Answer:
a. 2in
b. [tex]l(t)=0.002t^{3}-0.06t^{2}+0.87t+2cos(\frac{\pi}{12}t)+38[/tex]
c. l'(3)=0.1938 in/hr
Step-by-step explanation:
a.
In part a, the problem is asking us to find how much snow will melt during the 6 hour period. In order to do so we need to take the M(t) function and integrate it in the given period of time, so we get:
[tex]\int\limits^6_0 {\frac{\pi}{6}sin(\frac{\pi}{12}t)} \, dt[/tex]
So now we solve:
[tex]\frac{\pi}{6}\int\limits^6_0 {sin(\frac{\pi}{12}t)} \, dt[/tex]
this is a known integral, so we get:
[tex]\frac{\pi}{6}[-\frac{12}{\pi}cos(\frac{\pi}{12}t)]^{6}_{0}[/tex]
we can simplify this so we get:
[tex]-2[cos(\frac{\pi}{12}t)]^{6}_{0}[\tex]
[tex]-2[cos(\frac{\pi}{12}(6))-cos(\frac{\pi}{12}(0))][/tex]
[tex]-2[cos(\frac{\pi}{2})-cos(0)][/tex]
[tex]-2[0-1][/tex]
2 in
b)
For part b they want us to write an expression for l(t), the total number of inches of snow at any time t.
in order to do so we need to find an expression for the rate of change of snow. A snowmaker is adding some snow while another amountn of snow is melting, so this rate of change is found by subtracting the two functions, so we get:
l'(t)=S(t)-M(t)
so:
[tex]l(t)=\int {(0.006t^{2}-0.12t+0.87-\frac{\pi}{6}sin(\frac{\pi}{12}t))} \, dt[/tex]
so we integrate this to get:
[tex]l(t)=\frac{0.006}{3}t^{3}-\frac{0.12}{2}t^{2}+0.87t+2cos(\frac{\pi}{12}t)+C[/tex]
and we can simplify this:
[tex]l(t)=0.002t^{3}-0.006t^{2}+0.87t+2cos(\frac{\pi}{12}t)+C[/tex]
so now we need to find what C is equal to, we can use the fact that l(0)=40in so we get:
[tex]40=0.002(0)^{3}-0.006(0)^{2}+0.87(0)+2cos(\frac{\pi}{12}(0))+C[/tex]
which yields:
40=2+C
so
C=40-2
C=38
So the final function is:
[tex]l(t)=0.002t^{3}-0.06t^{2}+0.87t+2cos(\frac{\pi}{12}t)+38[/tex]
c)
for part c we need to find the rate of change of the total amount of snow at time t=3, so in this case we can use the equation we found previously:
l'(t)=S(t)-M(t)
[tex]l'(t)=(0.006t^{2}-0.12t+0.87-\frac{\pi}{6}sin(\frac{\pi}{12}t))[/tex]
and substitute t=3
[tex]l'(3)=(0.006(3)^{2}-0.12(3)+0.87-\frac{\pi}{6}sin(\frac{\pi}{12}(3)))[/tex]
which yields:
l'(t)=0.1938 in/hr
(2127*34534) : 122
pls need help
Answer:
36726909: 61
Step-by-step explanation:
2127 * 34534 = 73453818
therefore 73453818: 122
divide both sides to the simplest form
36726909: 61
Write an equation of the line with the given slope and y-intercept: m = -5,b=4
a. y = -5x + 4
b. y = 5x + 4
c. y= -57-4
d. y = 5x-4
Please select the best answer from the choices provided
Answer:
A.
I hope this will be useful
3b - 2a -9 when a =1/2 and b= 7
Answer: 11
Step-by-step explanation:
1. Evaluate 2a when a = 1/2
2a
2 x (1/2) = 1
2. Evaluate 3b when b = 7
3b
3x7 = 21
3. Put the pieces of the expression back together
21 - 1 -9
4. Solve
11
HELPPPP 69 POINTS!!!!
△FGH is translated up 2 units to form the image ∆F′G′H′.
