This loan has an interest 4. 5% compounded quarterly, account balance after 10 years:
The initial loan amount is $20,000, and it has an interest rate of 4.5% compounded quarterly. You would like to know the account balance after 10 years.
To calculate the account balance, we will use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the loan
P = the initial loan amount ($20,000)
r = the annual interest rate (0.045)
n = the number of times the interest is compounded per year (4, since it is compounded quarterly)
t = the number of years (10)
Plugging in the values:
A = 20000(1 + 0.045/4)^(4*10)
A = 20000(1.01125)^40
A ≈ 30,708.94
The account balance after 10 years will be approximately $30,708.94.
To know more about interest, refer here:
https://brainly.com/question/20406888#
#SPJ11
La maestra de Ciencia y Tecnología solicito a sus estudiantes que trajeran leche de vaca para elaborar yogur. Andrés trajo 2² litros, Bruno trajo 13/4 litros, Carlos trajo 1, 16 litros y Daniel 1,3 litros. ¿Qué estudiante trajo más leche? ¿Y quién menos?
Andres brought the most milk, and Carlos brought the least milk.
How to find the amount of milk bought ?To find out the student who bought the most milk, you need to convert the liters decimals so that they can be compared evenly.
Andrés brought 2²
= 2 x 2
= 4 liters of milk.
Bruno brought 13/4:
= 13 / 4
= 3.25 liters of milk.
Carlos bought 1. 16 liters and Daniel bough 1. 3 liters.
This shows that Andres bought the most milk and Carlos bought the least amount.
Find out more on liters at https://brainly.com/question/17433466
#SPJ1
A square has sides of length s. A rectangle is 6 inches shorter than the square and 1 inch longer. Which of the following expressions represents the perimeter of the rectangle?
The perimeter of the rectangle is represented by the expression 4s - 10.
How to calculate perimeter of a rectangle?
To calculate the perimeter of a rectangle, you need to add up the lengths of all four sides.
In the problem given, we know that the rectangle is 6 inches shorter than the square and 1 inch longer.
Let's call the length of the rectangle l and the width w.
We know that the length of the square is equal to its width (since it's a square), so the length of the rectangle must be l = s - 6, and the width must be w = s + 1.
To find the perimeter, we add up all four sides: P = 2l + 2w = 2(s-6) + 2(s+1) = 4s - 10.
Therefore, the expression that represents the perimeter of the rectangle is 4s - 10.
Learn more about perimeter
brainly.com/question/6465134
#SPJ11
solve the triangle.
angle C = 16°
angle c = 32
angle b = 92
Find angle B, a, and A
Answer:
Step-by-step explanation:
To solve the triangle, we can use the law of sines and the fact that the sum of the angles in a triangle is 180 degrees.
First, we can find angle A by using the fact that the sum of the angles in a triangle is 180 degrees:
A = 180 - B - C
A = 180 - 92 - 16
A = 72 degrees
Next, we can use the law of sines to find side a:
a/sin(A) = c/sin(C)
a/sin(72) = 32/sin(16)
a = (32*sin(72))/sin(16)
a ≈ 89.4
Finally, we can use the fact that the sum of the angles in a triangle is 180 degrees to find angle B:
B = 180 - A - C
B = 180 - 72 - 16
B = 92 degrees
Therefore, the triangle has angle B = 92 degrees, angle A = 72 degrees, and side a ≈ 89.4.
A cat darts around a room chasing a ball. The cat first travels along the vector −1, 2 and then chases the ball along the vector 2, 6 − . The cat darts after the ball 1.5 times along the vector 4, 3 . This is where the cat catches the ball and chews on it. What vector describes the cat’s final position? Show all your work.
To find the cat's final position, we need to add up all the vectors representing the cat's movements.
The cat first travels along the vector −1, 2.
Next, the cat chases the ball along the vector 2, 6 − , which we can write as (2, 6) − (0, 1) = (2, 5).
Then, the cat darts after the ball 1.5 times along the vector 4, 3, which we can write as 1.5(4, 3) = (6, 4.5).
Finally, the cat's position after catching the ball is the sum of all these vectors:
(-1, 2) + (2, 5) + (6, 4.5) = (7, 11.5)
Therefore, the vector describing the cat's final position is (7, 11.5).
