Answer:
= x^2 + 3 + √3x^2 - 1
Step-by-step explanation:
Remove parentheses: (a) = a
= x^2 + 3 + √x . 3x - 1
x . 3x = 3x^2
= x^2 + 3 + √3x^2 - 1
The dimensions of a closed rectangular box are measured as 60 centimeters, 50 centimeters, and 70 centimeters, with an error in each measurement of at most 0.2 centimeters. Use differentials to estimate the maximum error in calculating the surface area of the box.
Answer:
The maximum error in calculating the surface area of the box is 72 square centimeters.
Step-by-step explanation:
From Geometry, the surface area of the closed rectangular box ([tex]A_{s}[/tex]), in square centimeters, is represented by the following formula:
[tex]A_{s} = w\cdot l + (w + l)\cdot h[/tex] (1)
Where:
[tex]w[/tex] - Width, in centimeters.
[tex]l[/tex] - Length, in centimeters.
[tex]h[/tex] - Height, in centimeters.
And the maximum error in calculating the surface area ([tex]\Delta A_{s}[/tex]), in square centimeters, is determined by the concept of total differentials, used in Multivariate Calculus:
[tex]\Delta A_{s} = \left(l+h\right)\cdot \Delta w + \left(w+h\right)\cdot \Delta l + (w+l)\cdot \Delta h[/tex] (2)
Where:
[tex]\Delta w[/tex] - Measurement error in width, in centimeters.
[tex]\Delta l[/tex] - Measurement error in length, in centimeters.
[tex]\Delta h[/tex] - Measurement error in height, in centimeters.
If we know that [tex]\Delta w = \Delta h = \Delta l = 0.2\,cm[/tex], [tex]w = 60\,cm[/tex], [tex]l = 50\,cm[/tex] and [tex]h = 70\,cm[/tex], then the maximum error in calculating the surface area is:
[tex]\Delta A_{s} = (120\,cm + 130\,cm + 110\,cm)\cdot (0.2\,cm)[/tex]
[tex]\Delta A_{s} = 72\,cm^{2}[/tex]
The maximum error in calculating the surface area of the box is 72 square centimeters.
A walking path across a park is represented by the equation y = -4x + 10. A new path will be built perpendicular to this path. The paths will intersect at the point (4, -6). Identify the equation that represents the new path.
Answer: [tex]y=\frac{1}{4}x-7[/tex]
Step-by-step explanation:
The perpendicular slope of the line(m) = [tex]-\frac{1}{m}[/tex]:
m = -4 ⇒ [tex]-\frac{1}{m} =-\frac{1}{(-4)} =\frac{1}{4}[/tex]The function formula is y = mx + b, where the y-intercept(b) is found by substituting in the values of a point on the line ⇒ (4, -6):
[tex]y=\frac{1}{4}x+b\\-6=\frac{1}{4}(4)+b\\-6=1+b\\b=-6-1=-7[/tex]
So the perpendicular equation is [tex]y=\frac{1}{4}x-7[/tex].
Several factors influence the size of the F-ratio. For each of the following, indicate whether it would influence the numerator or the denominator of the F-ratio, and indicate whether the size of the F-ratio would increase or decrease. a. Increase the differences between the sample means. b. Increase the sample variances.
Answer:
(a) Increase the differences between the sample means this will increase the Numerator.
(b) Increase the sample variances will increase the denominator.
Step-by-step explanation:
F Ratio = Variance between treatments/ Variance within treatments.
Here,
(a) Increase the differences between the sample means:
- Will increase the Numerator and
- Size of the F-ratio would increase
(b) Increase the sample variances:
- Will increase the denominator and
- Size of the F Ratio would decrease.
Write an equation for the function that includes the following points (2,32) and (3,64)
Answer:
32 = a*2 +b
64 = a*3 + b
Then 32 = a
32 = 32*2 +b
b = - 32
So
Y = 32a - 32
Is the equation
In the diagram, WZ=StartRoot 26 EndRoot.
