The other diagonal of the rhombus is 4 cm.
The other diagonal of the rhombus can be found using the formula for the area of a rhombus, which is A = (d₁ × d₂)/2, where d₁ and d₂ are the lengths of the diagonals.
We're given that the area of the rhombus is 20 cm² and that one diagonal (d1) is 10 cm. Plugging these values into the formula, we get:
20 = (10 × d₂)/2
Simplifying, we get:
20 = 5 d₂
Dividing both sides by 5, we get:
d₂ = 4
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Jim wants to hang 4 pictures in a row on his wall. If he has 6 pictures to choose from , how many different arrangements are possible?
Answer:
180 possible arrangements
Step-by-step explanation:
To find the number of different arrangements possible when Jim hangs 4 pictures in a row from a set of 6 pictures, we can use the permutation formula:
nPr = n! / (n - r)!
where n is the total number of items in the set (in this case, 6), and r is the number of items being chosen (in this case, 4).
Substituting the values, we get:
6P4 = 6! / (6 - 4)!
= 6! / 2!
= (6 x 5 x 4 x 3 x 2 x 1) / (2 x 1)
= 360 / 2
= 180
Therefore, there are 180 different arrangements possible when Jim hangs 4 pictures in a row from a set of 6 pictures.
Answer:
Step-by-step explanation:
24
Pls help Which statement about the function y=x2−4x−12
is true?
Responses
The expression x2−4x−12
has factors (x−6)
and (x+2)
, and the function has zeros at x=−6
and x=2
.
The expression x 2 − − 4 x − − 12 has factors ( x − − 6 ) and ( x + 2 ) , and the function has zeros at x = − − 6 and x = 2 .
The expression x2−4x−12
has factors (x−6)
and (x+2)
, and the function has zeros at x=−2
and x=6
.
The expression x 2 − − 4 x − − 12 has factors ( x − − 6 ) and ( x + 2 ) , and the function has zeros at x = − − 2 and x = 6 .
The expression x2−4x−12
has factors (x−2)
and (x+6)
, and the function has zeros at x=−6
and x=2
.
The expression x 2 − − 4 x − − 12 has factors ( x − − 2 ) and ( x + 6 ) , and the function has zeros at x = − − 6 and x = 2 .
The expression x2−4x−12
has factors (x−2)
and (x+6)
, and the function has zeros at x=−2
and x=6
.
The expression x 2 − − 4 x − − 12 has factors ( x − − 2 ) and ( x + 6 ) , and the function has zeros at x = − − 2 and x = 6 .
Answer:
Step-by-step explanation:
The expression x2−4x−12 has factors (x-6) and (x+2), and the function has zeros at x=-2 and x=6.
Therefore, the correct statement is: "The expression x2−4x−12 has factors (x-6) and (x+2), and the function has zeros at x=-2 and x=6."
Find the value for that makes the statement true: sin = cos( + 40)
Answer:
[tex]\boxed{\theta=25}[/tex]
Step-by-step explanation:
I guess the correct equation is something like this:
[tex]\sin( \theta)= \cos(\theta + 40)[/tex]
I will use the following trigonometric identity:
[tex]\cos(x+y)=\cos(x) \cos(y)-\sin(x) \sin(y)[/tex]
rewriting the equation
[tex]\sin(\theta)=\cos(\theta) \cos(40)-\sin(\theta) \sin(40)\\\sin(\theta)+\sin(\theta) \sin(40)=\cos(\theta) \cos(40)[/tex]
common factor:
[tex]\sin(\theta)(1+\sin(40))=\cos(\theta) \cos(40) \\\\\frac{\sin(\theta)}{\cos(\theta)}= \frac{\cos(40)}{1+\sin(40))}[/tex]
And using also the following identity:
[tex]\frac{\sin(\theta)}{\cos(\theta)} =tan(\theta)[/tex]
rewriting the equation
[tex]\tan{\theta}= \frac{\cos(40)}{1+\sin(40))}\\\theta= \tan^{-1}(\frac{\cos(40)}{1+\sin(40))})\\\theta=25[/tex]
By this, we have solved the exercise.
