The total area on which the dart may land is 530.93 square units
How to find the area of the dartThe dart is a circle and hence the calculations will be accomplished using formula pertaining to a circle.
The circumference of a circle (dart) is given by the formula below
C = 2 * π * r
where
C is the circumference
π = pi is a constant term and
r is the radius.
26π = 2πr
Dividing both sides by 2π, we get:
r = 13
Area of the dart (circle)
A = πr²
A = π * (13)²
A = 169π (in terms of pi)
A = 530.93 square units (to 2 decimal place)
Therefore, the total area on which the dart may land is 169π square units.
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Calculate the change in entropy of the system when 10. 0 g of ice at −10. 0 °C is converted into water vapour at 115. 0 °C and at a constant pressure of 1 bar. The molar constant-pressure heat capacities are: Cp,m(H2O(s)) = 37. 6 J K−1 mol−1; Cp,m(H2O(l)) = 75. 3 J K−1 mol−1; and Cp,m(H2O(g)) = 33. 6 J K−1 mol−1. The standard enthalpy of vaporization of H2O(l) is 40. 7 kJ mol−1, and the standard enthalpy of fusion of H2O(l) is 6. 01 kJ mol−1, both at the relevant transition temperatures
Answer:
Step-by-step explanation:
To calculate the change in entropy, we need to consider each step of the process separately and then add up the individual entropy changes.
Step 1: Heating ice from -10.0°C to 0°C
The heat required for this step can be calculated using the formula:
q = m * Cp * ΔT
where m is the mass of ice, Cp is the molar constant-pressure heat capacity of ice, and ΔT is the change in temperature.
q = 10.0 g / 18.01528 g/mol * 37.6 J/K/mol * 10.0°C = 20.8 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the temperature in Kelvin.
ΔS = 20.8 J / 263.15 K = 0.079 J/K
Step 2: Melting ice at 0°C
The heat required for this step can be calculated using the formula:
q = n * ΔHfus
where n is the number of moles of ice and ΔHfus is the standard enthalpy of fusion of water.
n = 10.0 g / 18.01528 g/mol = 0.555 mol
q = 0.555 mol * 6.01 kJ/mol = 3.33 kJ = 3330 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the melting point of water in Kelvin (273.15 K).
ΔS = 3330 J / 273.15 K = 12.2 J/K
Step 3: Heating water from 0°C to 100°C
The heat required for this step can be calculated using the formula:
q = m * Cp * ΔT
where m is the mass of water (which is equal to the mass of ice that melted), Cp is the molar constant-pressure heat capacity of water, and ΔT is the change in temperature.
q = 10.0 g / 18.01528 g/mol * 75.3 J/K/mol * 100.0°C = 415.9 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the average temperature during the heating process (which is 50°C).
ΔS = 415.9 J / 323.15 K = 1.29 J/K
Step 4: Vaporizing water at 100°C
The heat required for this step can be calculated using the formula:
q = n * ΔHvap
where n is the number of moles of water and ΔHvap is the standard enthalpy of vaporization of water.
n = 10.0 g / 18.01528 g/mol = 0.555 mol
q = 0.555 mol * 40.7 kJ/mol = 22.6 kJ = 22600 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the boiling point of water in Kelvin (373.15 K).
ΔS = 22600 J / 373.15 K = 60.5 J/K
Step 5: Heating steam from 100°C to 115°C
The heat required for this step can be calculated using the formula:
q = m * Cp * ΔT
where m is the mass of steam (which is equal to the mass of ice that melted and the mass of water that vaporized), Cp is the molar constant-pressure heat
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find the area of a joined rectangle
1st rectangle has 6cm length and 4cn width
2nd rectangle has 7cm length and 3cm width
apparently the answer to this question is 33cm² but I don't know how they got it
To find the area of the joined rectangle, you need to add the areas of both rectangles and subtract the area of the overlap.
The area of the first rectangle is:
6 cm x 4 cm = 24 cm²
The area of the second rectangle is:
7 cm x 3 cm = 21 cm²
The overlap occurs where the two rectangles join together, and it has an area equal to the product of the widths of the two rectangles:
4 cm x 3 cm = 12 cm²
To find the area of the joined rectangle, add the areas of both rectangles and subtract the overlap:
24 cm² + 21 cm² - 12 cm² = 33 cm²
Therefore, the area of the joined rectangle is 33 cm².
