sin 2x cos 2x + sin^2 2x + cos^2 2x + 2sin 2x cos 2x)/(cos 2x + sin 2x)^2
dy/dx = 0/(cos 2x + sin 2x)^2
Therefore, dy/dx = 0.
can you help me to solve this question?
A=?
B=?
C=?
D=?
The slope of the secant line joining (2, f(2)) and (7, f(7)) is 8.6.
What is slope of secant line?Rise over run is the definition of a line's slope. A curve's secant line is a line that connects any two of its points. The slope of the secant line would change to the slope of the tangent line at the point when one of these points approaches the other. As a secant line is also a line, we may calculate its slope using the slope of a line formula.
The two points on the secant line are given as (2, f(2)) and (7, f(7)).
Substituting the values in the function we have:
f(x) = x² + 8x
f(2) = 2² + 8(2) = 20
f(x) = x² + 8x
f(7) = 7² + 8(7) = 63
Using the difference quotient the slope of the line is:
(f(7) - f(2)) / (7 - 2) = (63 - 20) / 5 = 8.6
Hence, the slope of the secant line joining (2, f(2)) and (7, f(7)) is 8.6.
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Question 11 (2 points)
Among the seniors at a small high school of 150 total students, 80 take Math, 41
take Spanish, and 54 take Physics. 10 seniors take Math and Spanish. 19 take Math
and Physics. 12 take Physics and Spanish. 7 take all three.
How many seniors take Math and Spanish, but not Physics?
Note: Consider making a Venn Diagram to solve this problem.
3
10
27
121
There are 3 seniors who take Math and Spanish, but not Physics.
What is Venn Diagram?
A diagram representing mathematical or logical sets pictorially as circles or closed curves within an enclosing rectangle (the universal set), common elements of the sets being represented by the areas of overlap among the circles.
To solve this problem, we can use a Venn diagram to organize the information given about the students.
First, we know that there are 150 seniors in total, so we can label the outer rectangle of the Venn diagram as having a total of 150 students.
Next, we can label the three circles as Math, Spanish, and Physics, with the numbers given in the problem:
80 seniors take Math, so we label the Math circle with 80.
41 seniors take Spanish, so we label the Spanish circle with 41.
54 seniors take Physics, so we label the Physics circle with 54.
We also know that 10 seniors take Math and Spanish, 19 take Math and Physics, 12 take Physics and Spanish, and 7 take all three. We can label these overlaps in the Venn diagram as follows:
The overlap of Math and Spanish is 10.
The overlap of Math and Physics is 19.
The overlap of Physics and Spanish is 12.
The overlap of all three is 7.
To find the number of seniors who take Math and Spanish, but not Physics, we need to subtract the number of seniors who take all three (because they are counted in all three circles) and the number of seniors who take Math, Spanish, and Physics (because they are counted in the overlap of all three circles). Then we add the number of seniors who take only Math and Spanish (because they are not counted in the Physics circle).
Using the formula for the number of elements in the union of three sets, we have:
Math or Spanish or Physics = Math + Spanish + Physics - (Math and Spanish) - (Math and Physics) - (Spanish and Physics) + (Math and Spanish and Physics)
So, the number of seniors who take Math and Spanish, but not Physics is:
Math and Spanish - (Math and Spanish and Physics) + (Math or Spanish or Physics - (Math + Spanish + Physics) + (Math and Spanish and Physics))
= 10 - 7 + (80 + 41 + 54 - 2(10) - 2(19) - 2(12) + 7)
= 3
Therefore, there are 3 seniors who take Math and Spanish, but not Physics.
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My little cousin needs help with this can anyone help please.
I’m busy with my tests and I don’t have the time to explain.
Answer:
I don't knowI am sorry I will let someone else answer
Step-by-step explanation:
TRUE OR FALSE to calculate the average of the numeric values in a list, the first step is to get the total of values in the list.
The given statement 'to calculate the average of the numeric values in a list the first step is to get the sum of all the given values ' is a true.
Average of the numeric values in a list,
First step is to get the sum of values in the list.
It is not the total number of values.
Once we have the sum, we can divide it by the number of values to get the average.
Here is an example,
Suppose we have a list of numeric values are as follow,
[2, 4, 6, 8, 10].
To calculate the average of these values, we first find their sum,
2 + 4 + 6 + 8 + 10 = 30
Next,
divide the sum by the number of values in the list
Number of values = 5
30 / 5 = 6
This implies,
The average of the values in the list is 6.
Therefore, to get the average first step is to get the total of all values is true statement.
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Please indicate which is the best answer to complete the figure below.
Answer:
Step-by-step explanation:
B because after having the star and the circle comes the square.
dy If x = a sin 2t, y = a(cos 2t + log tan t), then find dx
Step-by-step explanation:
We have:
x = a sin 2t
Differentiating with respect to t, we get:
dx/dt = 2a cos 2t
Next, we have:
y = a(cos 2t + log tan t)
Differentiating with respect to t, we get:
dy/dt = -2a sin 2t + (1/tan t)(1/ln 10)
Using the identity:
sin^2 t + cos^2 t = 1
We have:
sin 2t = 2sin t cos t
And:
cos 2t = cos^2 t - sin^2 t
cos 2t = 2cos^2 t - 1
Using these identities, we can rewrite dx/dt and dy/dt in terms of x and y:
dx/dt = 2a sqrt(1 - x^2/a^2)
dy/dt = -2a sqrt(1 - x^2/a^2) + (1/ln 10)(y - a cos 2t)
Therefore, we have:
dx/dy = dx/dt ÷ dy/dt
Substituting the expressions for dx/dt and dy/dt, we get:
dx/dy = (2a sqrt(1 - x^2/a^2)) / (-2a sqrt(1 - x^2/a^2) + (1/ln 10)(y - a cos 2t))
Simplifying, we get:
dx/dy = (-2 sqrt(1 - x^2/a^2)) / (2 sqrt(1 - x^2/a^2) - (1/ln 10)(y - a cos 2t))
. Higher Order Thinking This Venn diagram
shows the relationship of ratios to rates to unit
rates. Describe a real-world situation involving
a ratio relationship. Then write the ratio as
2 different equivalent rates and as a unit rate.
The ratio relationship of a car's fuel efficiency can be expressed as equivalent rates of miles per gallon and gallons per mile, or as a unit rate of either 30 miles per gallon or 1/30 gallons per mile.
What is a Real-World Situation that Involves a Ratio Relationship?A real-world situation involving a ratio relationship could be the fuel efficiency of a car. For example, suppose a car travels 60 miles using 2 gallons of gas.
To express this ratio relationship as equivalent rates, we can write:
60 miles ÷ 2 gallons = 30 miles per gallon
2 gallons ÷ 60 miles = 0.0333 gallons per mile
To express the ratio as a unit rate, we can divide the numerator and denominator by the same amount to simplify the fraction. Let's choose to divide by 2 to get:
60 miles ÷ 2 gallons = 30 miles per gallon
2 gallons ÷ 60 miles = 1/30 gallons per mile
In both cases, the ratio represents the same relationship between miles traveled and gallons of gas used, but it is expressed in different units or rates.
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