[tex]\text{-B$\mathfrak{randon}$VN}[/tex]
Help. You spin the spinner twice. 23456789
Help please
What is the probability of landing on an odd number and then landing on a number less than 4?
The spinner sections are numbered 2,3,4,5,6,7. 8,and 9
Write your answer as a percentage
The probability of landing on an odd number and then landing on a number less than 4 when you spin the spinner twice is 12.5%.
First, let's determine the probability of landing on an odd number on the first spin. Out of the 8 sections on the spinner, 4 are odd numbers (3, 5, 7, 9) and 4 are even numbers (2, 4, 6, 8). Therefore, the probability of landing on an odd number is 4/8 or 1/2.
Now, let's determine the probability of landing on a number less than 4 on the second spin. Out of the 8 sections on the spinner, only 2 sections are less than 4 (2 and 3). Therefore, the probability of landing on a number less than 4 is 2/8 or 1/4.
To determine the probability of both events occurring (landing on an odd number and then landing on a number less than 4), we need to multiply the probabilities of each event occurring. This is known as the multiplication rule of probability.
So, the probability of landing on an odd number and then landing on a number less than 4 is:
(1/2) x (1/4) = 1/8
To write this as a percentage, we can convert the fraction to a decimal by dividing the numerator (1) by the denominator (8) which equals 0.125. Then we can multiply by 100 to get the percentage:
0.125 x 100 = 12.5%
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Complete Question:
You spin the spinner twice. The spinner sections are numbered 2,3,4,5,6,7. 8, and 9
What is the probability of landing on an odd number and then landing on a number less than 4? Write your answer as a percentage
Mark sold half his video game collection to his brother and then bought 16 more games at a yard sale. He now has 36 games. How many did he start with?
Answer:
Step-by-step explanation:
Let's start by using algebra to solve the problem.
Let x be the number of games that Mark started with.
Mark sold half of his games to his brother, so he sold x/2 games. This means he had x - x/2 = x/2 games after selling half to his brother.
He then bought 16 more games, so he had x/2 + 16 games.
Finally, we're told he now has 36 games, so we can set up the equation:
x/2 + 16 = 36
Simplifying the equation, we get:
x/2 = 20
Multiplying both sides by 2, we get:
x = 40
Therefore, Mark started with 40 games.
Answer:
Mark had 40 games to start with.
Step-by-step explanation:
You know this because you can take away the 16 games he bought, which leaves him with half of what he started with which is 20. And if 20 is half of his games you can double it to give you his starting number of games.
:)
if the cost for your car repair is in the lower of automobile repair charges, what is your cost (to two decimals)?
The cost of your car repair will depend on the type of repair being performed, as well as the cost of the necessary parts and labour. To find out the exact cost, you will need to consult a qualified mechanic.
Assuming that the cost of your repair is in the lower range of automobile repair charges, you can calculate the cost by multiplying the cost of the parts and the cost of the labour together. You can then round the result to two decimal places. For example, if the cost of the parts is $100 and the cost of the labour is $200, the total cost of the repair will be $300. This can be rounded to two decimal places, giving you a cost of $300.00.\
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solve these questions
Answer:
a) The perimeter of a rectangle is given by the formula:
P = 2L + 2W
where P is the perimeter, L is the length, and W is the width. We are given that the width of the rectangle is 2x and the length is three times the width. So we can set up an equation that represents the given information:
P = 2L + 2W
168 = 2(3W) + 2W
168 = 8W
b) To solve for W, we can divide both sides of the equation by 8:
168/8 = W
21 = W
Therefore, the width of the rectangle is 21cm.
c) To find the length of the rectangle, we can use the expression that represents the length in terms of the width:
L = 3W
L = 3(21)
L = 63
Therefore, the length of the rectangle is 63cm.