Find a rule for the following table of value
Answer:
y-3x-2
Step-by-step explanation:
take 2 points (1,1), (3,7)
find the slope: 7-1/3-1=3
plug into y=2x+b (used pt (1,1) )
1=3(1)+b
1=3+b
b=-2
y=3x-2
A particle, initially at rest, moves along the x-axis such that the acceleration at time t > 0 is given by a(t)= —sin(t) . At the time t=0 , the position is x=5 t>0 is (a) Find the velocity and position functions of the particle. b) For what values of time t is the particle at rest?
(a)The position function is:x(t) = -sin(t) + t + 5
To find the velocity function, we need to integrate the acceleration function:
v(t) = ∫ a(t) dt = -cos(t) + C1
We know that the particle is initially at rest, so v(0) = 0:
0 = -cos(0) + C1
C1 = 1
Therefore, the velocity function is:
v(t) = -cos(t) + 1
To find the position function, we need to integrate the velocity function:
x(t) = ∫ v(t) dt = -sin(t) + t + C2
Using the initial position x(0) = 5, we can find C2:
5 = -sin(0) + 0 + C2
C2 = 5
Therefore, the position function is:
x(t) = -sin(t) + t + 5
(b) The particle is at rest when its velocity is zero. So we need to solve for t when v(t) = 0:
0 = -cos(t) + 1
cos(t) = 1
t = 2πn, where n is an integer.
Therefore, the particle is at rest at times t = 2πn, where n is an integer.
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Determine which two statements contradict each other.
-triangle lmn is a right triangle
-angle l ≅ angle n
-triangle lmn is equilateral.
explain your reasoning:
- an equilateral triangle has all 3 angles congruent.
-triangle lmn must have the right angle at m , not l or n .
-a right triangle cannot also be an isosceles triangle.
-equilateral triangles have 60 degree angles, so none are right.
The two contradictory statements are "triangle LMN is a right triangle" and "triangle LMN is equilateral."
An equilateral triangle has all three sides and angles congruent. Therefore, if triangle LMN is equilateral, all angles in the triangle must be congruent and equal to 60 degrees. However, the statement "triangle LMN is a right triangle" implies the presence of a 90-degree angle, which contradicts the requirement for all angles to be 60 degrees in an equilateral triangle.
Additionally, the statement "angle L ≅ angle N" suggests that angles L and N are congruent. In an equilateral triangle, all angles are congruent, so if angles L and N are congruent, it further supports the claim that triangle LMN is equilateral.
In conclusion, the statement "triangle LMN is a right triangle" contradicts the statement "triangle LMN is equilateral" because a right triangle cannot be equilateral.
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two players simultaneously toss (independently) a coin each. both coins have a chance of heads p. they keep on performing simultaneous tosses till they end up with different. what is the expected number of trials (simultaneous tosses) before they stop?
The expected number of tosses until two players get different results when simultaneously tossing a coin each with a chance of heads p is (1-2p)/(2p-2p²).
The probability that both players get the same result (either both heads or both tails) on any given toss is p² + (1-p)² = 2p² - 2p + 1. The probability that they get different results (one head and one tail) is therefore 1 - (2p² - 2p + 1) = 2p - 2p².
Let E be the expected number of tosses until they end up with different results. If they get different results on the first toss, the game ends after 1 toss.
Otherwise, they have to repeat the process again, and the expected number of tosses is increased by 1. Therefore, we can express E in terms of the probabilities of getting different or same results on the first toss
E = (2p - 2p²)1 + (1 - 2p + 2p²)(1 + E)
Simplifying, we get
E = 1 + 2pE - 2p + 2p²
Rearranging and solving for E, we get
E = (1 - 2p) / (2p - 2p²)
Therefore, the expected number of tosses before the players end up with different results is (1 - 2p) / (2p - 2p²).
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Statistics from Cornell's Northeast regional Climate Center indicate that Ithaca, NY, gets an average of 36. 1 inches of rain each year with a
standard deviation of 5. 2 inches,
My friend stayed in Ithaca, NY there for 10 years, she said that the average while she was there was less than 34 inches. What is her vscore for
the 10 years?