On a coordinate plane, parallelogram W X Y Z is shown. Point W is at (negative 2, 4), point X is at (2, 4), point Y is at (1, negative 1), and point Z is at (negative 3, negative 1).
What is the perimeter of parallelogram WXYZ?
units
units
units
units
Answer:
[tex]P = 8 + 2\sqrt{26}[/tex]
Step-by-step explanation:
Given
[tex]W = (-2, 4)[/tex]
[tex]X = (2, 4)[/tex]
[tex]Y = (1, -1)[/tex]
[tex]Z = (-3,-1)[/tex]
Required
The perimeter
First, calculate the distance between each point using:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 -y_2)^2[/tex]
So, we have:
[tex]WX = \sqrt{(-2- 2)^2 + (4-4)^2 } =4[/tex]
[tex]XY = \sqrt{(2- 1)^2 + (4--1)^2 } =\sqrt{26}[/tex]
[tex]YZ = \sqrt{(1- -3)^2 + (-1--1)^2 } =4[/tex]
[tex]ZW = \sqrt{(-3--2)^2 + (-1-4)^2 } =\sqrt{26}[/tex]
So, the perimeter (P) is:
[tex]P = 4 + \sqrt{26} + 4 + \sqrt{26}[/tex]
[tex]P = 8 + 2\sqrt{26}[/tex]
The perimeter of parallelogram WXYZ is 8 + 2√26 units
Perimeter of parallelogramIn order to determine the required perimeter of the parallelogram, we will use the distance formula as shown:
D= √(x2-x1)²+(y2-y1)²
Given the coordinate of the parallelogram shown as:
W(-2, 4)
X (2, 4)
Y(1, -1)
Z(-3, -1).
Since it is a parallelogram, the opposite sides are equal that is:
WX = YZ and XY = WZ
WX = YZ = √(x2-x1)²+(y2-y1)²
WX = YZ = √(2+2)²+(4-4)²
WX = YZ =√(4)²
WX = YZ = 4 units
Similarly
XY = WZ = √(2-1)²+(4+1)²
XY = WZ = √(1)²+(5)²
XY = WZ = √26
Perimeter = 2(4)+ 2(√26)
Perimeter = 8 + 2√26
Hence the perimeter of parallelogram WXYZ is 8 + 2√26 units
Learn more on perimeter of parallelogram here: https://brainly.com/question/11185474
The half life of carbon 14 is 5,730 year suppose a fossil found with 20 percent as much of its carbon 14 as compared to a living sample how old is the fossil
3,235 years
32,346 years
1331 years
13,307 years
13,305 years
Step-by-step explanation:
[tex]A = A_02^{-\frac{t}{5730}}[/tex]
Since only 20% of the original C-14 is left, then [tex]A=0.2A_0[/tex]. We can then write
[tex]0.2A_0=A_02^{-\frac{t}{5730}}[/tex]
Taking the log of both sides,
[tex]\log 0.2 = \left(-\dfrac{t}{5730}\right)\log 2[/tex]
Solving for t,
[tex]t = \dfrac{-(5730\:\text{years})\log 0.2}{\log 2}[/tex]
[tex]\:\:\:\:\:\:\:= 13,305\:\text{years}[/tex]
What is the prime factorization of 30?
O A. 2.2.3.5
O B. 5.6
O C. 3.10
O D. 2.3.5
D. 2.3.5 is the correct answer
Which choice is equivalent to(√6)( √8). How do you solve
A. 4√6
B. 4√3
C. 16√3
D. 3√16
Answer:
B
Step-by-step explanation:
(6)^1/2 × (8)^1/2
6^1/2 × 2 (2)^1/2
4 (3)^1/2
You play basketball at your school's
indoor stadium. You have two payment
options. Option A is to buy a membership
card for $20 and pay $2 each time you
go to the gym, t. Option B is to pay $4
each time you go. Write a a linear
equation to show how many trips to the
gym would the cost be the same?
Answer:
20 + 2x = 4x
Step-by-step explanation:
So you are setting the two expressions equal to each other.
buying a membership card and paying each time looks like this: 20 + 2x where x is the number of times you go to the gym. 20 dollars base then 2 each time you go.
