#1 Evaluate S² (x²+1) dx by using limit definition. (20 points) #2 Evaluate S x²(x²³ +8) ² dx by using Substitution. (10 points) #3 Evaluate Stift-4 dt (10 points) Sot at #4 Find flex) if f(x) = 5 * =_=_=_d² + x + ²/²₁ #5 Evaluate 5 | (t-1) (4-3) | dt (15 points) #6 Evaluate SX³ (x²+1) ³/²2 dx (15 points) (10 points) #7 Evaluate S sin (7x+5) dx (10 points) #8 Evaluate S/4 tan³ o sec² o do (10 points)
Answers
1. By applying the sum of powers formula, we find that ∫(x²+1)² dx diverges as n approaches infinity.
2. The final result is (1/23) * ((x²³ + 8)³/3) + C].
3. The final result is [\(-t^{(-3)}\) / 3 + C].
What is Riemann sum?A territory's approximate area, known as a Riemann sum, is calculated by summing the areas of various simplified slices of the region. Calculus uses it to formalise the process of exhaustion, which is used to calculate a region's area.
1) Using the limit definition of the integral,
we divide the interval [a, b] into n subintervals of width
Δx = (b - a)/n.
Then, the integral is given by the limit of the Riemann sum as n approaches infinity.
For ∫(x²+1)² dx,
we choose the interval [0, 1] and calculate the Riemann sum as Σ[(x⁴+2x²+1) Δx].
By applying the sum of powers formula,
we find that ∫(x²+1)² dx diverges as n approaches infinity.
2) To evaluate ∫x²(x²³ + 8)² dx using substitution,
let u = x²³ + 8
du = (23x²²) dx.
Rearranging, we have
dx = du / (23x²²).
Substituting these expressions, we get
∫(1/23)u² du
Integrating, we find
(1/23) * (u³/3) + C
Replacing u with x²³ + 8,
The final result is (1/23) * ((x²³ + 8)³/3) + C.
3) The integral ∫\(t^{(-4)}\) dt can be evaluated using the power rule of integration.
By adding 1 to the exponent and dividing by the new exponent, we find \(t^{(-4)}\) = ∫ \(-t^{(-3)}\) / 3 + C
To learn more about limit definition here:
https://brainly.com/question/30761744
#SPJ4
Related Questions
Discret Structure math
2.1.3 restate the theorem
a) The square root of every positive number less than one is greater than the number itself.
(c) Every real number besides 0 has a multiplicative inverse
2.2.2 sowing a statement is true or false by direct proof or counterexample Determine whether the statement is true or false. If the statement is true, give a proof. If the statement is false, give a counterexample. (Note: the definition of an even integer is an integer that can be expressed as 2k, where k is an integer.)
(b) If x+y is an even integer, then x and y are both even integers
Answers
The two given theorems are as follows:
a) The square root of every positive number less than one is greater than the number itself.
c) Every real number besides 0 has a multiplicative inverse.
To restate these theorems, we can write:
a) If a number is positive and less than one, then its square root is greater than the number itself.
c) For every real number x ≠ 0, there exists a real number y such that xy = 1.2.2.2 Determine whether the statement is true or false by direct proof or counterexample
The second part of the question asks to determine whether the given statement is true or false by direct proof or counterexample.
The statement is as follows:b) If x + y is an even integer, then x and y are both even integers.
To prove that the statement is true, we need to show that if x + y is an even integer, then x and y are both even integers. Let x = 2a and y = 2b, where a and b are integers. Then x + y = 2a + 2b = 2(a + b), which is even.
Hence, the statement is true.To show that the statement is false, we need to give a counterexample. Let x = 2 and y = 3.
Then x + y = 2 + 3 = 5, which is odd. However, x = 2 is even.
Hence, the statement is false.
To know more about counterexample click here
https://brainly.com/question/21738549
#SPJ11
Is 59 a prime number?
Answers
Answer: Yes, 59 is a prime number
Step-by-step explanation: 59 is a prime number, it has only two factors, such as one and the number itself. Hence, the factors of 59 are 1 and 59.
