Answers
It depends on how accurate you want to be, but two straight lines between 0° and 30° and 30° and 90° will not be too bad for Sine.
Thus for angles less than 30°
sinx≈x/60
and for angles greater than 30°
sinx≈(30+x)/120
For Cosine you use the identity
cosx=sin(90−x)
And for Tangent you use the identity
tanx=sinxcosx
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Related Questions
Need help with question
Answers
a) The decay formula for the mass of Strontium-90 is m(t) = 75 · [tex]e^{-t /40.395}[/tex].
b) The sample of Strontium-90 has a mass of approximately 13.258 miligrams after 70 days.
c) The sample of Strontium-90 takes a time of approximately 146.405 days.
How to model the mass decay of a sample of Strontium-90
The mass of Strontium-90 decays exponentially in time, whose model is described below:
m(t) = m' · [tex]e^{- t /\tau}[/tex]
Where:
m' - Initial mass of the isotope, in miligrams. m(t) - Current mass of the isotope, in miligrams. τ - Time constant, in days.And the time constant can be estimated by the following formula:
τ = t' / ㏑ 2
Where t' is the half-life of the isotope.
a) If we know that m' = 75 mg and t' = 28 d, then the expression for the mass of the sample is:
τ = 28 / ㏑ 2
τ ≈ 40.395 d
m(t) = 75 · [tex]e^{-t /40.395}[/tex]
b) And the mass of the isotope after 70 days is:
m(70) = 75 · [tex]e^{- 70 / 40.395}[/tex]
m(70) ≈ 13.258 mg
The current mass is approximately 13.258 miligrams.
c) If we know that m(t) = 75 · [tex]e^{-t /40.395}[/tex] and m(t) = 2 mg, then the time needed for the decay is:
75 · [tex]e^{-t /40.395}[/tex] = 2
[tex]e^{-t /40.395}[/tex] = 2 / 75
- t / 40.395 = ㏑ (2 / 75)
t = - 40.395 · ㏑ (2 / 75)
t ≈ 146.405 d
The needed time is approximately 146.405 days.
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Write a real world situation that could be modeled by the expression, 300+7x.
Answers
A real world situation that could be modeled by the expression, 300+7x is that Bob bought goods for $300 and then bought 6 pens that cost x dollar each.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both
In this case, Bob bought goods for $300 and then bought 6 pens that cost x dollar each. The total cost will be:
= 300 + (7 × x)
= 300 + 7x
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Use the table below to find d/dx[5f(x)-4x] x=2
Answers
The value of derivative of d/dx[5f(x)-4x] at x=2 = 16.
From the table:
At x=2,
f'(x) = 4
f(x) = 4x
= d/dx(5*4x - 4x)
= d/dx(20x - 4x)
= d/dx(16x)
= 16
Therefore the value of derivative of d/dx[5f(x)-4x] at x=2 = 16.
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What does s equal in 3s=24
Answers
Answer is 8
D degrees warmer than 50 degrees is 78 degrees
Answers
Answer:
28
Step-by-step explanation:
Translate words into math -- "warmer" means +, "is" means =
So D + 50 = 78
D = 78 - 50
D = 28
in a fruit punch drink, the 3 ingredients are apple juice, orange juice and cranberry juice. If 1/3 of the drink in apple juice and 1/2 is orange juice then write the ratio of cranberry juice to apple juice to orange juice in its simplest form
URGENT
Answers
The ratio of cranberry juice to apple juice to orange juice in the fruit punch is = 1 : 2 : 3
Let the total quantity of juice is 60 ml .
Now the apple juice is 1/3 of 60 = 20 ml
The orange juice is 1/2 of 60 = 30 ml
Therefore cranberry juice = 60 -(20+30) ml = 10 ml
Now the ratio of cranberry juice to apple juice to orange juice
= 10 : 20 : 30
= 1 : 2 : 3
We can exactly find out how much of one simple quantity is included in the other by simply comparing two amounts of the same units. Ratios can be divided into two smaller groups.