4 each time you go is just 4x
so just set the two equal to each other.
20 + 2x = 4x
If you solve it you will get x = something, which would be the number of times to make the two equal.
if f(x)=x+8 and g(x)=-4x-3 find (f+g)(x)
Answer:
for this case we have the following functions:
f (x) = x + 8
g (x) = -4x - 3
Subtracting the functions we have:
(f - g) (x) = f (x) - g (x)
(f - g) (x) = (x + 8) - (-4x - 3)
Rewriting:
(f - g) (x) = x + 8 + 4x + 3
(f - g) (x) = 5x + 11
Answer:
D. (f - g) (x) = 5x + 11
The vector w = ai + bj is perpendicular to the line ax + by = c and parallel to the line bx - ay = c. It is also true that the acute angle between intersecting lines that do not cross at right angles is the same as the angle determined by vectors that are either normal to the lines or parallel to the lines. Use this information to find the acute angle between the lines below.
5x + 9y = 2, 7x + 2y = 1
The angle is _______ radians.
(Type an exact answer, using pi as needed)
Answer:
fgvilgiuhuikj
Step-by-step explanation:??????????????
The mean weight of the packages Joan shipped was 2.5 pounds. If Joan mailed four packages and three of them had weights of 1.8, 3.2 and 2.7 pounds, then what did the other package weigh?
Answer:
2.3 pounds
Step-by-step explanation:
First, the mean is equal to the sum divided by the number of numbers.
There are four packages, so there are four numbers. Let's say the fourth package has a weight of x. We can then write
mean = sum / number of numbers
2.5 = (1.8+3.2+2.7+x)/4
multiply both sides by 4 to remove the denominator
10 = 1.8+3.2+2.7+x
10 = 7.7 + x
subtract 7.7 from both sides to isolate the x
x = 2.3 pounds
Find the area of the geometric figure.
3 yd
3 yd
Traperoid
7 yd
Step-by-step explanation:
The question isn't clear, so I'll just give you a formula to find the area of trapezoid,
(a+b)*h/2, where a = base side, b = top side, h = height.
So, let's say two sides are 3 yd and 7 yd, and height is 3 yd, so the area becomes,
(3+7)*3/2
= 10*3/2
= 30/2
= 15 yd²
Answered by GAUTHMATH
What is the volume of the composite figure if both the height and the diameter of the cylinder are 3.5 feet? Give the exact answer and approximate to two decimal places.
Answer:
Volume of composite figure = 44.9 feet³
Step-by-step explanation:
Given:
Height of cylinder = 3.5 feet
Diameter of cylinder = 3.5 feet
Diameter of hemisphere = 3.5 feet
Find:
Volume of composite figure
Computation:
Radius of cylinder and sphere = 3.5/2 = 1.75 feet
Volume of composite figure = Volume of cylinder + Volume of hemisphere
Volume of composite figure = πr²h + (2/3)πr³
Volume of composite figure = (3.14)(1.75)²(3.5) + (2/3)(3.14)(1.75)³
Volume of composite figure = (3.14)(3.0625)(3.5) + (2/3)(3.14)(5.359375)
Volume of composite figure = 33.656875 + 11.2189583
Volume of composite figure = 44.8758
Volume of composite figure = 44.9 feet³
in a class of 50 student,35 are boys.what is the ratio of girls to boys in the class?
Answer:
15:35
Step-by-step explanation:
50-35=Girls
50-35=15
The slope of diagonal OA is ? and its equation is ?
Answer:
Slope = [tex]\frac{4}{3}[/tex]
Equation of the line → [tex]y=\frac{4}{3}x[/tex]
Step-by-step explanation:
Let the equation of diagonal OA is,
y = mx + b
Here, m = Slope of the line OA
b = y-intercept
Slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, slope of the line passing through O(0, 0) and A(3, 4) will be,
m = [tex]\frac{4-0}{3-0}[/tex]
m = [tex]\frac{4}{3}[/tex]
Since, line OA is passing through the origin, y-intercept will be 0.
