Give your answer accurate to 3 decimal places.
The area of an equilateral triangle is decreasing at a rate of 5cm²/min. Find the rate (in centimeters per minute) at which the length of a side is decreasing when the are of the triangle is 300cm²
Answers
The rate at which the length of a side is decreasing when the area of the triangle is 300 cm² is approximately -0.083 cm/min, or -1/12 cm/min, accurate to 3 decimal places.
Let's use the formula for the area of an equilateral triangle to relate the rate of change of the area to the rate of change of the side length.
The area of an equilateral triangle with side length s is given by:
A = (√3/4) s²
Taking the derivative of both sides with respect to time t, we get:
dA/dt = (√3/2) s ds/dt
where ds/dt is the rate at which the side length is changing.
We know that dA/dt = -5 cm²/min (since the area is decreasing at a rate of 5 cm²/min), and we want to find ds/dt when A = 300 cm².
So we have:
-5 = (√3/2) s ds/dt
Solving for ds/dt, we get:
ds/dt = -10/(√3s)
When A = 300 cm², the side length can be found by rearranging the formula for the area:
s² = (4/√3) A
s² = (4/√3) (300)
s = 20√3 cm
Substituting this value into the expression for ds/dt, we get:
ds/dt = -10/(√3(20√3))
ds/dt = -1/12 cm/min
Therefore, the rate at which the length of a side is decreasing when the area of the triangle is 300 cm² is approximately -0.083 cm/min, or -1/12 cm/min, accurate to 3 decimal places.
To know more about triangle visit:
https://brainly.com/question/31240589
#SPJ11
Related Questions
There are 9 red, 8 blue, 5 green, and 15 white marbles in a jar. If I cannot see the marbles, what is the fewest number of marbles I must pick, without replacement, in order to guarantee that 3 of the marbles are of different colors?
Answers
Answer:
25
Step-by-step explanation:
2x+y=5
x - y = 4
Please answer this wuestion
Answers
Answer:
x=9
y=5
Step-by-step explanation:
Y = -1
This is because
2 * 3 + - 1 = 2 * 3 - 1 = 5
3 - - 1 = 3 + 1 = 4
The multiplication property of equality could be used to solve which of the following equations?
OX+2)x-3) = 0
m+7=-12
OD-2) = 18
03+y=7
Answers
Answer:
I pretty sure its C. OD-2) = 18
Step-by-step explanation:
Woof Chow Dog Food Company believes that it has a market share of 25 percent. It surveys n = 100 dog owners and ask whether or not Woof Chow is their regular brand of dog food, and 23 people say yes. Based upon this information, what is the critical value if the hypothesis is to be tested at the 0.05 level of significance?
Answers
The critical value for the 0.05 level of significance is k = 21.
To find the critical value, we can use the binomial distribution. The binomial distribution models the number of successes in n independent Bernoulli trials, each with probability p of success. In this case, the number of successes is the number of dog owners who say Woof Chow is their regular brand, and the number of trials is n = 100. The null hypothesis is that the true market share of Woof Chow is 25%, and the alternative hypothesis is that it is not 25%.
We can use the binomial cumulative distribution function (CDF) to find the critical value. The CDF gives the probability of getting k or fewer successes in n trials, given a probability of success p. The critical value is the smallest value of k such that the CDF at k is greater than or equal to 1 - alpha, where alpha is the level of significance. In this case, alpha = 0.05.
So, we want to find the smallest k such that:
P(X <= k) >= 1 - 0.05
where X is a random variable representing the number of dog owners who say Woof Chow is their regular brand. We can use a binomial calculator or a software package to calculate the binomial CDF, or we can use a table of critical values for the binomial distribution.
The critical value for the 0.05 level of significance is k = 21. This means that if the true market share of Woof Chow is 25%, then the probability of getting 23 or more dog owners who say Woof Chow is their regular brand is less than 0.05. Since the observed number of dog owners who say Woof Chow is their regular brand is 23, which is greater than 21, we can reject the null hypothesis that the true market share is 25%.