Yes, 59 is a prime number.
What is a prime number?
Any natural number greater than 1 that is not the sum of two smaller natural numbers is referred to as a prime number. A composite number is a natural number greater than one that is not prime.
In other terms, prime numbers are positive integers greater than one that only has the number itself and 1 as factors. 2, 3, 5, 7, 11, 13, and other prime numbers are just a few examples. Never forget that 1 is neither a prime number nor a composite. Apart from 1, the other numbers can all be categorised as prime and composite numbers. Except for 2, which is the smallest prime number and the only even prime number, all prime numbers are odd.
The number in question, which is 59, has only two factors: 1 and 59.
Therefore 59 is a prime number.
To learn more about prime numbers, follow the link.
https://brainly.com/question/145452
#SPJ4
PLEASE HELP DUE IN 1 HOUR, AND PLEASE DON'T PUT THOSE LINKS OR ELSE I WILL REPORT YOU.
Answers
Answer:
h ≤ 16
Step-by-step explanation:
If he plans to cook 16 of less hotdogs, h is going to be equal to or less than 16. The circle is closed because he could cook 16.
Answer:
For the first question it would be answer 4
Since they ask you "at most 16 hot dogs," that means that it has to be less than or equal to 16.
For the second question, you would put the endpoint on 16 and make the arrow going left.
mindy is saving money. she started with $0. after 6 weeks, she had $900 saved. mindy is not sure exactly how much money she saved each week. she assumes that saved money at a constant rate when she started saving money through week 6. Part A: create a graph that can be used to model the number of dollars,y, mindy saves in x weeks. Part B: explain what the slope of the line you drew represents. Part C: describe how you can use the line to predict the number of weeks it will take Mindy to save $150
Answers
It will take Mindy 1 week tο save $150.
What is Slοpe?The slοpe οf a line is the measure οf its steepness, defined as the ratiο οf the vertical change (rise) οver the hοrizοntal change (run) between any twο pοints οn the line.
Part A:
Tο create a graph that can be used tο mοdel the number οf dοllars Mindy saves in x weeks, we can use a linear equatiοn in slοpe-intercept fοrm:
y = mx + b
where y is the tοtal amοunt saved after x weeks, m is the slοpe (the cοnstant rate at which Mindy saves mοney), and b is the initial amοunt saved (which is 0 in this case).
Using the infοrmatiοn given, we can find the slοpe οf the line as fοllοws:
m = (change in y) / (change in x)
m = ($900 - $0) / (6 weeks - 0 weeks)
m = $150 per week
Sο the equatiοn fοr the line is:
y = $150x
We can graph this line by plοtting the pοints (0,0) and (6, $900), and then drawing a straight line cοnnecting them.
Part B:
The slοpe οf the line represents the cοnstant rate at which Mindy saves mοney each week. In this case, the slοpe is $150 per week, which means that Mindy is saving $150 every week.
Part C:
Tο use the line tο predict the number οf weeks it will take Mindy tο save $150, we can plug in the value fοr y (which is $150) intο the equatiοn and sοlve fοr x:
$150 = $150x
x = 1
Sο it will take Mindy 1 week tο save $150.
To learn more about Slope from the given link
https://brainly.com/question/16949303
#SPJ1
Can someone explain how you got the answer!!
Answers
9514 1404 393
Answer:
20 square units
Step-by-step explanation:
The area is given by the formula ...
A = bh
where b is the base of the parallelogram, and h is the perpendicular distance between the parallel bases. Using the numbers from the figure, we have ...
A = 5·4 = 20 . . . . square units
_____
Additional comment
You will notice this is the same formula as is used for a rectangle. You can consider the parallelogram to have the same area as a rectangle of these dimensions if you look at what happens when you cut the right triangle from the right end and add it to the left end. The result is a rectangle 5 units wide and 4 units high.
The same formula applies even if the skew is so great that the bases do not overlap. (That much skew would not result in a triangle of the kind shown in this diagram.)