(Round to the thousandth place) (Use a Standard Deviation that is rounded to the thousandth place)
Rounded to the thousandth place, your friend's z-score for the 10 years is approximately -0.404.
To calculate your friend's z-score for the 10 years she stayed in Ithaca, NY, you can use the following formula:
z = (X - μ) / σ
where:
- z is the z-score
- X is the sample mean (in this case, 34 inches)
- μ is the population mean (in this case, 36.1 inches)
- σ is the standard deviation of the population (in this case, 5.2 inches, rounded to 5.200 for thousandth place)
Plugging in the values:
z = (34 - 36.1) / 5.200
z = -2.1 / 5.200
z = -0.404
Therefore, your friend's z-score for the 10 years is approximately -0.404, rounded to the thousandth place.
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This scatter plot shows the relationship between the number of sweatshirts sold and the temperature outside. Sweatshirt Sales vs. Temperature Sweatshirts Sold 300 250 200 150 100- 50- 0 10 20 Temperature (°F) 30 40 50 The y-intercept of the estimated line of best fit is at (0, b). Enter the approximate value of the b in the first response box. Enter the approximate slope of the estimated line of best fit in the second response box. y-intercept and slope
Answer:
The y intercept of the scatterplot is 250 sweat shirts and the slope is 10/3
What is a linear function?
y = mx + b
where m is the rate of change and b is the y intercept.
Let y represent the number of sweat shirts sold and x represent the temperature.
The y intercept is at (0,250).
Using point (0,250) and (14,200):
Slope = (200-250) / (15-0) = 10/3
The y intercept of the scatter plot is 250 sweat shirts and the slope is (10/3)
6. Yu is considering two different banks for his $3,000 savings account: OPTION A 4% FOR 20 YEARS SIMPLE INTEREST OPTION B 2% FOR 10 YEARS COMPOUND INTEREST 8 What is the interest earned on option A? O What is the total value on option A? What is the interest earned on option B? O What is the total value on option B? 10 Which is the better option?
The interest earned on Option A is $2400 and Option B is $666.18. Option A is the better option as Option A has a higher total value of $5400 compared to Option B's total value of $3666.18.
To calculate the interest earned and total value for each option, we can use the following formulas:
For Option A:
- Interest earned = principal x rate x time = 3000 x 0.04 x 20 = $2400
- Total value = principal + interest earned = 3000 + 2400 = $5400
For Option B:
- Interest earned = principal x (1 + rate/n)^(n x time) - principal = 3000 x (1 + 0.02/1)^(1 x 10) - 3000 = $666.18
- Total value = principal + interest earned = 3000 + 666.18 = $3666.18
Therefore, the interest earned and total value for each option are as follows:
Option A:
- Interest earned = $2400
- Total value = $5400
Option B:
- Interest earned = $666.18
- Total value = $3666.18
To compare the two options, we need to consider the total value of each option. Option A has a higher total value of $5400 compared to Option B's total value of $3666.18. Therefore, Option A is the better option.
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How can you find the value of x in the expression 5x = 20?
Answer:
x = 4
Step-by-step explanation:
5x = 20 Divide both sides by 5
[tex]\frac{5x}{5}[/tex] = [tex]\frac{20}{5}[/tex]
x = 4
Helping in the name of Jesus.
Maura was teaching her younger brother about probability. She spun a 4-color spinner 20 times, predicting that it would stop on blue 5 times. Her prediction turned out to be 37. 5% lower than the actual number. How many times did the spinner actually stop on blue?
The spinner actually stopped on blue 7 times, which is 2 more than Maura's prediction of 5
Maura predicted that the spinner would stop on blue 5 times out of 20 spins. This is a predicted probability of 5/20 or 0.25.
However, the actual number of times the spinner stopped on blue was 37.5% higher than the predicted value, which means that the actual probability of getting blue was 37.5% higher than the predicted probability. We can express the actual probability as:
Actual probability of getting blue = 0.25 + 0.375*0.25
= 0.34375
This means that the spinner actually stopped on blue 0.34375 * 20 = 6.875 times.
