Write each expression as an algebraic (nontrigonometric) expression in u, u > 0.
sin(2sec^-1 u/10)
Answer:
[tex]\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0[/tex]
Step-by-step explanation:
We want to write the trignometric expression:
[tex]\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)\text{ where } u>0[/tex]
As an algebraic equation.
First, we can focus on the inner expression. Let θ equal the expression:
[tex]\displaystyle \theta=\sec^{-1}\left(\frac{u}{10}\right)[/tex]
Take the secant of both sides:
[tex]\displaystyle \sec(\theta)=\frac{u}{10}[/tex]
Since secant is the ratio of the hypotenuse side to the adjacent side, this means that the opposite side is:
[tex]\displaystyle o=\sqrt{u^2-10^2}=\sqrt{u^2-100}[/tex]
By substitutition:
[tex]\displaystyle= \sin(2\theta)[/tex]
Using an double-angle identity:
[tex]=2\sin(\theta)\cos(\theta)[/tex]
We know that the opposite side is √(u² -100), the adjacent side is 10, and the hypotenuse is u. Therefore:
[tex]\displaystyle =2\left(\frac{\sqrt{u^2-100}}{u}\right)\left(\frac{10}{u}\right)[/tex]
Simplify. Therefore:
[tex]\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0[/tex]
¡4 = -1
O True
False
Answer:
Apparently that's false because 4 does not equal -1, 4 is totally 10 times greater than -1
Hopefully that helps
Step-by-step explanation:
simplify - root (9+y)^2 if y <-10
Answer:
− √ ( 9 + y ) 2 > 1
Explanation:
− √ ( 9 + y ) 2 , where y < − 10
Simplify the expression,
− √ ( 9 + y ) 2 = − ( 9 + y ) = − 9 − y
When y < − 10 , − y > 10
Subtract 9 from both sides,
− 9 − y > 1 Hence,
− √ ( 9 + y ) 2 > 1
The value of the expression -√(9 + y)² is -9 which is more than -10. So, it is incorrect.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ -√(9 + y)²
Simplify the expression, then we have
-√(9 + y)² = 0
(9 + y) = 0
9 + y = 0
y = - 9
More about the Algebra link is given below.
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please help i am stuck and trying not to fail lol. also if you can show work pls
Given:
The figure of rectangle.
To find:
a. The diagonal of the rectangle.
b. The area of the rectangle.
c. perimeter of the rectangle.
Solution:
(a)
In a right angle triangle,
[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\sin 30=\dfrac{12}{Hypotenuse}[/tex]
[tex]\dfrac{1}{2}=\dfrac{12}{Hypotenuse}[/tex]
[tex]Hypotenuse=12\times 2[/tex]
[tex]Hypotenuse=24[/tex]
So, the diagonal of the of the rectangle is 24 units.
(b)
In a right angle triangle,
[tex]\tan \theta=\dfrac{Perpendicular}{Base}[/tex]
[tex]\tan 30=\dfrac{12}{Base}[/tex]
[tex]\dfrac{1}{\sqrt{3}}=\dfrac{12}{Base}[/tex]
[tex]Base=12\sqrt{3}[/tex]
Length of the rectangle is 12 and width of the rectangle is [tex]12\sqrt{3}[/tex]. So, the area of the rectangle is:
[tex]Area=length \times width[/tex]
[tex]Area=12 \times 12\sqrt{3}[/tex]
[tex]Area=144\sqrt{3}[/tex]
So, the area of the rectangle is [tex]144\sqrt{3}[/tex] sq. units.
(c)
Perimeter of the rectangle is:
[tex]P=2(length+width)[/tex]
[tex]P=2(12+12\sqrt{3})[/tex]
[tex]P=24+24\sqrt{3}[/tex]
[tex]P\approx 65.57[/tex]
Therefore, the perimeter of the rectangle is about 65.57 units.
i need help on this one too sorry to ask much
Answer:
I can't really see the pic :(
Step-by-step explanation:
Answer:
8^2
Step-by-step explanation:
8*8=8^2 or 64
x+1/2=2 Plssssssssssssssssssssssssssssss help need anwser fast
Answer:
3/2
Step-by-step explanation:
Step-by-step explanation:
[tex]x + \frac{1}{2} = 2 \\ x = 2 - \frac{1}{2} \\ x = \frac{3}{2} [/tex]
Find the area of the following figure: 14ft 6ft 9ft
hi I am sorry I don't know.
Which of the following scenarios represents a possible impulse purchase?
Bryce researches interest rates on the purchase of a new car before deciding to make a purchase.
Bryce budgets for his first new car and decides to purchase a car through a dealership offering 0% interest to first-time buyers.
Bryce purchases the car of his dream by financing the entire cost of the car with a high interest bank loan.
