Final answer:
To find the interval of increase for the function F(x) = 9*sin(x) + cot(x), we need to find where the derivative is positive. The interval of increase for the function is (0, π/2) and (π, 3π/2).
Explanation:
In order to find the interval of increase for the function F(x) = 9*sin(x) + cot(x), we need to find where the derivative is positive. Let's first find the derivative of F(x). The derivative of sin(x) is cos(x) and the derivative of cot(x) is -csc^2(x).
So, the derivative of F(x) is 9*cos(x) - csc^2(x). Now, to find where the derivative is positive, we need to find the intervals where 9*cos(x) - csc^2(x) > 0. We can solve this inequality by analyzing the sign changes of the derivative function.
By analyzing the sign changes of 9*cos(x) - csc^2(x), we find that the derivative is positive when x is in the intervals (0, π/2) and (π, 3π/2). Therefore, the interval of increase for the function F(x) = 9*sin(x) + cot(x) is (0, π/2) and (π, 3π/2).
A 34 - m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 36 m . Find the length of the shadow. If necessary, round your answer to the nearest tenth.
Answer:
Length of the shadow is 11.8 meters.
Step-by-step explanation:
In the figure attached,
AB is a 34 meter tall building casting a shadow BC.
Let the measure of BC = x meters
It is given that the distance between A and C is 36 meters.
To find the length of BC we will apply Pythagoras theorem in the triangle.
AB² + BC² = AC²
(34)² + x² = (36)²
1156 + x² = 1296
x² = 1296 - 1156
x² = 140
x = √140
x = 11.832 meters
≈ 11.8 meters
Therefore, length of the shadow will be 11.8 meters.
f(x) = 2/3 x -5 what is the value f(6)?
How is inductive reasoning used in geometry?
Answer:
Inductive reasoning draws general conclusions from specific details / observations - in other words, going from specific --> general.
Example:
Specific: I break out when I eat peanuts.
Observation: This is a symptom of being allergic.
General Conclusion: I am allergic to peanuts.
hope this helps! <3
Final answer:
Inductive reasoning in geometry involves observing patterns in specific instances and formulating general rules or hypotheses, such as the sum of angles in a triangle or the properties of parallel lines intersected by a transversal.
Explanation:
Inductive reasoning in geometry is used to derive broad generalizations from specific observations or instances. One way inductive reasoning is applied is by observing patterns or properties in a set of geometric figures and then formulating a hypothesis or general rule that applies to all similar figures. For example, after measuring the angles of several triangles and finding that they always add up to 180 degrees, one might assume that all triangles have this property. Another example is when looking at multiple parallel lines cut by a transversal and noticing the corresponding angles are equal, thus generalizing that this is the case for any parallel lines intersected by a transversal.
Scientists, including mathematicians, use inductive reasoning to construct hypotheses, which are then tested using deductive reasoning. The conclusions drawn from inductive reasoning may not always be correct, but they are essential for advancing scientific and mathematical knowledge by suggesting relationships and rules that can be rigorously tested.
Would you measure walls using inches or yards
A league of 19 teams is playing a "round-robin" style tournament, where each team plays every other team exactly once. How many games total need to be played? Justify your answer using a graph model—say what the vertices and edges of your graph represent, and what (if any) theorems you use. (Upload your file below.)
The directions for mixing an insect spray say to use 1 3/4 ounces of chemical in each gallon of water. How many ounces of chemical should be mixed with 4 1/5 gallons of water?
7 7/20 ounces of chemical should be mixed with 4 1/5 gallons of water.
To determine the amount of chemical to mix with 4 1/5 gallons of water, you need to use the given ratio of 1 3/4 ounces of chemical per gallon of water.
1.) Convert 4 1/5 gallons to a mixed number:
4 1/5 = 21/5 gallons.
2.) Multiply the amount of water by the chemical-to-water ratio:
(21/5) gallons * (7/4) ounces = 147/20 ounces.
3.) Convert 147/20 ounces to a mixed number:
147/20 = 7 7/20 ounces.
Therefore, 7 7/20 ounces of chemical should be mixed with 4 1/5 gallons of water.
81.54 is what percent of 75.5
which number is a factor of 20, but not a multiple of 2? 12, 5, 10 or 4?
an ellipse has a center at the origin, a vertex along the major axis at (13, 0), and a focus at (12, 0). What is the equation of the ellipse?
Answer: The equation of the ellipse is
[tex]\dfrac{x^2}{169}+\dfrac{y^2}{25}=1.[/tex]
Step-by-step explanation: We are given to find the equation of an ellipse that has a center at the origin, a vertex along the major axis at (13, 0) and a focus at (12, 0).
