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 swimming pool is circular with a 20-ft diameter. The depth is constant along east-west lines and increases linearly from 1 ft at the south end to 6 ft at the north end. Find the volume of water in the pool. (Round your answer to the nearest whole number.)
Answer:
1100 ft³
Step-by-step explanation:
Use the formula for the volume of a cylinder. For height, use the average of the minimum and maximum depths.
V = πr²h
r = d/2 = 20 ft/2 = 10 ft
h = (1 ft + 6 ft)/2 = 3.5 ft
V = π(10 ft)²(3.5 ft)
V = 1100 ft³
On a coordinate plane, a line goes through points (negative 1, 0), (0, 1), and (1, 2). Which table goes with the graph?
Answer:
Table B
Step-by-step explanation:
correct on edge :)
Would you rather?
buy 2 lollypops for $2
buy 30 lollypops for $40
Answer:
Buy 2 lollipops for $2.
Step-by-step explanation:
If you divide the total price by total items purchased, you get the price per unit. 2/2=1 or around $1, while 40/30=4/3 or around $1.3. You are paying 1$ per lollipop for the 2 lollipop choice and paying 1.3 dollars per lollipop for the 30 lollipop choice.
Convert 1.5% to decimal and a fraction. Show and explain your method.
Answer:
0.015
Step-by-step explanation:
1.5% = means 1.5 per 100 or simply 1.5/100.if you divide 1.5 by 100 you will get 0.015
Deon bought a desk on sale for $105.60. This price is 67% less than the original price. What was the original price?
Answer:
.33x = 105.60
$371
Step-by-step explanation:
Answer:
63.44
Step-by-step explanation:
its 63.44697 but you round so its 63.44
need help with algebra problem
Answer:
[tex]option \: d \: 4.2 \times {10}^{ - 3} [/tex]
Step-by-step explanation:
Multiplication,
[tex] = 8.4 \times {10}^{ 8 } \times 5 \times {10}^{ - 11} \\ = 8.4 \times 5 \times {10}^{8 + ( - 11)} \\ = 4.2 \times {10}^{8 - 11} \\ = 4.2 \times {10}^{ - 3} [/tex]
in a school there are 650 girls. It is 26% of the whole students, how many boys are there in the school?
Answer:
Step-by-step explanation:
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help please i don't know how to do this
If a projectile is fired with an initial speed of vo ft/s at an angle α above the horizontal, then its position after t seconds is given by the parametric equations x=(v0cos(α))t andy=(v0sin(α))t−16t2
(where x and y are measured in feet).
Suppose a gun fires a bullet into the air with an Initial speed of 2048 ft/s at an angle of 30 o to the horizontal.
(a) After how many seconds will the bullet hit the ground?
(b) How far from the gun will the bullet hit the ground? (Round your answer to one decimal place.)
(c) What is the maximum height attained by the bullet? (Round your answer to one decimal place.)
Answer:
a) The bullet hits the ground after 64 seconds.
b) The bullet hits the ground 113,511.7 feet away.
c) The maximum height attained by the bullet is of 16,384 feet.
Step-by-step explanation:
Equations of motion:
The equations of motion for the bullet are:
[tex]x(t) = (v_0\cos{\alpha})t[/tex]
[tex]y(t) = (v_0\sin{\alpha})t - 16t^2[/tex]
In which [tex]v_0[/tex] is the initial speed and [tex]\alpha[/tex] is the angle.
Initial speed of 2048 ft/s at an angle of 30o to the horizontal.
This means that [tex]v_0 = 2048, \alpha = 30[/tex].
So
[tex]x(t) = (v_0\cos{\alpha})t = (2048\cos{30})t = 1773.62t[/tex]
[tex]y(t) = (v_0\sin{\alpha})t - 16t^2 = (2048\sin{30})t - 16t^2 = 1024t - 16t^2[/tex]
(a) After how many seconds will the bullet hit the ground?
It hits the ground when [tex]y(t) = 0[/tex]. So
[tex]1024t - 16t^2 = 0[/tex]
[tex]16t^2 - 1024t = 0[/tex]
[tex]16t(t - 64) = 0[/tex]
16t = 0 -> t = 0 or t - 64 = 0 -> t = 64
The bullet hits the ground after 64 seconds.
