Answer:
Step-by-step explanation:
I'm going to go through this as I would when teaching it to my students for the first time. This is a super simple one, so it shouldn't be too hard. Begin with what you know:
A snowball is a sphere. Since we are told that the surface area is changing (decreasing, to be exact), it would make sense to know the formula for the surface area of a sphere:
[tex]S=4\pi r^2[/tex] where r is the radius. Let's take the derivative of this using implicit differentiation to see what it is we need to solve this:
[tex]\frac{dS}{dt}=4\pi*2r\frac{dr}{dt}[/tex], where dr/dt is the rate at which the radius is changing. If we look at the problem, we are looking for the rate at which the DIAMETER is changing. So instead of using the radius in the original formula, we need to write it in terms of the diameter. We know that
d = 2r so
[tex]r=\frac{d}{2}[/tex] and we will put that into the formula for r to get:
[tex]S=4\pi(\frac{d}{2})^2[/tex] and simplify a bit:
[tex]S=4\pi(\frac{d^2}{4})[/tex] and the 4's cancel each other out, leaving us with simply:
[tex]S=\pi d^2[/tex] Now let's take the derivative:
[tex]\frac{dS}{dt} =\pi 2d\frac{dD}{dt}[/tex] where the rate of the surface area is -8 ("decreasing" rate makes this number a negative) when the diameter is 11. Filling in:
[tex]-8=\pi(2)(11)\frac{dD}{dt}[/tex] and solving for the rate at which the diameter is changing:
[tex]\frac{dD}{dt}=-\frac{8}{22\pi}[/tex] , which rounds to
[tex]\frac{dD}{dt}=-1.142\frac{cm}{min}[/tex] and again, the negative means that the diameter is decreasing.
Solve for x using the
distributive property.
6(2 - 6x) = -24
X ?
⇛6(2 - 6x) = -24
⇛12 - 36x = -24
⇛-36x = -24 - 12
⇛-36x = -36
⇛x = -36/-36
⇛x = 1
pls halllllllpppppppp
Answer:
85 degrees
Step-by-step explanation:
To find the range, take the high temperature and subtract the low temperature
40 - -45
40 + 45
85
The range is 85 degrees
Answer:
85
Step-by-step explanation:
The definition of range is the subtraction between the highest and lowest numbers.
In this problem, there are only two numbers so they will be subtracted.
40 - -45
40 + 45 = 85
The range is 85.
Hope this helped.
Find the surface area of a rectangular prism with a height of 16 feet, a width of 10 feet, and a length of 13 feet.
988 ft2
996 ft2
980 ft2
1000 ft2
Answer: 996 ft2
Step-by-step explanation:
Add up the area of all 6 sides of the prism:
(10 · 13) + (10 · 13) + (10 · 16) + (10 · 16) + (16 · 13) + (16 · 13)
= 130 + 130 + 160 + 160 + 208 + 208
=996 ft²
Answer:
B) 996 ft2
Step-by-step explanation:
the image is located below
Answer:
288 ft³
Step-by-step explanation:
Volume of the pyramid,
base area × height × (1/3)
= (9×8)×12/3
= 72×4
= 288 ft³
Find the missing side. Round your answer to the nearest tenth
Answer:
14.7
Step-by-step explanation:
tan(73)=48/x
or, x=48/tan(73)
or, x=14.7 (rounded to the nearest tenth)
Answered by GAUTHMATH
A collection of 30 coins consists of dimes and nickels. The total value is $1. 95How many dimes are there?
please help me with this
9514 1404 393
Answer:
92°
Step-by-step explanation:
The "givens" tell you the E and F are midpoints of their respective segments. That means EF ║ AB and angles DBF and EFC are "corresponding" angles with respect to transversal BC and those parallel lines. Corresponding angles are congruent, so ...
m∠DBF = m∠EFC = 92°
Joes bait shop brought in a gross profit in sales of $4,100.00 in the month of June. During the same month their operating expenses totaled $1990.00. Calculate the net income of the bait shop for the month of June
Answer:
2110
Step-by-step explanation:
4100-1990=2110
Heather has $20 in her purse she earn some money at work and add it to the money in her purse at the end of the day she has $95 in her purse use M as a variable
Answer:
M=$75
Step-by-step explanation:
I used M for money that Heather earned.