What are the coordinates of the vertices of ∆F′G′H′ ?
Enter your answer by filling in the boxes.
F′ = ( , )
G′ = ( , )
H′ = ( , )
Answer:
I hope the Picture Helps!
Step-by-step explanation:
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The required coordinates of the vertices of ∆F′G′H′ is F' = (-5, 2), G'= (0, 2), and H' = (0, 6).
What is coordinate?Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.
As mentioned in the question, a given triangle on coordinate axes translated 2 units up. The term "2 unit up" implies that each ordinate of the coordinates of the triangle is increased by 2 units,
So the trasformation equation for the triangle is given as,
(x, y) ⇒ (x, y+2)
Now, the coordinates of the vertices of ∆FGH,
F = (-5, 0), G= (0, 0) H = (0, 4)
After the trasformation coordinate of ∆F′G′H′
F' = (-5, 0 + 2), G'= (0, 0 + 2) H' = (0, 4 + 2)
F' = (-5, 2), G'= (0, 2) H' = (0, 6)
Thus, the required coordinates of the vertices of ∆F′G′H′ is F' = (-5, 2), G'= (0, 2), and H' = (0, 6).
Learn more about coordinate here:
brainly.com/question/13498438
#SPJ2
ahdjfvjxbxnxjzjsjnsmsnsns
Answer:
b sorry if wrong
Step-by-step explanation:
Tatiana earns money by babysitting her little cousin. When she babysits for 2 hours she earns $27. When she babysits for 7 hours she earns $94.50. Which equation represents her total wages based on the hours that she works?
Answer:
36$
Step-by-step explanation:
I took the test
Who ever Answers first gets a good review
Answer:
Do we do all of them???
Step-by-step explanation:
If the ribbon cost 10￠ (0.10) per foot, what is the total cost of the ribbon in Dollars? Explain your reasoning.
Answer:
How many feet are you going to buy that is the real question.
Step-by-step explanation:
It depends on how many feet you buy.
Simplify the given polynomial expressions, and determine the degree and number of terms in each expression
Answer: What is the "given polynomial expressions?"
A 100-square grid has 70 shaded squares. Explain how you could express this model as a fraction, percent, and decimal
Answer:
the answer would be 70/100 in fraction form, 70% in percent, and (i believe) 0.7 min decimal form. Hope this helps!
Answer:
70 out of 100 is the ratio 70 Over 100 apostrophe , so it represents 70%. 70 Over 100 can be reduced by dividing the numerator and the denominator by 10 to get the reduced fraction 7 Over 10. Dividing 7 by 10 results in the decimal equivalent 0.70.
Step-by-step explanation:
Which best illustrates the distinction between statistical significance and practical importance?
A. In 2016, 240 out of 400 statistics students at Oxnard Technical College sold their textbooks at the end of the semester, compared with 220 out of 330 students in 2015, a significant decrease.
B. Our new manufacturing technique has increased the life of the 80 GB USB AsimoDrive external hard disk significantly, from 240,000 hours to 250,000 hours.
C. In 50,000 births, the new vaccine reduced the incidence of infant mortality in Morrovia significantly from 14.2 deaths per 1000 births to 10.3 deaths per 1000 births.
D. The new Sky Penetrator IV business jet's cruising range has increased significantly from 3,975 miles to 4,000 miles.
Answer:
The distinction between statistical significance and practical importance is best illustrated by:
C. In 50,000 births, the new vaccine reduced the incidence of infant mortality in Morrovia significantly from 14.2 deaths per 1000 births to 10.3 deaths per 1000 births.
Step-by-step explanation:
Current state Previous state Change
A. Textbooks sold 240/400 (0.6) 220/330 (0.67) 0.07
B. Life of hard disk 250,000 hrs 240,000 hrs 0.04
C. Infant mortality 10.3 per 1000 14.2 per 1000 0.27
D. Cruising range 4,000 miles 3,975 miles 0.006
Statistical significance, which depends on the p-value established before the test, relates to whether an effect exists, while practical significance determines the magnitude or size of the effect. A statistical test cannot tell whether the magnitude is large enough to be important. Mathematically, the change can be determined, which establishes the practical significance or importance of the change.
need help with this please!!
