pls
solve a,b,c. show full process thanks
(Each 5 points) Let (t) = + + 6 + 1 and y(t) = 2t - be parametric equations for a path traced out as t increases. (a) Find the equation of the tangent line when t= 2? (b) Find any values of t where th
Answers
The equation of the tangent line when t = 2 is x + y = 32. (a) to find the equation of the tangent line when t = 2, we need to find the derivative of the parametric equations with respect to t and evaluate it at t = 2.
given:
x(t) = t³ + 3t² + 6t + 1
y(t) = 2t - 5
to find the Derivative , we differentiate each equation separately:
dx/dt = d/dt(t³ + 3t² + 6t + 1)
= 3t² + 6t + 6
dy/dt = d/dt(2t - 5)
= 2
now, we evaluate dx/dt and dy/dt at t = 2:
dx/dt = 3(2)² + 6(2) + 6
= 12 + 12 + 6
= 30
dy/dt = 2(2) - 5
= 4 - 5
= -1
so, at t = 2, dx/dt = 30 and dy/dt = -1.
the tangent line has a slope equal to dy/dt at t = 2, which is -1. the point (x, y) on the curve at t = 2 is (x(2), y(2)).
plugging in t = 2 into the parametric equations, we get:
x(2) = (2)³ + 3(2)² + 6(2) + 1
= 8 + 12 + 12 + 1
= 33
y(2) = 2(2) - 5
= 4 - 5
= -1
so, the point (x, y) on the curve at t = 2 is (33, -1).
using the point-slope form of a line, we can write the equation of the tangent line:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the point (33, -1).
plugging in the values, we have:
y - (-1) = -1(x - 33)
simplifying, we get:
y + 1 = -x + 33
rearranging, we obtain the equation of the tangent line:
x + y = 32 (b) to find any values of t where the tangent line is horizontal, we need to find the values of t where dy/dt = 0.
from our previous calculations, we found that dy/dt = -1. to find when dy/dt = 0, we solve the equation:
-1 = 0
this equation has no solutions.
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Related Questions
O
3÷7=2/1/201
+7=21
Which equation calculates the number of foot pieces that can be cut from a piece of
wood that is 7 feet long?
7÷ 3 = 10
7÷3=21
CLEAR
CHECK
Answers
The The The The The The The The The The
With Alpha set to .05, would we reduce the probability of a Type
I Error by increasing our sample size? Why or why not? How does
increasing sample size affect the probability of Type II Error?
Answers
With Alpha set to .05, increasing the sample size would not directly reduce the probability of a Type I error. The probability of a Type I error is determined by the significance level (Alpha) and remains constant regardless of the sample size.
However, increasing the sample size can indirectly affect the probability of a Type I error by increasing the statistical power of the test. With a larger sample size, it becomes easier to detect a statistically significant difference between groups, reducing the likelihood of falsely rejecting the null hypothesis (Type I error).
Increasing the sample size generally decreases the probability of a Type II error, which is failing to reject a false null hypothesis. With a larger sample size, the test becomes more sensitive and has a higher likelihood of detecting a true effect if one exists, reducing the likelihood of a Type II error. However, it's important to note that other factors such as the effect size, variability, and statistical power also play a role in determining the probability of a Type II error.
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Drake says that 8 cups is equal to a quart because there are two cups in a pint and 4 pints in a quart. Is drake correct or not?
Answers
Answer:
drake is not correct
Step-by-step explanation:
Since we currently realize that there are 16 cups in a gallon, half-gallon milk would have 8 cups on it. So it would be a half of a gallon not a quart. Hope this helps! <3
Answer:
he is not
Step-by-step explanation:
8 cups equal 2 quarts
1 quart equal 4 cups so 2 quart equal 8
Sin x = - 1/2
where (-360 < x < 360)
Answers
Answer:
-30, 210 and 330 degrees
Step-by-step explanation:
Given the expression Sin x = - 1/2
x = arcsin(-1/2)
x = -30 degrees
Since sin is negative in the third and fourth quadrant
x = 180 + 30
x = 210 degrees
In the fourth quadrant
x = 360 - 30
x = 330
Hence the value of x within the interval -360 < x < 360 are -30, 210 and 330 degrees
What is the perimeter of triangle XYZ?