The width and length of the rectangle are 21cm and 63cm, respectively.
what topics will be covered in this unit? logarithmic functions quadratic functions linear functions matrices exponential functions
The unit will cover linear functions, quadratic functions, exponential functions, logarithmic functions, and matrices.
We have,
Based on the topics, the unit will cover the following topics:
Linear functions: This topic typically includes concepts such as slope, intercepts, equations of lines, and graphing linear functions.
Quadratic functions: This topic covers quadratic equations, factoring, completing the square, quadratic formula, vertex form, and graphing parabolas.
Exponential functions: This topic involves exponential equations, growth and decay, properties of exponential functions, and their graphs.
Logarithmic functions: This topic focuses on logarithmic equations, properties of logarithms, solving logarithmic equations, and the relationship between exponential and logarithmic functions.
Matrices: Matrices are a topic in linear algebra and involve operations on matrices, matrix multiplication, determinants, inverse matrices, and solving systems of linear equations using matrices.
It's important to note that the exact content and depth of each topic may vary depending on the specific curriculum or course.
However, the mentioned topics generally form the core concepts of a unit covering functions, algebra, and matrices.
Thus,
The unit will cover linear functions, quadratic functions, exponential functions, logarithmic functions, and matrices.
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Let Θ be an angle in standard position. What is the terminal point (x,y) of Θ= π on the unit circle?
In the present scenario, the angle of Θ= π terminates in the second quadrant, where the x-coordinate is negative and the y-coordinate is positive.
the terminal point (x, y) of Θ= π on the unit circle can be calculated with the help of the following steps:
Step 1: Firstly, let’s recall the unit circle, which is a circle having a radius of 1 unit, and it is centered at the origin of a coordinate plane.
Step 2: Draw the angle of Θ= π on the unit circle. We can see that this angle has been formed by rotating in the clockwise direction along the unit circle from its initial position on the positive x-axis.
Step 3: As we know that the terminal point (x, y) of an angle in standard position is given by (cos Θ, sin Θ). Therefore, we can apply this formula to calculate the coordinates of the terminal point for the given angle of Θ= π on the unit circle.
Here, cos π= -1 and sin π= 0. Thus, the coordinates of the terminal point are (-1, 0). Hence, the correct answer is (-1, 0).Note: The coordinates of the terminal point for an angle in standard position can be negative, positive, or zero, based on the quadrant in which the angle terminates.
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DUE FRIDAY WELL WRITTEN ANSWERS ONLY!!!!!!!!!!!
Complete the table
All the trigonometric values for sin θ, cos θ and tan θ are valued below. Each trigonometric value is mentioned.
sin θ has boundaries from 0 to 1.
sin [tex]-\pi /2[/tex] = -1
sin [tex]-\pi /3[/tex] = -0.87
sin [tex]-\pi /6[/tex] = -0.5
sin 0 = 0
sin [tex]\pi /6 \\[/tex] = 0.5
sin [tex]\pi /3[/tex] = 0.87
sin [tex]\pi /2[/tex] = 1
sin [tex]2\pi /3[/tex] = [tex]\sqrt{3}/2[/tex]
sin [tex]5\pi /6[/tex] = 1/2
sin [tex]\pi[/tex] = 1
sin [tex]7\pi /6[/tex] = -0.5
sin [tex]4\pi /3[/tex] = -0.87
sin [tex]3\pi /2[/tex] = -1
sin [tex]5\pi /3[/tex] = -0.87
sin [tex]11\pi /6[/tex] = -0.5
sin [tex]2\pi[/tex] = 0
Similarly cos θ has boundaries.