$20+M=$95
6.(a) A laptop was bought at Canadian $ 770. If the tax of 20% and 13% VAT should be paid, find the least selling price of it in Nepali rupee that prevents the shopkeeper from loss?
The LEAST selling price of the laptop should be ;
$1024.1 in other to avoid loss.
Price of laptop = $770
Tax = 20%
VAT = 13%
TO avoid loss ;
both the VAT percentage and TAX must be added to the price of the laptop:
Total percentage = VAT + TAX = (20 + 13) = 33%
THEREFORE, Least selling price should be :
Price of laptop * (1 + 33%)
770 * 1.33
= $1024.1
Learn more about TAX :
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A speed training service wants to explore the effectiveness of some of the classes offered to their clients. They randomly select 300 high school athletes and record their 50-meter dash time. The 300 high school athletes are then randomly assigned to three groups with 100 in each. One hundred athletes will take a circuit training class, 100 athletes will take an interval training class, and 100 athletes will take a plyometrics training class. At the end of 10 weeks of taking these classes, their 50-meter dash time will be recorded a second time. Their times will be analyzed to see which class showed the greatest overall improvement in times.
Select all the sentences that correctly identify the components of the experiment.
The experimental units are subjects.
The subjects are the 50 athletes.
There is one treatment, the 50-meter dash.
There are three treatments.
One treatment is a circuit training class.
The factor is the type of class.
There are 10 levels of the factor.
Answer:
A,D,E,F
1,4.5,6
The experimental units are subjects.
There are three treatments.
One treatment is a circuit training class.
The factor is the type of class.
ED2021
Please help‼️
Given O below, if XY and YZ are congruent, what is the measure of chord XY?
Answer:
11.2
Step-by-step explanation:
yz = 11.2
since the corresponding arc of yz and xy are same, their measures will ba same too
Answered by GAUTHMATH
Answer:
11.2
Step-by-step explanation:
good luck!
Can someone please help
Me
Answer:
$3735
Step-by-step explanation:
2/5 = 8/20
8/20 + 7/20 = 15/20 = 3/4
3/4*4980 = 3735
A swimmer dove off a board that was 50 ft above the water. The swimmer reached a depth of 15 ft in the pool. What number represents the swimmer's original height, in feet?
9514 1404 393
Answer:
50
Step-by-step explanation:
The number you choose depends on the location you consider to be zero height.
If we consider the surface of the pool to be zero height, and "up" to be the positive direction for measuring height, then the appropriate number for the original 50-ft height is 50.
solve for y then find the slope and y intercept and graph
y=4x+3
y=
b=
m=
Answer:
y = 4x+3
m =4
b =3
Step-by-step explanation:
y=4x+3
This is already solved for y
This is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = 4x+3
m =4
b =3
Solve the equation for the given variable
-2(-2x + 3) = -3x + 10
Round your answers to the nearest tenths place
Help meee
[tex] - 2( - 2x + 3) = - 3 x+ 10[/tex]
[tex]4x - 6 = - 3x + 10[/tex]
[tex]4x + 3x = 16[/tex]
[tex]7x = 16[/tex]
[tex]x = \frac{16}{7} [/tex]
[tex]x = 2.2857[/tex]
[tex]x = 3[/tex]
Write a 6-digit number that fits the description.
1. The value of its thousands digit is 5,000.
2. The value of its hundreds digit is 700.
3. Its tens digit is 2 less than the thousands digit.
4. Its hundred thousands digit is the same as the hundreds digit.
The number is?
Answer:
175731 is one of the answers of the 6 digit number
some others are:
275732
375733
475734
575735
675735
775734
875732
The 6-digit number is 175731.