This means that based on the survey results, we cannot conclude that Woof Chow has a market share of 25%. The survey results suggest that Woof Chow may have a market share that is greater than 25%.
To learn more about critical value here:
https://brainly.com/question/30168469
#SPJ4
Compute ( x⋅x
x⋅w
)x using the vectors w= ⎣
⎡
3
−2
−5
⎦
⎤
and x= ⎣
⎡
6
−2
1
⎦
⎤
( x⋅x
x⋅w
)x= (Simplify your answer. Type an integer or simplified fraction for each matrix element.)
Answers
To compute (x⋅x)(x⋅w)x, we first need to calculate the dot product between vectors x and x, and between vectors x and w. Let's perform these calculations:
Dot product of x and x:
x⋅x = (6 * 6) + (-2 * -2) + (1 * 1)
= 36 + 4 + 1
= 41
Dot product of x and w:
x⋅w = (6 * 3) + (-2 * -2) + (1 * -5)
= 18 + 4 - 5
= 17
Now, we can substitute these values into the expression (x⋅x)(x⋅w)x:
(41 * 17) * x = (697) * x
Therefore, the result of (x⋅x)(x⋅w)x is 697 times the vector x.
What is the product of 12.54 and 82.11?
10.296594
102.96594
1,029.6594
10,296.594
Answers
Answer: 1029.6594 (Third one)
Step-by-step explanation:
12.54·82.11=1029.6594
Answer: 1,029.6594
Step-by-step explanation:
Product means the answer by way of multiplication.
The cost of 9 scarves is $87.75. What is the unit price?
Answers
Answer:
the answer is 9.75 for one
Step-by-step explanation:
divide 87.75/9
hope this helped
Which of the following options have the same value as %70, percent of 80?
Answers
Answer:
A, C and E.
Step-by-step explanation:
\(70 \% \times 80\)
\(70/100 \times 80\)
\(560/10\)
\(=56\)
\(0.7 \times 80\)
\(=56\)
\(7/10 \times 80\)
\(=56\)
Rewrite by completing the square 2x^2+7x+6=0
Answers
Answer:
\(2x^2+7x+6=0\\\\2(x^2+\frac72x+3)=0\\\\2[x^2+2\cdot x\cdot\frac74+(\frac74)^2-(\frac74)^2+3]=0\\\\2[x^2+2\cdot x\cdot\frac74+(\frac74)^2]-2(\frac74)^2+6=0 \\\\2(x+\frac74)^2-2\cdot\frac{49}{16}+6=0\\\\2(x+\frac74)^2-\frac{49}8+\frac{48}8=0\\\\2(x+\frac74)^2-\frac18=0\)
Answer:
(x+7/4)^2=1/16
Step-by-step explanation:
What angles must be congruent to QPS?
Answers
Answer:
QTS & TQS
Step-by-step explanation:
so as PQ=QT is given & QS is an common side, you can take the triangle PQS & TQS as isosceles triangles.
so then the angles PSQ=QST becoz the angles opposite to equal sides of an isosceles triangle are also equal in measures.
PQ=QT (given)
QS = common side
PSQ=QST (the angles opposite to equal sides of an isosceles triangle are also equal in measures.)
Therefore PQS is congruent to QTS (S.S.A)
Frereise !
Calculate the coordinates of the intersection point of the two lines (4.) and ((,)
1) (d): y = 4x-2 and (d): y = 8v+6 2)(a); y .-2x + 7 and (d): y = 3x - 3
3)(y *d
4) (4): y
and (d): y -
1
1
1
3
4
5
Exercise 2
1) The straight line (d): y = 5x + 2 cuts (x'x) and (y'y) at two points E and F respectively,
Calculate the coordinates of E and F
2) The straight line (d): y = cuts (x'x) and (y'y) at two points E and F respectively,
Calculate the coordinates of E and F
3
5
.
