Answer:
42
Step-by-step explanation:
6*4+3*6= 42
Answer:
42
Step-by-step explanation:
6*4+3*6=42
find the volume V of the solid generated by revolving the region bounded by the given lines and curves about x axis for y = x^2, y =0, x =2.
The volume of the solid generated is V=8π and 32/5π
Given functions are x=y², x=2 and y=0
The equation y=x² is a parabola opening to right and has a vertex at O(0,0)
and another y=0 is the x-axis and x=2 is a line parallel to the y-axis
The region bounded by the above will be formed once their intersection points are known.
y²=2⟹y=±√2
OFB is bounded by O(0,0), F(2,0) and B(2,√2)
Let V be the volume of solid generated when the region OFB is revolved around line x=2.
[tex]V=\pi \int\limits^2_0 {x^4} \, dx \\[/tex]
V=π[x⁵/5]²₀
V=π[(2)⁵/5]
V=32/5 π.
[tex]V=\pi \int\limits^4_0 {(2^2)_2-(\sqrt{y}^2)_3 } \, dy\\\\ V=\int\limits^4_0 {(4-y)} \, dx[/tex]
V=8π.
when the shaded region revolves the bout x-axis:
[tex]V=\pi \int\limits^b_a {y^2} \, dx \\\\V=\pi \int\limits^2_0 {y^2} \, dx =\pi \int\limits^2_0 {x^4} \, dx =\pi [\frac{1}{5}.x^5]_0^2\\\\ V=\pi [\frac{32}{5}-0][/tex]
V=32/5
when the shaded region revolves the bout y-axis:
[tex]V=\pi \int\limits^c_d [(x^2)_2-(x^2)_1} \, dx \\V=\pi \int\limits^4_0 [(2^2)_2-(\sqrt{y} ^2)_1} \, dy \\V=\pi \int\limits^4_0 {(4-y)} \, dy =\pi [4y-\frac{1}{2}y^2]_0^4[/tex]
V=π[16-8]
V=8π
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In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 25 pieces of carry-on luggage was collected and weighed.
The average weight was 18 pounds. Assume that we know the standard deviation of the population to be 7.5 pounds. If we wanted to establish the 95% confidence interval estimate, determine the margin of error to be used.
The average weight of carry-on luggage by passengers in airplanes is (15.7, 20.3) pounds.
The margin of error to be used is 2.3 pounds.
Confidence Interval Estimate CalculationThe margin of error can be calculated using the formula:Margin of Error = z * (standard deviation / sqrt(sample size))where z is the Z-score that corresponds to the desired confidence level (95% confidence corresponds to a Z-score of 1.96), standard deviation is the population standard deviation (7.5 pounds), and sample size is the number of items in the sample (25).
Plugging in the values, we get:Margin of Error = 1.96 * (7.5 / sqrt(25)) = 2.3 pounds
So, the 95% confidence interval estimate of the average weight of carry-on luggage would be:(average weight - margin of error, average weight + margin of error)
= (18 - 2.3, 18 + 2.3) = (15.7, 20.3) pounds.
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Stefan borrowed twice as much on his 8 % car loan as on his 7% student loan. The annual interest
on the car loan is $360 more than the interest on the student loan. How much did Stefan borrow on
each loan?
a. Write an equation about the principals on the loans, using for the amount of money he borrowed
for his car and y for the amount of money he borrowed for his student loan.
b. Write another equation about the interest on the loans.
c. Solve your system and answer the question for much he borrowed at each rate.
Car: $
Student: $
Answer:
Stefan borrowed $8000 on his car loan and $4000 on his student loan.