900,000=x+y+z
79,750=0. 08x+0. 09y+0. 01z
2x=z
Answer:
since 2x = z
replace z with 2x
900000 = x+y+z
900000 = x+y+2x
900000 = 3x+y - eqn (1)
79750= 0.08x +0.09y+0.01z
79750 = 0.08x +0.09y+0.01(2x)
79750 = 0.08x+0.09y+0.02x
79750 = 0.10x +0.09y - eqn(2)
from eqn(1)
900000 = 3x + y
y = 900000-3x - eqn(3)
substitute eqn(3) in eqn(2)
79750 = 0.1x +0.09y
79750=0.1x + 0.09(900000-3x)
79750=0.1x+ 81000 - 0.27x
collect like terms
79750 -81000 = 0.1x-0.27x
-1250 = -0.17x
to find x divide both sides by -0.17
x = -1250/-0.17 ~= 7353
since 2x = z
2*7353 = 14706
in eqn(3)
y = 900000-3x
y= 900000-3(7353)
y = 900000-22059
y = 877941
x =7353,y= 877941,z=14706
Anne's Road Paving Company mixed 16 1/4 tons of cement. They used 6 3/4 tons of the cement to pave a street downtown. How much cement did they have left?
Answer is 9.5 tons of cement
Anne's Road Paving Company initially mixed 16 1/4 tons of cement. They used 6 3/4 tons for paving a street downtown. To find the remaining amount of cement, subtract the used amount from the initial amount:
16 1/4 - 6 3/4 = 15 1/4 - 5 3/4 = 9 1/2 tons.
So, they had 9 1/2 tons of cement left.
To know more about subtraction calculations:
https://brainly.com/question/28669193
#SPJ11
Of the following options, what could be a possible first step in solving the
equation -7x- 5 = x + 3? (6 points)
Adding 7x to both sides of the equation
O Subtracting 5 from both sides of the equation
Adding x to both sides of the equation
O Combining like terms, -7x + x = - 6x
A company is designing a new cylindrical water
bottle. The volume of the bottle will be 170 cm³.
The height of the water bottle is 8.1 cm. What is
the radius of the water bottle? Use 3.14 for л.
Height: 8.1 cm
Answer: around 2.6 cm because I rounded to the tenth.
Step-by-step explanation:
r^2=170/8.1×3.14
r^2=170/25.434
r^2≈6.68
Next square root both sides so r^2 becomes r and 6.68 square rooted is about 2.6 cm is the radius.
R≈2.6cm
A farm grew 19.8 tons of wheat in 2013. the farm's wheat output increased by 9.8% from 2013-2014, and by 5.1 % from 2014 to 2015. which expression represents a strategy for estimating the farm's output for 2015?
The expression that represents a strategy for estimating the farm's output for 2015 is 1.153w, where w is the farm's wheat output in 2013.
Let w be the farm's wheat output in 2013. We know that the output increased by 9.8% from 2013 to 2014, so the output in 2014 can be estimated as:
w + 0.098w = 1.098w
This expression represents a strategy for estimating the farm's output for 2014.
Similarly, the output in 2015 can be estimated as:
(1.098w) + 0.051(1.098w) = (1 + 0.051)(1.098w)
Simplifying this expression, we get:
1.153w
Therefore, the expression that represents a strategy for estimating the farm's wheat output for 2015 is:
1.153w
where w is the farm's wheat output in 2013 (i.e., 19.8 tons).
So we can estimate the farm's wheat output in 2015 as:
1.153(19.8) = 22.82 tons (rounded to two decimal places)
Note that this is only an estimate, based on the assumption that the percentage increases from 2013 to 2014 and from 2014 to 2015 will continue to hold in the future.
Know more about expression here:
https://brainly.com/question/1859113
#SPJ11
Robert takes out a loan for $7200 at a 4. 3% rate for 2 years. What is the loan future value?
(Round to the nearest cent)
The loan future value is $7726.73.
To find the loan future value, we need to calculate the total amount that Robert will owe at the end of the 2-year loan term, including both the principal (initial loan amount) and the interest.