: y
2
Answers
Answer:
Mastong by skoger넞호오ㅗ노아ㅗ너너엉
can you apply the properties of rational exponents to an example?
Answers
We can simplify \((16x^4)^(-1/2) to 1/(4x^2)\) using the properties of rational exponents.
Certainly! Here's an example:
Simplify the expression: \((16x^4)^(-1/2)\)
We can apply the property of rational exponents which states that \((a^m)^n = a^(m*n)\). Using this property, we get:
\((16x^4)^(-1/2) = 16^(-1/2) * (x^4)^(-1/2)\)
Next, we can simplify \(16^(-1/2)\) using the rule that \(a^(-n) = 1/a^n\):
\(16^(-1/2) = 1/16^(1/2) = 1/4\)
Similarly, we can simplify \((x^4)^(-1/2)\) using the rule that \((a^m)^n = a^(m*n)\):
\((x^4)^(-1/2) = x^(4*(-1/2)) = x^(-2)\)
Substituting these simplifications back into the original expression, we get:
\((16x^4)^(-1/2) = 1/4 * x^(-2) = 1/(4x^2)\)
Therefore, the simplified expression is \(1/(4x^2).\)
Learn more on rational exponents here
brainly.com/question/20726608
#SPJ1
Please help thanks!
Answers
Answer:
10
Step-by-step explanation:
=13+ 3^3 ÷9 we can change it to:
=13+ 3^3/-9
3^3 can be changed to 27
13+ 27/9
=13+−3
=10
Hello! This is 6th grade math, i was wondering if y'all knew this. Correct answer gets a brainliest
Answers
Answer:
6
Step-by-step explanation:
2(6-4)+3=7
2(2)+3=7
4+3=7
7=7
Answer:
The answer is 6.
Step-by-step explanation:
2(x-4)+3=7.
1. Multiply the 2 by each number/variable inside of the parenthesis.
2x-8+3=7
2. Combine like terms
2x-5=7
3. Take the 5 from the left side and add it to 7 on the right side
2x-5=7
+5 +5
2x = 12
4. Divide both sides by 2
2x/2= X and 12/2 = 6
5. The 2 cancels out, leaving you with x, and 12 divided by 2 is 6.
X = 6
Let the long-run profit function for a representative firm is given by π i
=p 2
−2p−399, where p is the price of computer. The inverse market demand for computer is given by p=39−0.009q, where q is unit of computers. Suppose technology for producing computers is identical for all firms and all firms face identical input prices. (a) Find the firm's output supply function. (b) Find the market-equilibrium price and the equilibrium number of firms. (c) Find the number of computers sold by each firm in the long run.
Answers
(a) The firm's output supply function is given by q = (p + 199) / 2.
(b) The market-equilibrium price is $32.56, and the equilibrium number of firms is 10.
(c) Each firm sells 70 computers in the long run.
To find the firm's output supply function, we need to maximize the firm's profit function, which is given by π = p^2 - 2p - 399. In the long run, firms will produce where marginal cost equals marginal revenue. Marginal revenue can be obtained by differentiating the inverse market demand function with respect to q, and marginal cost is equal to the derivative of the profit function with respect to q. Equating the two, we get:(39 - 0.009q) = (2q - 2) / q
Simplifying the equation, we find:
q = (p + 199) / 2
This represents the firm's output supply function.
To find the market-equilibrium price and the equilibrium number of firms, we need to find the intersection point of the market demand and supply. Substituting the output supply function into the inverse market demand function, we have:p = 39 - 0.009((p + 199) / 2)
Simplifying and solving for p, we get:
p ≈ $32.56
Substituting this price back into the output supply function, we find:
q = (32.56 + 199) / 2 ≈ 115.78
Given that each firm produces 70 computers in the long run, we can calculate the equilibrium number of firms:
Number of firms = q / 70 ≈ 10
Since each firm sells 70 computers in the long run, and there are 10 firms, the total number of computers sold by each firm is:70 * 10 = 700
Learn more about Equilibrium
brainly.com/question/30694482
#SPJ11
What is the probability of not picking a red face card when you draw a card at random from a pack of 52 cards?