cos [tex]-\pi /2[/tex] = 0
cos [tex]-\pi /3[/tex] = 0.5
cos [tex]-\pi /6[/tex] = 0.87
cos 0 = 1
cos [tex]\pi /6 \\[/tex] = 0.87
cos [tex]\pi /3[/tex] = 0.5
cos [tex]\pi /2[/tex] = 0
cos [tex]2\pi /3[/tex] = -0.5
cos [tex]5\pi /6[/tex] = -0.87
cos [tex]\pi[/tex] = -1
cos [tex]7\pi /6[/tex] = -0.87
cos [tex]4\pi /3[/tex] = -0.5
cos [tex]3\pi /2[/tex] = 0
cos [tex]5\pi /3[/tex] = 0.5
cos [tex]11\pi /6[/tex] = 0.87
cos [tex]2\pi[/tex] = 1
But tan θ has no boundaries.
tan [tex]-\pi /2[/tex] = undefined
tan[tex]-\pi /3[/tex] = -0.8
tan [tex]-\pi /6[/tex] = -1.73
tan 0 = 0
tan[tex]\pi /6 \\[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex]
tan [tex]\pi /3[/tex] = [tex]\sqrt{3}[/tex]
tan [tex]\pi /2[/tex] = undefined
tan [tex]2\pi /3[/tex] = -3
tan [tex]5\pi /6[/tex] = -0.5774
tan [tex]\pi[/tex] = undefined
tan [tex]7\pi /6[/tex] = -1.73
tan[tex]4\pi /3[/tex] = 1.73
tan [tex]3\pi /2[/tex] = undefined
tan [tex]5\pi /3[/tex] = -1.73
tan [tex]11\pi /6[/tex] = -0.58
tan [tex]2\pi[/tex] = 0
Hence, all the values mentioned in the table, were written above.
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Simplify 4 x + 3 y 2 − 7 z 4 + 5 z 4 + 11 − 4 x + y 2
Answer:
[tex]4y {}^{2} - 2z {}^{4} + 11[/tex]
Step-by-step explanation:
[tex]1. \: (4x - 4x) + (3y {}^{2} + y {}^{2} ) + ( - 7z {}^{4} + 5z {}^{4} ) + 11 \\ 2. \: 4y {}^{2} - 2z {}^{4} + 11[/tex]
fatouma is lifting wieghts over a 10 week training period . every week , she lifts 2 kg more than she lift the previous week . during the tenth week she lifts 120 kg . what mass did she lift during the week
Fatouma lifted 1 kg during the first week and 120 kg during the tenth week. Fatouma lifted 120 kg in 10 weeks, increasing by 2 kg each week.
What is linear equation ?Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0
Say the mass Fatouma lifted during the first week "x". According to the problem, she increases the weight she lifts by 2 kg every week. So, the mass of second week is "x + 2" kg, during the third week is "x + 4" kg, and so on.
Since there are 10 weeks of training, the mass she lifted during the 10th week is:
x + (10 - 1) × 2 = x + 18
We also know that during the 10th week, she lifted 120 kg. So, we can set up an equation:
x + 18 = 120
Solving for x, we get:
x = 102
Thus, Fatouma lifted 102 kg during the first week of training.
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what is x2=20 show your work
Answer:
x=10
Step-by-step explanation:
x2=20
2*x=20
2*10=20
so, x=10
BRAINLIST! HELP ME PLS
SHOW HOW U GOT IT AND SHOW ALL STEPS! IF CORRECT WILL MAKE U BRAINLIST!
Answer: 948 [tex]ft^{2}[/tex]
Step-by-step explanation:
2(18*20) + 2(18*3) + 2(20*3) = 2(360) + 2(54) + 2(60) = 720 + 108 + 120 = 948
Matt wants to buy a tie. The prices of similar ties offered by four different online retailers are listed. $15.50, $17.50, $16.00, $18.00 What is the mean absolute deviation of the prices of the ties?