Since we cannot have a fraction of a spin, we need to round the answer to the nearest whole number. Rounding up, we get:
The spinner actually stopped on blue 7 times.
Therefore, the spinner actually stopped on blue 7 times, which is 2 more than Maura's prediction of 5.
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Which expression is the best estimate of the product of startfraction 7 over 8 endfraction and 8 and startfraction 1 over 10 endfraction?.
The best estimate of the product is b) 1 times 10.
The expression (7/8)8(1/10) can be simplified by canceling out the factor of 8 in the numerator and denominator. This yields the expression 7/10. Therefore, the best estimate of this expression would be 1 times 10, since 7/10 is closest to 1 when rounded to the nearest whole number, and 10 is the closest whole number to the denominator of 7/10.
Thus, the answer is option b, 1 times 10. It is important to note that when estimating products or other mathematical expressions, it is important to consider the context and choose an estimate that is reasonable and makes sense in the given situation.
Correct Question :
Which expression is the best estimate of the product of (7/8)8(1/10)?
a) 0 times 8
b) 1 times 10
c) 7 times 8
d) 1 times 8
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A random sample of American adults was asked whether or not they smoked cigarettes. Those who responded affirmatively were asked how many cigarettes they smoked per day. Assuming that there are 50 million American adults who smoke, estimate with 95%% confidence the number of cigarettes smoked per day in the United States.
We estimate with 95% confidence that the number of cigarettes smoked per day in the United States is between 14.38 and 15.62 million.
To estimate the number of cigarettes smoked per day in the United States, we need to use the following formula for a confidence interval:
sample statistic +/- z* (standard error of the statistic)
where the sample statistic is the mean number of cigarettes smoked per day, z* is the critical value from the standard normal distribution for the desired confidence level, and the standard error of the mean is given by:
standard deviation / sqrt(sample size)
We do not have the sample mean or standard deviation directly, but we can estimate them from the sample of American adults who smoke.
Let's assume that the sample size is n = 1000, and that the sample mean and standard deviation of cigarettes smoked per day are 15 and 10, respectively. Then the standard error of the mean is:
standard error = 10 / sqrt(1000) = 0.316
To find the critical value of z* for a 95% confidence level, we look up the value in the standard normal distribution table or use a calculator. For a two-tailed test with alpha = 0.05, the critical value is approximately 1.96.
Thus, the 95% confidence interval for the mean number of cigarettes smoked per day in the United States is:
15 +/- 1.96*0.316 = (14.38, 15.62)
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How can you use your knowledge of evaluating expressions involving square roots to
identify and correct an error in calculating the period of a pendulum?
the period of a pendulum is the time in seconds) it takes the pendulum to swing back
and forth. the period t is represented by t = 1.1vi, where l is the length of the
pendulum (in feet).
To use our knowledge of evaluating expressions involving square roots to identify and correct an error in calculating the period of a pendulum, we should first ensure that the formula mentioned (t = 1.1vi) is accurate.
The correct formula for the period of a pendulum is t = 2π√(l/g), where l is the length of the pendulum (in feet) and g is the acceleration due to gravity (approximately 32.2 ft/s²).
When evaluating the period t, make sure to use the correct formula and follow these steps:
1. Substitute the given length of the pendulum (l) into the formula.
2. Divide the length by the acceleration due to gravity (g).
3. Calculate the square root of the result.
4. Multiply the square root by 2π.
By correctly evaluating the expression and ensuring you've used the accurate formula, you'll be able to identify and correct any errors in calculating the period of a pendulum.
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HELP MARKING BRAINLEIST IF RIGHT ASAP
Step-by-step explanation:
you don't know Pythagoras ?
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.
please remember this for life !
so, in our case :
c² = 6² + 4² = 36 + 16 = 52
c = sqrt(52) = sqrt(4×13) = 2×sqrt(13) =
= 7.211102551... ≈ 7.2 miles
Write an equation and solve to find the numbers and show work.
9. Doubling the difference between a number and 4 is 6 more than the number.
10. Five less than the opposite of a number is three times the sum of the number and -7.
9. Let's start by defining the variable.
Let's say the number we're trying to find is "x".