Answer:
a 1/4 cuz perpendicular m × m original line is -1
us
Solve for x using the
distributive property.
8(4 + 2x) = 16
Answer: x=-1
Step-by-step explanation:
Do 8(4) + 8(2x)=16 to use the distributive property. You should get 32+16x=16. Then, subtract 32 from both sides of the equation and you will get 16x=-16. Finally, divide both sides of the equation by 16 and you will get you answer, x=-1. Hope I helped.
a. [-1, 1]
b. [0, pi]
c. [-pi/2, pi/2]
d. -♾, ♾]
f(x) = sin(x)
Domain (–∞, ∞)
Range [–1, 1]
y = arcsine(x)
y = f–¹(x)
Domain [–1, 1]
Range [–π/2, π/2]
Determine the value of w, then x, then y, and finally z.
Answer:
w 20x35y try to make it work
Chloe invests money in an account paying simple interest. She invests $200 and no money is added or removed from the investment. After one year, she has $204. What is the simple percent interest per year?
Answer:
2%
Step-by-step explanation:
Chloe's simple interest for 1 year is $4. You can get this by subtracting the amount she invested from the total amount she got after one year.
$204 - $200 = $4Now that we know the simple interest, we can now get the simple interest rate or simple percent interest per year by dividing $4 by $200.
$4 ÷ $200 = 0.02Let's change 0.02 into a percentage.
0.02 x 100 = 2%This means that every year, her investment will earn a 2% simple interest.
Answer:
2%
Step-by-step explanation:
can somebody pls help
I need the answer quickly. 6(3-2)/6
Answer:
I think the answer would be 1
Step-by-step explanation:
1 is the answer
3-2=1
6(1)=6
6/6=1
Music Magic offers live streaming for $9.99 a month, with downloads at $0.50 a song. You have $30 a month budgeted for this service. The equation 0.5s + 9.99 = 30 describes the situation. The solution to this equation is s = 40.02. Explain what this means in terms of service.
Step-by-step explanation:
$30 a month budget includes:
$9.99 monthly fee$20.01 to download songs, each for $0.50, this makes $20.01/$0.50 = 40.02 songs. So we can download 40 songs with this service.Previous
1
Next
Solving Real-World Problems involving Rational Numbers: Mast Submit Test
Tools
Info
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
A rectangle is 12 feet long and 5 feet wide. If the length of the rectangle is increased by 25% and the width is decreased by 20%, what is the change in
the area of the rectangle?
The change in the area of the rectangle is
square feet
Reset
Next
No change in area
Step-by-step explanation:
The area is 60 square feet for both rectangles.
Answer:
0 square feet
Step-by-step explanation:
i got it right
Calculate the federal income taxes. In 1980, the federal income tax was 14 percent on incomes between $2,300 and $3,400 per year, 16 percent
on incomes between $3,400 and $4,400 per year, and 21 percent on incomes between $8,500 and 10,800 per year. In 1980, you made $3,000.
What was your income tax this year?
O $42.00
O $420
$480
$630
Answer: 420
Step-by-step explanation: 14 percent of 3000 is 420
Correct Answer: $420
Corbin is selling cheese at the farmers’ market. One wheel of cheese has a diameter of 11 inches.
Part A Calculate the area of the wheel of cheese. Use 3.14 for π.
Part B
If the 11-inch wheel of cheese costs $21.35, what is the cost per square inch?