Answer: mean-16.75
population size- 4
Step-by-step explanation:
9. a soccer field is a rectangle 90 meters wide and 120 meters long. the coach asks players to run from one corner to the other corner diagonally across. what is this distance? round your answer to the nearest tenth. (4 points)
The distance from one corner to the other corner diagonally across the soccer field is 169.7 meters.
To calculate this, use the Pythagorean theorem, which states that [tex]a^2 + b^2 = c^2[/tex], where a and b are the two sides of a right triangle, and c is the hypotenuse, or the longest side.
In this problem, a is 90 meters, b is 120 meters, and c is the distance from one corner to the other diagonally across the field.
So, [tex]90^2 + 120^2 = c^2[/tex]. To solve this, take the square root of both sides, and c = 169.7 meters.
To round this answer to the nearest tenth, we need to round it to 169.7 meters.
This question can be used to demonstrate the importance of knowing the Pythagorean theorem, which can be used to calculate the distance of a right triangle when the lengths of two sides are known. It is a useful tool to solve a variety of geometry problems.
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. a student is calculating the surface area of a single sheet of paper. he measures the length to be he measures the width to be the student should record the area of the paper as (a) 602.64 cm2 . (b) 602.6 cm2 . (c) 602 cm2 . (d) 603 cm2 .
The student should record the area of the paper as option (c) 602 cm^2
The student measured the length and width of a single sheet of paper and was asked to calculate its surface area. The surface area of the paper is the product of its length and width, which can be calculated by multiplying the two measurements together.
The surface area of the paper can be calculated as the product of the length and the width
Surface area = length × width
Substituting the given measurements, we get
Surface area = 43 cm × 14 cm
Surface area = 602 cm^2
Therefore, the correct option is (c) 602 cm^2
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The given question is incomplete, the complete question is;
A student is calculating the surface area of a single sheet of paper. he measures the length to be 43 cm he measures the width to be 14cm the student should record the area of the paper as (a) 602.64 cm^2 . (b) 602.6 cm^2 . (c) 602 cm^2 . (d) 603 cm^2 .
John wants to store his golf club inside a box. If the box has a length of 20in, width of 13 in,
and height of 11 in. If his golf club is 26 inches exactly, will it fit inside the box?
Answer: No
Step-by-step explanation:
Because the length of the box is shorter than the length of the club
20in<26in
The width of the box is also shorter than the width of the club
13in<16in
The height of the box is also shorter than the height of the club
11in<16in
But what about putting it at an angle?
So we know [tex]a^{2} +b^{2} =c^{2}[/tex]
so let's try [tex]20^{2} +13^{2} =x^{2}[/tex]
[tex]x^{2}[/tex]=569
[tex]x=\sqrt{159}[/tex]
x is near 23.85 in, but 23.85<26. So no.
Penny Banks purchased a new washer and dryer for $1,526.39. She used the store's credit plan and made a 25% down payment. How much did she finance?
Penny Banks made a 25% down payment, which means she paid 75% of the total cost through financing.
The amount she paid as a down payment is:
25% of $1,526.39 = 0.25 x $1,526.39 = $381.60
So the amount she financed is:
$1,526.39 - $381.60 = $1,144.79
Therefore, Penny Banks financed $1,144.79.
Can someone help me?!??
Answer:
4,320
Step-by-step explanation:
answer is 4,320
9x2x3x8x2x5
Answer:
66 km²
Step-by-step explanation:
To solve this, you should find the area of the rectangle as if it were complete and then subtract the area of the missing section.
Step one: Finding the area of the big rectangle
A = length x width
A = 9 x 8
A = 72 km²
Step two: Find the area of the smaller rectangle
A = 2 x 3 = 6 km²
Step three: Subtract the area of the small rectangle from the area of the big rectangle
72 - 6 = 66
The price of a new car is $28,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 6%/year compounded monthly. (Round your answers to the nearest cent.)
(a) What monthly payment will she be required to make if the car is financed over a period of 36 months? Over a period of 60 months?