Therefore, equation of OA will be,
[tex]y=\frac{4}{3}x[/tex]
what the mining of althoe
[tex]y \geqslant 3[/tex]
The question isn't well stated ; If the question intends to ask the meaning of the inequality :
Answer:
Kindly check explanation
Step-by-step explanation:
Given the inequality : y ≥ 3
This inequality statement or expression means that :
y is true for all values beginning from 3 and beyond
That is values from 3 makes the expression a true statement.
Therefore values of y for which the inequality holds or is true are :
(3,....)
Find the length of side ab, give your answer to 1 decimal place 62 and 12
Answer:
Huh? is it triangle? and right triangle? if it is its 62^2 = 12^2 + x^2
Step-by-step explanation:
Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that 110 hours will be required to complete the project. The firm's three graphic designers available for assignment to this project are Lisa, a senior designer and team leader; David, a senior designer; and Sarah, a junior designer. Because Lisa has worked on several projects for Lake View Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. To provide label designing experience for Sarah, the junior designer must be assigned at least 15% of the total project time. However, the number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers. Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18 for Sarah. (a) Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize total cost (in dollars). (Assume L is the number of hours Lisa is assigned to the project, D is the number of hours David is assigned to the project, and S is the number of hours Sarah is assigned to the project.)
Answer:
z (min) = 2079
L = 26 D = 39.6 S = 16.5
Step-by-step explanation:
L numbers of hours assigned to Lisa
D numbers of hours assigned to David
S numbers of hours assigned to Sara
Objective Function to minimize:
z = 30*L + 25*D + 18*S
Constraints:
Total time available
L + D + S ≤ 110
Lisa experience
L ≥ 0.4 * ( L + D ) then L ≥ 0.4*L + 0.4*D
0.6*L - 0.4*D ≥ 0
To provide designing experience to Sara
S ≥ 0.15*110 then S ≥ 16.5
Time for Sara
S ≤ 0.25 * ( L + D ) S ≤ 0.25*L + 0.25*D or -0.25*L - 0.25*D + S ≤0
Availability of Lisa
L ≤ 50
The Model is:
z = 30*L + 25*D + 18*S to minimize
Subject to:
L + D + S ≤ 110
0.6*L - 0.4*D ≥ 0
S ≥ 16.5
-0.25*L - 0.25*D + S ≤0
L ≤ 50
L ≥ 0 ; D ≥ 0 , S ≥ 0
After 6 iterations optimal ( minimum ) solution is:
z (min) = 2079
L = 26 D = 39.6 S = 16.5
The formula that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize the total cost is z = 30L + 25D + 18S and the minimum z is 2079.
Given :
The company estimates that 110 hours will be required to complete the project.Lisa has worked on several projects for Lake View Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers.To provide a label designing experience for Sarah, the junior designer must be assigned at least 15% of the total project time.The number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers.Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18 for Sarah.The formula that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize the total cost is given by:
z = 30L + 25D + 18S
The constraints are given by:
1) L + D + S [tex]\leq[/tex] 110
2) L [tex]\geq[/tex] 0.4(L + D)
L [tex]\geq[/tex] 0.4L + 0.4D
0.6L - 0.4D [tex]\geq[/tex] 0
3) S [tex]\geq[/tex] 0.15(110)
S [tex]\geq[/tex] 16.5
Now, to minimize 'z' then use:
[tex]\rm -0.25L-0.25D+S\leq 0[/tex]
L [tex]\leq[/tex] 50
L [tex]\geq[/tex] 0, D [tex]\geq[/tex] 0, S [tex]\geq[/tex] 0
Now, the minimum z is given by:
z = 2079
L = 26, D = 39.6, S = 16.5
For more information, refer to the link given below:
https://brainly.com/question/23017717
Find the mean or average of these savings accounts $215, $156,$318, $75, and $25
Answer:
157.8
Step-by-step explanation:
Add them all up to get 789 and divide them by 5 as there are five numbers to get the answer:)
HELP WILL MARK BRAINLIESG
Write an equation that represents the line,
Use exact numbers.