To begin, we can use the formula for calculating compound interest:
[tex]A = P(1 + r/n)^{(nt)[/tex]
where A is the final amount, P is the principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, we know that the principal is $7200, the interest rate is 4.3% (or 0.043 as a decimal), the loan term is 2 years, and the interest is compounded once per year (n = 1).
Substituting these values into the formula, we get:
A = 7200(1 + 0.043/1)²
A = 7200(1.043)²
A = 7726.73
Therefore, the loan future value is $7726.73. This means that at the end of the 2-year loan term, Robert will owe a total of $7726.73, which includes the original $7200 loan amount and $526.73 in interest.
Know more about future value here:
https://brainly.com/question/14860893
#SPJ11
How do you solve the cube root function of x²/³ = 16?
The cube root of the given function is [tex]x=2\sqrt[3]{2}[/tex].
The given function is x³=16.
Here, the given function can be written as
[tex]x=\sqrt[3]{16}[/tex]
[tex]x=\sqrt[3]{2\times2\times2\times2}[/tex]
[tex]x=\sqrt[3]{2^3\times2}[/tex]
[tex]x=2\sqrt[3]{2}[/tex]
Therefore, the cube root of the given function is [tex]x=2\sqrt[3]{2}[/tex].
Learn more about the radical form here:
brainly.com/question/27272065.
#SPJ1
"Your question is incomplete, probably the complete question/missing part is:"
How do you solve the cube root function of x³=16.
A spring gun at ground level fires a golf ball at an angle of 45 degrees. The ball lands 10 m away.
a) What was the ball's initial speed?
b) For the same initial speed, find the two firing angles that make the range 6 m.
Recall that the Ideal Projectile Motion Equation is
r=(vo*cos(theta))ti+((vo*sin(theta)t-1/2*g*t^2)j.
Answer: a) vo=sqrt(10g)
b) theta=1/2*arcsin(3/5),
theta=pi-1/2*arcsin(3/5).
And is arcsin the same thing as sin^-1?
Yes, arcsin and sin^-1 both represent the inverse sine function.
process of finding inital speed:
a) To find the ball's initial speed, we can use the range formula for projectile motion:
R = (v₀² * sin(2θ)) / g
where R is the range (10 m),
v₀ is the initial speed,
θ is the launch angle (45 degrees), and
g is the acceleration due to gravity (9.81 m/s²).
We can solve for v₀:
10 = (v₀² * sin(90)) / 9.81
10 = (v₀²) / 9.81
v₀² = 10 * 9.81
v₀ = sqrt(10 * 9.81)
The ball's initial speed is sqrt(10 * 9.81) m/s.
b) For the same initial speed, we can find the two firing angles that make the range 6 m:
6 = (v₀² * sin(2θ)) / 9.81
Now, we can use the initial speed found in part (a):
6 = (10 * 9.81 * sin(2θ)) / 9.81
0.6 = sin(2θ)
To find the two angles, we can use the arcsin function:
θ₁ = 1/2 * arcsin(0.6)
θ₂ = π - 1/2 * arcsin(0.6)
The two firing angles are 1/2 * arcsin(0.6) and π - 1/2 * arcsin(0.6).Yes, arcsin is the same as sin^(-1);
To know more about sin functions:
https://brainly.com/question/24500215
#SPJ11
In milling operations, the spindle speed S (in revolutions per minute) is directly related to the cutting speed C (in feet per minute) and inversely related to the tool diameter D (in inches). A milling cut taken with a 3-inch high-speed drill and a cutting speed of 70 feet per minute has a spindle speed of 88.2 revolutions per minute. What is the spindle speed for a cut taken with a 4-inch high-speed drill and a cutting speed of 30 feet per minute?
The spindle speed for a cut taken with a 4-inch high-speed drill and a cutting speed of 30 feet per minute is approximately 35.1 revolutions per minute.
Speed is a measure of how fast an object is moving. It is usually measured in units of distance per unit time, such as miles per hour or meters per second. Speed is an important concept in physics, engineering, and everyday life
We can use the formula for spindle speed that relates spindle speed to cutting speed and tool diameter:
S = (C × 12) / (π × D)
where S is spindle speed, C is cutting speed in feet per minute, D is tool diameter in inches, and π is the mathematical constant pi.