What is the place value strategy?The place value strategies are defined as math strategies that use to assist you in resolving your elementary math problems, use your places values, such as tens and hundreds. It is possible to employ enlarged notation or compensation. Using regrouping techniques, you can make the problem easier by compensating for addition.
Let the number would be ABCDEF
Given the condition that the value of its thousands of digits is 5,000.
So C = 5
Given the condition that the value of its hundreds of digits is 700.
So D = 7
Given the condition that Its tens digit is 2 less than the thousand digits.
So E = 5-2 = 3
Given the condition that Its hundred thousand digits is the same as the hundred digits.
So B = 7
Therefore, all possible answers:
275732
375733
475734
575735
675735
775734
875732
Hence, the 6-digit number is 175731
Learn more about the place value strategy here:
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PLEASE HELP THIS IS DUE ASAP!!!!!!!!!!!!!!
the answer is 1/12
the first rolling a 4 has a 1/6 chance of happening and half of the numbers on the die are odd, so 1/6*1/2=1/12
50% of 80
50% of 48
50% of 15
25% of 120
25% of 90
A one lane highway runs through a tunnel in the shape of one half a sine curve cycle
The sine curve equation, y = 10·sin(x·π/24), that models the entrance of the
tunnel with a cross section that is the shape of half of a sine curve and the
height of the tunnel at the edge of the road, (approximately 7.07 ft.) are
found by applying the following steps
(a) The equation for the sine curve is y = 10·sin(x·π/24)
(b) The height of the tunnel at the edge of the road is approximately 7.07 feet
The reason for the above answers are presented as follows;
(a) From a similar question posted online, the missing part of the question
is, what is the height of the tunnel at the edge of the road
The known parameters;
The shape of the tunnel = One-half sine curve cycle
The height of the road at its highest point = 10 ft.
The opening of the tunnel at road level = 24 ft.
The unknown parameter;
The equation of the sine curve that fits the opening
Method;
Model the sine curve equation of the tunnel using the general equation of a sine curve;
The general equation of a sine curve is y = A·sin(B·(x - C) + D
Where;
y = The height at point x
A = The amplitude = The distance from the centerline of the sine wave to the top of a crest
Therefore;
The amplitude, A = The height of half the sine wave = The height of the tunnel = 10 ft.
D = 0, C = 0 (The origin, (0, 0) is on the left end, which is the central line)
The period is the distance between successive points where the curve passes through the center line while rising to a crest
Therefore
The period, T = 2·π/B = 2 × Opening at the road level = 2 × 24 ft. = 48 ft.
T = 48 ft.
We get;
48 = 2·π/B
B = 2·π/48 = π/24
By plugging in the values for A, B, C, and D, we get;
y = 10·sin((π/24)·(x - 0) + 0 = 10·sin(x·π/24)
The equation of the sine curve that fits the opening is y = 10·sin(x·π/24)
(b) The height of the tunnel at the edge of the road is given by substituting
the value of x at the edge of the road into the equation for the sine curve
as follows;
The width of the shoulders = 6 feet
∴ At the edge of the road, x = 0 + 6ft = 6 ft., and 6 ft. + 12 ft. = 18 ft.
Therefore, we get;
y = 10 × sin(6·π/24) = 10 × sin(π/4) = 5×√2
y = 10 × sin(18·π/24) = 10 × sin(3·π/4) = 5×√2
The height of the, y, tunnel at the edge of the road where, x = 6, and 18 is y = 5·√2 feet ≈ 7.07 ft.
Learn more about the sine curve here;
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What is the distance between point C and point D?
Question 5 options:
A)
17 units
B)
13 units
C)
12 units
D)
√85 units
Answer:
B. 13 units
Step-by-step explanation:
let
(x1 , y1) = (-4 , -6)
(x2 , y2) = (1 , 6)
distance between CD = root (x2 - x1)^3 + (y2 - y1)
= root {1 - ( -4)}^2 + {6 - ( -6)}^2
= root {1 +4}^2 + {6+6}^2
= root 5^2 + 12^2
= root 25 + 144
= root 169
= 13 units ans
Which of the following shows the extraneous solution to the logarithmic equation below?