(b) How far from the gun will the bullet hit the ground?
This is the horizontal distance, that is, the x value, x(64).
[tex]x(64) = 1773.62(64) = 113511.7[/tex]
The bullet hits the ground 113,511.7 feet away.
(c) What is the maximum height attained by the bullet?
This is the value of y when it's derivative is 0.
We have that:
[tex]y^{\prime}(t) = 1024 - 32t[/tex]
[tex]1024 - 32t = 0[/tex]
[tex]32t = 1024[/tex]
[tex]t = \frac{1024}{32} = 32[/tex]
At this instant, the height is:
[tex]y(32) = 1024(32) - 16(32)^2 = 16384[/tex]
The maximum height attained by the bullet is of 16,384 feet.
What is the amount f rainfall that Miami receives, round to the nearest half or whole? 55 9/10"
Answer:
56"
Step-by-step explanation:
Date Page The male population of a village is 9840 and the female population is 8965. Find the total population of the village ii) How many more males are there than females
Find the limit of f as or show that the limit does not exist. Consider converting the function to polar coordinates to make finding the limit easier. f(x,y)
Answer:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]
Step-by-step explanation:
Given
[tex]f(x,y) = \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]
Required
[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex]
[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex] becomes
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]
Multiply by 1
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}\cdot 1[/tex]
Express 1 as
[tex]\frac{y^2}{y^2} = 1[/tex]
So, the expression becomes:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} \cdot \frac{y^2}{y^2}[/tex]
Rewrite as:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} \cdot \frac{\sin^2y}{y^2}[/tex]
In limits:
[tex]\lim_{(x,y) \to (0,0)} \frac{\sin^2y}{y^2} \to 1[/tex]
So, we have:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} *1[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2}[/tex]
Convert to polar coordinates; such that:
[tex]x = r\cos\theta;\ \ y = r\sin\theta;[/tex]
So, we have:
[tex]\lim_{(x,y) \to (0,0)} \frac{(r\cos\theta)^2 (r\sin\theta;)^2}{(r\cos\theta)^2+2(r\sin\theta;)^2}[/tex]
Expand
[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2\cos^2\theta+2r^2\sin^2\theta}[/tex]
Factor out [tex]r^2[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2(\cos^2\theta+2\sin^2\theta)}[/tex]
Cancel out [tex]r^2[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]
Express [tex]2\sin^2 \theta[/tex] as [tex]\sin^2\theta+\sin^2\theta[/tex]
So:
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+\sin^2\theta+\sin^2\theta}[/tex]
In trigonometry:
[tex]\cos^2\theta + \sin^2\theta = 1[/tex]
So, we have:
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]
Evaluate the limits by substituting 0 for r
[tex]\frac{0^2 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]
[tex]\frac{0 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]
[tex]\frac{0}{1+\sin^2\theta}[/tex]
Since the denominator is non-zero; Then, the expression becomes 0 i.e.
[tex]\frac{0}{1+\sin^2\theta} = 0[/tex]
So,
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]
jimmy had twice as many oranges as grapefruit, 5 more grapefruits than pineapples, how many of each fruit did jimmy have?
Answer:
Step-by-step explanation:
I think he has 7 oranges and 5 grapefruit and ten pineapples
What is the value of x in the triangle?
Answer:b
Step-by-step explanation:
Ive done this
it is estimated that 50% of emails are spam emails. Some software has been applied to filter these spam emails before they reach your inbox. A certain brand of software claims that it can detect 99% of spam emails and the probability for a flase positive is 5%. What is the probability that an email is detected as spam
Answer:
0.52 = 52% probability that an email is detected as spam.
Step-by-step explanation:
Probability that an email is detected as spam:
99% of 50%(are spam).
5% of 100 - 50 = 50%(false positives, that is, e-mails that are not spam but are detected as spams).
What is the probability that an email is detected as spam?
[tex]p = 0.99*0.5 + 0.05*0.5 = 0.52[/tex]
0.52 = 52% probability that an email is detected as spam.
Two cell phone companies charge a flat fee plus an added cost for each minute or part of a minute used. The cost is represented by C and the number of minutes is represented by t.
Call-More: C = 0.40t + 25 Talk-Now: C = 0.15t + 40
Answer:
The call more is cheaper than talk-now.