We know that for a 3-inch high-speed drill with a cutting speed of 70 feet per minute, the spindle speed is 88.2 revolutions per minute. We can use this information to solve for the constant of proportionality k:
88.2 = (70 × 12) / (π × 3)
k = 88.2 × (π × 3) / (70 × 12)
k ≈ 0.0039
Now we can use the value of k to find the spindle speed for a 4-inch high-speed drill with a cutting speed of 30 feet per minute:
S = k × C × 12 / D
S = 0.0039 × 30 × 12 / 4
S = 35.1
Therefore, the spindle speed for a cut taken with a 4-inch high-speed drill and a cutting speed of 30 feet per minute is approximately 35.1 revolutions per minute.
To know more about speed visit:
brainly.com/question/28224010
#SPJ1
Ted spent 1 hour 21 minutes less than Jared reading last week. Jared spent 52 minutes less than Pete. Pete spent 3 hours reading. How long did Ted spend reading?
Ted spent 67 minutes reading.
Ted spent 1 hour and 21 minutes less Jared reading last week. Jared spent 52 minutes less Pete. Pete spent 3 hours reading. How long did Ted spend reading?
First, let's determine how long Jared spent reading:
Jared = Pete - 52 minutes
Jared = 3 hours * 60 minutes/hour - 52 minutes
Jared = 148 minutes
Now we can use the fact that Ted spent 1 hour 21 minutes less than Jared:
Ted = Jared - 1 hour 21 minutes
Ted = 148 minutes - 81 minutes
Ted = 67 minutes
Learn more about minutes
brainly.com/question/15600126
#SPJ11
I NEED SERIUOS HELPPP
The regression line equation, can be found to be y = 0.90x - 3.79
How to find the regression equation ?Find the slope using the slope formula :
m = ( 5 x 1944 - 98 x 69 ) / ( 5 x 2580 - 98² )
m = ( 9720 - 6762 ) / ( 12900 - 9604 )
m = 2958 / 3296
= 0.8975
Then find the y - intercept :
b = ( 69 - 0. 8975 x 98) / 5
b = ( 69 - 87. 945) / 5
b = - 18. 945 / 5
= - 3.789
The regression equation is:
y = 0.90x - 3.79
Find out more on regression equation at https://brainly.com/question/27997774
#SPJ1
x^2+8x+16 What is the perfect factored square trinomial
Answer:
The perfect factored square trinomial that is equivalent to the expression x^2 + 8x + 16 is:
(x + 4)^2
To see why this is the case, you can expand the expression (x + 4)^2 using the FOIL method:
(x + 4)^2 = (x + 4) * (x + 4)
= x^2 + 4x + 4x + 16
= x^2 + 8x + 16
So, x^2 + 8x + 16 can be factored as (x + 4)^2, which is a perfect square trinomial.
Greg, Harry and Ian share their electricity bill in the ratio 2:4:5.
how much dies each of them pay when their electricity bill are 1) 110$ 2) 165$ 3) 352$
pls answer quickly
The amount each of them pays when their electricity bill is $110, $165, and $352 respectively, in the ratio 2:4:5, are:
1) $20, $40, $50
2) $30, $60, $75
3) $64, $128, $160
1. How much do they pay for a $110 electricity bill?To find out how much each of them pays, we'll use the given ratio of 2:4:5 and divide the total bill among them accordingly.
Total bill: $110
The total ratio is 2+4+5=11.
Greg's share: (2/11) * $110 = $20
Harry's share: (4/11) * $110 = $40
Ian's share: (5/11) * $110 = $50
Therefore, Greg pays $20, Harry pays $40, and Ian pays $50.
2. How much do they pay for a $165 electricity bill?Total bill: $165
The total ratio is still 2+4+5=11.
Greg's share: (2/11) * $165 = $30
Harry's share: (4/11) * $165 = $60
Ian's share: (5/11) * $165 = $75
Therefore, Greg pays $30, Harry pays $60, and Ian pays $75.
3. How much do they pay for a $352 electricity bill?Total bill: $352
The total ratio remains the same: 2+4+5=11.
Greg's share: (2/11) * $352 = $64
Harry's share: (4/11) * $352 = $128
Ian's share: (5/11) * $352 = $160
Therefore, Greg pays $64, Harry pays $128, and Ian pays $160.