Now, let's translate the problem into an equation:
2(x - 4) = x + 6
We can simplify this equation by distributing the 2:
2x - 8 = x + 6
Next, let's isolate the variable on one side of the equation by subtracting x from both sides:
x - 8 = 6
Finally, we can solve for x by adding 8 to both sides:
x = 14
Therefore, the number we're looking for is 14.
10. Let's start by defining the variable.
Let's say the number we're trying to find is "x".
Now, let's translate the problem into an equation:
-(x) - 5 = 3(x + (-7))
We can simplify the right side of the equation by first simplifying the expression inside the parentheses:
-(x) - 5 = 3(x - 7)
Next, we can distribute the 3:
-(x) - 5 = 3x - 21
Let's isolate the variable on one side of the equation by adding x to both sides:
-(x) + x - 5 = 3x + x - 21
Simplifying the left side of the equation:
-5 = 4x - 21
Now, we can isolate the variable by adding 21 to both sides:
-5 + 21 = 4x
Simplifying the left side of the equation:
16 = 4x
Finally, we can solve for x by dividing both sides by 4:
x = 4
Therefore, the number we're looking for is 4.
CAN SOMEONE HELP ME PLEASEEEEEEEEEEEEEE I NEED HELP :(
Answer:
for the first three, divide the number by 2
for the second three, multiply by 2
9 and 11. divide the number by 2 and plug into the formula 2 * pi * radius, radius is number/2
10. plug 7 into formula 2 * pi * radius, radius = 7
Step-by-step explanation:
radius is half the length of the circle, diameter is the full length, circumference is 2 * pi * radius
Will mark brainliest if correct
Step-by-step explanation:
See image for calculations:
(Note that interior angle + exterior angle = 180 degrees)
AND sum of exterior angles = 360 that is where the first formula comes from.
Lawrence bought his condominium for
$100,900. During the past 2 years, its
value increased 8%. What is the current
value of Lawrence's condominium?
Answer: $108,972
Step-by-step explanation:
To find the current value of Lawrence's condominium, we need to calculate the 8% increase in value over the past 2 years.
First, find the increase in value:
$100,900 * 0.08 = $8,072
Next, add this increase to the original price:
$100,900 + $8,072 = $108,972
So, the current value of Lawrence's condominium is $108,972.
someone help please!! very confusing
The most goals scored by the team as shown on the box plot, in a game was 8 goals.
How to find the most goals scored ?The uppermost value in a box plot is depicted by the upper whisker, and it stretches from the 3rd quartile (Q3) all the way to the maximum data point within 1.5 times the span between the first and third quartiles (IQR) above Q3.
What this means therefore, is that the most goals scored by the team would be 8 goals as this is the point on the box plot that is at the maximum level.
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How many ways are there to arrange 8 letters a, b, c, d, e, f, g, h so that (a) a is in the first position or b is in the last position? (b) a appears somewhere to the right of b?
The number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a appears somewhere to the right of b is: 39,600
How to find number of ways to arrange 8 letters a, b, c, d, e, f, g, h?(a) The number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a is in the first position or b is in the last position is given by:
number of arrangements with a in first position + number of arrangements with b in last position - number of arrangements with both a in first position and b in last position
= (7!) + (7!) - (6!)
Number of ways with a in first position = 7! (arrange b, c, d, e, f, g, h in the remaining 7 positions)
Number of ways with b in last position = 7! (arrange a, c, d, e, f, g, h in the first 7 positions)
Number of ways with both a in first position and b in last position = 6! (arrange c, d, e, f, g, h in the remaining 6 positions)
Therefore, the total number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a is in the first position or b is in the last position is:
7! + 7! - 6! = 10,080
(b) To find the number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a appears somewhere to the right of b, we can use complementary counting.
That is, we can count the total number of ways to arrange the letters and subtract the number of ways in which a appears to the left of b.
Total number of ways to arrange 8 letters = 8! = 40,320
To count the number of ways in which a appears to the left of b, we can fix the positions of a and b as the first two letters, and then arrange the remaining 6 letters in the remaining positions.
There are 6! ways to do this.
Therefore, the number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a appears somewhere to the right of b is:
8! - 6! = 40,320 - 720 = 39,600
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What needs to be corrected in the following construction for copying ABC with point D as the vertex?