Answer:
3/2 + 7
Step-by-step explanation:
A square coffee shop has sides that are 10 meters long. What is the coffee shop's area?
square meters
100
SOLUTION:
10•10= 100
Find the distance between the two points.
(3,-9) and (-93,-37)
Answer:
100
Step-by-step explanation:
√(x2 - x1)² + (y2 - y1)²
√(-93 - 3)² + [-37 - (-9)]
√(-96)² + (-28)²
√9216 + 784
√10000
= 100
Write the ratio 4 3/5 to 1 1/5 as a fraction in lowest terms
Answer:
23/6
Step-by-step explanation:
Given fractions
4 3/5 to 1 1/5
Write 4 3/5 as improper fraction= 23/5
Write 1 1/5 as improper fraction= 6/5
Then find the ratio
23/5 : 6/5
Ratio is finding division of two terms
(23/5) / (6/5)
= 23/5 × 5/6
5 at the denominator cancel out 5 at numerator then we have
= 23/6
Hence, fraction in lowest terms here is
23/6
Your money grows at a rate of 8% a year if you originally invest $2,000 what is the function that represents your money after t years
Answer:
2000*(1.08)^t where t is years after deposit
Step-by-step explanation:
What is the following product? Assume d>0 3vd•3vd•3vd
Answer:
A. d
Step-by-step explanation:
If you find the 3rd square root or whatever its called, and multiply it by itself again 3 times, You end up with d again.
a+in=√1+i÷1-i,prove that a^2+b^2=1
Answer with Step-by-step explanation:
We are given that
[tex]a+ib=\sqrt{\frac{1+i}{1-i}}[/tex]
We have to prove that
[tex]a^2+b^2=1[/tex]
[tex]a+ib=\sqrt{\frac{(1+i)(1+i)}{(1-i)(1+i)}}[/tex]
Using rationalization property
[tex]a+ib=\sqrt{\frac{(1+i)^2}{(1^2-i^2)}}[/tex]
Using the property
[tex](a+b)(a-b)=a^2-b^2[/tex]
[tex]a+ib=\sqrt{\frac{(1+i)^2}{(1-(-1))}}[/tex]
Using
[tex]i^2=-1[/tex]
[tex]a+ib=\frac{1+i}{\sqrt{2}}[/tex]
[tex]a+ib=\frac{1}{\sqrt{2}}+i\frac{1}{\sqrt{2}}[/tex]
By comparing we get
[tex]a=\frac{1}{\sqrt{2}}, b=\frac{1}{\sqrt{2}}[/tex]
[tex]a^2+b^2=(\frac{1}{\sqrt{2}})^2+(\frac{1}{\sqrt{2}})^2[/tex]
[tex]a^2+b^2=\frac{1}{2}+\frac{1}{2}[/tex]
[tex]a^2+b^2=\frac{1+1}{2}[/tex]
[tex]a^2+b^2=\frac{2}{2}[/tex]
[tex]a^2+b^2=1[/tex]
Hence, proved.
The population of a city this year is 200,000. The population is expected to increase by 2.5% per year over the next 10 years. Which exponential equation models this situation?
Answer:
[tex]A = 200,000(1+.025) ^{t}[/tex]
[tex]A = 200,000(1+.025) ^{10}[/tex]
Step-by-step explanation:
Solve the equation 2sin^2(x) = 1 for x ∈ [-π,π], expressing all solutions as exact values. please help its urgent !!
Answer:
2sin.2(x) sd s
Step-by-step explanation:
سا (a) From the definition of derivatives determine dy÷dx if y = -2÷x
Step-by-step explanation:
Given: [tex]y = -\dfrac{2}{x}[/tex]
Derivative of a power function [tex]x^n[/tex]:
[tex]\dfrac{d}{dx}(x^n) = nx^{n-1}[/tex]
Therefore,
[tex]\dfrac{dy}{dx}=-2(-1)x^{-2} = \dfrac{2}{x^2}[/tex]