Pls help me, I’m desperate lm.ao
its been so long and no one is answering ??? xD
Answer:
I. 94.99 in²
II. $0.23
Step-by-step explanation:
Given the following data;
Diameter of wheel = 11 inches
[tex] \pi = 3.14[/tex]
Cost of wheel = $21.35
[tex] Radius, r = \frac {diameter}{2} [/tex]
[tex] Radius, r = \frac {11}{2} = 5.5 \; inches [/tex]
Part A
To find the area;
We know that a wheel is circular in nature. Thus, the area of a circle is given by the formula;
[tex] Area, A = \pi r^{2} [/tex]
Substituting into the equation, we have;
[tex] Area, A = 3.14 * 5.5^{2} [/tex]
[tex] Area, A = 3.14*30.25[/tex]
Area, A = 94.99 in²
Part B
To find cost per square inch;
[tex] Cost \; per \; square \; inch = \frac {Cost \; per \; wheel}{Area \; of \; wheel} [/tex]
[tex] Cost \; per \; square \; inch = \frac {21.35}{94.99} [/tex]
Cost per square inch = $0.23
8 Susie has 1 cup of ice cream. How many 9 4 cup servings can she make? 0 alo c 9 32 G over 8 0012 15
Answer: c. 3 and 5 over 9
Step-by-step explanation:
There is a 8/9 cup of ice cream. The number of 1/4 cup servings that can be made from this is:
= 8/9 ÷ 1/4
= 8/9 * 4/1
= 32/9
= 3⁵/₉ cups
Triangle ABC is similar to triangle ADE. Find x, the distance from point B to point C.
Answer:
30 feet^2
Step-by-step explanation:
eeeeet eeeees what eeeeet eeeees
Write the ratio of the first measurement to the second measurement. Compare in millimeters.
diameter of ball A:30mm
diameter of ball B: 5.7 cm
The ratio of the diameter of ball A to the diameter of ball B is-
Answer:
The ratio of the diameter of ball A to the diameter of ball B is 10:19.
Step-by-step explanation:
Ratios
A ratio is a relation between two quantities and it's calculated as a division. For example, the ratio between 8 and 4 is 8:4 = 8 / 4 = 2.
We are given the diameters of two balls as follows:
The diameter of the ball A=30mm
The diameter of the ball B=5.7 cm = 57 mm
The ratio of the diameter of ball A to the diameter of ball B is 30:57. Dividing both numbers by 3, we have: ratio=10:19
The ratio of the diameter of ball A to the diameter of ball B is 10:19.
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations and inequalities about the y-axis.x2 - y2 = 64, x \geq 0, y = -8, y = 8
Answer:
The Volume of the solid
V = π(1365.33) cubic units
Step-by-step explanation:
Step(I):-
Given curves are x²- y² = 64 , x=0 , y=-8 and y=8
The given function x = f(y)
x²- y² = 64
x² = y² +64
The Volume of the solid generating by revolving the region bounded by the graphs of the equations
[tex]V = \pi \int\limits^a_b {x^2} \, dx[/tex]
Step(ii):-
the limits are y = a = -8 and y = b=8
The Volume of the solid
[tex]V =\pi \int\limits^8_8 {(y^2+64)} \, dx[/tex]
[tex]V = \pi (\frac{y^{3} }{3} + 64 y )_{-8} ^{8}[/tex]
[tex]V = \pi (\frac{(8)^{3} }{3} + 64 (8) - (\frac{(-8)^{3} }{3} +64(-8) )[/tex]
[tex]V = \pi (\frac{(8)^{3} }{3} + 64 (8) - (\frac{(-8)^{3} }{3} +64(-8) ) = \pi (\frac{1024}{3} + 1024)[/tex]
V = π(1365.33) cubic units
How to divide with partial quotiants?
Answer:
You can search it up on Gxogle! It will tell you step by step.
"Step 1: Write a list of easy facts for the divisor.
Step 2: Subtract from the dividend an easy multiple of the divisor (e.g. 100x, 10x, 5x, 2x). Record the partial quotient in a column to the right of the problem.
Step 3: Repeat until the dividend has been reduced to zero or the remainder is less than the divisor."
I hope this helped!

A and B are equidistant from the line l. How many circles can be drawn with their centres on line l and that pass through both A and B?
A. 1
B. 2
C. 3
D. 4
E. >10
Answer:
just one.. so A
Step-by-step explanation:
2.865 in expanded form
Answer: 2.865
Step-by-step explanation:
Plz Help fast WILL MARK BRAINLIEST