Sam and Andre shared a number of pennies in the ratio 8:3. They received a total of 671 pennies. How many more pennies did Sam receive than Andre?
Answers
Answer:
Sam had 488
Andre had 183
488:183
please mark brainllest
What number is represented by point A? Explain or show how you know.
Answers
Point A is between the 7th and 8th tick marks.
Once you zoom in, you can see that the decimal would be 7.4. So the number could be represented by the expression 7.4 times 10 to the 11th power.
Since, In Geometry and Mathematics, a number line refers to a type of graph that is usually composed of a graduated straight line, which typically comprises both negative and positive numerical values (numbers) that are located at equal intervals along its length.
In this scenario and exercise, we would determine the numerical value (number) that is represented by point A by solving as follows;
10¹² × 7/10 = 7 × 10¹¹
10¹² × 4/10 = 4 × 10¹¹
By adding the numbers, we have:
7 × 10¹¹ + 4/10 × 10¹¹ = 7.4 × 10¹¹
Read more on number line here:
brainly.com/question/22515080
#SPJ1
Missing information:The question is incomplete and the complete question is shown in the attached picture.
What number is represented by point A? Explain or show how you know. Point A is between the__ th and__ th tick marks. Once you zoom in, you can see that the decimal would be__ So the number could be represented by the expression__times 10 to the __th power.
Which set of ordered pairs satisfies an inverse variation?
Answers
93 is what percent of 620?
%
Answers
Answer:
15%
Step-by-step explanation:
Answer:
15%
Step-by-step explanation:
This table contains equivalent ratios between x and y
x
6
8
10
12
y
3
4
6
Enter the missing value from the table.
Answers
The missing value from the table of values is y = 5
Calculating the missing value from the table.From the question, we have the following parameters that can be used in our computation:
x 6 8 10 12
y 3 4 6
From the above table of values, we can see that
x is divided by 2 to get y
using the above as a guide, we have the following:
y = 1/2x
When the value of x is 10, we have
y = 1/2 * 10
Evaluate
y = 5
Hence, the missing value from the table. is y = 5
Read mroe about equivalent ratio at
https://brainly.com/question/2328454
#SPJ1
4-6-5 3-5-4 2-8-?
Ok, can somebody please help me.
You need to find ?. This is not math this is brain game and i can't solve it!!!!
please help
Answers
Answer:
345678
Step-by-step explanation:
a scientist produces zinc iodine. This is the method used:
1.weight 0.500 g of iodine 2.dissolve the iodine in ethanol
3.add the excess of zinc
4. stir the mixture until there's no further change
5. filter the excess zinc
6. evaporate off the ethanol
explain why the scientist adds excess zinc rather then excess iodine
answer is given, explain the full process including final steps
Answers
Given the curve:
\(y=\frac{18}{x^2+2}\)You need to find the equation for the tangent to that curve at the point:
\((1,6)\)Then, you need to follow these steps:
1. Derivate the function given in the exercise using these Derivative Rules:
\(\frac{d}{dx}(\frac{1}{u(x)})=-\frac{u^{\prime}(x)}{u(x)^2}\)\(\frac{d}{dx}(x^n)=nx^{n-1}\)\(\frac{d}{dx}(k)=0\)Where "k" is a constant.
Then, you get:
\(=18\cdot\frac{(x^2+2)^{\prime}}{(x^2+2)^2}\)\(=-18\cdot\frac{(x^2+2)^{\prime}}{(x^2+2)^2}\)\(=-18\cdot\frac{2x}{(x^2+2)^2}\)\(y^{\prime}=-\frac{36x}{(x^2+2)^2}\)2. Substitute this value of the x-coordinate of the given point into the derivated function and then evaluate, in order to find the slope of the line:
\(m=-\frac{36(1)}{(1^2+2)^2}=-\frac{36}{9}=-4\)4. The Point-Slope Form of the equation of a line is:
\(y-y_1=m(x-x_1)\)Where "m" is the slope of the line and this point is on the line:
\((x_1,y_1)\)In this case:
\(\begin{gathered} m=-4 \\ x_1=1 \\ y_1=6 \end{gathered}\)Therefore, you can substitute values:
\(y-6=-4(x-1)\)5. Convert the equation from Point-Slope Form to Slope-Intercept Form.