Answers
Answer:
3/13
Step-by-step explanation:
Answer:
13/3
Step-by-step explanation: There are 6 red face cards in all red cards
Total number of possible outcomes=26
P (red face card) =
26/6=3/13
What is the angle GXI
Answers
Answer:
60
Step-by-step explanation:
They're made up of two 30 degree angles so it's 60 because 30 + 30 = 60.
Complete the statements about circle Z. A central angle, such as angle ____ of circle Z, is an
Answers
Answer:
A central angle, such as angle of circle Z, is an angle whose vertex is and whose sides are radii of the circle.
Answer:
do you have a pic of the circle
Step-by-step explanation:
which of these events could permanently shift an individual's demand curve for umbrellas to the right?
Answers
There are several events that could permanently shift an individual's demand curve for umbrellas to the right. A demand curve represents the relationship between the price of a good and the quantity of that good that consumers are willing to buy. When the demand curve shifts to the right, it means that consumers are willing to buy more of the good at every given price.
One event that could permanently shift an individual's demand curve for umbrellas to the right is an increase in income. When consumers have more disposable income, they are more likely to purchase umbrellas as they can afford to do so. This would result in an increase in demand for umbrellas, which would shift the demand curve to the right.
Another event that could shift an individual's demand curve for umbrellas to the right is a change in weather patterns. If there is an increase in rainfall or storms in a particular region, consumers are more likely to purchase umbrellas. This would result in an increase in demand for umbrellas, which would shift the demand curve to the right.
To know more about consumers visit:-
https://brainly.com/question/30132393
#SPJ11
Calculate the following unit rates.
The cookie recipe calls for 2/3 cup of brown
sugar for 1/2 batch of cookies.
Answers
Using proportions, it is found that the unit rate is of 1.33 cups of brown sugar for a batch of cookies.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
2/3 cups of brown sugar are used for half a batch of cookies. The unit rate is the amount used for one batch. Hence, the rule of three is given by:
2/3 cups - 1/2 batch
x cups - 1 batch.
Applying cross multiplication:
\(\frac{1}{2}x = \frac{2}{3}\)
\(x = \frac{4}{3}\)
The unit rate is of 1.33 cups of brown sugar for a batch of cookies.
More can be learned about proportions at https://brainly.com/question/24372153
Consider the accompanying matrix as the augmented matrix of a linear system. State in words the next two elementary row operations that should be performed in the process of solving the system. [ 1-4 4 0 - 2 0 3 -6 0 4 0 0 1 4 -4 0 0 3 7 8 ]
What should be the first elementary row operation performed? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. Interchange row 3 and row 2.
B. Scale row 1 by (Type an integer or a simplified fraction.) C. Replace row 2 by its sum with times row 4. (Type an integer or a simplified fraction.) D. Replace row 4 by its sum with -3 times row 3. (Type an integer or a simplified fraction.) What should be the second elementary row operation performed? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. Scale row 4 by (Type an integer or a simplified fraction.) B. Replace row 1 by its sum with times row 4. (Type an integer or a simplified fraction.)
C. Replace row 3 by its sum with times row 2. (Type an integer or a simplified fraction.) D. Interchange row 1 and row 2.
Answers
The first elementary row operation that should be performed is D. Replace row 4 with its sum with -3 times row 3. The second crude row operation that should be performed is C. Replace row 3 with its sum with 2 times row 2.
I understand you have provided an accompanying matrix representing a linear system, and you would like to know the first two elementary row operations to perform in solving the system. The matrix you provided appears to be incomplete or not properly formatted. However, I can still guide you on how to approach the problem.