Answers
Answer:
126
Step-by-step explanation:
A catering company charges a $65 set-up and delivery fee
and $7.50 per plate with a minimum total of $140 dollars pls
Answers
Answer:
to get to 140$ you need to get 10 plates
Step-by-step explanation:
65$
7.5 x 10 =75
75+65=140.
I need help with this someone please explain it to me
Answers
The length of the Antenna will be;
⇒ h = 18 meters
What is Proportional?
Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
Tyler is 1.8 meters and his shadow is 6 meters.
And, Tyler is standing 54 meters from the antenna.
Now,
Since, Tyler is 1.8 meters and his shadow is 6 meters.
And, Tyler is standing 54 meters from the antenna.
Let the length of the Antenna = x
Hence, We get by definition of proportional, we get;
⇒ 1.8 / 6 = h / (54 + 6)
⇒ 0.3 = h / 60
⇒ h = 0.3 × 60
⇒ h = 18 meters
Thus, The length of the Antenna will be;
⇒ h = 18 meters
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7
A basketball player attempts 15 baskets in a game. He makes 9 of the attempted baskets. Which
ratio describes the number of baskets the player made to the number of baskets the player
attempted?
Answers
Answer:
3:5 Let me know if It helped
Step-by-step explanation:
We are looking for the ration of baskets made to baskets attempted.
Made:attempted
9:15
we can divide each number by 3
9/3:15/3
so the ratio is 3:5 the ratio of baskets made : attempted
Dominic runs a farm stand that sells peaches and grapes. Yesterday Dominic sold 34 pounds of peaches and 45 pounds of grapes for a total revenue of $192.25. Today he sold 47 pounds of peaches and 16 pounds of grapes for a total revenue of $208. Write a system of equations that could be used to determine the price of each pound of peaches and the price of each pound of grapes. Define the variables that you use to write the system.
Answers
Answer:
34x + 45y = 192.25
47x + 16y = 208
Step-by-step explanation:
Let x stand for peaches.
Let y stand for grapes.
Since we know that yesterday he sold 35 pounds of peaches ( x ) and 45 pounds of grapes ( y ) for $192.25, we can create an equation to represent this using two variables; peaches and grapes.
We can do the same thing with the amount of peaches and grapes he sold today. Once we make this equation, we will have two equations to make the system of equations to solve for x and y.
Mr. Deutsch ran 42 miles in 8 hours. What was his miles per hour?
Answers
Answer:
3 miles
Step-by-step explanation:
8 hours ----> 42 miles
1 hour
= 24 / 8
= 3 miles
So, His miles per hour is 3 miles.
Answer:Answer:
3 miles
Step-by-step explanation:
8 hours ----> 42 miles
1 hour
= 24 / 8
= 3 miles
Hope this helps
Two objects are moving along separate linear paths where each path is described by position, d, and time, t. The variable d is measured in meters, and the variable t is measured in seconds. The equation describing the graph of the position of the first object with respect to time is d = 2. 5t 2. 2. The graph of the position of the second object is a parallel line passing through (t = 0, d = 1). What is the equation of the second graph? A. D = 2. 5t 1 B. D = t 2. 5 C. D = -0. 4t 1 D. D = 2. 5t 3. 2.