2 log Subscript 5 Baseline (x + 1) = 2
Answer:
x=4
Step-by-step explanation:
log5(x+1)=1, (x+1)=5, x=4
Answer:
x= -6
Step-by-step explanation:
i got it wrong and the answer is -6
please help me asap!!!!!
Answer:
392
Step-by-step explanation:
1.49×10⁸/3.8×10⁵ = 392
What is the volume of this regular prism?
54.97 cubic inches
8.91 cubic inches
109.95 cubic inches
21.99 cubic inches
Answer:
A
Step-by-step explanation:
The volume of prism is b*h, base area is (2.5)*(3.24*(1.1)=8.91. Hence volume is 8.91*6.17=54.97
Help
Plz!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
angle G
sin inverse (21/29) = 46.4
GH
c^2 - b^2 = a^2
29^2 - 21^2 = a^2
a = √(29^2 - 21^2)
GH = 20
therefore ans is B) <G = 46.4º, <I = 43.6º, GH = 20
Hey I need helping with solving thank you
Answer:
the answer to this equation is c (10)
what is the circumference of a circle with 60 in. as the radius
Answer:
60π
Step-by-step explanation:
circumference of a circle = 2πr, where r = radius
given r = 60 in
2πr = 2×π×60
= 60π
= 188.5 (rounded to the nearest tenth)
What is the solution to the system of equations below?
2x+3y=6
x-3y=9
Answer:
Step-by-step explanation:
2x + 3y = 6
2x = 6-3y
x = (6-3y)/2
x - 3y = 9
(6-3y)/2 -3y = 9
(6-3y)/2 -6y/2 = 9
(6-9y)/2 = 9
6 - 9y = 9×2
-9y = 18-6
y = 12/-9
y = -4/3
2x + 3y = 6
2x + 3(-4/3) = 6
2x -4 = 6
2x = 6+4
2x = 10
x = 10/2
x = 5
Therefore x = 5 and y = (-4/3)
I used subsitution method
please click thanks and mark brainliest if you like :)
Answer:
x = 5; y = -4/3
Step-by-step explanation:
One equation has 3y. The other equation has -3y. Add the equations to eliminate y and solve for x.
2x + 3y = 6
(+) x - 3y = 9
---------------------
3x = 15
x = 5
2x + 3y = 6
2(5) + 3y = 6
3y + 10 = 6
3y = -4
y = -4/3
Answer: x = 5; y = -4/3
Two cards are selected with replacement from a standard deck of 52 cards. Find the probability of selecting a heart and then selecting a diamond.
Answer: 50.2 is it
Step-by-step explanation: thats easy
Probability helps us to know the chances of an event occurring. The probability of selecting a heart and then selecting a diamond is 144/2652.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given that Two cards are selected with replacement from a standard deck of 52 cards. Therefore, the probability of selecting a heart and then selecting a diamond is,
Probability = (12/52) × (12/51)
Probability = 144/2652
Hence, The probability of selecting a heart and then selecting a diamond is 144/2652.
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Tại sao số mắt xích không được là bội số của số răng đĩa xích
Answer:
Nên sử dụng số răng lẻ cho đĩa xích dẫn động kết hợp với số lượng mắt xích chẵn để mài mòn đồng đều trên răng và trục lăn. Trong trường hợp này, một răng cụ thể của bánh xích không tiếp xúc với một mắt xích cụ thể của xích trong mỗi lần quay.
Step-by-step explanation:
Translated
It is preferable to use an odd number of teeth for the driving sprocket in combination with an even number of chain links for uniform wear and tear on the teeth and rollers. In this case, a particular tooth of the sprocket wheel does not come in contact with a particular link of the chain for every rotation.
