The number of solutions to the trigonometric equation is; 1 solution which is x = 270°
How to find the trigonometric solution?The trigonometric equation is given as;
sin²x - 2sin x - 3 = 0
Now, factorizing this gives us;
(sin x - 3)(sin x + 1) = 0
Thus, we now have;
sin x - 3 = 0
sin x = 3
At this point, x has no real solution
For the second factor, we have;
sin x + 1 = 0
sin x = -1
x = sin⁻¹ -1
x = 270°
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needs E15,000 on his
E16,000 so on. Until what age will he have enough money G
(4marks)
Q171
Amal, Balu and Chandran each has some sweets, Amal gives one third of his sweets to
Balu. Balu gives one third of all the sweets he now has to Chandran. Then Chandran gives
one third of all the sweets he now has to Amal. All of them end up having the same
number of sweets, Chandran begins with 40 sweets, How many sweets does Balu have
originally?
(4marks
Answer: Balu originally had 40 sweets.
Step-by-step explanation:
Let x be the number of sweets Balu originally had.
After Amal gives one third of his sweets to Balu, Balu's number of sweets becomes x + (1/3)x = (4/3)x.
After Balu gives one third of his sweets to Chandran, Chandran's number of sweets becomes 40 + (1/3)(4/3)x = 40 + (1/3)x.
After Chandran gives one third of his sweets to Amal, Amal's number of sweets becomes (2/3)x + (1/3)(40 +(1/3)x) = (2/3)x + (1/3)x + 40/3 = (5/3)x + 40/3.
Since all three of them now have the same number of sweets, we can set the number of sweets each of them has equal:
(4/3)x = (5/3)x + 40/3.
Now, we will isolate x by rearranging the equation. Subtracting (5/3)x from both sides, we get:
(4/3)x - (5/3)x = 40/3
Simplifying the left side:
-x/3 = 40/3
Dividing both sides by -1/3:
x = 40
Thus, Balu originally had 40 sweets.
Analyze the function f(x) = - tan 4x. Include:
- Domain and range
- Period
- Two Vertical Asymptotes
For the function f(x) = -tan 4x,
Domain = π[(2n+1)/8] < x < π[(2n+3)/8] Range = set of all real numbers The period = π /4Two vertical asymptotes = π/8 and -π/8Given the function
f(x) = -tan 4x
The domain of the function is the set of all possible inputs of the function
The range is set of all possible outputs of the function
Here the function is
f(x) = -tan 4x
Domain of the function will be
π[(2n+1)/8] < x < π[(2n+3)/8]
The range of the given function is set of all real numbers
The period = π /4
Two vertical asymptotes are π/8 and -π/8
Therefore, the domain, range period and the two vertical asymptotes of the function has been found
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You are given the three vectors X, Y, and Z. Vector
X=(3, 2), vector Y= {-4, 3), and vector Z= {7, -1}.
What is the magnitude of the resultant vector X-Z+Y?
F. -10
G.-8
H. 8
J. 10
K. 12
Answer:
J.10
Step-by-step explanation:
You just have to add the numbers:
3 + 2 + (-4) + 3 + 7 + (-1) = 10
hope u like it, bye
Please help me with this question
Answer: it’s C. My dear <3
Step-by-step explanation: hope this helps (btw I’m just being nice so don’t ask)
In △ABC', BD is the perpendicular bisector of ADC . Based upon this information, which statements below can be proven? I.BD is a median. II. BD bisects ABC III. △ABC is isosceles.
(1) I and II, only
(3) II and III, only
(2) I and III. only (4) L I and II
Based upon this information, (2) I and III only statements can be proven.
From the given information, we can prove that statement II is true, i.e., BD bisects ABC.
Proof:
Since BD is the perpendicular bisector of ADC, we have AD = CD and ∠ADB = ∠CDB = 90°. Thus, triangles ABD and CBD are congruent (by the hypotenuse-leg congruence criterion), which implies AB = BC and ∠ABD = ∠CBD. Therefore, BD bisects ∠ABC.
However, we cannot prove that statements I or III are true based solely on the given information.
Statement I (BD is a median) would be true if we had additional information that AD = DB = DC, but this is not necessarily true based on the given information.
Statement III (△ABC is isosceles) would be true if we had additional information that AB = BC, but this is not necessarily true based on the given information. In fact, it is only guaranteed that AB = BC if AD = BD = DC, which is not necessarily the case.
Therefore, the correct answer is (2) I and III, only.
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You have a wire that is 35 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minimum?