Answers
The equation of second graph is \(d = 2.5 t + 1\)
We have given the linear equation is
\(d = 2.5 t +2.2,\)
If the graph of the position of the second object is parallel to
\(d = 2.5 t +2.2,\)
What is the form of linear equation?The equation of slope intercept form is
\(d=mt+b\)
compare the given equation with the slope intercept form
we get m = 2.5
t = 0, d = 1
1 = 2.5 · 0 + b
b = 1
Therefore,the equation of second graph is \(d = 2.5 t + 1\)
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Answer both parts it is not two questions it is only one
question
a)When it comes to Avocados, the Chipotle store has a weekly
demand of 200 avocados for their delicious guacamole, with a
standard deviation of 10. Cost of stockout (Cs) is $4.50 and Cost of excess (Ce)$ 1.25 (Avocados, like everything else, have gotten expensive!). Find the optimal weekly stocking level for avocados.
b)The Chipotle store is going strong and data shows that it goes through 45 bottles of the Tapatio Red sauce per week (some like their burritos hot!). Weekly usage has a standard deviation of 2.75. The manager will accept no more than an 8% risk of stockout during lead time, which is two weeks. Assume distribution of usage is normal. 1. Determine the value of Z (1 point) 2. Determine the ROP (1 point) 3. If acceptable risk were to go down to 5%, what would be the new ROP?
Answers
The optimal weekly stocking level for avocados can be found by using the Economic Order Quantity (EOQ) formula. Thus, the new ROP would be 97.
The formula is given as: EOQ = sqrt(2DS/H), where
D = Annual demand (52 weeks × 200 avocados) = 10,400S
Cost of stockout = $4.50H
Cost of excess = $1.25Using the given values,
EOQ = sqrt(2 × 10,400 × 4.5/1.25)
EOQ = 381.75 ≈ 382
Thus, the optimal weekly stocking level for avocados is 382.
b)To find the Reorder Point (ROP), we need to use the formula ROP = dL + zσL
where, d = Average demand during the lead time
L = Lead time
z = Z value corresponding to the required service level
σL = Standard deviation of demand during lead time
From the given data, Average demand during the lead time is: dL = 45 × 2 = 90
Since the manager will accept no more than an 8% risk of stockout during lead time, the Z value corresponding to the required service level is 1.28 (as per the standard normal distribution table).
The standard deviation of demand during lead time is: σL = √(2.75² × 2) = 3.89
Thus, 1. The value of Z is 1.28. 2. The Reorder Point (ROP) can be calculated as: ROP = dL + zσL
ROP = 90 + 1.28 × 3.89
ROP = 95.01 ≈ 953
If acceptable risk were to go down to 5%, the new Z value corresponding to the required service level would be 1.64 (as per the standard normal distribution table).
Using this value in the formula for ROP, the new ROP can be calculated as:
ROP = dL + zσL
ROP = 90 + 1.64 × 3.89
ROP = 96.37 ≈ 97
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Please help me in geomotry.
Answers
Answer:
distance between (3,7) and (-6,-4) is \(\sqrt{202}\)
Step-by-step explanation:
3rd point = (3, -4)
from (3,7) to (3, -4) is 11 units
from (-6,-4) to (3, -4) is 9 unites
hypothenuse
a^2 + b^2 = c^2
(11)^2 + (9)^2 = c^2
121 + 81 = c^2
c^2 = 202
c = \(\sqrt{202}\)
9)
Robert bought 3 pound of grapes and
divided them into 6 equal portions. What
is the weight of each portion?
Answers
Answer:
each portion would be 8 ounces
Answer:1/2 lb or 9 oz
Step-by-step explanation: 1 pound = 18 oz
3lbs*18oz/lb = 54oz
54oz/6 = 9 oz in each portion [9oz*1lb/18oz = 1/2 lb]
How can you apply it triangle congruence to real life situation?
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Congruent triangles are also frequently employed in architectural designs, carpet patterns, stepping stone patterns, and geometric art.
The following are the two most typical instances of this: Equilateral triangles are used to make truss bridges, which are built on both sides.
Congruence :
If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. A term used to describe an object and its mirror counterpart is congruence. If two things or shapes superimpose on one another, they are said to be congruent. They are identical in terms of size and shape. Line segments having the same length and angles with the same measure are congruent in the context of geometric figures.
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Blue Line Red Line
y-intercept
slope
Inequality
Answers
Answer:
Y-intercept
Step-by-step explanation:
Because they both meet
Mr. Walker gave his class the function f(x) = (x + 3)(x + 5). Four students made a claim about the function. Each student’s claim is below.