Learn more about ratio
brainly.com/question/13419413
#SPJ11
PLEASE HELP
Nathaniel is moving the dresser in his bedroom so it is against a different wall.
The length of the wall is feet and the dresser is feet long.
Which estimation is best for centering the dresser along the wall?
A.
The dresser should be placed about 6 feet from each end of the wall.
B.
The dresser should be placed about 8 feet from each end of the wall.
C.
The dresser should be placed about 10 feet from each end of the wall.
D.
The dresser should be placed about 12 feet from each end of the wall
To determine the best estimation for centering the dresser along the wall, we need to consider the length of the wall and the length of the dresser. Let's call the length of the wall "W" and the length of the dresser "D".
Since we don't know the actual values of W and D, we'll have to work with the given options.
Option A suggests placing the dresser about 6 feet from each end of the wall. This would leave a space of W - 12 feet in the middle of the wall, which would be the total space available for the dresser to be centered.
Option B suggests placing the dresser about 8 feet from each end of the wall. This would leave a space of W - 16 feet in the middle of the wall, which would be the total space available for the dresser to be centered.
Option C suggests placing the dresser about 10 feet from each end of the wall. This would leave a space of W - 20 feet in the middle of the wall, which would be the total space available for the dresser to be centered.
Option D suggests placing the dresser about 12 feet from each end of the wall. This would leave a space of W - 24 feet in the middle of the wall, which would be the total space available for the dresser to be centered.
To find the best estimation for centering the dresser along the wall, we need to determine which option provides the closest match between the available space in the middle of the wall and the length of the dresser.
Without knowing the actual values of W and D, it's difficult to say for certain which option is best. However, we can make an educated guess by considering the lengths of typical bedroom walls and dressers.
Based on this, option C (placing the dresser about 10 feet from each end of the wall) seems like a reasonable estimation for centering the dresser along the wall. This option provides a space of W - 20 feet in the middle of the wall, which is likely sufficient for most dressers.
Of course, the actual placement of the dresser will depend on other factors as well, such as the layout of the room and the location of other furniture. It's always a good idea to measure carefully and test different arrangements before settling on a final placement for any piece of furniture.
To know more about length refer here
https://brainly.com/question/30100801#
#SPJ11
Complete parts a through c for the given function. 2 f(x) = xº(x-2) on [ -2,2] O A. The local minimum/minima is/are at x = and there is no local maximum. (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) B. The local maximum/maxima is/are at x = and the local minimum/minima is/are at x = (Use a comma to separate answers as needed. Type integer or simplified fractions.) C. The local maximum/maxima is/are at x = 1 and there is no local minimum. (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) O D. There is no local maximum and there is no local minimum. c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist). Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The absolute maximum is at x= and there is no absolute minimum. (Use a comma to separate answers as needed. Type integers or simplified fractions.) B. The absolute maximum is at x = and the absolute minimum is at x= 11. (Use a comma to separate answers as needed. Type integer or decimals rounded to two decimal places as needed.) O C. The absolute minimum is at x= and there is no absolute maximum. (Use a comma to separate answers as needed. Type integers or simplified fractions.)
The absolute maximum occurs at x = -2 and the absolute minimum occurs at x = 0 and x = 2 and The absolute maximum is at x = -2 and the absolute minimum is at x = 0, 2.
a. The local minimum is at x=2 and there is no local maximum.
b. The local maximum is at x=1 and the local minimum is at x=-2 and x=2.
c. The absolute maximum is at x=0 and the absolute minimum is at x=2.
(Note: To find the absolute maximum and minimum, we need to evaluate the function at the critical points and endpoints of the interval. The critical points are x=0 and x=2, and the endpoints are x=-2 and x=2. The absolute maximum is the largest value among these, which is f(0)=0. The absolute minimum is the smallest value among these, which is f(2)=-4.)
Given the function f(x) = x²(x - 2) on the interval [-2, 2]:
A. To find the local minima and maxima, we need to take the first derivative and find its critical points.
f'(x) = 3x² - 4x
Solving for x, we get x = 0 and x = 4/3.
However, x = 4/3 is not within the interval [-2, 2], so the only critical point within the interval is x = 0.