36 months=$
60 months=$
(b) What will the interest charges be if she elects the 36-month plan? The 60-month plan?
36-month plan =$
60-month plan=$
With a 25% down payment, the interest for the 60-month plan therefore equals $3,372.60.
what is compound interest ?A loan's or investment's principle and any accrued interest from earlier periods are both considered when calculating compound interest. In other words, it is the interest charged on a deposit or loan that is computed on both the initial principal and the cumulative interest. This means that the principal amount is increased by the interest earned during each period, and the succeeding interest is computed using the new sum. This causes the investment or debt to grow over time and can have a big impact on the amount received or due in comparison to simple interest calculations.
given
(b) The amount funded can be subtracted from the total amount paid over the loan term to determine the interest fees.
The total sum paid for the 36-month plan is:
The amount paid is monthly payment multiplied by the number of payments ($630.70 x 36 = $22,743.60).
These are the interest fees:
Interest costs equal Total paid - Financed amount ($22,743.60 - $21,000) to equal $1,743.60.
Hence, the 36-month plan's interest costs come to $1,743.60.
(ii) The total sum paid for the 60-month plan is:
Amount paid equals Monthly Payment * Number of Payments, or $406.21 * 60, for a total of $24,372.60.
These are the interest fees:
Interest costs are calculated as follows: Total paid - Total financed: $24,372.60 - $21,000 = $3,372.60
With a 25% down payment, the interest for the 60-month plan therefore equals $3,372.60.
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This is due tomorrow so please help me ASAP! Thanks!
The value of the given lengths are as follows:
a.) KL = 11.1ft
LO = 5.7ft
b.) m<OMN = 45°
How to calculate the missing length of the given triangles?For Side LO ;
7/11 = 7√2/7√2+LO
7(7√2+LO) = 11×7√3
69.3+7LO = 108.9
7LO = 108.9-69.3
LO = 39.6/7
LO = 5.7 ft
For KL ;
This can be solved using the Pythagorean theorem;
c²= b²+a²
C = 5.7+7√2 = 15.6
b = 11
a²= 15.6²-11²
= 243.36 - 121
= 122.36
a= √122.36
a= 11.1ft
For angle OMN;
This can be solved using SOHCAHTOA.
Sin∅ = opposite/hypotenuse
opposite = 7
hypotenuse = 7√2
sin∅ = 7/7√2
sin∅ = 0.707106781
∅= sin-1 0.707106781
∅ = 45°
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Lin's job pays $12.50 an hour. She also gets paid $25 per week to cover uniform cleaning and
other expenses. To meet her budget, Lin needs to be paid at least $300 per week.
Answer:
I think it is because 3,500
you have 8 red roses and 4 yellow rose. if you line them up in a row, how many different arrangements can you get
There are 27,720 different arrangements of red and yellow roses.
The total number of roses is 8 + 4 = 12. To find the number of different arrangements, we can use the formula for permutations, which is:
n! / (n - r)!
where n is the total number of objects and r is the number of objects we want to arrange.
In this case, we want to arrange all 12 roses, so n = 12. The number of red roses is 8, so r = 8. Therefore, the number of different arrangements of the roses is:
12! / (12 - 8)! = 12! / 4! = 27,720
So there are 27,720 different arrangements of the 8 red roses and 4 yellow roses.
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James invested 20,000 for one year and earned 1470 interest. If part of the money is invested at 10% and the remainder is invested at 6% how much is the invested at each rate
Linear equation.
Answer:
Let's represent the amount invested at 10% as x and the amount invested at 6% as y. Then we can set up a system of two equations to represent the given information:
x + y = 20,000 (since the total amount invested is 20,000)
0.10x + 0.06y = 1,470 (since the interest earned is 1,470 and the interest rate at which x is invested is 10% and the interest rate at which y is invested is 6%)
We can use the first equation to solve for one of the variables in terms of the other:
x = 20,000 - y
Now we can substitute this expression for x into the second equation and solve for y:
0.10(20,000 - y) + 0.06y = 1,470
2,000 - 0.10y + 0.06y = 1,470
-0.04y = -530
y = 13,250
So $13,250 was invested at 6%. We can find the amount invested at 10% by plugging in this value of y into the first equation:
x + 13,250 = 20,000
x = 6,750
So $6,750 was invested at 10%.