The circumference of the circle is 110 m.
What is the circumference of the circle?Let us assume that the wire has been cut into two equal halves thus the radius of the circle would be 35 m/2 = 17.5 m
Then;
C = 2πr
C = circumference
r = radius
"pi" is a mathematical constant approximately equal to 3.14 and "r" is the radius of the circle. If the diameter of the circle is known, the radius can be calculated by dividing the diameter by 2.
C = 2 * 3.142 * 17.5
C = 110 m as we can see here
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You have a job with a gross pay of $49946.
to answer the following questions based on the 2021 federal income tax brackets:
a. What is your tax bracket?
%
b. How much do you owe for federal taxes on:
filled tax brackets?
$
the partially filled tax bracket?
$
Based on the 2021 federal income tax brackets, the gross pay of $49,946 puts you in the 22% tax bracket. For the fully filled tax bracket, you would owe $10,890.50 in federal taxes, and for the partially filled tax bracket, you would owe $4,994.60 in federal taxes.
You're flying from Joint Base Lewis-McChord (JBLM) to an undisclosed location 44 km south and 227 km east. Mt. Rainier is located approximately 56 km east and 40 km south of JBLM. If you are flying at a constant speed of 800 km/hr, how long after you depart JBLM will you be the closest to Mt. Rainier?
The time JBLM will you be the closest to Mt. Rainier will be 5.12 minutes.
What is Distance?A measurement of the distance between two places along a line or line segment.
The plane's flight route follows the line.
y = -125/135x = -25/27x
The direction of the perpendicular line passing across Mt. Rainier is,
y = 27/25(x -56) -40
In standard form, these two equations are,
25x +27y = 0
27x -25y = 2512
The coordinates at the closest approach are the answers to these two equations:
(x, y) = (33912/677, 31400/677)
The Pythagorean theorem (distance formula) states that the distance d from the origin to this point is as follows:-
d = 1256√(2/677) km
The airplane's speed can be used to convert this distance to time:
1256√(2/677) X 60/800 = 94.2√(2/677) ≈ 5.120019 mins
So, 5.12 minutes after leaving JBLM, Mt. Rainier will be the nearest.
The attached graph shows the geometry of the problem.
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The Surface area of a cell phone screen is 5900mm². Use the fact that 10mm = 1cm to Convert this area to cm²
When the surface area of the cell phone is converted to Cm² it would be. = 59cm²
How to convert mm² to cm² ?The surface area of the cell phone screen = 5900mm²
But 10 mm = 1 cm
When squared after calculating the area,
100 mm² = 1 cm²
5900 mm² = X cm²
Make X cm² the subject of formula;
X cm² = 5900/100 = 59cm²
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Suppose X is a random variable with mean X and standard deviation oXSuppose Y is a random variable with mean Y and standard deviation oY. The mean of X + Y is:a. MX+MYb.uX/oX) + (Y /oY). c. 1X+uY, but only if X and Y are independent. d (uX/oX) + (Y/oY), but only if X and Y are independent.
The answer is (a) MX + MY. Whether or not X and Y are independent, we cannot simplify (a) or (b) further.
The mean of X + Y is:
E(X + Y) = E(X) + E(Y)
So the answer is not (a) or (b).
(c) is incorrect because the formula given is only true if X and Y are independent, but no such assumption is given in the problem.
(d) is also incorrect because we cannot simply divide the means by the standard deviations to get the standard normal variables, especially when the variables X and Y have different means.
Therefore, the answer is (a) MX + MY.
Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.
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7. During a sale at the Honda dealership, Mr. Sherman notices the great 10 points
sales price ($33,500) and purchases two cars for his daughters. What will
he pay in total for the two cars, including 8.875% sales tax?
A. $72,946.25
B. $36,473.13
C. $41,372.50
D. $82,745
Answer: A
Step-by-step explanation:
First you add up the total prices of both cars
$67,000
Next find 8.875% of that and add to total price of both cars
Answer= $72,946.25
What is the answer to the problem 8(w+3)=_w+_ ?
what is the volume of the prism?
The volume of the prism with a trapezoidal base is 312 m³
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
The volume of the prism is the product of the base area and the height. It is given by:
Volume = area of base * height
The prism shown in the diagram is a trapezoid prism, hence:
Area of base = (1/2)(5 + 8)(4) = 26 m²
Volume = area of base * height
Volume of prism = 26 m² * 12 m = 312 m³
The volume of the prism is 312 m³
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7x7+24x5(1x+24)=1
SOlve for x
solve for x
....................
