Answer:
there are approximately 5.035 months when there is less than 9 million square meters of sea ice around the North Pole in a year.
Step-by-step explanation:
Given the data in the question;
Let S(t) represent the amount sea ice around the North Pole in millions of square meters at a given time t,
t is the number of months since January.
Now, we use a cosine curve to model this scenario
Vertical shift will be;
D = ( 6 + 14 ) / 2 = 20 / 2
D = 10
Next is the Amplitude;
|A| = ( 6 - 14 ) / 2
|A| = 4
Now, the horizontal stretch factor will be;
B = 2π / 12
B = π/6
Hence;
S(t) = 4cos( π/6 × t ) + 10 ----------- let this be equation 1
Now we find when there will be less than 9 million square meters of sea ice;
S(t) = 9
so we have
9 = 4cos( π/6 × (t-2) ) + 10
9 - 10 = 4cos( π/6 × (t-2) )
-1 = 4cos( π/6 × (t-2) )
-1/4 = cos( π/6 × (t-2) )
so we have;
cos⁻¹( -1/4 ) = π/6 × (t₁-2) -------- let this be equation 2
2π - cos⁻¹( -1/4 ) = π/6 × (t₂-2) -------- let this be equation 3
so we solve equation 2 and 3
we have'
t₁ - t₂ = 6/π × ( 2π - cos⁻¹( -1/4 ) - cos⁻¹( -1/4 ) )
t₁ - t₂ = 6/π × ( 2π - 2cos⁻¹( -1/4 )
t₁ - t₂ = 6/π × ( π - cos⁻¹( -1/4 )
t₁ - t₂ = 6/π × ( π - 104.4775 )
t₁ - t₂ = 6/π × ( π - 104.4775 )
t₁ - t₂ = 5.035
therefore, there are approximately 5.035 months when there is less than 9 million square meters of sea ice around the North Pole in a year.
explain how to write an equation of a line given the slope and one point on the line
33. Given the following algebraic expression 5x² + 10 Which statement is true?
a. The coefficient is 5
b. The constant is 2
C. The power is 10
d. The constant is 5
Answer:
Given the following algebraic expression 5x² + 10 Which statement is true?
a. The coefficient is 5. ( true)
b. The constant is 2
C. The power is 10
d. The constant is 5
Here are the population figures of five different cities. 371,265 635,155 226,710 468,920 724,435 What is the difference between the largest population and the smallest population?
Answer:
497,725
just subtract smallest from largest to get the difference
724,435 - 226,710
Answer:
largest population 724,435Smallest population 226,710Solve the equation for w 5(w-2)+10=2w+6
Answer:
w=2
Step-by-step explanation:
See image below:)
Answer:
w = 1/2 or w = 3/6
Step-by-step explanation:
5(w-2) + 10 = 2w + 6
5(w-2) + 10 = 5w + 10 - 10 = 5w (the 5 outside of the bracket multiplies with the digits inside, including the w)
Now you have : 5w = 2w+6
Transfer the 2w to the left side, which would make it negative, therefore
5w - 2w= 6
3w = 6
w = 3/6
or
w = 1/2 (simplified)
Determine the value of y, if x is 1.
y = |x| +7
Help plsss
Answer:
8
Step-by-step explanation:
The absolute value (the lines both sides of x) simply mean the number in between is positive. Since 1 is already positive, just add it to 7!
Which of the following values could be an absolute value?
Answer:
Step-by-step explanation: It could be 8,7, or 2. Because these are all positive
:)
7) Point P is located at (4,8) on a coordinate plane. Point P will be relfected over y = x. What will bee
the coordiantes of the image of point P?
A. (28,4)
B. 24,8)
C. (4,28)
D. (8,4)
Use the order of operations to simplify the expression
(5.4)² - 5.4²
Answer:
0
Step-by-step explanation:
(5.4)^2 - 5.4^2
= 5.4^2 - 5.4^2
= 5,4^2(1 - 1)
= 5.4^2(0)
= 0
Answer to the question?
Answer:
35
Step-by-step explanation:
AEC and AEB form a straight angle(180°)
180-40=140
AEV and AED are equal
140 divided by 4 = 35
Question in in picture, please help
Step-by-step explanation:
256 mm3
cause volume of rectangular prism is l*b*h
Complete the explanation on why it is a good idea to use multiple samples when making comparative inferences about two populations.