Since the focus lies on the X-axis, so the standard equation of an ellipse with major axis as X-axis is given by
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
According to given information, we have
a vertex along the major axis, (a, 0) = (13, 0)
⇒ length of the major axis, a = 13,
co-ordinates of focus, (c, 0) = (12, 0)
⇒ c = 12.
We know that
[tex]c^2=a^2-b^2.[/tex]
Therefore,
[tex]12^2=13^2-b^2\\\\\Rightarrow 144=169-b^2\\\\\Rightarrow b^2=169-144\\\\\Rightarrow b^2=25\\\\\Rightarrow b=5.[/tex]
Thus, from equation (i), we get
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\\\\\\\Rightarrow \dfrac{x^2}{13^2}+\dfrac{y^2}{5^2}=1\\\\\\\Rightarrow \dfrac{x^2}{169}+\dfrac{y^2}{25}=1.[/tex]
The equation of the ellipse is
[tex]\dfrac{x^2}{169}+\dfrac{y^2}{25}=1.[/tex]
The equation of the ellipse along the major axis at (13, 0), and a focus at (12, 0) is; x²/169 + y²/25 = 1
Equation of an ellipseThe equation of an ellipse whose center is the origin, (0,0) usually takes the form;
x²/a² + y²/b² = 1The coordinates of the vertex on the major axis is given as; (13,0) and the focus at (12,0)
Hence, the square of the length of the minor axis;
b² = a² - c²b² = 169 - 144b² = 25.Hence, the equation of the described ellipse is;
x²/169 + y²/25 = 1Read more on equation of an ellipse;
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There are 9 more pencils then pens in a container. There are 25 writing utensils in the container in all. How many pens are there in the container?
For what value of a does 9=(1/27)^a+3
The value of a in the equation [tex]9=(\frac{1}{27})^{a+3}[/tex] is a = -11/3
Solving indical equationsThe given equation is:
[tex]9=(\frac{1}{27})^{a+3}[/tex]
This can be rewritten as:
[tex]9=27^{-1(a+3)}[/tex]
Which can be further simplified as:
[tex]3^2=3^{-3(a+3)}[/tex]
Since the bases are equal, they cancel out
The equation becomes:
2 = -3(a + 3)
2 = -3a - 9
2+9 = -3a
-3a = 11
a = -11/3
Therefore, the value of a in the equation [tex]9=(\frac{1}{27})^{a+3}[/tex] is a = -11/3
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can someone pls answer
9y = -11x +36
y = -11/9 +4
y = 4
what is the least common multiple of 20 and 52
The least common multiple of 20 and 52 is, 420
What is Least common multiple?The Least common multiple of two or more numbers are the smallest number that is multiple of two or more numbers.
Given that;
The numbers are,
⇒ 20 and 52
Now, The factors of numbers are,
⇒ 20 = 2 × 2 × 5
⇒ 42 = 2 × 3 × 7
Hence, The least common multiple of 20 and 52 is,
⇒ LCM of {20, 52} = 2 × 2 × 5 × 3 × 7
= 420
Thus, The least common multiple of 20 and 52 is, 420
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What is the value of this expression? (-8)3
Answer:
Step-by-step explanation:
You could, if you wished, take out the negative sign, obtaining -(8)(3). That would be -24.
But if you meant exponentiation, it would look like (-8)^3, or (-8)³, and that would be equal to 8*8*8 = 512.
2.5 million deaths per is how many deaths per minute
Two parallel lines are crossed by a transversal. What is the value of x?
A. x = 12
B. x = 14
C. x = 22
D. x = 24
Answer
x = 12
Explanation
The two given angles are supplementary angles. That means that the add up to 180 degrees.
(5x + 5) + 115 = 180
5x +5 + 115 = 180
5x + 120 = 180
5x= 180 - 120
5x = 60
x = 12
a car is traveling at a rate of of 55 miles per hour. how many feet oer hour does the car travel?
write a formula for the nth term of the sequence. Identify your formula as recursive or explicit. -3,3,-3,3,-3,3
4.4 mi/h how many ft/s
Answer:
about 6.45 ft/s
Step-by-step explanation:
The conversion factor for mph to fps is ...
1 mph = 22/15 fps
Multiplying by 4.4 gives ...
4.4 mph = 96.8/15 fps = 484/75 fps = 6 34/75 fps
≈ 6.4533333... ft per second
Find the amount of time to the nearest day it would take a deposit of $1300 to grow to 1 million at 17% compounded continuously. The amount of time it would take to grow the deposit to $1 million is____ years ___ days
It would take approximately 39 years and 183 days for the deposit to grow to $1 million.