One is the part to the whole ratio; the other is the part to the part ratio. The exact relationship that is between the two distinct entities or groupings is only exactly depicted by the part-to-part ratio.
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4.8 is what percent of 12
Answers
Answer:40%
Step-by-step explanation:
3. Use the graph of f(x) below to answer the following questions. Approximate answers are okay.
Answers
Answer:
Step-by-step explanation:
f(0) = 4
f(x)=0 when x = 0.75
f(x) =5 when x =3
A{ x ∈ R ║ 3≤x}
4.5÷0.9= what is 4.5 divided by 0.9 equal to .explain
Answers
Answer: The answer is 5.
Step-by-step explanation:
4.5 ÷ 0.9 = 450/90.
Convert decimal 4.5 to fraction 45/10
Convert decimal 0.9 to fraction 9/10
Divide 450/90
Simply 450/90 = 5
Answer:
5
Step-by-step explanation:
Consider triangle XYZ with altitude WZ. What is XZ?
X
W
N
28
21
Y
Answers
The value for the side of rectangle XZ is equal 14, using the trigonometric ratios of cosine and sine of angles.
What is trigonometric ratios?The trigonometric ratios concerns the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;
sine, cosine and tangent.
Considering the triangle WYZ, the cosine of angle Y;
cos(Y) = 21/YZ {adjacent/hypotenuse}
YZ = [21/cos(Y)] {cross multiply}
Considering the triangle XYZ, the cosine of angle Y;
cos(Y) = YZ/28
YZ = 28 × cos(Y)
Therefore,
28cos(Y) = [21/cos(Y)]
cos²(Y) = 21/28 {cross multiply}
cos(Y) = √(21/28) {take the square root of both sides}
cos(Y) = 0.8660
Y = cos^(-1)(0.8660) {cross multiply}
Y = 30°
To get the side XZ, considering the triangle XYZ the sine of 30°;
sin30° = XZ/28 {opposite/hypotenuse}
by cross multiplication
XZ = 28 × sin30°
XZ = 14
Therefore, by proper application of the trigonometric ratios of cosine and sine of the angle for the given triangle, the side XZ = 14.
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If Pam has 40 dollars in her account, how much money does her brother have in his account? Use a tape diagram to
support your answer.
Answers
Answer:
[tex] \binom{?}{?} [/tex]
Step-by-step explanation:
$40 Pam use type diagram
$45. bro
find the value of f(4) for the function f(a)=7(a+2) "-7"
Answers
Answer: 35
Step-by-step explanation:
[tex]f(4)=7(4+2)-7\\\\f(4)=7(6)-7\\\\f(4)=7(5)\\\\f(4)=35[/tex]
Which expression shows the distance on the number line between -12 and negative one
Answers
Answer: (-12,-1)
Step-by-step explanation: Point A=-1 and Point B=-12
:)
On a map, 2 inches equals 180 miles. The distance that a family travels is 3.5 inches on the map. Represent the scale as two different ratios. What is the actual distance the family travels?
Answers
Answer:
315
Step-by-step explanation:
2/180=3.5/x
2x=630
x=315
How much money must be deposited today to become $2250 in 20 years at 5.5%
compounded continuously?
The deposit must be $
(Round to the nearest cent as needed.)
Answers
The amount of money that must be deposited today is $749 .
In the question ,
it is given that ,
the amount that is need to be made (A) = $2250
time (t) = 20 years
rate percent (r) = 5.5% = 0.055
let the amount that must be deposited today be P .
The amount that is needed to be deposited today at 5.5% compounded continuously can be calculated using the formula .
A = P×[tex]e^{r\times t}[/tex]
Substituting the values , we get
2250 = P × [tex]e^{0.055\times 20}[/tex]
2250 = P × [tex]e^{1.1}[/tex]
P = 2250/ [tex]e^{1.1}[/tex]
P = 748.9599
P ≈ 749
Therefore , The amount of money that must be deposited today is $749 .