Step-by-step explanation:
The companies charge a flat fee plus an added cost for each minute or part of a minute used for two companies are as follows :
Call-More: C = 0.40t + 25 Talk-Now: C = 0.15t + 40
We need to find which company is cheaper if a customer talks for 50 minutes.
For call more,
C = 0.40(50) + 25 = 45 units
For talk-now,
C = 0.15(50) + 40 = 47.5 units
So, it can be seen that call more is cheaper than talk-now.
How many fixed-requirement constraints does a transportation problem with 5 factories and 6 customers have?a. 30.b. 11.c. 6.d. 5.
Answer:
Option B
Step-by-step explanation:
From the question we are told that:
Demand point [tex]m=5[/tex]
Supply Point [tex]n=6[/tex]
Generally the equation for fixed-requirement constraints is mathematically given by
[tex]X=m+n[/tex]
[tex]X=5+6[/tex]
[tex]X=11[/tex]
Therefore the correct option is
Option B
I need help pls!! 20 points I need it!!
Answer: About 6.71 units
Step-by-step explanation:
You use the distance formula: [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex].
Assign the the two points to the variables:
[tex](x_{1}, y_{1}) = (1, 3)\\(x_{2}, y_{2}) = (4, -3)[/tex]
Substitute them in the formula:
[tex]\sqrt{(4-1)^{2}+(-3-3)^{2}}[/tex]
And solve it:
[tex]\sqrt{(4-1)^{2}+(-3-3)^{2}}\\=\sqrt{(3)^{2}+(-6)^{2}}\\=\sqrt{9+36}\\=\sqrt{45}\\=6.71[/tex]
Answer:
I got the answer as 6.70 .here's how
Step-by-step explanation:
c= ( 1,3)
d=(4,-3)
Now , formula of distance
√(x2 - x1)^2 +(y2 - y1)^2
or, √(4-1)^2+(-3-3)^2
or, √(3)^2+(-6)^2
or,√9+36
or√45
√45 = 6.70 units approx
Anyone know this question?
Answer:
All of these
Step-by-step explanation:
Given
[tex]f(5) = 11[/tex]
[tex]f(x)[/tex] at [tex](5,11)[/tex]
Required
Interpret
[tex]f(5) = 11[/tex] mean that: the function is at [tex](5,11)[/tex]
In other words:
[tex]x = 5; y = 11[/tex]
It also means:
Substitute 5 for x and the result will be 11
Hence, all options are true
5x5+90
I honestly have no idea wth this answer is . Please help meeee
The standard form of an absolute value function is R(x) = a|x-h|+k Which of the following represents the vertex?
o (-k,h)
o (-1,K)
o (k,h)
o (h,k)
Answer:
o (h,k)
Step-by-step explanation:
The top and bottom ends of a windshield wiper blade are R = 24 in. and r = 14 in., respectively, from the pivot point. While in operation, the wiper sweeps through 135°. Find the area swept by the blade. (Round your answer to the nearest whole number.)
Answer:
Area swept by the blade = 448[tex]in^{2}[/tex]
Step-by-step explanation:
The arc the wiper wipes is for 135 degrees angle.
So, find area of sector with radius 24 inches. And the find area of arc with r=14 inches.
Then subtract the area of sector with 14 inches from area of sector with radius as 24 inches.
So, area of sector with r=24 in =[tex]\frac{135}{360} *\pi *24^{2}[/tex]
Simplify it,
=216[tex]\pi[/tex]
Now, let's find area of sector with radius 14 inches
Area of sector with r=14 in = [tex]\frac{135}{360} *\pi *14^{2}[/tex]
Simplify it
=73.5[tex]\pi[/tex]
So, area swept by the blade = 216[tex]\pi[/tex] -73.5[tex]\pi[/tex]
Simplify it and use pi as 3.14.....