Use the concept of compound interest defined as:
The interest that is computed using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Given that,
Initial deposit: $1300
Target amount: $1 million
Interest rate: 17%
Compounding: Continuous
Time to calculate: To the nearest day
To find the amount of time it would take,
Use the formula:
[tex]t = \dfrac{ln(\frac{M}{P})}{r}[/tex]
Where,
t = time in years
M = final amount ($1 million)
P = initial deposit ($1300)
r = interest rate (17% or 0.17)
Find the natural logarithm of the ratio M/P:
ln(1,000,000 / 1,300) ≈ 6.64
Divide the result by the interest rate:
t = 6.64 / 0.17
t ≈ 39.05 years
So, it would take approximately 39 years to grow the deposit to $1 million.
To determine the number of days,
Multiply the decimal part of the years by 365 (assuming a non-leap year):
0.05 x 365 ≈ 183 days
Hence,
Rounding to the nearest day, it would take approximately 39 years and 183 days for the deposit to grow to $1 million.
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A tree is 6 feet 4 inches tall. How tall is it in inches?
The number of inches in 6 feet 4 inches tall is 76 inches.
Given that, a tree is 6 feet 4 inches tall.
Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
We know that, 1 feet = 12 inches
So, 6 feet = 6×12
= 72 inches
Now, in inches = 72+4
= 76 inches
Therefore, the number of inches in 6 feet 4 inches tall is 76 inches.
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Erica bought 3 1/2 yards of Frederick if she uses 2/3 of the fabric to make a curtain how much will she have left
1) Which number rounds up when rounded to the nearest tenth?
55. 24
170.93
0.12
8.15
___________
2)
Estimate the value of 2968 + 9912 by rounding each number to the thousands.
14,000
13,000
12,000
7000
___________
3)
Which statement below shows the best use of friendly numbers to estimate the value of 27 ·times 4
25 times 4 = 100
30 times 5 = 150
27 times 4 = 108
20 times 4 = 80
_____________
4)
Marcus has 78 baseball cards and 45 basketball cards. Estimate the total number of cards Marcus has.
30
33
123
130
___________
5)
Determine which answer is reasonable for 4. 8 times 9.2.
14
45.36
432
870.4
(please be 100 sure)
the slope of a line is 2/3. what is the slope of a line that is perpendicular to this line? Type a numerical answer in the space provided. do not include spaces in your answer. if necessary, use the / key to represent a fraction bar and only type improper fractions (no mixed numbers).
What is the eighth term of the geometric sequence 4,-20,100,...?
The eighth term of the geometric sequence 4, -20, 100,... is 9600, calculated using the formula aₙ = arⁿ⁻¹ with a = 4, r = -5, and n = 8.
The eighth term of the geometric sequence 4, -20, 100,... is 9600.
To find the eighth term of a geometric sequence, you can use the formula: aₙ = arⁿ⁻¹, where a is the first term, r is the common ratio, and n is the term number. In this case, a = 4, r = -5, and n = 8.
Plug the values into the formula: 4 x (-5)⁸⁻¹ = 9600.
Given the function value of the acute angle find the other five trigonometric function values cos a= Sqrt 7/7
Makers Corp. had additions to retained earnings for the year just ended of $395,000. The firm paid out $195,000 in cash dividends, and it has ending total equity of $5.3 million. What is the net income?
Write the ratio of 4 teachers to 134 students in simplest form.?
divide 134/4 = 33.5 that would be 1/33.5
since you can't have .5 student, multiply each side by 2
33.5*2 = 67
so 2/67 would be the simplest form using whole numbers
vito just put some money into a cd that pays 12.7 interest compound quarterly. according to the rule of 72,in the approximately how years will he have 4 times the amount of money that he has now
Answer:
11.34 years.
Step-by-step explanation:
We have been Vito put some money into a cd that pays 12.7 interest compound quarterly.
Since the rule of 72 states that to find the number of years it will take an amount to double, we need to divide 72 by annual interest rate.
First of all let us find the number of years it will take to double Vito's money by dividing 72 by 12.7.
[tex]\text{Time it will take to double Vito's money}=\frac{72}{12.7}[/tex]
[tex]\text{Time it will take to double Vito's money}=5.66929133858\approx 5.669[/tex]
Since it will take 5.669 years to double Vito's money, so to find the time it will take Vito to have 4 times the money, we will multiply 5.669 by 2.
[tex]\text{Time it will take to have 4 times Vito's money}=5.669*2[/tex]
[tex]\text{Time it will take to have 4 times Vito's money}=11.338\approx 11.34[/tex]
Therefore, approximately in 11.34 years Vito will have 4 times the amount of money that he has now.
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A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then the unit cost is given by the function C(x) =x^2-320x+40,052 . What is the minimum unit cost? Do not round your answer.