The solution of x in the rhombus is 3
How to determine the solution of x in the shapeFrom the question, we have the following parameters that can be used in our computation:
The rhombus
Also, we have
LN = 14
AN = x + 4
Using the above as a guide, we have the following equation:
LN = 2 * AN
substitute the known values in the above equation, so, we have the following representation
2 * (x + 4) = 14
Evaluate the expression
x + 4 = 7
Subtract 4 from both sides
so, we have the following representation
x = 3
Hence, the solution is 3
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Write an equation for the line that contains the points (4,-2) and (-2,0)
The linear equation that passes through the two given points is:
y = (-1/3)*x - 2/3
How to write the equation of the line with the two points?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If a line passes through the points (x₁, y₁) and (x₂, y₂) then the slope can be written as:
a = (y₂ - y₁)/(x₂ - x₁)
Here we know that the line passes through (4, -2) and (-2, 0), then the slope is:
a = (0 + 2)/(-2 - 4)= 2/-6 = -1/3
y = (-1/3)*x + b
To find the value of b, we can replace the values of any of the points in the equation, if we use (-2, 0) we will get:
0 = (-1/3)*-2 + b
0 = 2/3 + b
-2/3 = b
The linear equation is y = (-1/3)*x - 2/3
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Need help really please
Answer:
Step-by-step explanation:
No pressure. You just need to look for the number that when added to the other given number, will give the same as the sum on the other side.
For instance, The top-left question:
4+6 = x+8 (let x be the box)
x= 4+6-8
x=2.
OR, since 4 + 6 =10,
you look for a number when added to 8, that gives 10.
That number is 2.
Hope this helps :]
mz1 = (2x +29)° and mz2 = (5x+20)°. If 21 and
22 are vertical angles, what are mz1 and mz2?
Answer:
Step-by-step explanation:
m∠2 = 90° - 56° = 34°. So, m∠1 = m∠2 = 34°
here the answers
its (3,-2) i did the test
I jsut need some answers thank you mwa
ill give brainliest to whoever can answer
Robert uses f(x) = 1000(1.06)^x to calculate the interest he earns each year for his savings account. What is the yearly interest rate as a percent?
The GCF of 20 and another number is 4. Which of these could be the other
number? Select all that apply.
A 4
B 8
C 10
D 20
E 80
Answer:
Step-by-step explanation:
A because the gcf of 20 is 4 and the gcf of 4 is 4
Answer:
b
..,..............................................is my answer
A bakery can make 42 cheesecakes for every 6 blocks of cream cheese. Which table represents the relationship between the number of cheesecakes the bakery makes and the number of blocks of cream cheese the bakery uses?
Answer:
Step-by-step explanation:
Assume a TCP sender is continuously sending 1,126-byte segments. If a TCP receiver advertises a window size of 6,353 bytes, and with a link transmission rate 10 Mbps an end-to-end propagation delay of 14.4 ms, what is the utilization? Assume no errors, no processing or queueing delay, and ACKs transmit instantly. Also assume the sender will not transmit a non-full segment. Give answer in percentages, rounded to one decimal place, without units (e.g. for an answer of 10.43% you would enter "10.4" without the quotes).
If a TCP receiver advertises a window size of 6,353 bytes, and with a link transmission rate 10 Mbps an end-to-end propagation delay of 14.4 ms, then the utilization is 0.4%.
What is Round trip time?
The round-trip time (RTT) is the time it takes from when a browser submits a request to when it receives a response from a server, measured in milliseconds.
The time it takes for a segment to be transmitted over the link is:
time per segment = 1,126 bytes / 10 Mbps = 0.00009008 seconds
The end-to-end propagation delay is 14.4 ms, or 0.0144 seconds.
The time it takes for an ACK to be sent back from the receiver is the propagation delay plus the time it takes for the ACK segment to be transmitted over the link:
time for ack = 0.0144 seconds + (1 segment / 10 Mbps) = 0.014508 seconds
The time it takes for the sender to receive an ACK after sending a segment is the time it takes for the segment to be transmitted, plus the time it takes for the ACK to be sent back:
round trip time = time per segment + time for ack = 0.00009008 + 0.014508 = 0.0145
The number of segments that can be in flight at any given time is the window size divided by the segment size:
segments in flight = 6,353 bytes / 1,126 bytes = 5.645 segments
We can now calculate the maximum sending rate of the sender by dividing the number of segments in flight by the round-trip time:
max sending rate = segments in flight / round trip time = 387.165 segments per second
The utilization of the link is the sending rate divided by the link rate, multiplied by 100 to get a percentage:
utilization = (max sending rate / 10 Mbps) * 100 = 0.00387165 * 100 = 0.387165%
Rounding to one decimal place, the utilization is 0.4%.