The equation of a line in Slope-Intercept Form is:
\(y=mx+b\)Where "m" is the slope and "b" is the y-intercept.
Then, by solving for "y", you get:
\(y-6=(-4)(x)-(-4)(1)\)\(y-6=-4x+4\)\(y=-4x+4+6\)\(y=-4x+10\)Hence, the answer is:
1. Derivate the function.
2. Find the slope of the tangent line by substituting the x-coordinate of the given point into the function derivated.
3. Write the equation of the tangent line in Point-Slope Form using the given point and the slope.
4. Rewrite the equation in Slope-Intercept Form by solving for "y".
Equation for the tangent of the curve:
\(y=-4x+10\)Pls help me with this math..... its kind of easy...
Answers
a=9.2
b=1 5/8
c=4
d=24
e=2.3
f=8.5
g= 2.6
B) 1 5/8
C) 4
D) 24
E) 2.3
F) 8/5
G) 2.6
do eight-digit numbers with no digits 9 in their decimal representations constitute more than half of all eight-digit numbers?
Answers
Answer:
No.
Step-by-step explanation:
To determine whether eight-digit numbers with no digits 9 in their decimal representations constitute more than half of all eight-digit numbers, we need to calculate the total number of eight-digit numbers and the number of eight-digit numbers with no digit 9.There are 10 possible digits for each position in an eight-digit number, so there are 10^8 (or 100,000,000) total eight-digit numbers.
To count the number of eight-digit numbers with no digit 9, we can note that each digit in the number has 9 possible choices (0, 1, 2, 3, 4, 5, 6, 7, or 8), and since there are eight digits in the number, there are 9^8 (or 43,046,721) eight-digit numbers with no digit 9.Therefore, the proportion of eight-digit numbers with no digit 9 is:
9^8 / 10^8 = 0.43046721
This is less than half, so we can conclude that eight-digit numbers with no digits 9 in their decimal representations do not constitute more than half of all eight-digit numbers.
No, eight-digit numbers with no digit 9 in their decimal representations do not constitute more than half of all eight-digit numbers.
There are a total of 9 digits (0-9) in the decimal system, and an eight-digit number can have any of these digits in each of its eight places.
So, the total number of eight-digit numbers that can be formed is:
9 × 9 × 9 × 9 × 9 × 9 × 9 × 9 = 43,046,721
Out of these, there are 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 = 16,777,216 numbers that can have digits other than 9 in each of the eight places.
Therefore, the remaining numbers (43,046,721 - 16,777,216 = 26,269,505) will have at least one 9 in their decimal representations.
So, the eight-digit numbers with no digit 9 in their decimal representations constitute:16,777,216 / 43,046,721 = 0.3906 or approximately 39.06%of all eight-digit numbers. Therefore, they do not constitute more than half of all eight-digit numbers.
No, eight-digit numbers with no digit 9 in their decimal representations do not constitute more than half of all eight-digit numbers.
To learn more about the decimal system visit:
https://brainly.com/question/28222265?
#SPJ11
Wesley says that the equation 2(2x + 7) = 6x +4
can be used to calculate DF.
Is Wesley correct?
Yes, the equation is correct
O No. it's not quite right. Here's the correct equation...
There's not enough information provided.
Answers
Answer:
2(9x)=18x
Step-by-step explanation:
parentheses first (2x+7)=9x then multiply 2(9x)=18x+4=22x
Corry collects cube containers. She fills them with water and pours them into a rectangular prism. She was playing with them and discovered something interesting. She had three cube containers. One cube was 1 inch by 1 inch by 1 inch. A second cube was 2 inches by 2 inches by 2 inches and a third cube was 3 inches by 3 inches by 3 inches.She filled all three with water. Then Corry poured all three cubes into a rectangular prism filling it exactly! The rectangular prism has a square base with a side length (1+2+3 = 6) inches and the height is 1 inch.Corry wonders whether she has found a pattern. Investigate using more cube containers to fill square base prisms with heights of 1 in. Describe any conjectures you discover.