When solving a linear system using an augmented matrix, you would generally perform the following steps:
1. Rearrange the rows, if necessary, so that the pivot (leading entry) in each row is 1 and positioned to the right of the pivot in the row above it.
2. Use row operations to create zeros below the pivots.
3. Use row operations to create zeros above the pivots.
4. Scale each row so that the pivot in each row is 1.
For the first row operation, you can either:
A. Interchange rows to position the pivots correctly, or
B. Scale a row by an integer or a simplified fraction so that the pivot is 1.
For the second row operation, you will most likely replace a row by its sum with a multiple of another row, so that there is a zero below the pivot. Without the correctly formatted matrix, it's difficult to provide a specific answer. However, I hope this general guidance helps you solve the given linear system.
Learn more about pivots here:- brainly.com/question/31261482
#SPJ11
What dose 10x+9-6x=-19 mean
Answers
Answer:
it algebra
Step-by-step explanation:
10x-6x=4x
Then the equation becomes
4x+9=-19
Then you subtract the 9 from -19
4x=-28
Now you have to separate the 4 from x
4x/4 and -28/4
So now you get
X=-7
A rectangle has a perimeter of 45 ft. The length and width are scaled by a factor of 1.5.
What is the perimeter of the resulting rectangle?
Enter your answer in the box.
Answers
Perimeter is the sum of the 4 sides. If the sides are scaled by a factor of 1.5, then the perimeter is also scaled by a factor of 1.5.
New perimeter: 45 ft x 1.5 = 67.5 feet.
Alice purchased paint in a bucket with a radius of 3.5 inches and a height of 8 inches The paint cost $0.05 per cubic inch. What was the total cost of the paint
Answers
The total cost of the paint is $15.40.
What is the first step is to find the volume of the bucket?The first step is to find the volume of the bucket.
The volume of a cylinder is given by the formula:
V = πr²h
where V is the volume, r is the radius, and h is the height.
Plugging in the values, we get:
V = π(3.5 inches)²(8 inches)
V = 308 cubic inches
The total cost of the paint can then be found by multiplying the volume of the bucket by the cost per cubic inch:
Total cost = 308 cubic inches × $0.05/cubic inch
Total cost = $15.40
Therefore, the total cost of the paint is $15.40.
Learn more about paint
brainly.com/question/15008921
#SPJ11
Triangle ABC has vertices at A(8,3), B(8,5), and C(4,3).
What is the area of Triangle ABC?
Answers
Answer: 4 units squared
Step-by-step explanation:
A = (l * w) / 2
5 - 3 = 2
8 - 4 = 4
4 * 2 = 8
8 / 2 = 4
Solve pls brainliest
Answers
Answer:
The correct answers are D and E
Step-by-step explanation:
D is correct because according to exponent rules, you add them when you multiply.
E is correct because the expression will equal 64 when calculated.
suppose we have five coins, and each coin has a different probability of showingheads when flipped. the probabilities of getting heads for each coin are 0.1, 0.2,0.3, 0.4 and 0.5. assume we toss all five coins at the same time. what is theexpected value of the number of heads?
Answers
The expected number of heads when all the 5 coins are tossed at the same time is 1.5, under the condition that the probabilities of getting heads for each coin are 0.1, 0.2,0.3, 0.4 and 0.5.
Then the expected value of the number of heads can be evaluated by multiplying each probability with its corresponding number of heads and suming them.
For the given case, we possess five coins with different probabilities of getting heads when flipped.
Therefore, getting heads for each coin in context of probability are 0.1, 0.2, 0.3, 0.4 and 0.5
Now, the expected value of the number of heads is
Expected value = \((0.1 * 1) + (0.2 * 1) + (0.3 * 1) + (0.4 * 1) + (0.5 * 1)\)
= 0.1 + 0.2 + 0.3 + 0.4 + 0.5
=1.5
The expected number of heads when all the 5 coins are tossed at the same time is 1.5, under the condition that the probabilities of getting heads for each coin are 0.1, 0.2,0.3, 0.4 and 0.5.