Jeremiah: The y-intercept is at (15, 0).
Lindsay: The x-intercepts are at (–3, 0) and (5, 0).
Stephen: The vertex is at (–4, –1).
Alexis: The midpoint between the x-intercepts is at (4, 0).
Answers
the only student that is correct is Stepheh. "The vertex is at (–4, –1)."
Which claims are true?
Here we have the quadratic equation:
f(x) = (x + 3)*(x + 5)
The first claim is: "The y-intercept is at (15, 0)."
This is clearly false, as the y-intercept is at x = 0, and in that point we have x = 15.
The second claim is:
"The x-intercepts are at (–3, 0) and (5, 0)"
This is false, in the factored equation we can see that the x-intercepts are x =-3 and x = -5.
Third claim:
"The vertex is at (-4, -1)"
The middle value between the zeros is:
(-3 + (-5))/2 = -4
Evaluating the function in x = -4 we get the y-value of the vertex:
f(-4) = (-4 + 3)*(-4 + 5) = -1*1 = -1
So the vertex is at (-4, -1), this claim is true.
The fourth claim is:
"The midpoint between the x-intercepts is at (4, 0)."
Which is false, we already saw that the midpoint between the x-intercepts is at x = -4
Then the only student that is correct is Stepheh. "The vertex is at (–4, –1)."
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A regular hexagonal shape is made using 6 match sticks. If 3 such hexagons are made how many matchsticks are used. What is the perimeter of the shape if each match box is 4cm
Answers
To create a single hexagon, 6 matchsticks are needed. When three hexagons are formed, the total number of matchsticks needed is 3 × 6 = 18.
The perimeter of the hexagon is calculated using the formula: P = 6s, where P is the perimeter and s is the length of each side of the hexagon. For a matchbox of 4 cm, the length of one matchstick is 4 cm.The perimeter of the hexagon is, therefore, 6 × 4 cm = 24 cm.
It is known that a regular hexagonal shape requires 6 matchsticks. Therefore, to create 3 hexagons, the total number of matchsticks used is 3 × 6 = 18.Therefore, the number of matchsticks used is 18. This is the main answer.To determine the perimeter of the hexagon, we'll use the formula P = 6s, where P is the perimeter and s is the length of each side of the hexagon. Since the length of one matchstick is 4 cm, we can say that s = 4 cm.Thus, P = 6 × 4 cm = 24 cm.
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The association placed a track marker on the ground every four hundred yards. Every 900 yards, the association put up a water station. What is the shortest distance a runner will have to travel to see a water station and a track marker in the same location?
Answers
Answer:
ima take my dagn points back smh dont answer on my questions if ur not gonna do them and say thanks ma'am like wt dude such a lame move god
Step-by-step explanation:
How much is 500 grams to cups?
Answers
500 grams would be approximately equal to 4 cups. Understanding conversions between different units of measurement is an important skill for anyone who loves to cook or bake.
One of the most common conversions you may need to make is between grams and cups.
When converting 500 grams to cups, it is important to keep in mind that the conversion factor will depend on the type of ingredient being measured. For example, a cup of sugar weighs much differently than a cup of flour. However, in general, there is an average conversion factor of approximately 1 cup of flour being equal to approximately 125 grams.
Therefore, it is always best to use a reliable conversion chart or online converter to ensure accuracy, especially if you are following a recipe that requires precise measurements. Additionally, it is also a good idea to use a kitchen scale when measuring ingredients in grams, as it is more accurate than measuring cups.
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Q А A of sc S 12 10 6 4 2. - 20-18-16-14-12-10 -8 6 4-2 -2 2 4 CO 8 10 12 14 16 18 20 R 26 S -8. -10 – 12 Quadrilateral PORS is transformed by translating it 6 units to the right and then rotating it 90° clockwise about the origin. Which coordinate pairs represent vertices of P'O'R'S' after these two transformations?