What is the greatest common factor of 9, 24, and 30
Answer: 3
Step-by-step explanation:
9/3=3
24/3= 8
30/3=10
If h = 13 units and r = 6 units, then what is the volume of the cone shown above?
The vοlume οf the cοne is 156π cubic units
What is cοne?A cοne is a three-dimensiοnal geοmetric fοrm with a flat base and a smοοth tapering tip οr end. A cοne is made up οf a cοllectiοn οf line segments, half-lines, οr lines that link the apex—the cοmmοn pοint—tο every pοint οn a base that is in a plane οther than the apex.
Given,
h = 13 units and r = 6 units
We knοw the fοrmula tο determine vοlume οf cοne; that is
(1/3)πr²h
Where r= radius οf the cοne
h= height οf the cοne
We put the value οf h and r in the fοrmula
(1/3)πr²h
= (1/3)π6² *13
=156π cubic units
The vοlume οf the cοne is 156π cubic units
Hence the cοrrect answer is 156π cubic units
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5000+800+20+1+0. 3+0. 04+0. 006+0. 0009 in standard form
The number in standard form is 5.821346 x [tex]10^{3}[/tex].
To write a number in standard form, we express it as a number between 1 and 10, multiplied by a power of 10.
First, let's add up the numbers:
5000 + 800 + 20 + 1 + 0.3 + 0.04 + 0.006 + 0.0009 = 5821.346
the value of sum is 5821.346
To express this number in standard form, we need to move the decimal point to the left until we have a number between 1 and 10. We moved the decimal point 3 places to the left, so we need to multiply by [tex]10^{3}[/tex]:
5821.346 = 5.821346 x [tex]10^{3}[/tex]
Therefore, the number in standard form is 5.821346 x[tex]10^{3}[/tex] .
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a)Find the number c that satisfies the conclusion of the Mean Value Theorem for this function f(x) = x + 3/x and the interval [1,14]
The number c that satisfies the conclusion of the Mean Value Theorem for the function f(x) = x + 3/x on the interval [1, 14] is approximately c = 3.75.
To find the number c that satisfies the conclusion of the Mean Value Theorem for the function f(x) = x + 3/x on the interval [1, 14], follow these steps:
1. Verify the conditions of the Mean Value Theorem:
The function f(x) = x + 3/x is continuous on the closed interval [1, 14] and differentiable on the open interval (1, 14).
2. Calculate the average rate of change of the function on the interval:
f(14) = 14 + 3/14 ≈ 14.214
f(1) = 1 + 3/1 = 4
Average rate of change = (f(14) - f(1)) / (14 - 1) ≈ (14.214 - 4) / 13 ≈ 0.786
3. Differentiate the function to find the instantaneous rate of change:
f'(x) = 1 - 3/x²
4. Set f'(x) equal to the average rate of change and solve for x:
1 - 3/x² = 0.786
x² = 3 / (1 - 0.786)
x² ≈ 14.056
x ≈ √14.056 ≈ 3.75
The number c that satisfies the conclusion of the Mean Value Theorem for the function f(x) = x + 3/x on the interval [1, 14] is approximately c = 3.75.
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What is the area of a circle with the radius of 11.5 meters? Use 3.14 for pi or put pi in your answer for an exact answer.
Answer:
Area = [tex]415.265 m^2[/tex]
Step-by-step explanation:
Area of a circle = [tex]\pi r^2[/tex]
[tex]A = (3.14)(11.5^2)=(3.14)(132.25)=415.265[/tex]