To learn more about probability
https://brainly.com/question/13604758
#SPJ4
It is given that A⃗ −B⃗ =(−51.4m)x^,C⃗ =(62.2m)x^, and A⃗ +B⃗ +C⃗ =(13.8m)x^.
Find the vector A⃗ . Find the vector B⃗ .
Answers
The vector A is (49.9m) x and vector B is (1.5m) x.
In the given question, A − B = (−51.4m)x, C =(62.2m)x, and A +B +C =(13.8m)x.
Find the vector A. Find the vector B.
We may disregard the vector x and treat the issue as an arithmetic one since all of the measurements are in the same direction (simultaneous equations).
A − B = −51.4.............................(1)
C = 62.2.............................(2)
A + B + C = 13.8.............................(3)
Now putting the value of C from Equation (2) in Equation (3)
A + B + C = 13.8
A + B + 62.2 = 13.8
Subtract 62.2 on both side, we get
A + B = 13.8 - 62.2
A + B = - 48.4.....................(4)
Adding the equation (1) and (4), we get
2A = - 99.8
Divide by 2 on both side, we get
A = - 49.9
Now subtracting the equation (1) and (4), we get
2B = -48.4 - ( -51.4)
2B = 3
Divide by 2 on both side, we get
B = 1.5
Since all of the calculations are done in terms of the unit vector x.
So the answer is vector B = (1.5m) x and vector A = (49.9m) x.
To learn more about vector link is here
brainly.com/question/29740341
#SPJ4
A Jésica le piden hacer dos esculturas triangulares idénticas. En la primera le solicitan que su perímetro sea de 80 centímetros mientras que en la segunda requiere que sus lados midan x+4 , 3x+2 , y , 2x-2 ¿ que dimensiones tendrá la esculturas triangulares ?
me podrían ayudar ☹️ porfavor
Answers
La esculturas triangulares tendrán las siguientes medidas 16.66 cm, 40 cm y 23.32 cm.
¿Qué e el perímetro?Es la suma total de los lados del triángulo, en este caso el perímetro total es de 80.
¿Cómo calcular las dimensiones del triángulo?Se pueden calcular usando el total y la información sobre cada lado:
x+4 + 3x+2 + 2x-2 = 806x + 4 = 806x = 80 - 46x = 76x = 76/ 6x = 12.66Finalmente calcule cada lado:
A. x+4 = 12.66 + 4 = 16.66B. 3x + 2 = 3 x 12.66 + 2 = 39.98 o 40C. 2x - 2 = 23.32Aprenda más sobre perímetro en: https://brainly.com/question/24514946
Show two different ways to complete the multiplication problem
314x5?
Answers
One way to complete the multiplication problem 314 x 5 is to use the standard algorithm of multiplying the digits from right to left. First, we multiply 5 by 4, which gives us 20. We write down the 0 and carry over the 2. Next, we multiply 5 by 1 and add the carry-over digit of 2, which gives us 7. We write down the 7 in the second place from the right. Finally, we multiply 5 by 3 and add the carry-over digit of 0, which gives us 15. We write down the 5 and carry over the 1. Therefore, the product of 314 and 5 is 1570.
Method 2:Another way to complete the multiplication problem 314 x 5 is to use the distributive property. We can break down 314 into 300 + 10 + 4 and multiply each term by 5. First, we multiply 300 by 5, which gives us 1500. Next, we multiply 10 by 5, which gives us 50. Finally, we multiply 4 by 5, which gives us 20. Then, we add these three products together: 1500 + 50 + 20 = 1570. Therefore, the product of 314 and 5 is 1570.
To learn more about problem click here: brainly.com/question/30142700
#SPJ11