Answers
ANSWER
The pairs that represent vertices from these options are:
• (-7, -3)
• (7, -3)
,• (12, -10)
EXPLANATION
The rule for the translation 6 units right is:
\((x,y)\rightarrow(x+6,y)\)So after the translation the vertices are:
\(\begin{gathered} P(-3,7)\rightarrow(3,7) \\ Q(4,12)\rightarrow(10,12) \\ R(4,-2)\rightarrow(10,-2) \\ S(-3,-7)\rightarrow(3,-7) \end{gathered}\)Then, the rule for a 90º clockwise rotation about the origin is:
\((x,y)\rightarrow(y,-x)\)So, after the rotation, the vertices are:
\(\begin{gathered} (3,7)\rightarrow P^{\prime}(7,-3) \\ (10,12)\rightarrow Q^{\prime}(12,-10) \\ (10,-2)\rightarrow R^{\prime}(-2,-10) \\ (3,-7)\rightarrow S^{\prime}(-7,-3) \end{gathered}\)read the picture plsssssssssss
Answers
2. 2x - 5(3x^2)
3. 8x + 2x/3 +6
4. x + 3 - y - 6
Pls help me with this
Answers
Independent Practice
Which model is most appropriate for the set of points?
(–2, 5), (–1, –1), (0, –3), (1, –1), (2, 5)
A.
exponential
B.
linear
C.
quadratic
Answers
The selling price of an item is $600. It is marked down by 30%, but this sale price is still marked up from the cost of $350. Find the markup from cost to the sale price.
Answers
Answer:
I believe that it is $420
Step-by-step explanation:
First convert 30% to a decimal which is .30. Then you multiply 600 and .30 you get 180. Finally, you subtract 180 from 600 and that leaves you with 420.
Answer:
70
Step-by-step explanation:
hope this helps
The junior class at Summerfield High school sold a total of 375 ticket for their spring festival. The adult tickets sold for $7.50 each and the atudent tickets sold for $4.50 each. If the junior class collected $2,212.50 in ticket sales, how many student tickets did the class sell?
Answers
Answer:y=200 students
Step-by-step explanation:Let x = the number of adult tickets sold
Let y = the number of student tickets sold
x + y = 375 x = 375 - y
7.50x + 4.50y = 2212.50 Multiply both sides of this equation by 10 to remove the decimal points.
75x + 45y = 22,125
75(375-y) + 45y = 22,125
28,125 - 75y + 45y = 22,125
-30y = -6000
y = 200 student tickets
What is the value of n? enter your answer in the box.
Answers
The value of "n" is 6.
"n" is related to a circle with intersecting chords labeled 5, n+4, 7, and n+8 [1]. To find the value of "n", we can use the property that states that if two chords intersect inside a circle, the products of their segments are equal. Using this property, we can set up the following equation:
7(n+4) = 5(n+8)
Expanding the brackets, we get:
7n + 28 = 5n + 40
Simplifying, we get:
2n = 12
n=6
A circle is a two-dimensional geometric shape that is defined as a set of all points in a plane that are at a fixed distance (called the radius) from a given point (called the center). It is a closed shape, meaning that it has no beginning or end, and its boundary is a continuous curve.
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Out of the 20 students in Mrs. Green's class, 8 have a pet. What percent of the students in Mrs. Green's
class have a pet?
The percent of students in Mrs. Green's class that have a pet is _____
%.
Answers
You just have to divide 8/20 = .4 and then move the decimal twice to the right to get the percentage
Which ordered pair is a solution of the equation?
y = 3x+5
Answers
Answer:
Step-by-step explanation:
Y=1/3y+-5/3
this to two (2) Change Significant figure. 40.505734
Answers
Answer:
Step-by-step explanation:
To change the number 40.505734 to two significant figures, we need to round it to the nearest value with two significant figures.
Looking at the third digit after the decimal point (5), we see that it is greater than or equal to 5. Therefore, we need to round up the second digit after the decimal point (0) by adding 1 to it.
Thus, the number 40.505734 rounded to two significant figures is 41.