Answers
Answer:
\(\displaystyle\sum_{i=1}^n{i^3}=\left(\sum_{i=1}^n{i}\right)^2\)
Step-by-step explanation:
The only sum of three cubes that has a total equal to the square of the sum of their dimensions is the one Corry found.
However, we notice that ...
1³ +2³ +3³ +4³ = (1 +2 +3 +4)² = 100
If we add the next number in sequence, we get ...
100 +5³ = 225 = (10 +5)²
225 +6³ = 441 = (15 +6)²
So, it seems that the sum of the first n cubes is equal to the square of the sum of the first n natural numbers.
A phone company offers two monthly plans. Plan A costs $30 plus an additional $0.03 for each minute of calls. Plan B has no initial fee but costs $0.18 for each minute of calls. What is the cost when the two plans cost the same for a set number of minutes? (asap)
Answers
Answer: YE
Step-by-step explanation:
TOTALLY
Help me please. You get brownies.
Answers
Find the surface area of each figure. Round your answers to the nearest hundredth, if necessary
Answers
Answer:
506π ft^2
Step-by-step explanation:
here's your solution
=> height of cylinder = 12 ft
=> radius of cylinder = 11 ft
=> surface area of cylinder = 2πr(h+r)
=> SA = 2*11(12+11)*π
=> SA = 22*23π
=> SA = 506π ft^2
hope it helps
MATHHHHH!!!! HELP ME OUTTT
Answers
Answer:a
Step-by-step explanation:hhehenndherndur
help me answer this please!!! i will mark you brainliest
Answers
Answer:
363 ft.
Step-by-step explanation:
To calculate the base side which is b we use the trigonometric identity called cosine.
\(cos \theta=\frac{base}{hypotenuse} \\\\cos25 = \frac{b}{400}\\\\b=400*cos 25\\b=400*0.906\\b=362.5\ ft\)
Since we the answer to the nearest whole number it would be b = 363 ft.
Americans consume the equivalent 22.2 teaspoons (tsp) of sugar per day, on average, with a standard deviation of 6.5 tsp. Assuming sugar consumption follows a normal distribution respond to the following:
1) What is the probability that a randomly selected American will consume more than 30 tsp in a day?
2)What proportion of Americans consume between 20 and 25 tsp in a day?
3) If you were to consume 10 tsp of sugar today, approximately what percentile would that place you in?
4) What is the 95th percentile of daily sugar consumption?
Answers
The 95th percentile of daily sugar consumption is approximately 32.97 tsp.
To answer the questions, we can use the normal distribution and Z-scores.
Z | 0.00 | 0.01 | 0.02 | 0.03 | 0.04
------------------------------------------------------------------------
-3.4 | 0.0003 | 0.0003 | 0.0003 | 0.0002 | 0.0002
-3.3 | 0.0005 | 0.0005 | 0.0004 | 0.0004 | 0.0003
-3.2 | 0.0007 | 0.0007 | 0.0006 | 0.0006 | 0.0005
-3.1 | 0.0010 | 0.0009 | 0.0009 | 0.0008 | 0.0007
-3.0 | 0.0013 | 0.0013 | 0.0012 | 0.0011 | 0.0010
-2.9 | 0.0019 | 0.0018 | 0.0017 | 0.0016 | 0.0015
-2.8 | 0.0026 | 0.0025 | 0.0023 | 0.0022 | 0.0021
-2.7 | 0.0035 | 0.0034 | 0.0032 | 0.0031 | 0.0030
-2.6 | 0.0047 | 0.0045 | 0.0043 | 0.0041 | 0.0040
-2.5 | 0.0062 | 0.0060 | 0.0059 | 0.0057 | 0.0055
Given information:
Mean (μ) = 22.2 tsp
Standard deviation (σ) = 6.5 tsp
Probability of consuming more than 30 tsp in a day:
To find this probability, we need to calculate the area under the normal distribution curve to the right of 30 tsp. We can use the Z-score formula.