There is a local minimum at x = 0, and no local maximum. Therefore, the answer is:
A. The local minimum is at x = 0 and there is no local maximum. (Type an integer or a simplified fraction.)
B. For the absolute maximum and minimum, we need to evaluate the function at the endpoints and the critical point within the interval.
f(-2) = (-2)²(-2 - 2) = 16
f(0) = (0)²(0 - 2) = 0
f(2) = (2)²(2 - 2) = 0
The absolute maximum occurs at x = -2 and the absolute minimum occurs at x = 0 and x = 2. The answer is:
B. The absolute maximum is at x = -2 and the absolute minimum is at x = 0, 2. (Use a comma to separate answers as needed. Type integers or simplified fractions.)
To know more about absolute maximum click here:
brainly.com/question/29030328
#SPJ11
find the angle between the vectors. (round your answer to two decimal places.) u = (4, 3), v = (5, −12), u, v = u · v
The angle between u and v is approximately 104.66 degrees. To find the angle between two vectors u and v, we can use the dot product formula:
cos(theta) = (u · v) / (||u|| ||v||)
where ||u|| and ||v|| are the magnitudes of u and v, respectively.
First, let's compute the dot product of u and v:
u · v = [tex](4)(5) + (3)(-12) = 20 - 36 = -16[/tex]
Next, we need to find the magnitudes of u and v:
[tex]||u||[/tex] = sqrt([tex]4^2[/tex] + [tex]3^2[/tex]) = 5
[tex]||v||[/tex] = sqrt([tex]5^2[/tex] + (-12[tex])^2[/tex]) = 13
Now we can substitute these values into the formula for cos(theta):
cos(theta) = [tex](-16) / (5 * 13) = -0.246[/tex]
To find the angle theta, we take the inverse cosine of cos(theta):
theta = [tex]cos^-1[/tex](-0.246) = 104.66 degrees
Therefore, the angle between u and v is approximately 104.66 degrees.
Learn more about vectors ,
https://brainly.com/question/29740341
#SPJ4
help mif with dis math probles pwees
For this above box plot prompt, the answer are given below.
What is the explanation for the response?Part A
From the box plots, we can see that the Red Team has the least variability and spread of times, followed by the Blue Team and then the Green Team.
The Red Team's box is the smallest, indicating that their times are more tightly clustered together.
Blue Team:
Q1: 75
Q2: 82
Q3: 87
IQR: 12
Upper fence: Q3 + 1.5IQR = 87 + 1.512 = 105
There are no outliers
Green Team:
Q1: 70
Q2: 75
Q3: 80
IQR: 10
Upper fence: Q3 + 1.5IQR = 80 + 1.510 = 95
There is one outlier at 90
Red Team:
Q1: 80
Q2: 83
Q3: 87
IQR: 7
Upper fence: Q3 + 1.5IQR = 87 + 1.57 = 98.5
There are no outliers
Learn more about box plots;
https://brainly.com/question/1523909
#SPJ1
Find the radius of the circle with equation x² + y² = 12²
Answer:
The equation of a circle with center (a,b) and radius r is given by:
(x - a)² + (y - b)² = r²
Comparing this to the equation x² + y² = 12², we can see that the center of the circle is (0,0) and the radius is 12. Therefore, the radius of the circle is 12 units.
A clown made purple and green balloon animals at a party. He kept track of the requests.
What is the probability that a randomly selected balloon animal is green and is shaped like a dog?
The probability that a randomly selected balloon animal is green and shaped like a dog is 0.231.
What is the probability?The probability is found using the data table given below:
Purple and giraffe = 3; Purple and dog = 3; Green and giraffe = 4; Green and dog = 3
Out of the total number of balloon animals made, the number of green dog balloon animals is 3.
The probability of randomly selecting a green dog balloon animal is found using the formula:
Probability = (number of green dog balloon animals) / (total number of balloon animals)Probability = 3 / (3 + 3 + 4 + 3) = 3/13
Probability = 0.231
Learn more about probability at: https://brainly.com/question/24756209
#SPJ1
Please help solve
Use Mean value theorem to prove √ 6a+3
1. Using methods other than the Mean Value Theorem will yield no marks
The Mean Value Theorem can be used to prove that the square root of 6a+31 lies between two values, where one value is equal to the function evaluated at a divided by the square root of 6, and the other value is equal to the function evaluated at a plus one divided by the square root of 6.