Step-by-step explanation:
a. Let x be the amount of money Stefan borrowed on his car loan and y be the amount he borrowed on his student loan. According to the problem, Stefan borrowed twice as much on his car loan as on his student loan, so x = 2y.
b. The annual interest on the car loan is $360 more than the interest on the student loan. We can set up an equation as follows:
0.08x - 0.07y = 360
c. Substituting x = 2y from equation (a) into equation (b), we get:
0.08(2y) - 0.07y = 360
0.16y - 0.07y = 360
0.09y = 360
y = 4000
So, Stefan borrowed $4000 on his student loan. Using equation (a), we can find the amount he borrowed on his car loan:
x = 2y = 2(4000) = 8000
Therefore, Stefan borrowed $8000 on his car loan and $4000 on his student loan.
Using MATLAB, plot Bode diagrams of G1(s) and G2(s) given below: G1(s)=1+s/1+2s G(s) = 1-s/1-2s Note that the second transfer function is a non-minimum phase system; meaning it has a zero on the right-half plane. Note how the phase plot is affected.
Bode plots depict the frequency response, or the magnitude and phase changes as a function of frequency. This is accomplished using two semi-log scale plots. Using MATLAB, plot Bode diagrams of G1(s) and G2(s) given below.
(a) The first function is:
G1(s) = (1 + s)/(1 + 2s)
MATLAB Code:
%G1(s)
n1 = [1 1] %coefficients of numerator
d1 = [2 1] %coefficients of denominator
sys1 = f(n1,d1) %the transfer function
bode(sys1) %bode plot
grid on
Command Window:
>> Untitled
n1 = 1 1
d1 = 2 1
sys1 = (1 + s)/(1 + 2s)
Continuous-time transfer function.
(b) The second function is:
G(s) = (1 - s)/(1 - 2s)
MATLAB Code:
%G2(s)
n2 = [-1 1] %coefficients of numerator
d2 = [2 1] %coefficients of denominator
sys2 = f(n2, d2) %the transfer function
bode(sys2) %bode plot
grid on
Command Window:
>> Untitled
n2 = -1 1
d2 = 2 1
sys2 = (1 - s)/(1 - 2s)
Continuous-time transfer function.
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The complete question is:
Using MATLAB, plot Bode diagrams of G1(s) and G2(s) given below:
G1(s) = (1 + s)/(1 + 2s)
G2(s) = (1 - s)/(1 - 2s)
Note that the second transfer function is a non-minimum phase system; meaning it has a zero on the right-half plane. Note how the phase plot is affected.
work out an estmate of the mean age in this table
a)
The class modal interval is 24 ≤ a < 26.
b)
The Mean age of the employee is 23.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
Age Frequency (f) Midpoint (x) fx
18 ≤ a < 20 3 19 57
20 ≤ a < 22 2 21 42
22 ≤ a < 24 7 23 161
24 ≤ a < 26 8 25 200
26 ≤ a 0
Now,
Sum of all the frequencies.
N = 3 + 2 + 7 + 8 = 20
Sum of fx.
= 57 + 42 + 161 + 200
= 460
Now,
Mean = 460/20
Mean = 23
Now,
Class modal interval.
= 24 ≤ a < 26
Because in the class interval, the frequency is the highest.
Thus,
The class modal interval is 24 ≤ a < 26.
The Mean is 23.
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A politician's support increases from 32% to 53% Determine the absolute and relative change in this situation.
Absolute Change: The politician's support has increased by percentage points.
Relative Change: The politician's support has increased by %.
Round your answer to the nearest tenth of a percent.
Answer:
Step-by-step explanation:
Absolute Change:
The absolute change in the politician's support is calculated as the difference between the final support percentage (53%) and the initial support percentage (32%):
53% - 32% = 21 percentage points
So, the absolute change in the politician's support is 21 percentage points.
Relative Change:
The relative change in the politician's support is calculated as the absolute change divided by the initial support percentage, multiplied by 100 to express it as a percentage:
(21 / 32) * 100 = 65.625%
Rounding to the nearest tenth of a percent, the relative change in the politician's support is 65.6%.
So, the absolute change in the politician's support is 21 percentage points, and the relative change is 65.6%.
In this case, the absolute change in the politician's support is an increase of 21 percentage points, and the relative change is an increase of 65.6%.