Z = (X - μ) / σ
Substituting the values, we get:
Z = (30 - 22.2) / 6.5 ≈ 1.2
Using a Z-table or calculator, we can find the probability associated with a Z-score of 1.2, which is approximately 0.8849. Therefore, the probability that a randomly selected American will consume more than 30 tsp in a day is approximately 0.8849 or 88.49%.
Proportion of Americans consuming between 20 and 25 tsp:
To find this proportion, we need to calculate the area under the normal distribution curve between 20 and 25 tsp. We can again use Z-scores.
Z1 = (20 - 22.2) / 6.5 ≈ -0.3385
Z2 = (25 - 22.2) / 6.5 ≈ 0.4308
Using the Z-table or calculator, we find the area to the left of Z1 is approximately 0.3676, and the area to the left of Z2 is approximately 0.6645. Therefore, the proportion of Americans consuming between 20 and 25 tsp in a day is approximately 0.6645 - 0.3676 = 0.2969 or 29.69%.
Percentile for consuming 10 tsp:
To determine the percentile, we need to find the area under the normal distribution curve to the left of 10 tsp. Again, we use Z-scores.
Z = (10 - 22.2) / 6.5 ≈ -1.8769
Using the Z-table or calculator, we find the area to the left of Z is approximately 0.0301. This means that consuming 10 tsp of sugar would place you at approximately the 3rd percentile.
95th percentile of daily sugar consumption:
To find the 95th percentile, we need to find the Z-score corresponding to the area to the left of 0.95. Using the Z-table or calculator, we find the Z-score is approximately 1.645.
Using the Z-score formula, we can find the corresponding value (X) from the mean and standard deviation:
X = Z * σ + μ
X = 1.645 * 6.5 + 22.2 ≈ 32.97
Therefore, the 95th percentile of daily sugar consumption is approximately 32.97 tsp.
To know more about normal distribution refer here:
https://brainly.com/question/15103234
#SPJ11
Two cars travel at the same speed to different destinations. Car A reaches its destination in 12 minutes. Car B reaches its destination in 18 minutes. Car B travels 4 miles farther than Car A. How fast do the cars travel? Write your answer as a fraction in simplest form.
Answers
Answer:
chatGPT
Step-by-step explanation:
Let's denote the speed of each car as v, and the distance that Car A travels as d. Then we can set up two equations based on the information given:
d = v * (12/60) (since Car A reaches its destination in 12 minutes)
d + 4 = v * (18/60) (since Car B travels 4 miles farther than Car A and reaches its destination in 18 minutes)
Simplifying the equations by multiplying both sides by 60 (to convert the minutes to hours) and canceling out v, we get:
12v = 60d
18v = 60d + 240
Subtracting the first equation from the second, we get:
6v = 240
Therefore:
v = 240/6 = 40
So the cars travel at a speed of 40 miles per hour.
this cylindrical fish tank has a height of 38 inches and diameter of 26 inches. what is the volume of the fish tank.
Answers
Answer:
using π as 3.14: 20165.08 cubic inches
in terms of π: 6422π cubic inches
Step-by-step explanation:
» Concepts
The volume of a cylinder is how much space the cylinder can take inside of it. The formula to find this volume is πr²h, where r = radius and h = height. In addition, it's important to know that the radius is half the diameter.
» Application
We're given the radius as 13 inches (26/2 = 13), and the height is 38 inches. Now, we just have to plug in the values and simplify.
» Solution
Using π as 3.14:
\(3.14*13^2*38\) \(3.14*169*38\)\(20165.08\)In terms of π:
\(\pi *169*38\) \(6422\pi\)Identify the polygon that has vertices J(12,−4), U(0,−4), S(4,3), and T(8,3), and then find the perimeter and area of the polygon.