Let f(x) = √(6x + 31) and choose any value of a such that a > -31/6.
By the Mean Value Theorem, there exists some c in (a, a+1) such that:
f(a+1) - f(a) = f'(c)
where f'(c) is the derivative of f(x) evaluated at c.
We have:
f'(x) = 3/√(6x+31)
Thus, we can write:
f(a+1) - f(a) = (3/√(6c+31)) * (a+1 - a)
Simplifying, we get:
f(a+1) - f(a) = 3/√(6c+31)
Since a < c < a+1, we have:
a < c
√(6a+31) < √(6c+31)
√(6a+31) < (3/√(6c+31)) * √(6c+31)
√(6a+31) < f(a+1) - f(a)
Therefore, we can write:
f(a) < √(6a+31) < f(a+1)
f(a) = √(6a + 31)/√6
f(a+1) = √(6(a+1) + 31)/√6
Substituting these values, we get:
(√(6a + 31))/√6 < √(6a+31) < (√(6(a+1) + 31))/√6
Simplifying, we get:
√(6a + 31)/√6 < √(6a+31) < √(6a + 37)/√6
Hence, we have shown that the square root of 6a+31 lies between two values, where one value is equal to the function evaluated at a divided by the square root of 6, and the other value is equal to the function evaluated at a plus one divided by the square root of 6.
For more questions like Function click the link below:
https://brainly.com/question/16008229
#SPJ11
A rectangle garden measuring 13 m x 50 m it’s a have a gravel pathway of constant with built all around it. There is enough gravel to cover 80 meters. Answer and equality that represents all possible with (w) in meters of the pathway?
The width of the gravel pathway is 7 meters.
The length of the rectangular garden is 50m and the width is 13m. Let's assume the width of the gravel pathway to be w meters.
The length of the rectangular garden including the two widths of the pathway would be 50+2w meters, and the width including the two widths of the pathway would be 13+2w meters.
The area of the rectangular garden including the pathway is the product of the length and the width:
(50+2w)(13+2w)
We can now set up an equation using the area of the garden and the amount of gravel available:
(50+2w)(13+2w) - 50*13 = 80
Simplifying this equation gives:
4w^2 + 126w - 3196 = 0
This is a quadratic equation that we can solve for w using the quadratic formula:
w = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 4, b = 126, and c = -3196.
Plugging in these values and solving for w gives:
w = 7 or w = -22.75
Since the width of the pathway cannot be negative, the only valid solution is w = 7.
Therefore, the width of the gravel pathway is 7 meters.
Learn more about width at https://brainly.com/question/26813183
#SPJ11
how many favorable outcomes will there be for spinning the same color twice?
The number of favorable outcomes for spinning the same color twice will depend on the number of colors on the spinner.
If there are only two colors on the spinner, such as red and blue, then there will be only one favorable outcome, which is spinning either red or blue twice.
If there are more than two colors on the spinner, the number of favorable outcomes will depend on the number of times each color appears on the spinner.
For example, if there are four colors on the spinner, and each color appears equally, then there will be four favorable outcomes: spinning red twice, spinning blue twice, spinning green twice, or spinning yellow twice.
In general, if there are n colors on the spinner and each color appears with equal probability, then the number of favorable outcomes for spinning the same color twice will be n.
To know more about probability refer here
https://brainly.com/question/34187875#
#SPJ11
Aimie is looking for a golf ball that he hit into the air towards a fence surrounding the golf course. The fence has a height of 2 yards and is located at a distance of 120 yards from where Jaimie hit the ball. Jaimie wants to determine if his golf ball landed inside or outside of the fence.
The golf ball's height, h, in yards with respect to time, t, in seconds, can be modeled by the quadratic function h=−0. 6t2+3t. Jaimie's golf ball reached its maximum height at the fence.
What is the maximum height, in yards, the golf ball reached before landing back on the ground?
_____yards
The maximum height the golf ball reached before landing back on the ground is 3.75 yards.
To find the maximum height the golf ball reached before landing back on the ground, we need to find the vertex of the quadratic function[tex]h(t) = -0.6t^2 + 3t.[/tex] The vertex of a quadratic function in the form of[tex]f(x) = ax^2 + bx + c[/tex] is given by the formula x = -b/(2a).