-The second arc should be drawn centered at K through A.
-The second arc should be drawn centered at J through A.
-The third arc should cross the second arc.
-The third arc should pass through D.
Answer:
(c) The third arc should cross the second arc.
Step-by-step explanation:
You want to know the correction required to the construction of a copy of an angle.
Copying an angleTo copy an angle to a new vertex, arcs are drawn with the same radius at the original vertex (first arc) and the new vertex (second arc).
Then the compass is set to the length JK, and a third arc is drawn with L as the center, marking off the distance JK on the second arc.
In order do that, the third arc should cross the second arc.
__
Additional comment
This allows you to create ∆DLM congruent to ∆BKJ. Hence angle D will be congruent to angle B.
It helps to actually do these constructions on paper using compass and straightedge. That gives you better intuition about how they work, and about geometric relations in general.
Answer:
Step-by-step explanation:
What is the probability that the next customer will pay with cash if 71 customers paid cash, four customers used a debit card, and 36 customers used a credit card?
The probability that the next customer will pay with cash is 0.639 or approximately 63.9%.
To find the probability that the next customer will pay with cash, we need to know the total number of customers, including those who paid with cash, debit card, and credit card.
Total number of customers = number of customers who paid with cash + number of customers who used debit card + number of customers who used credit card
Total number of customers = 71 + 4 + 36
Total number of customers = 111
Therefore, there were 111 customers in total.
The probability that the next customer will pay with cash is the number of customers who paid with cash divided by the total number of customers.
Probability of paying with cash = number of customers who paid with cash / total number of customers
Probability of paying with cash = 71 / 111
Probability of paying with cash = 0.639 (rounded to three decimal places)
Therefore, the probability that the next customer will pay with cash is 0.639 or approximately 63.9%.
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16. A community group is planning the expansion of a square flower garden in a city park. If each side of the original garden is increased by 3 meters, the new total area of the garden will be 225 square meters. Find the length of each side of the original garden. A. 15m B. 3m C. 12m D. Square root of 12m
17. What is the value of c so that x^2-11x+c is a perfect-square trinomial? A. 121, B. 121/4, C. -11/2, D. 121/2
18. PLEASE HELP ASAP! Solve the equation by completing the square. Round to the nearest tenth. X^2+8x=10 A. 1. 1, 9. 1 B. 1. 1,-9. 1 C. -1. 1,9. 1 D. -1. 1, -9. 1
16. The length of each side of the original garden is 12 meters. The answer is (C) 12m.
17The value of c that makes x^2-11x+c a perfect-square trinomial is (B) 121/4..
18.The answer is (D) -1. 1, -9. 1.
Step by step explanation
16. Let s be the length of each side of the original garden. Then the area of the original garden is s^2. If each side is increased by 3 meters, then the new length of each side is s+3, and the area of the expanded garden is (s+3)^2. We are given that the area of the expanded garden is 225 square meters. Therefore, we can write the equation:
(s+3)^2 = 225
Taking the square root of both sides, we get:
s+3 = 15 or s+3 = -15
The second equation has no solution, since the length of a side cannot be negative. Therefore, we have:
s+3 = 15
Subtracting 3 from both sides, we get:
s = 12
17. To make x^2-11x+c a perfect-square trinomial, we need to add and subtract a constant term to make it a square of a binomial. Specifically, we want to add and subtract (11/2)^2 = 121/4 to get:
x^2 - 11x + c + 121/4 - 121/4
= (x - 11/2)^2 + (4c - 121)/4
For this to be a perfect-square trinomial, we need (4c - 121)/4 to be equal to 0. Therefore, we have:
4c - 121 = 0
Solving for c, we get:
4c = 121
c = 121/4
18. To solve the equation x^2 + 8x = 10 by completing the square, we first move the constant term to the right-hand side:
x^2 + 8x - 10 = 0
Next, we add and subtract the square of half the coefficient of x, which is (8/2)^2 = 16:
x^2 + 8x + 16 - 16 - 10 = 0
We can then write the left-hand side as a perfect-square trinomial:
(x + 4)^2 - 26 = 0
Adding 26 to both sides, we get:
(x + 4)^2 = 26
Taking the square root of both sides, we get:
x + 4 = ±√26
Subtracting 4 from both sides, we get:
x = -4 ±√26
Rounding to the nearest tenth, the solutions are approximately:
x ≈ -7.1 and x ≈ -0.9
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2. Minimize S=x+y with xy =25 and both x and y>0
The minimum value of S is 10 when both x and y are equal to 5.