Explanation:In this situation, the absolute change in the politician's support can be calculated by subtracting the original value from the new value. So, 53% (new value) - 32% (original value) = 21%. Thus, the absolute change in support is 21 percentage points.
The relative change is the absolute change divided by the original value. So, 21% (absolute change) ÷ 32% (original value) = 0.65625. To get the relative change as a percentage, we need to multiply this decimal by 100, and round to the nearest tenth of a percent, which gives us 65.6%.
Therefore, the politician's support has increased by an absolute change of 21 percentage points, and a relative change of 65.6%.
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Given f(x) = 2x² - 6, find f(7)
Answer:
92
Step-by-step explanation:
2x49=98-6=92
Answer:
f(7) = 92
Step-by-step explanation:
To find f(7), substitute x = 7 into the given function.
[tex]\begin{aligned}f(7)&=2(7)^2-6\\&=2(49)-6\\&=98-6\\&=92\end{aligned}[/tex]
The equations that represent the balance in three different savings accounts x years after 2012,
A
=
900
(
1.05
)
x
A
=
900
(
1.05
)
x
B
=
1100
(
1.038
)
x
B
=
1100
(
1.038
)
x
C
=
5000
(
0.85
)
x
C
=
5000
(
0.85
)
x
Which of the following statements are TRUE? Check all that apply.
Account C had the largest balance in the year 2012.
The balance of Account A is growing at a rate of 5% per year.
The balance of Account C is decreasing at a rate of 85% per year.
Account A is growing faster than account B.
all the applications are true.
What is simple interest?
A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,
Solution: Start by using:
2012 indicates that x=1
So A = 900 (1.05) = 900 × 1,05=945
B = 1100 (1.038) = 1100 × 1038 = 1141.8 \sC = 5000 (0,85) = 5000 x0.85 = 4250 \s4250 1141.8945
So, Ture is the first applicant.
Applying the second: 1.05-1=0.055% Ture
The third application is 1-0.85=0.15=15%. False
Applying the fourth: A 1.05+=0.05=5%
B: \s11038-1=0.038=3.8% \s5% > 3.8% Ture
Hence all the apply are true.
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find dy/dx, y= 4x²sinxcosx
The derivative of y relative to x is given as follows:
dy/dx = 8xsin(x)cos(x) + 4x²(cos²(x) - sin²(x)).
How to obtain the derivative?The function for this problem is defined as follows:
y = 4x²sin(x)cos(x)
The function is a product of three functions, hence the product rule is applied, as follows:
dy/dx = [4x²]'sin(x)cos(x) + 4x²[sin(x)]'cos(x) + 4x²sin(x)[cos(x)]'.
The derivatives are given as follows:
[4x²]' = 8x.[sin(x)]' = cos(x).[cos(x)]' = -sin(x).Hence the derivative of the function is defined as follows:
dy/dx = 8xsin(x)cos(x) + 4x²cos²(x) - 4x²sin²(x)
dy/dx = 8xsin(x)cos(x) + 4x²(cos²(x) - sin²(x)).
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Ty and Leo are walking along linear routes in a city. On a map of the city, Ty’s route passes through the coordinates (−1,3) and (0,1) and Leo's route passes through the coordinates (1,4) and (0,2) . Will Ty and Leo pass through a common coordinate, walk along the same route, or never cross routes?
Ty and Leo will
The two lines have same slope with opposite signs thus, the linear routes are perpendicular, and Ty and Leo will pass through a common coordinate.
What is a perpendicular line?A perpendicular is a straight line in mathematics that forms a right angle (90 degrees) with another line. In other words, two lines are perpendicular to one another if they connect at a right angle. If two segments PQ and RS connect at right angles, we may say that they are perpendicular to one another.
For the given coordinates of Ty and Leo let us calculate the slope of the line.
The slope of the line is given as:
m = (y2 - y1) / (x2 - x1)
For Ty:
m = (1 - 3) / (0 + 1) = -2
For Leo:
m = (2 - 4) / (0 - 1) = 2
The two lines have same slope with opposite signs thus, the lines are perpendicular, and Ty and Leo will pass through a common coordinate.
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I am so clueless with this mess
Answer:
3 miles
Step-by-step explanation:
The distance between Arati and Ava can be calculated using the Law of Cosines. Let's call the distance between Arati and Ava as "d". We know that:
a = 2 (distance skied by Arati)
b = 3 (distance skied by Ava ) c = d (distance between Arati and Ava) A = 45 (angle between a and b)
Plugging these values into the Law of Cosines formula:
d^2 = 2^2 + 3^2 - 2 * 2 * 3 * cos(45)
d^2 = 4 + 9 - 12 * (√2 / 2)
d^2 = 13 - 12 * √2
d = √(13 - 12 * √2)
To the nearest mile, the distance between Arati and Ava is approximately 3 miles.
Can anyone help me? Find m
Answer:
m∠Y = 60
WY = 7 in
Step-by-step explanation:
It's an isosceles triangle (2 sides are equal), therefore m∠W = m∠Y because the base angles of an isosceles triangle are equal.
Sum of interior angles of a triangle is 180.
let x = m∠W = m∠Y
2x + 60 = 180
2x = 180 - 60 = 120
x = 120/2 = 60
m∠Y = 60
Since all 3 angles = 60, now we know it's an equilateral triangle, therefore WY = 7 in
m+c<n<d-m
In the inequality above, c and d are constants.
If m= 1 and n = 2 is a solution of the inequality, which of the following statements concerning c and d must be true?
I. cd is negative
II. d-c>2
III. d+ c> 2
(A) II only
(B) I and II only
(C) II and III only
(D) I, II, and III
Answer: the right option is (A) II only
Step-by-step explanation:
This problem refers to right triangle ABC with C = 90°. Solve for all the missing parts using the given information. Find B, a,c. (Round your answers to three decimal places.) A = 9° 36', b = 5.812 cm.
So, adjusted to three decimal places, the lacking angles in the triangle are B = 80°24', a = 1.042 cm, and c = 5.852 cm.
What is the formula for decimal places?The number of important digits is the total number of digits, excluding the decimal point, all leading zeros, and some following zeroes. The number of decimal points is the number to the left of the decimals.
We are given that triangle ABC is a right triangle with C = 90°, A = 9° 36', and b = 5.812 cm.
To find B, we can use the fact that the sum of the angles in a triangle is 180°. Therefore, we have:
B + A + C = 180°
B + 9°36' + 90° = 180°
B = 80°24'
To find a, we can use the trigonometric function tangent.
We have:
tan A = opposite/adjacent
tan 9°36' = a/b
Solving for a, we get:
a = b tan A = 5.812 cm tan 9°36' ≈ 1.042 cm
The Pythagorean theorem, which says that in a right triangle, the square of the hypotenuse equals the total of the squares of the two sides (a and b), can be used to determine c.
We have:
c² = a² + b²
c² = (1.042 cm)² + (5.812 cm)²
c² ≈ 34.235 cm²
c ≈ √34.235 cm²
c ≈ 5.852 cm
Therefore, the missing parts of the triangle are B ≈ 80°24', a ≈ 1.042 cm, and c ≈ 5.852 cm, rounded to three decimal places.
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Koji is installing a rectangular window in an office building. The window is 8 2/3 feet wide and 5 3/4 feet high.
The formula for the area of a rectangle is A=bh.
What is the area of the window?
Enter your answer as a mixed number in simplest form by filling in the boxes.
In a case whereby Koji is installing a rectangular window in an office building. The window is 8 2/3 feet wide and 5 3/4 feet high using the formula for the area of a rectangle is A=bh, the area of the window is 49 5/6.
How can the area of the windowbe calculated?The concept that will be used here is area of a rectangle. Since window can be seen to be like a rectangle then area of window can be take as area of rectangle which can be calculated as
Area = Length × breadth
The Length=82/3 = 26/3
the breadth= 5 3/4 = 23/4
Then Area =( 26/3 * 23/4) = 299/6 = 49 5/6
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Answer: 49 5/6 square feet
Step-by-step explanation: The width/breadth = 8 2/3 = 26/3
the height = 5 3/4 = 23/4
Area = (26/3 * 23/4) = 598/12 = 49 5/6
sin2 80° + cos2 80° without calculator
Answer:
1
Step-by-step explanation:
Because of the Pythagorean Identity [tex]\sin^2\theta+\cos^2\theta=1[/tex], then the answer is simply 1 as the angle does not matter.
If 20% of a length is 23km.what is the complete length?
The total length is 115 km.
Step-by-step explanation:1. Create an equation.Let "x" be the complete lengh. So, in order to find 20% of that length we need to multiply by 0.2, which equals 20%. And it needs to equal 23 km. Hence the equation should be the following:
[tex]0.2x=23[/tex]
2. Divide by "0.2" on both sides of the equation.[tex]\frac{0.2x}{0.2} =\frac{23}{0.2} \\ \\x=115[/tex]
3. Verify the answer.To verify the answer, calculate 20% of the result (115), and it should equal 23 km. Let's see!
[tex]115*0.2=\\ \\23[/tex]
4. Conclude.The total length is 115 km.
-------------------------------------------------------------------------------------------------------
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Use the compound interest formula to compute the total amount accumulated and the interest earned.
$2,000 for 3 years at 5% compounded semiannually.
The amount in the account is $ ( )enter your response here.
(Do not round until the final answer. Then round to the nearest cent as needed.)
Answer:
$12,000
Step-by-step explanation:
2000([tex](1 + \frac{.05}{2}) ^{2(3)}[/tex]
12,000
truth table for (P^Q)
In the attachment......
I have two cans of paint. Can A has 9 parts of blue paint to one part of yellow paint. Can B is 20 percent blue paint and the rest is yellow paint. How much paint should I use from each can to obtain 5 liters of paint which is half blue and half yellow.
3.43 liters of Can A, and 4.57 liters of Can B should be used from each can to obtain 5 liters of paint which is half blue and half yellow.
What is word problem?A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
From the question,
Can A is 9 parts of blue 1 part yellow= 90% blue, 10% yellow
Can B is 20% blue, 80% yellow.
let
A + B = 8 Liters
90% A + 20% B = 50% (Blue)
10% A + 80% B = 50% (Yellow)
resolving
90% A + 20% B = 10% A + 80% B
80% A = 60% B
Go back to A + B = 8 and solve for one of the variables.
B = 8 - A
80% A = 60% (8 - A)
80% A = 480% - 60% A
140% A = 480%
A = 3 43 liters
B = 8 - A = 4.57 liters
Hence, 3.43 liters of Can A, and 4.57 liters of Can B should be used.
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Find the global extreme values of the function f(x, y) = x^2 + 2(y^2)
on the circle x^2 + y^2 = 1.
The global extreme values of the function f(x, y) = x² + 2(y²) on the circle x² + y² = 1 are,
The maximum value of f on the circle x² + y² = 1 is,
⇒ f(0, ±1) = 2
And, the minimum value is,
⇒ f(±1, 0) = 1
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
Function is,
f(x, y) = x² + 2(y²)
And, Equations of circle is,
x² + y² = 1
Hence, The maximum value of f on the circle x² + y² = 1 is,
⇒ f(0, ±1) = 0² + 2(1²) = 2
And, the minimum value is,
⇒ f(±1, 0) = 1² + 2 × 0 = 1
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Find the shortest distance between the line L1 passing through the points A =
(3, 2, 1) and B = (2, 1, 0) and the line L2 passing through the points C = (2, 4, −1) and
D = (3, 0, −2).
The shortest distance between the two lines L1 and L2 is 0.
How did we get the value?The shortest distance between two lines can be found using the cross product of their direction vectors.
The direction vectors of line L1 and L2 can be found as:
L1 = B - A = (2 - 3, 1 - 2, 0 - 1) = (-1, -1, -1)
L2 = D - C = (3 - 2, 0 - 4, -2 - (-1)) = (1, -4, -3)
The cross product of the direction vectors of L1 and L2 gives the normal vector to the plane formed by the two lines:
cross(L1, L2) = (1 + 4, -1 - 4, 3 + 1) = (5, -5, 4)
The normal vector of the plane formed by the two lines, and a point on line L1 (A = (3, 2, 1)), can be used to find the equation of the plane:
5x - 5y + 4z = d
5 * 3 - 5 * 2 + 4 * 1 = d
15 - 10 + 4 = d
9 = d
So the equation of the plane formed by the two lines is:
5x - 5y + 4z = 9
The shortest distance between the two lines is equal to the distance between a point on line L1 (A = (3, 2, 1)) and the plane formed by the two lines:
d = abs(9 - (5 * 3 - 5 * 2 + 4 * 1)) / sqrt(5^2 + (-5)^2 + 4^2)
d = abs(9 - 9) / sqrt(29)
d = 0 / sqrt(29)
d = 0
Therefore, the shortest distance between the two lines L1 and L2 is 0.
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11 ≥ 2x-5 or 2x-5 > 15
Answer:
Step-by-step explanation:
11≥2x-5
or
2x-5≤11
2x≤11+5
x≤16/2
x≤8
2x-5>15
2x>15+5
2x>20
x>20/2
x>10
so either x≤8
or
x>10
Answer: x</= 8 and x>10
Not sure what you are specifically asking for here is the answers for both
Step-by-step explanation:
Step 1: Move the terms
Step 2: Calculate
Step 3: Divide both sides
K
For each of the following five independent situations, journalize the adjusting entry and the related transaction (either
before or after it). (Record debits first, then credits. Select the explanation on the last line of the journal entry
table. Round amounts to the nearest whole dollar.)
(Click the icon to view the situations.)
a. December 1-business receives $6,000 for a 10-month service contract.
Accounts and Explanation
alculator
Date
December 1
Clear all
Debit
Credit
Check answer
The journal entry for the business receiving $ 6, 000 for a 10 month service contract is :
Date Account and Explanation Debit Credit
December 1 Cash $ 6, 000
Unearned Service Revenue $ 6, 000
Being revenue received for services
not yet rendered
How to record unearned service revenue ?When a business receives money for a service that it is yet to perform for the client, this is called unearned service revenue. The amount is to be debited to the cash account as it is an asset and assets are debited when they increase.
Unearned service revenue will then be credited by the same amount because it represents a liability that the company owes to the client.
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Oskar has a map showing this trip is 165 kilometers long. Oskar is from Texas and is more familiar with miles as a unit of measure for distance. Write three paragraphs explaining how to help Oskar determine the distance of his trip in miles.
Paragraph 1: Identify a conversion rate on your formula sheet that will help Oskar? How will this help?
Paragraph 2: Explain the steps Oskar will need to use to convert 165 kilometers into miles.
Paragraph 3: Where do you think Oskar might be traveling in which the maps are labeled in kilometers instead of miles? What is the difference between these two units of measure?
1. Using the conversion rate of 1 kilometer = 0.621371 miles, Oskar determine the distance of his trip in miles.
2. Oskar's 165 kilometer trip is equivalent to 101.87995 miles.
3. The difference between kilometers and miles is that a kilometer is a metric unit of length and a mile is an imperial unit of length.
How to Apply Conversion Rate?Paragraph 1: To convert kilometers to miles, Oskar will need to use the conversion rate of 1 kilometer = 0.621371 miles.
This conversion rate can be found on any formula sheet, and it will help Oskar determine the distance of his trip in miles.
Paragraph 2: To convert 165 kilometers into miles, Oskar will simply need to multiply 165 by 0.621371.
The result will give him the distance in miles.
For example, 165 * 0.621371 = 101.87995 miles. Therefore, Oskar's 165 kilometer trip is equivalent to 101.87995 miles.
Paragraph 3: Oskar might be traveling in a country where the maps are labeled in kilometers instead of miles. This is common in many countries, including most of Europe and many countries in Asia. The difference between kilometers and miles is that a kilometer is a metric unit of length and a mile is an imperial unit of length. A kilometer is equal to 0.621371 miles, while a mile is equal to 1.60934 kilometers. It's important to be aware of the units used in different countries to ensure accurate navigation.
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A sine function has the following key features:
Period = 12
Amplitude = 4
Midline: y = 1
y-intercept: (0, 1)
The function is not a reflection of its parent function over the x-axis.
Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
Answer:
The sine function for the given parameters is y = 4 sin ( pi/2 * x ) + 1. The period is 12, the amplitude is 4, the midline is y = 1 and the y-intercept is (0, 1). The function is not a reflection of its parent function over the x-axis.
Step-by-step explanation:
To solve a sine function with the given features, one must first identify the midline, amplitude, period, and phase shift of the function. The midline is the average of the maximum and minimum values of the graph, while the amplitude is half of the difference between these two values. The period is the length of one cycle in radians, and the phase shift is how much it has been shifted from its parent function over the x-axis.
If tant=74, what is tan(t−π) ?
The tan(t−π) = 74of the given trigonometric function, tan(t−π), is 74
Evaluating trigonometric functionsFrom the question, we are to determine the value of trigonometric function tan(t−π) using the given information.
The given information is tan(t) = 74
We can use the following identity to solve this problem:
tan(t - π) = tan(t) - tan(π) / 1 + tan(t)tan(π)
Since tan(π) = 0
This can be simplified into
tan(t - π) = tan(t) / (1 - 0)
tan(t - π) = tan(t)
Thus,
We just need to find tan(t)
Given that tan(t) = 74.
Hence, tan(t−π) = 74
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let sn be the sum of the reciprocals of the non-zero digits of the integers from 1 to 10n inclusive. find the smallest positive integer n for which sn is an integer?
The smallest positive integer n for which Sn is an integer is 063.
What is integer?
The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.
Let [tex]K=^9E_{i=11}\frac{1}{i}[/tex].
Examining the terms in S1, it can be seen that S1 = K + 1 since each digit n appears once and 1 appears an extra time.
Now consider writing out S2.
Each term of K will appear 10 times in the units place and 10 times in the tens place (plus one extra 1 will appear), so -
S2 = 20K + 1
In general, the equation is -
[tex]S_n=(n10^{n-1})K+1[/tex]
Because each digit will appear [tex]10^{n-1}[/tex] times in each place in the numbers [tex]1,2,......,10^{n-1}[/tex]and there are n total places.
The denominator of K is [tex]$D = 2^3\cdot 3^2\cdot 5\cdot 7$[/tex] .
For Sn to be an integer [tex]n10^{n-1}[/tex] must be divisible by D.
Since, [tex]10^{n-1}[/tex] only contains the factors 2 and 5 (but will contain enough of them when n ≥ 3), we must choose n to be divisible by [tex]$3^2\cdot 7$[/tex] .
The smallest such n, the answer is 063.
Therefore, the integer is 063.
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Find the distance between the following numbers on the real number line. a=12, b=3
Answer:
Step-by-step explanation:
The distance between two numbers on the real number line is simply the absolute value of their difference. So, to find the distance between the numbers a = 12 and b = 3, we calculate:
distance = |a - b| = |12 - 3| = |9| = 9
Therefore, the distance between the numbers a = 12 and b = 3 on the real number line is 9 units.
Answer:
Step-by-step explanation:
12.1+|-11|=12
What is the volume of a sphere with a diameter of 30in
The radius of the sphere is half of its diameter, so the radius is 30/2 = 15 inches.
The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius.
Substituting the given values, we get:
V = (4/3)π(15)³
V = (4/3)π(3375)
V = 4500π
Therefore, the volume of the sphere is 4500π cubic inches.