Area of swept =678.584 - 230.907
=447.6769
Round to nearest whole number
So, area swept by the blade = 448[tex]in^{2}[/tex]
What is the common ratio of the sequence? -2, 6, -18, 54,...
a.-3
b.-2
c.3
d.8
Answer:
a. -3
Step-by-step explanation:
-2 turns into 6 by multiplying it by -3.
the same from 6 to -18, from -18 to 54, ...
so, an/an+1 = -3
Feedback:Correct answer
Question 2 of 10
10.0 Points
3
Find the interquartile range for a data set having the five-number
summary: 4.6, 14.3, 19.7, 26.1, 31.2
A. 26.6
B. 11.8
C. 11.5
D. 15.1
(URGENT!!) Which graph models the function f(x) = -4(2)x? (2 points)
Answer:
2nd Graph
Step-by-step explanation:
Bases off the graphs, you gave me, I assume your the equation is
[tex]f(x) = - 4(2) {}^{x} [/tex]
The parent equation of this function is
[tex]f(x) = b {}^{x} [/tex]
Let say x=0
Using the rules of exponets, the y value must be 1 so a critical point is
(0,1)
The function is multiplied by -4.
This means the function is stretched in the y direction by 4 and reflected over the x axis. So our new point will be
(0,-4).
The base 2 the function will get compressed by 1/2.
The best graph that represents this is the second graph
Find the equation of the lines in problem 1 (0,0) slope =2.
Answer:
y = 2x
Step-by-step explanation:
Given that , the line passes through the point (0,0) and has a slope of 2. So here we can use the point slope form of the line as ,
[tex]\implies y- y_1 = m( x - x_1) \\\\\implies y - 0 = 2( x - 0 ) \\\\\implies y = 2(x) \\\\\implies \underline{\underline{y = 2x }}[/tex]
5. A cylindrical pipe is placed in a rectangular trench that is 5m x 4m
and 2.5m deep, is placed across the shorter side of the trench.
5.1 How much volume of cement will be needed to cover this hollow
pipe?
Answer:
The volume (density) of cement that will be needed to cover this hollow pipe is:
= 50,000 kg/m³
Step-by-step explanation:
Length of a cylindrical pipe = 5m
Width of the cylindrical pipe = 4m
Depth of the cylindrical pipe = 2.5m
The cubic meters of the cylindrical pipe = 5 * 4 * 2.5 = 50m³
1 cubic meter is equal to 1,000 kilogram
Therefore, the volume (density) of cement that will be needed to cover this hollow pipe is:
= 50 * 1,000
= 50,000 kg/m³
In the xy-plane, the slope of the line y = mx − 4 is
less than the slope of the line y = x − 4. Which of the
following must be true about m?
[Show Workings}
I will give brainlist to the person with the right
If the slope of the line y = mx − 4 is less than the slope of the line y = x − 4, this shows that m will be any values less than 1 i.e. m < 1. This gives a true statement
The slope of a line defines the steepness of such a line. It is the ratio of the rise to the run of a line.
The general formula for calculating an equation of a line is expressed as:
[tex]y = mx + b[/tex] where:
m is the slope of the line
Given the equation of the line, [tex]y=x-4[/tex] the slope of the line will be derived through comparison as shown:
[tex]mx=1x\\[/tex]
Divide through by x
[tex]\dfrac{mx}{x} = \dfrac{1x}{x}\\ m=1[/tex]
Hence the slope of the line y = x - 1 is 1.
According to the question, since we are told that the slope of the line
y = mx − 4 is less than the slope of the line y = x − 4, this shows that m will be any values less than 1 i.e. m < 1. This gives a true statement
Learn more about the slope of a line here: https://brainly.com/question/16949303
Answer:
Step-by-step explanation:
Applying the translation (x, y) - (x - 3, y + 7) maps the point (-4,7) onto the point
9
O A) (14, -7)
12
B) (7, -14)
15
C) (14, 7)
D) (-7, 14)
Answer: Choice D. (-7, 14)
Work Shown:
[tex](x,y) \to (x-3, y+7)\\\\(-4,7) \to (-4-3, 7+7)\\\\(-4,7) \to (-7, 14)\\\\[/tex]
The point has moved 3 units to the left and 7 units up. See the diagram below.
Recall the creative calligraphy case we discussed in class. Suppose you have received a rush order of 55 invitations that have to be created in the next (four hour) work session. What is the most time You (i.e. not Susie) can spend writing on the card and envelope for each invitation and still fill the order
Answer:
About 4 minutes and 3 seconds
Step-by-step explanation:
If I have 55 invitations to be created in four hours.
4 hours × 60 =240 minutes
240/55= 4.36 minutes
So if I spend 4 minutes and 3 seconds on an invitation, I should be able to fill the order.