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describe how to map line p onto line q
Answers
Answer:r
Step-by-step explanation:r
Which of the following are characteristics of the graph of the absolute value
parent function?
Check all that apply.
A. It goes through the origin.
B. It is in quadrants I and II.
C. The left half has a slope of 1.
D. It is V-shaped.
Answers
Answer: All Are correct
Step-by-step explanation:
Look at graph, the vertex hits the origin, the parent function is on the top half of the graph (quads 1 and 2), both the left and right side have a slope of 1, and it is v shaped!
Please help. Find x and y. NEED ASAP
Answers
Answer:
x=10
y=5
Step-by-step explanation:
you have to find the length
I need the answer and work please.
Answers
Answer: you prob fininshed 5,3
Step-by-step explanation:
also this is easy im srry for doing this
A teacher is four times as old as a student in 20 years the student age will be half of the teacher age how old are they now
Answers
Let the present age of student be x
Present of teacher will be 4x
After 20 years,
Age of student = x + 20
Age of teacher = 4x + 20
According to the given condition after 20 years,
x + 20 = (4x + 20)/2
x + 20 = 2x + 10
2x - x = 20 - 10
x = 10
So student's present age is 10 years while teacher's is 4 x 10 i.e 40 years.
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How long will it take to double your money if you invest in an account that pays 8% interest, compounded continuously
Answers
The time that would be taken for the money to double is 9 years.
How long would it take to double the money?Given that a compound interest has to do with the type of interest that is charged both on the principal and on the interest. We know that the principal is the money that was invested.
Let the principal be P and let the time taken be t. Let us now apply the formula;
A = P(1 + r)^n
Where A = 2P and r = 0.08
2P = P(1 + 0.08)^n
2P/P = (1.08)^n
2 = (1.08)^n
ln2 = nln1.08
n = ln2/ln1.08
n = 0.693/0.077
n = 9
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How many ways are there to split the integers 1 through 14 into 7 pairs so that in each pair the
greater number is at least 2 times the lesser number?
Answers
The number of ways to split the integers, given the condition and using the Fundamental Counting Theorem, is of:
144.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes considering all trials is calculated by the multiplication of the factorials as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
Given the condition that the greater number is at least 2 times the lesser number we have that the pairs are composed by one number between 1 and 7 and another number between 8 and 14.
Hence the pairs of each number are built as follows:
For the pair of the number 7, there are only one possible outcome, which is of 14.For the pair of the number 6, there are two possible outcomes, which are of either 12 or 13.For the pair of the number 5, there are three possible outcomes, which are of either 10, 11, and whichever of 12 or 13 is not paired with 6.For the pair of the number 4, there are four possible outcomes, which are of either 8, 9, and the two remaining numbers that are not paired with 5 or 6.For the pair of the number 3, there are three possible outcomes, which are the remaining numbers that are not paired with 4, 5 or 6.For the pair of the number 2, there are two possible outcomes, which are the remaining numbers that are not paired with 3, 4, 5 or 6.For the pair of the number 1, there is one possible outcome, which is the remaining numbers that is not paired with 2,3, 4, 5 or 6.Hence the number of ways to split the numbers is:
2 x 3 x 4 x 3 x 2 = 144.
(the numbers were multiplied because of the Fundamental Counting Theorem).
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The sum of two numbers is 42. The sum of 5 times the 1st number and 9 times the 2nd number is 190. What are the two numbers?
Answers
Step-by-step explanation:
x + y = 42
5x + 9y = 190
x = 42 - y
5(42 - y) + 9y = 190
210 - 5y + 9y = 190
210 + 4y = 190
4y = -20
y = -5
x = 42 - y = 42 - -5 = 42 + 5 = 47
The height of a plant grew linearly over the course of a month. Initially the plant was 2 inches tall and it grew at an average rate of change of 0.125 inches per day.
a. Find an equation that models the height of the plant H in terms of the number of days d.
b. Determine the height of the plant after 15 days.
Answers
The equation that models the height of the plant H in terms of number of days is H = 1.875+0.125d and the height of the plant after 15 days is 3.75 inches.