In this case, a = -0.6 and b = 3. Plugging these values into the formula:
t = -3 / (2 * -0.6) = 3 / 1.2 = 2.5
Now that we have the time at which the ball reaches its maximum height, we can plug this value back into the height function to find the maximum height:
[tex]h(2.5) = -0.6(2.5)^2 + 3(2.5) = -0.6(6.25) + 7.5 = -3.75 + 7.5 = 3.75[/tex]
So, the maximum height the golf ball reached before landing back on the ground is 3.75 yards.
To know more about golf ball refer here:
https://brainly.com/question/263622
#SPJ11
The diagonal of rectangle ABCD is 42. 3 cm, and it forms an angle of 53° with the shorter side AD of the rectangle
Using trignometric functions the shorter side AD has length a ≈ 25.75 cm and the longer side AB has length b ≈ 34.25 cm.
In the given scenario, we have a rectangle with sides AD and AB. The length of AD is represented as 'a' and is approximately 25.75 cm, while the length of AB is denoted as 'b' and is approximately 34.25 cm. The diagonal AC of the rectangle has a length of 42.3 cm and forms an angle of 53° with AD.
To find the lengths of sides a and b, we can utilize trigonometric functions, specifically cosine and sine. Since we have the length of the diagonal AC and the angle it forms with AD, we can set up the following equations:
cos(53°) = a/42.3
sin(53°) = b/42.3
By rearranging the equations, we can solve for a and b:
a = 42.3 * cos(53°) ≈ 25.75 cm
b = 42.3 * sin(53°) ≈ 34.25 cm
By substituting the given values into the equations, we can determine that the length of AD (a) is approximately 25.75 cm, and the length of AB (b) is approximately 34.25 cm.
These calculations allow us to find the side lengths of the rectangle based on the given information about the diagonal length and angle. Understanding trigonometric relationships enables us to solve geometric problems involving angles, sides, and diagonals in various shapes and configurations.
To know more about trignometric functions refer to
https://brainly.com/question/25618616
#SPJ11
Val needs to find the area enclosed by the figure. The figure is made by attaching semicircles to each side of a 56m-by-56m square. Val says the area is 1,787.52m. Find the area enclosed by the figure. Use 3.14 for . What error might have made?
Val's calculation of 1,787.52 m² is incorrect.
What is area of semicircle?
The area of a semicircle is half the area of the corresponding circle. If r is the radius of the semicircle, then the area of the semicircle is:
A(semicircle) = (1/2) π r²
To find the area enclosed by the figure, we need to add the areas of the square and the four semicircles.
The area of the square is:
[tex]A_{square}[/tex] = (56 m)² = 3,136 m²
The area of one semicircle is half the area of the corresponding circle, and the radius of the circle is equal to the side length of the square. Therefore, the area of one semicircle is:
[tex]A_{semicircle}[/tex] = (1/2) π (56/2)²= 1,554.56 m²
The total area enclosed by the figure is:
[tex]A_{total}[/tex] = [tex]A_{square}[/tex]+ 4 [tex]A_{semicircle}[/tex] = 3,136 + 4(1,554.56) = 9,901.44 m²
Therefore, Val's calculation of 1,787.52 m² is incorrect.
To know more about areas visit:
brainly.com/question/16952186
#SPJ9
Question:
Val needs to find the area enclosed by the figure. The figure is made by attaching semicircles to each side of a 56m-by-56m square. Val says the area is 1,787.52m. Find the area enclosed by the figure. Use 3.14 for π. What error might have Val made?
Which postulate or theorem can be used to prove that ΔABC ≅ ΔDCB
The postulate or theorem that can be used to prove that ΔABC ≅ ΔDCB is the "Side-Side-Side (SSS) theorem".
Hence, the correct option is A.
Since in both triangles ΔABC and ΔDCB, we have
BC = BC (Common line)AB = CD (given)AC = BD (given)Therefore, by SSS theorem, we can conclude that ΔABC ≅ ΔDCB.
Hence, the correct option is A.
To know more about theorem here
https://brainly.com/question/12725344
#SPJ1