It is a good idea to use multiple random samples to see how statistical measure vary among the ————-(different/same) samples.
Find the length of the third side. If necessary, round to the nearest tenth.
Answer: 14.4
Step-by-step explanation:
Levers are not a problem in the mechanical system. But, if you put two different simple machines that do not cooperate, they will be able to make the question that you need to. T or F
Answer:
True
Step-by-step explanation:
I am assuming that you are asking if two different simple machines that do not cooperate will work or not.
The answer to that is True.
Two things that do not work together will not work together. The two simple machines can not work with each other.
So, the answer is True. Best of Luck!
The pyramid shown below has a square base, a height of 7, and a volume of 84 cubic units.
What is the length of the side of the base?
12
36
6
18
please help! (listing BRAINLIST and giving points) :)
Answer:
(a) = 60
(b) = 70
Step-by-step explanation:
(a) Sum of all the angles of a triangle is 180
This is an equilateral Triangle
which means all the sides are equal since all the sides are equal that means all the angles are equal
[tex]x + x + x = 180 \\ 3x = 180 \\ x = \frac{180}{3} \\ x = 60[/tex]
(b) this is an isosceles triangle with two equal sides that means the two opposite angles are equal
[tex]40 + x + x = 180 \\ 40 + 2x = 180 \\ 2x = 180 - 40 \\ 2x = 140 \\ x = 70[/tex]
Please help a girl out, math is not my forte
Answer:
80 ft²
Step-by-step explanation:
You are given the formula
a = (1/2)bh
Just plug in the base and height, then multiply
a = (1/2) * 8 *20
a = (1/2) * 160
a = 80 ft²
Answer:
80 [tex]ft^{2}[/tex]
Step-by-step explanation:
Area = [tex]\frac{1}{2} bh[/tex]
Area = [tex]\frac{1}{2}[/tex] 8 · 20
Area = [tex]\frac{1}{2}[/tex] 160
Area = 80 [tex]ft^{2}[/tex]
Three consecutive integers have a sum of 30. Which equation can be used to find x, the value of the smallest of the three numbers? (x + 1) + (x + 2) = 30 x + (x + 1) + (x + 2) = 30 x (x + 1) (x + 2) = 30 3 x (x + 1) (x + 2) = 30
Answer:
X+(X+1)+X+2)=30
Step-by-step explanation:
A license plate begins with three letters. If the possible letters are A, B, C, D and E, how many different permutations of these letters can be made if no letter is used more than once?
Answer:
60 different permutations of these letters can be made.
Step-by-step explanation:
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
How many different permutations of these letters can be made if no letter is used more than once?
3 letters from a set of 5. So
[tex]P_{(5,3)} = \frac{5!}{(5-3)!} = \frac{5!}{2!} = 5*4*3 = 60[/tex]
60 different permutations of these letters can be made.
Is this the correct answer?
Answer:
Correct.
Step-by-step explanation:
It looks good to me.
Good job!
Write the simplified expression that represents the perimeter of the triangle below.
X - 3
4x + 4
2x + 1
Show Work
Answer:
Just plus everything together
X-3+4X+4+2X+1
Step-by-step explanation:
A ramp is in the shape of a triangle
Answer:
Step-by-step explanation:
PLEASE HELP ME!!! I need to simplify these equations, not answer them.
Answer:
Step-by-step explanation:
a= 2qr^3 quotent 6p^2
The radius of a circle is 10 cm. Find its circumference in terms of \piπ.
[tex]{ \bf{ \underbrace{Given :}}}[/tex]
Radius of the circle "[tex]r[/tex]" = 10 cm.
[tex]{ \bf{ \underbrace{To\:find:}}}[/tex]
The circumference of the circle.
[tex]{ \bf{ \underbrace{Solution :}}}[/tex]
[tex]\sf\orange{The\:circumference \:of\:the\:circle\:is\:20\:π\:cm.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
We know that,
[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:2πr }[/tex]
[tex] = 2 \: \pi \times 10 \: cm \\ \\ = 20 \: \pi \: cm[/tex]
Therefore, the circumference of the circle is 20 π cm.
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]
help answer please help
Answer:
The best was to display a set of data with a wide range would be
a histogram.