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Algebra: let f(x)= 3x+7 f^-1 (x)=
Answer:
Step-by-step explanation:
To find the inverse of a function, we need to switch the x and y values and solve for y (or x, depending on how the original function is written). The inverse of the function f(x) = 3x + 7 is written as f^-1(x). To find f^-1(x), we can follow these steps:
Replace the function f(x) with y to make it easier to manipulate: y = 3x + 7.
Swap the x and y variables: x = 3y + 7.
Solve for y:
Subtract 7 from both sides to get x - 7 = 3y.
Divide both sides by 3 to get (x - 7) / 3 = y.
Write the inverse function using f^-1(x) instead of y:
f^-1(x) = (x - 7) / 3
So, the inverse of the function f(x) = 3x + 7 is f^-1(x) = (x - 7) / 3.
Simplify: 3√28 + 4√7 + 2√32
HELP!!!
Answer:
[tex]10\sqrt{7}+8\sqrt{2}[/tex]
Step-by-step explanation:
Lets simplify.
[tex]3\sqrt{28}+4\sqrt{7} +2\sqrt{32}[/tex]
Rewrite [tex]28[/tex] as [tex]2^2*7[/tex]
[tex]3\sqrt{2^2*7}+4\sqrt{7} +2\sqrt{32}[/tex]
Pull terms out from under the radical.
[tex]3\left(2\sqrt{7} \right)+4\sqrt{7} +2\sqrt{32}[/tex]
[tex]6\sqrt{7} \right)+4\sqrt{7} +2\sqrt{32}[/tex]
Add [tex]6\sqrt{7}[/tex] and [tex]4\sqrt{7}[/tex].
[tex]10\sqrt{7} +2\sqrt{32}[/tex]
Rewrite [tex]32[/tex] as [tex]4^2*2[/tex].
[tex]10\sqrt{7} +2\sqrt{4^2*2}[/tex]
Pull terms out from under the radical.
[tex]10\sqrt{7}+2\left(4\sqrt{2}\right)[/tex]
[tex]10\sqrt{7}+8\sqrt{2}[/tex]
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A. 600 square inches
B. 768 square inches
C. 648 square inches
D. 792 square inches
Answer:
Step-by-step explanation:
area of pole=75×8=600 square inch
area if sign=12×12+1/2×12×4
=144+24
=168 square inches
total area=600+168
=768 square inches
what is the value of 8.4n - 3.2p, when n=4 and p=-2
Answer:
33.6-(-6.4)=40
Step-by-step explanation:
1. 8.4×4
2. 3.2x-2
3. 33.6-(-6.4)
4. 40
the two negatives become positive
Which of the following is an example of a continuous random variable?a. A Bernoulli trial
b. Binomial random variable
c. Normal random variable
d. Discrete uniform random variable
An example of a continuous random variable is a Normal random variable.
What is a normal random variable?
A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. A random variable can be either discrete (having definite values) or continuous (any value in a continuous range).
Here, we have
We have to determine the example of a continuous random variable.
We concluded that the example of a continuous random variable is a normal random variable.
Hence, an example of a continuous random variable is a Normal random variable.
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$10000 is deposited in an account earning 8% interest compounded continuously. Use the continuous interest formula below to determine how long it takes for the amount in the account to double. Round answer to 2 decimal places.
A=Pe^rt
____Years?
By using the continuous interest formula, we get 8.54 years that the amount will take to double itself.
What is continuous interest formula?The continuous interest formula is used to calculate the future value of a compound interest investment. It is written as follows:
Future Value = Principal × [tex](1 + r)^{n}[/tex]
where Principal is the original investment, r denotes the yearly interest rate, and n denotes the number of compounding periods.
The continuous interest formula is used to compute the future worth of an investment given its current value, yearly interest rate, number of times the interest is compounded each year, and number of years held.
In the given question,
A = A_0[tex]e^{rt}[/tex]
2A_0 = A_0[tex]e^{rt}[/tex]
2 = [tex]e^{rt}[/tex]
ln(2) = rt
t = [tex]\frac{2}{r}[/tex]
t = [tex]\frac{2}{0.08}[/tex]
t = 8.54 years
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