According to the question,
We have the following information:
Initially the plant was 2 inches tall and it grew at an average rate of change of 0.125 inches per day.
2, 2.125, ...
Now, this series will become an arithmetic progression.
Formula to find the nth term:
an = a+(n-1)d
H = 2+(d-1)0.125
H = 1.875+0.125d
Now, the height after 15 days will be:
H = 1.875+0.125*15
H = 1.875+1.875
H = 3.75 inches
Hence, the equation that models the height of the plant H in terms of number of days is H = 1.875+0.125d and the height of the plant after 15 days is 3.75 inches.
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Is it possible for a number to be a product of 2, a product of 5,
and a product of 10? Explain.
Answers
Answer: Yes
Step-by-step explanation:
Yes, it is because if you multiply 2 and 5, you get 10. 2 and 5 LCM is also 10. If you check 2 and five multiples you see this is also proved true.
2 - 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 ...
5 - 5, 10, 15, 20 ...
The number of men and women receiving bachelor's degrees each year has been steadily increasing. For the years 1970 through the projection of 2014, the number of men receiving degrees (in thousands) is given by the equation y= 3.9x+446, and for women, the equation is y= 14.2x+316, where x is the number of years after 1970.
Answers
Answer:
if what I think you want is the number of bachelor degrees from from 1970 to 2014 for both men and women is then:
men: 617.6
women: 940.8
Step-by-step explanation:
from 1970 to 2014 it is 44 years so we plug 44 into x for both equations
Men:
y = 3.9(44) + 446
y = 171.6 + 446
y = 617.6
Women:
y = 14.2(44) + 316
y = 624.8 + 316
y = 940.8
The ratio of boys to girls in a class is 5:4. There are 36 students in the class. How many
students are girls?
Answers
Answer:
Let the girls be x
then, 5:4 = 5x and 4x
,
total stud.=36 so,
5x+4x=36
9x=36
x=36÷9
hence
x=4
now, boys = 5x=5×4=20
girls= 4x=4×4=16
so there are 16 girls
IXL Help Fast Please!
Answers
The equation of the line d that is parallel to line c is y = -5x + 4.
How to find the equation of a line in slope intercept form?The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, c has an equation y = -5x + 3. Line d is parallel to line c. Therefore, they have the same slopes. Parallel lines have the same slope.
Hence, let's find the equation of line d passing through (2, -6)
Let's find the y-intercept
-6 = -5(2) + b
-6 = -10 + b
b = -6 + 10
b = 4
Therefore, the equation of the line d is y = -5x + 4
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it is given that the rainfall in 2017 of 420mm was 25% more than in 2016. Find the annual rainfall in 2016
Answers
The annual rainfall in 2016 is 336 mm.
Let the annual rainfall in 2016 be 100x mm.
Now it is given that rainfall in 2017 is 25% more than rainfall in 2016.
So. rainfall in 2017 is = 100x + 100x*(25/100) = 100x+25x = 125x mm
Also given that the amount of rainfall in 2017 = 420 mm.
According to question the suitable equation is,
125x = 420
x = 420/125
x = 3.36
Hence the rainfall in 2016 is = 100x = 100*3.36 = 336 mm.
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A container ship left port last week carrying some goods that weighed a total of 130,980 tons. Today, it stopped in another port to unload. The weight of the goods on the ship is now 91,686 tons. By what percent has the weight of the goods on the ship decreased?
help please annnd thaannks
Answers
Answer:
30%
Step-by-step explanation:
130980-91686=39294
39294/130908=0.3
Answer: 168,609 ton
Hi, to answer this question, first we have to calculate the amount of the weight decrease by multiplying the original weight of the goods (240,870) by the percentage decrease in decimal form ( divided by 100)
Mathematically speaking:
240,870 (30/100) =72,261 ton
Finally we have to subtract that value to the original weight:
240,870-72,261 = 168,609 ton
Feel free to ask for more if needed or if you did not understand something.
Step-by-step explanation: