Answer:
[tex]L(f(t)) = \dfrac{6}{S^2+1} [\sqrt{3} \ S +1 ][/tex]
Step-by-step explanation:
Given that:
[tex]f(t) = 12 cos (t- \dfrac{\pi}{6})[/tex]
recall that:
cos (A-B) = cos AcosB + sin A sin B
∴
[tex]f(t) = 12 [cos\ t \ cos \dfrac{\pi}{6}+ sin \ t \ sin \dfrac{\pi}{6}][/tex]
[tex]f(t) = 12 [cos \ t \ \dfrac{3}{2}+ sin \ t \ sin \dfrac{1}{2}][/tex]
[tex]f(t) = 6 \sqrt{3} \ cos \ (t) + 6 \ sin \ (t)[/tex]
[tex]L(f(t)) = L ( 6 \sqrt{3} \ cos \ (t) + 6 \ sin \ (t) ][/tex]
[tex]L(f(t)) = 6 \sqrt{3} \ L [cos \ (t) ] + 6\ L [ sin \ (t) ][/tex]
[tex]L(f(t)) = 6 \sqrt{3} \dfrac{S}{S^2 + 1^2}+ 6 \dfrac{1}{S^2 +1^2}[/tex]
[tex]L(f(t)) = \dfrac{6 \sqrt{3} +6 }{S^2+1}[/tex]
[tex]L(f(t)) = \dfrac{6( \sqrt{3} \ S +1 }{S^2+1}[/tex]
[tex]L(f(t)) = \dfrac{6}{S^2+1} [\sqrt{3} \ S +1 ][/tex]
Someone help me understand
Answer:
f¯¹(x) = 23/ (6x + 3)
Step-by-step explanation:
f(x) = (23 – 3x)/6x
The inverse, f¯¹, for the above function can be obtained as follow:
f(x) = (23 – 3x)/6x
Let y be equal to f(x)
Therefore, f(x) = (23 – 3x)/6x will be written as:
y = (23 – 3x)/6x
Next, interchange x and y.
This is illustrated below:
y = (23 – 3x)/6x
x = (23 – 3y)/6y
Next, make y the subject of the above expression. This is illustrated below:
x = (23 – 3y)/6y
Cross multiply
6xy = 23 – 3y
Collect like terms
6xy + 3y = 23
Factorise
y(6x + 3) = 23
Divide both side by (6x + 3)
y = 23/ (6x + 3)
Finally, replace y with f¯¹(x)
y = 23/ (6x + 3)
f¯¹(x) = 23/ (6x + 3)
Therefore, the inverse, f¯¹, for the function f(x) = (23 – 3x)/6x is
f¯¹(x) = 23/ (6x + 3)
Write an equation for a line perpendicular to y = − 5 x + 5 and passing through the point (5,5)
Answer:
The answer is
[tex]y = \frac{1}{5} x + 4[/tex]Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the line perpendicular to
y = -5x + 5 we must first find the slope of
Comparing with the general equation above
Slope = - 5
The slope of the perpendicular line is the negative inverse of the slope of the original line
Slope of perpendicular line = 1/5
Equation of the line using point (5,5) and slope 1/5 is
[tex]y - 5 = \frac{1}{5} (x - 5)[/tex][tex]y - 5 = \frac{1}{5} x - 1[/tex][tex]y = \frac{1}{5} x - 1 + 5[/tex]We have the final answer as
[tex]y = \frac{1}{5} x + 4[/tex]Hope this helps you
Answer:
y=0.2x+4 or y=1/5 x+4.
Step-by-step explanation:
When one line is perpendicular to another, you have to find the opposite reciprocal for the slope of the given equation.
For instance, if you have the number 5, the reciprocal of 5 is 1/5 or 0.2. The opposite of positive is negative. Therefore, it is -0.2.
Therefore, if the slope of the first equation is -5, the slope for the next equation is 1/5. Reciprocal of -5 is -1/5. The opposite of -1/5 is positive 1/5. Or, the opposite of negative is positive. Therefore, it would be 1/5x.
However, we are not done.
Since we are given that the line passes through the point (5,5), we need to find the y-intercept of this equation.
The formula for slope-intercept is y=mx+b.
M is your slope
B is your y-intercept.
We can find the y-intercept by actually plugging in the point (5,5) into the new equation.
5=0.2(5)+b.
5 is x and 5 is also y.
(x,y).
Simplify the equation by multiplying 0.2 times 5. That is equal to 1.
We now have 5=1+b.
Isolate for the letter "b" by subtracting 1 from both sides.
1-1 is 0.
5-1 is 4.
Therefore, b=4.
Finally, we can plug in the y-intercept into the new equation.
y=0.2 or 1/5x+4.
I hope this helps! I also hope you have a great rest of your day!
Each corner of a rectangular prism is cut off. Two (of the eight) cuts are shown. How many edges does the new figure have? Assume that the planes cutting the prism do not intersect anywhere in or on the prism. EXPLAIN PLS
Answer:
36
Step-by-step explanation:
Each cut creates a triangular face where the corner used to be. That face adds three edges to the figure. The 8 cuts add a total of 8×3 = 24 edges to the 12 edges the prism already had.
The new figure has 12+24 = 36 edges.
how many hours are there from 10:30 on Monday to 11:30 on Tuesday
Answer:
25 hours.
Step-by-step explanation:
We are to find the number of hours from:
Monday at 10:30
to
Tuesday at 11:30
Since the question does not state whether the times are in A.M / P.M ,
There are 24 hours upto 10:30 on Tuesday.
Adding 1 hour gives 11:30
So the answer = 24 + 1 = 25 hrs
Answer:
25 hours
Step-by-step explanation:
1 day=24 hours
11.30-10.30=1 hour
----------------------------
add the total 25 hours
Classify the expression: 5x + 3x^2 − 7x^3 + 2
A. Linear Expression
B. Quadratic Expression C. Cubic Expression
D. Quartic Expression
Answer:
C. Cubic expression.
Step-by-step explanation:
The highest exponent is 3 ( in the term 7x^3) so it is cubic.
Answer:
C. Cubic Expression.
Step-by-step explanation:
5x + 3x^2 - 7x^3 + 2
= 3x^2 - 7x^3 + 5x + 2
= -7x^3 + 3x^2 + 5x + 2
The highest value of exponent in the equation is 3.
For a linear expression, the highest exponent is 1.
For a quadratic expression, the highest exponent is 2.
For a cubic expression, the highest exponent is 3.
For a quartic expression, the highest exponent is 4.
So, this is C. Cubic Expression.
Hope this helps!
Which parent functions have an intercept at (0,0)Choose all that are correct.
Linear
Quadratic
Radical
Absolute Value
Rational
Exponential
Logarithmic (Log)
Cubic
Cube Root
Answer:
Linear, Quadratic, Radical, Absolute Value, Cubic, Cube Root
Step-by-step explanation:
To find:
Which functions have an intercept at (0, 0).
That means, when we put a value [tex]x=0[/tex] in the [tex]y =f(x)[/tex], value of [tex]y=0[/tex].
Let us discuss each parent function one by one:
1. Linear:
[tex]y = x[/tex]
When we put x = 0, y = 0
Therefore, it has intercept at (0, 0).
2. Quadratic:
[tex]y = x^2[/tex]
When we put x = 0, y = 0
Therefore, it has intercept at (0, 0).
3. Radical:
[tex]y = \sqrt x[/tex]
When we put x = 0, y = 0
Therefore, it has intercept at (0, 0).
4. Absolute Value:
[tex]y = |x|[/tex]
When we put x = 0, y = 0
Therefore, it has intercept at (0, 0).
5. Rational:
[tex]y = \dfrac{1}{x}[/tex]
When we put [tex]x = 0\Rightarrow y \rightarrow \infty[/tex]
Therefore, it does not have intercept at (0, 0).
6. Exponential:
[tex]y = b^x[/tex]
b is any base
When we put [tex]x = 0\Rightarrow y =1[/tex]
Therefore, it does not have intercept at (0, 0).
7. Logarithmic:
[tex]y = logx[/tex]
When we put [tex]x = 0 \Rightarrow y\rightarrow[/tex] Not defined
Therefore, it does not have intercept at (0, 0).
8. Cubic:
[tex]y = x^3[/tex]
When we put [tex]x = 0\Rightarrow y =0[/tex]
Therefore, it has intercept at (0, 0).
9. Cube Root:
[tex]y = \sqrt[3]x[/tex]
When we put [tex]x = 0\Rightarrow y =0[/tex]
Therefore, it has intercept at (0, 0).
Find the sum to infinity of the series 2+5/4+11/16+23/64+..........up to the infinity.
infinity
We have
[tex]2+\dfrac54+\dfrac{11}{16}+\dfrac{23}{64}+\cdots=\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}{4^n}[/tex]
(notice that each denominator is a power of 4, and each numerator is one less than some multiple of 3, in particular 3 times some power of 2)
Recall for [tex]|x|<1[/tex], we have
[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]
So we have
[tex]\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}4=3\sum_{n=0}^\infty\left(\frac12\right)^n-\sum_{n=0}^\infty\left(\frac14\right)^n=\frac3{1-\frac12}-\frac1{1-\frac14}=\boxed{\frac{14}3}[/tex]
rate = 45 mph time=4 hours distance =
━━━━━━━☆☆━━━━━━━
▹ Answer
180 miles
▹ Step-by-Step Explanation
Distance = mph * hours
Distance = 45 mph * 4 hrs
Distance = 180 miles
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Simplify to create an equivalent expression.
\qquad{7n-(4n-3)}7n−(4n−3)
Answer:
[tex]3n + 3[/tex]
[tex]3(n+1)[/tex]
Step-by-step explanation:
Given
[tex]7n - (4n - 3)[/tex]
Required
Simplify
To simplify the given expression, you start by opening the bracket
[tex]7n - (4n - 3)[/tex]
[tex]7n - 4n + 3[/tex]
Next, you perform arithmetic operations on like terms
[tex]3n + 3[/tex]
The answer can be further simplified;
Factorize [tex]3n + 3[/tex]
[tex]3(n+1)[/tex]
Hence;
[tex]7n - (4n - 3)[/tex] when simplified is equivalent to [tex]3n + 3[/tex] or [tex]3(n+1)[/tex]
Answer:
3n+n
Step-by-step explanation:
Describe all numbers x that are at a distance of 2 from the number 8. Express this using absolute value notation.
Answer:
The numbers that are at a distance of 2 from the number 8 can be expressed using absolute value notation as:
|x - 8| = 2
Step-by-step explanation:
The numbers that are at a distance of 2 from the number 8 are the numbers that are satisfied by the equation:
|x - 8| = 2
The equation is written in the notation of absolute value as required.
Stock prices used to be quoted using eighths of a dollar. Find the total price of the transaction. 400 shares of national semi at 135 1/2
Answer:
The value is [tex]T = \$54200[/tex]
Step-by-step explanation:
From the question we are told that
The number of shares is n = 400
The rate of each share is [tex]k = 135\frac{1}{2} = 135.5[/tex]
Generally the total price is mathematically represented as
[tex]T = 400 * 135.5[/tex]
[tex]T = \$54200[/tex]
Joseph is 33 years old. Five years ago, He was twice as old as Ann. How old will Ann be in 5 years time?
Answer:
19 years oldStep-by-step explanation:
[tex]Joseph = 33 \:years \:old\\ \\Let \: ann's \:age be x\\\\33-5 = 2x\\\\28 = 2x\\\\Divide \:both \:sides \:of \:the \:equation \: by \:2\\\\\frac{2x}{2} = \frac{28}{2} \\\\x = 14\\\\Ann's \:present \:age \:= 14\\\\In \:5 \:years \:time ; \\\\14+5 = 19\\[/tex]
Which of the following units is incommensurable with kilograms
Answer:
All units of measurement that are not based on or do not measure mass or weight and volume are incommensurable with kilograms.
Step-by-step explanation:
A measure unit is said to be incommensurable with another if it does not have the same measurement basis with the other measure unit. For example, a measure in time cannot be measured in kilograms because time is measured in hours, minutes, seconds, days, etc. But, if a measurement base can be applied to two or more measurement units, then the measurement units are commensurable with the measurement base.
You calculate the correlation between height and weight for a simple random sample of 50 students from your college. Another student does the same for a simple random sample of 200 students from the college. The other student should get:_________.
A. a correlation greater than 1.
B. a higher value for the correlation.
C. about the same value for the correlation.
D. a lower value for the correlation.
E. a correlation less than-1.
Answer:
B
Step-by-step explanation:
A researcher wishes to examine the relationship between years of schooling completed and the number of pregnancies in young women. Her research discovers a linear relationship, and the least squares line is: ˆ y = 3 − 5 x y^=3-5x where x is the number of years of schooling completed and y is the number of pregnancies. The slope of the regression line can be interpreted in the following way:
1.) When amount of schooling increases by one year, the number of pregnancies decreases by 4.
2.) When amount of schooling increases by one year, the number of pregnancies increases by 4.
3.) When amount of schooling increases by one year, the number of pregnancies increases by 5.
4.) When amount of schooling increases by one year, the number of pregnancies decreases by 5.
Answer:
1. When amount of schooling increases by one year, the number of pregnancies will decrease by 4.
Step-by-step explanation:
Regression analysis is a statistical technique which is used for forecasting. It determines the relationship between two variables. It determines the relationship of two or more dependent and independent variables. It is widely used in stats to find trend in the data. It helps to predict the values of dependent and independent variables. In the given question, there is regression equation given. X and Y are considered as dependent variables. When number of schooling increases by 1 year then number of pregnancies will decrease by 4
An aluminum bar 4 feet long weighs 24 pounds. What is the weight of a similar bar that is 3 feet 3 inches long? WILL MARK BL
Answer:
19.5 pounds
Step-by-step explanation:
1 foot = 12 inches
3 inches = 3/12 = 0.25 feet
3 feet 3 inches = 3.25 feet
then:
24 pounds is 4 feet
A pounds is 3.25 feet
A = 24*3.25/4
A = 19.5 pounds
Answer:
19.50 pounds
Step-by-step explanation:
1 foot = 12 inches
3 inches = 3/12 = 0.25 feet
3 feet 3 inches = 3.25 feet
then:
24 pounds is 4 feet
A pounds is 3.25 feet
A = 24*3.25/4
A = 19.50 pounds
What is the value of x to the nearest tenth?
Step-by-step explanation:
Hello!!!
Let's workout with this figure.
BC is a chord, O is the centre and OA is the perpendicular bisector.
AB = 1/2 of BC (according to circle's theorem)
so, A B = 1/2 × 25.6
Therefore, the measure of AB is 12.8.
now, let's have a small work with triangle AOB.
as it is a Right angled triangle, taking angle B as refrence angle we get,
p=x
b=12.8
h= OB = 16 (it is also a radius.)
now,
by Pythagoras relation we get,
[tex]p = \sqrt{ {h}^{2} - {b}^{2} } [/tex]
or, x = root 16^2- 12.8 ^2
by simplification, we get;
the measure of x is 9.6.
Therefore, the value of x is 9.6.
Hope it helps...
Claire has to go to the movie theater the movie starts at 4:15 pm it is a 25min walk to the theater from her home what time dose the have to leave the house to get there on time
Answer:
3:50 pm
Step-by-step explanation:
Count backwards with the 25 min.
4:15 - 15 min >
25 - 15 = 10 >
4:00 - 10 = 3:50
Answer:
3:50 pm
Step-by-step explanation:
Starting Time + Time Interval = Ending Time
=> Ending Time - Time Interval = Starting Time
Ending Time = 4:15 pm
Time Interval = 25 minutes
Starting Time = x
=> 4:15 - 25 = x
=> 4:15 - 15 - 10 = x
=> (4:15 - 15) - 10 = x
=> 4:00 - 10 = x
=> 3:50 pm = x
So, she needs to leave the house at 3:50 pm to get to the movie theater on time.
Solve the following equation for x to find the total number of sale items stocked on the shelves of a toy store for a certain week: x = 0.7x + 24 How many total items were stocked for that week? 14 56 80 10
Answer:
80
Step-by-step explanation:
The total of 80 items were stocked for that week.
What is a system of equations?
A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Solve equation for x to find the total number of sale items stocked on the shelves of a toy store for a certain week:
x = 0.7x + 24
We need to find How many total items were stocked for that week
Solving;
x = 0.7x + 24
x - 0.7x = 24
0.3x = 24
x = 80
Therefore, the total of 80 items were stocked for that week.
Learn more about equations here;
https://brainly.com/question/10413253
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What is the approximate diameter of a sphere whose surface area is 83.96 square inches? Use π = 3.14.
Answer:
5.17
Step-by-step explanation:
The surface area of a sphere is 4[tex]\pi[/tex]r².
83.96=4[tex]\pi[/tex]r²
Divide by 4
20.99=3.14r²
divide by 3.14
6.6847=r²
take the square root
2.585=r
mulitply by 2 (diameter is twice the radius)
5.17
The diameter of the sphere is 5.17 inches.
What is surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any object is called as the surface area.
The surface area of a sphere is 4πr².
83.96=4πr²
Divide by 4
20.99=3.14r²
Divide by 3.14
6.6847=r²
Take the square root.
2.585=r
Multiply by 2 (diameter is twice the radius).
r= 2 x 2.585
r = 5.17 inches
Therefore, the diameter of the sphere is 5.17 inches.
To know more about a surface area follow
https://brainly.com/question/1293273
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To paint his apartment, Alex but 6 gallons of paint to cover 1440 ft.². What is the ratio of square feet to gallons of paint?
Answer & Step-by-step explanation:
The ratio of square feet to gallons of paint:
[tex]1440:6[/tex]
This can also be written as:
[tex]\frac{1440}{6}[/tex]
This fraction can be simplified by dividing the numerator and denominator by 6:
[tex]\frac{1440}{6}=\frac{240}{1}[/tex]
So, the ratio of square feet to gallons of paint is:
1 gallon for every 240 ft².
:Done
Translate and solve: 54 greater than x is greater than 216
Answer:
x >162
Step-by-step explanation:
x+54 > 216
Subtract 54 from each side
x+54-54 > 216 - 54
x >162
Answer:
[tex]\huge \boxed{{x>162}}[/tex]
Step-by-step explanation:
[tex]x+54 > 216[/tex]
[tex]\sf Subtract \ 54 \ from \ both \ parts.[/tex]
[tex]x+54 -54> 216-54[/tex]
[tex]x>162[/tex]
Jerry walked a dog from 6:40 a.m. to 7:30 a.m. one day. If he was paid at the rate of $6 per hour, how much did he cam that day?
You want to construct a pool that will hold 3496 ft. of water if the pool is to be 23 feet long and 19 wide how deep will it need to be
Answer:
8 feet deep
Step-by-step explanation:
volume = length x width x depth
3496 = 23 x 19 x d
3496 = 437 x d
divide both sides by 437
d = 8
What is numbers 1-30 added all together
Answer:
465
Step-by-step explanation:
The sum of consecutive numbers has a formula, and it's
[tex]\frac{n(n+1)}{2}[/tex].
Where n is the amount of numbers.
From 1-30, it's 30 numbers, so:
[tex]\frac{30(30+1)}{2} \\\\\frac{30(31)}{2} \\\\\frac{930)}{2} \\\\\\465[/tex]
Hope this helped!
WILLL GIVE 5 STARS BRAINIEST AND THANKS AND 20 POINTS EACH ANSWER In Minot, North Dakota, the temperature was 15 degrees Fahrenheit at 4:00 P.M. By 11:00 P.M. the temperature had fallen 17 degrees. What was the temperature at 11:00 P.M.?
Answer:
-2 degrees
Step-by-step explanation:
Our original temperature is 15. We're asked to find the temperature at 11:00 P.M., which is 17 less than 15. We can set up the equation 15 - 17 to get -2. This is your answer.
Answer:
The temperature was -2 degrees Fahrenheit
Step-by-step explanation:
The starting temperature was 15 degrees
It fell 17 degrees
15 -17 = -2
The temperature was -2 degrees Fahrenheit
Please help with this
Answer:
B) x=80°
Step-by-step explanation:
This is a hexagon, so it has interior angles equaling 720°. (N-2)*180
So the equation would be
78+134+136+132+2x+x=720
480+3x=720
3x=720-480
3x=240
x=80°
According to the U.S. Energy Information Administration the average number of televisions per household in the United States was 2.3. A college student claims the average number of TV’s per household in the United States is different. He obtains a random sample of 73 households and finds the mean number of TV’s to be 2.1 with a standard deviation of 0.84. Test the student’s claim at the 0.01 significance level.
Let [tex]\mu[/tex] be the average number of televisions per household in the United States .
As per given ,
[tex]H_0:\mu =2.3\\\\ H_a:\mu\neq2.3[/tex]
Since [tex]H_a[/tex] is two-tailed and population standard deviation is unknown, so the test is two-tailed t-test.
For sample : Sample size : n= 73, sample mean: [tex]\overline{x}[/tex] = 2.1, sample standard deviation : s= 0.84.
[tex]t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}[/tex]
[tex]t=\dfrac{2.1-2.3}{\dfrac{0.84}{\sqrt{73}}}\\\\ t=-2.034[/tex]
T-critical value for degree of freedom n-1 = 73-1=72 and 0.01 significance level is 2.646 . [By students' t-distribution table]
Since, [tex]|2.034|<2.646[/tex] i.e. [tex]|T_{cal}|<|T_{crit}|[/tex]
This means we cannot reject null hypothesis.
We conclude that the average number of televisions per household in the United States is 2.3 at the 0.01 significance level.
simplify radical -50
Answer:
[tex]5i\sqrt{2}[/tex]
Step-by-step explanation:
If we want to convert [tex]\sqrt{-50}[/tex] into a radical simplified, we need to find two numbers that multiply to be -50 and one of them can be squared.
[tex]\sqrt{-50} = \sqrt{-25 \cdot 2}[/tex]
The square root of -25 is 5i.
So:
[tex]5i\sqrt{2}[/tex]
Hope this helped!
Answer: [tex]=5i\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\sqrt{-50}=\sqrt{-1}\sqrt{50}[/tex]
[tex]\sqrt{-1}\sqrt{50}[/tex]
[tex]\sqrt{5^2\cdot \:2}[/tex]
[tex]=\sqrt{2}\sqrt{5^2}[/tex]
[tex]\sqrt{5^2}=5[/tex]
[tex]=5\sqrt{2}[/tex]
g Which of the following is equivalent to P( A|B)? a. P(A and B) b. P(B|A) c. P(A)/P(B) d. None of these choices.
Answer:
The correct option is D.
But option B is correct if P(A) = P(B).
Step-by-step explanation:
P(A|B) is read as "The probability of A given B".
It is different from the options A, B, and C.
It is equal to option B only if the probability of A is equal to the probability of B. That is P(A|B) = P(B|A) if P(A) = P(B).