Answers
Answer:P= 16 + 2\|65 units; A= 56 units2
Step-by-step explanation:
Enzo says that he can draw an enlarge rectangle that is 16 cenimeters by 13 cenimeters which explain enzo is correct
Answers
Enzo's statement that he can draw an enlarged rectangle that is 16 centimeters by 13 centimeters is correct. To explain this, we need to understand what it means to enlarge a shape.
Enlargement is the process of making a shape bigger or smaller while maintaining its shape and proportions. In other words, if we enlarge a rectangle, we need to make sure that the length and width are increased by the same factor.
In this case, Enzo has specified the new dimensions of the rectangle as 16 centimeters by 13 centimeters. To create an enlarged rectangle with these dimensions, we need to know the scale factor of the enlargement. The scale factor is the ratio of the length of the enlarged shape to the length of the original shape. In this case, we can find the scale factor by dividing the length of the new rectangle (16 centimeters) by the length of the original rectangle.
Let's assume that the original rectangle has a length of 8 centimeters and a width of 6 centimeters. Dividing 16 by 8 gives us a scale factor of 2. This means that we need to multiply the length and width of the original rectangle by 2 to get the dimensions of the enlarged rectangle.
So, the length of the enlarged rectangle will be 8 x 2 = 16 centimeters, and the width will be 6 x 2 = 12 centimeters. However, Enzo has specified that the width of the enlarged rectangle should be 13 centimeters. This means that we need to adjust the scale factor to make the width of the enlarged rectangle 13 centimeters. Dividing 13 by 6 gives us a scale factor of approximately 2.17.
Multiplying the length and width of the original rectangle by this scale factor gives us the new dimensions of the enlarged rectangle. The length will be 8 x 2.17 = 17.36 centimeters (rounded to two decimal places), and the width will be 6 x 2.17 = 13.02 centimeters (rounded to two decimal places). Therefore, Enzo is correct in saying that he can draw an enlarged rectangle that is 16 centimeters by 13 centimeters.
To know more about enlarged rectangle, refer to the link below:
https://brainly.com/question/9248968#
#SPJ11
What are the values of x and y
Answers
A carpenter wishes to make a rain gutter with a rectangular cross-section by bending up a flat piece of metal that is 18 feet long and 44 inches wide. The top of the gutter is open. What values of x, length of metal bent up, will give a cross-sectional area of at most 50 square inches? Round your answer to three decimal places.
Answers
Answer:
x = 20.996 , 1.002 square inches.
Step-by-step explanation:
We assume that the sides are bent at right angles
Dimensions of the given metal sheet are
Length = 18feet = 216 inches
Width = 44 inches
When we will bend the width part of the given metal sheet
let the bent length be x
so the cross sectional dimensions will be
width = 44-2x
length = x
Area = x(44-2x)
The given are should be at most 50 square inches
so the equation becomes
x(44-2x)\(\leq 50\)
-2x^2 + 44x \(\leq 50\)
\(2x^2 -44x +50\geq 0\)
\(x^2 -22x +25\geq 0\) (dividing the equation by 2)
upon solving the above quadratic equation we get
x = 20.996 , 1.002
both the solutions are possible.
Therefore we have the are using the values of x as 20.996 and 1.002 are
42.159968 and 42.079992 which is less than 50 square inches.
please help i don’t get this lol
Answers
Answer:
sorry i dont know the answer
Step-by-step explanation:
Consider the function f(x). Select all of the following that include a horizontal compression of f(x).
Answers
ANSWER
f(3x)
f(6x) + 9
EXPLANATION
A function is said to undergo horizontal compression if it changes as follows:
\(\begin{gathered} f(x)\Rightarrow\text{ f(bx)} \\ \text{given that b > 1} \end{gathered}\)This means that the functions that include a horizontal compressions are functions that have that form of transformation in them.
Note: b must be greater than 1
Therefore, the correct options are:
f(3x)
f(6x) + 9