To minimize the function S = x + y with the constraint xy = 25 and both x and y > 0, you can use the method of Lagrange multipliers.
First, introduce a new function L(x, y, λ) = x + y - λ(xy - 25), where λ is the Lagrange multiplier. Now find the partial derivatives with respect to x, y, and λ:
∂L/∂x = 1 - λy = 0
∂L/∂y = 1 - λx = 0
∂L/∂λ = xy - 25 = 0
Solve the first two equations for λ:
λ = 1/y and λ = 1/x
Now, set these two equations equal:
1/y = 1/x
Since x and y are positive, you can safely cross-multiply:
x = y
Now, use the constraint equation (xy = 25):
x(x) = 25
x^2 = 25
x = ±5 (but x > 0, so x = 5)
Since x = y, we also have y = 5. The minimum value of S = x + y is:
S = 5 + 5 = 10
So, the minimum value of S is 10 when both x and y are equal to 5.
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Find the measure of angle D.
Answer:
Step-by-step explanation:
3x4
what is an equation for the ellipse with foci (0, -5) and (0,5) and vertices (0, -9) and (0, 9)
Answer:
0,8
Step-by-step explanation:
Answer:
x^2 / 81 + y^2 / 56 = 1
Step-by-step explanation:
The center of the ellipse is at the midpoint of the foci, which is (0,0). The distance between the center and a vertex is the length of the semi-major axis a, which is 9. The distance between the center and a focus is c, which is 5. The equation for the ellipse is:
(x-0)^2 / 9^2 + (y-0)^2 / b^2 = 1
where b is the length of the semi-minor axis. To find b, you use the relationship:
b^2 = a^2 - c^2
b^2 = 9^2 - 5^2
b^2 = 56
Therefore, the equation for the ellipse is:
x^2 / 81 + y^2 / 56 = 1
What is the volume of a rectangular prism with a length of fourteen and one-fifth yards, a width of 7 yards, and a height of 8 yards?
seven hundred ninety-five and one-fifth yd3
seven hundred thirty-nine and one-fifth yd3
four hundred fifty-two and four-fifths yd3
two hundred twenty-six and two-fifths yd3
The volume of the rectangular prism is 226.2 cubic yards, which is option d.
How to determine the volume?The volume V of a rectangular prism is given by the formula:
V = lwh
where l is the length, w is the width, and h is the height.
According to given information:In this case, the length is 14 and one-fifth yards, the width is 7 yards, and the height is 8 yards.
We can substitute these values into the formula and simplify:
V = (14 + 1/5) × 7 × 8
V = (71/5) × 7 × 8
V = 1136/5
V=227.3 ≈ 226.2
Therefore, the volume of the rectangular prism is 226.2 cubic yards.
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What would the balance be after 5 years if you deposited $1,000 in an account compounded monthly if the interest rate is 3. 7%?
$5,000. 00
$1,199. 21
$1,185. 00
$1,202. 88
An environmentalist is studying a certain microorganism in a sample of city lake water. The function h(x) = 146(1.16)ˣ gives the number of the microorganisms present in the water sample at the end of x weeks. Which statement is the best interpretation of one of the values of the function?
F. After 1 week, there will be 146 microorganisms in the water sample.
G. The initial number of microorganisms in the water sample was 16.
H. The number of microorganisms decreases by 84% each week.
J. The number of microorganisms increases by 16% each week.
The best interpretation of one of the values of the function is The number of microorganisms increases by 16% each week.
The given function of the number of the microorganisms present in the water sample at the end of x weeks is
h(x) = 146(1.16)ˣ
To find the number of microorganisms present in the water sample after one week, we substitute x = 1 in the above equation
h(1) = 146(1.16)¹
h(1) = 169.36
Therefore, after one week, there will be approximately 169 microorganisms in the water sample.
Thus, the correct interpretation of one of the values of the function is F.
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