Step-by-step explanation:
It's a graphical display of bars which will help you measure the central tendency.
question : Suppose you have VND 100 million to save orspend. If you lend, you will receive 112 million after a year. Inflation is 14% / year.
a. What is the nominal interest rate you get?
b. What is the real interest rate?
c. Should you save or spend that money?
d. Question (c) how will be answered if inflation is 10% / year, nominal interest rates do not change?
Answer:
Step-by-step explanation:
Which system of equations can be used to find the roots of the equation 4x2 = x3.
ly=-4x²
ly=x²+2x
(y = x² - 4x² + 2x
»
O
ly=0
0
o y
Jy = 4x²
Lva-x-2x
ly=44²
ly=x²+2x
o
Answer:
The second answer
Y=X³-4X²+2X
Y=0
The system of equations can be used to find the roots of the given equation is y = 4x², y = x³+2x
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
For example, 3x – 5 = 16 is an equation.
Given is an equation, 4x² = x³+2x, we need to identify the system of equations can be used to find the roots of this,
An equality can be transformed in a system of equations by making each side equal to a new variable. In this case the variable y was made equal to each side.
See that may find the solution of such system by graphing both functions in a same coordinate system, where the intersection of the functions would show the solution of the system.
The attached image. In such graph, the red curve is the function y = x² and the blue function is y = x³ + 2x.
The intersection point is (0,0) meaning that the solution is x = 0, y = 0.
Hence, the system of equations can be used to find the roots of the given equation is y = 4x², y = x³+2x
Learn more about equations, click;
https://brainly.com/question/29657992
#SPJ7
The retail cost of a TV is 50 % more than its wholesale cost. Therefore, the retail cost is ____ times the wholesale cost.
Answer:
Let the retail cost be x and the wholesale cost be y
Step-by-step explanation:
x = y + 0.50y
x = 1.50y
Therefore the retail cost is 1.50 times the wholesale cost.
[tex] {x}^{2} + \sqrt{x} + \sqrt[5]{x} [/tex]
what is f'(3) of this equation?
Answer:
[tex]3 + \frac{1}{2\sqrt{3} } + \frac{1}{5\sqrt[5]{81} }[/tex]
Step-by-step explanation:
Just to make it easier to see, [tex]\sqrt{x} = x^{\frac{1}{2} }[/tex] and [tex]\sqrt[5]{x} = x^{\frac{1}{5} }[/tex] This way we could more easily use the power rule of derivatives.
So if f(x) = [tex]x^{2} +x^{\frac{1}{2} } +x^{\frac{1}{5} }[/tex] then f'(x) will be as follows.
f'(x) = [tex]x^{1} +\frac{1}{2} x^{-\frac{1}{2} } +\frac{1}{5} x^{-\frac{4}{5} } = x +\frac{1}{2x^{\frac{1}{2} }} +\frac{1}{ 5x^{\frac{4}{5} }} = x +\frac{1}{2\sqrt{x}} +\frac{1}{ 5\sqrt[5]{x^4} }[/tex]
to find f'(3) just plug 3 into f'(x) so [tex]3 + \frac{1}{2\sqrt{3} } + \frac{1}{5\sqrt[5]{81} }[/tex]
The company has only two division division eight and division be last year division a made 60% of the companies total revenue and division be made 40% of the total revenue this year division as revenue has decreased by 35% and division bees revenue has decreased by 5% which division had higher revenue this year?
9514 1404 393
Answer:
Division A
Step-by-step explanation:
Suppose last year's revenue for the company was 100 units.
Last year's Division A revenue was 0.60×100 = 60. This year's revenue is 1-35% = 65% of last year's, so is ...
60 × 0.65 = 39 . . . . units
__
Last year's Division B revenue was 0.40×100 = 40. This year's revenue is 1-5% = 95% of last year's, so is ...
40 × 0.95 = 38 . . . . units
__
At 39 units this year, Division A still has the higher revenue than Division B at 38 units.
Which inequality has the solution shown below?
-18 -17 -16 -15 -14 -13 -12
Answer:
0.2x+5>2
Step-by-step explanation:
0.2 is the same as 2/10;
(2/10)x>2-5
(2/10)x>-3
2x>-30
X>-15( since -15 is lesser than -14,-13,-12 and so on. the sign should be >