Answer: Bryce purchases the car of his dream by financing the entire cost of the car with a high interest bank loan.
Step-by-step explanation: Please mark brainliest I am trying to level up
can someone solve these for me? its factoring trinomials
you can dm the answers on ig as well if you'd like
Answer:
1.) [tex]\left(x-3\right)\left(x+6\right)[/tex]
2.) [tex]\left(a-3\right)^2[/tex]
3.) [tex]=\left(t+8\right)\left(t-9\right)[/tex]
4.) [tex]=\left(b+7\right)^2[/tex]
Step-by-step explanation:
2.) [tex]=a^2-2a\cdot \:3+3^2[/tex], [tex]\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a-b\right)^2=a^2-2ab+b^2[/tex].
[tex]a=a,\:b=3[/tex]
[tex]=\left(a-3\right)^2[/tex]
3.) [tex]=\left(t^2+8t\right)+\left(-9t-72\right)[/tex][tex]=t\left(t+8\right)-9\left(t+8\right)[/tex], [tex]\mathrm{Factor\:out\:common\:term\:}t+8[/tex].
[tex]=\left(t+8\right)\left(t-9\right)[/tex]
Help......................
plsssssssssssssssss help
Answer:
x = 7
Step-by-step explanation:
Find the point on the graph that has the y-value of 8. Determine its x-value.
1.An electronic prize wheel is programmed to land on "win” 25% of the time on weekdays and 10% of the
time on weekends, and consecutive plays produce winners independently. Suppose we observe a random
sample of 50 outcomes from this machine on a weekday and 100 outcomes from this machine on a
weekend. Which of the following descritts the shape, mean, and standard deviation of the sampling
distribution of the difference in the two sample proportions?
(a) Shape = approximately normal, mean = 0.15, standard deviation = 0.07
(b) Shape = approximately normal, mean = 0.15, standard deviation = 0.05
(c) Shape = approximately normal, mean = 0.35, standard deviation = 0.07
(d) Shape = skewed right, mean = 0.35, standard deviation = 0.05
(e) Shape = skewed right, mean 0.35, standard deviation = 0.0
Answer: D
Step-by-step explanation:
The shape, mean, and standard deviation of the sampling distribution of the difference in the two sample proportions is Shape = skewed right, mean = 0.35, standard deviation = 0.05.
What is the standard deviation?In statistics, the standard deviation of a random variable, data is the square root of its variance.
An electronic prize wheel is programmed to land on "win” 25% of the time on weekdays and 10% of the time on weekends, and consecutive plays produce winners independently.
A random sample of 50 outcomes from this machine on a weekday and 100 outcomes from this machine on a weekend.
[tex]P_{1} = 25%\\ =0.25\\P_{2} = 0.10\\[/tex]
[tex]n_{1} = 50\\n_{2} =100[/tex]
Let x be a random variable for weekdays
[tex]x= N[0.25, 0.25\times(1-0.25)/50]\\x = N[0.25, 0.00375][/tex]
Let y be randomly variable for weekdays
[tex]Y= N[0.10, 0.10\times(1-0.10)/100]\\Y= N[0.10, 0.0009][/tex]
Thus, the shape, mean, and standard deviation of the sampling distribution of the difference in the two sample proportions is Shape = skewed right, mean = 0.35, standard deviation = 0.05.
Learn more about standard deviation;
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guys help asap plsss!
Given:
The triangle ABC rotated 270 degrees clockwise.
The rule of rotation is
[tex](x,y)\to (-y,x)[/tex]
To find:
The coordinates of point B after the given rotation.
Solution:
From the given graph, it is clear that the coordinates of point B are (4,4).
The given rule of rotation is:
[tex](x,y)\to (-y,x)[/tex]
Using this rule, we get
[tex]B(4,4)\to B'(-4,4)[/tex]
The coordinates of point B after the given rotation are (-4,4).
Therefore, the correct option is C.
Help is for now please
find the total service area of this cone. leave your answer in terms of pi.
r=10in h=24in
Answer:
36pie inch²
Step-by-step explanation:
Answer attached
Hope it helps :)
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Answer:
lol dababy ur my idol
Step-by-step explanation:
84b /32b
3b
Answer:
3b^2
Step-by-step explanation:
12b^7 / 4b^5
=12b^7/ 4b^5
=12b^2/4
=3b^2
What is one of the best methods to multiply these binomials: (x+8)(x+7)
A Use the quadratic formula
B Take the square root of both sides
C Distribute everything and one set parentheses to the other set
D Factor out the GCF
Answer:
A for me
Step-by-step explanation:
hope that helps you
how do you add an equation vertically
"Vertically" probably refers to stacking the polynomials on top of each other and aligning them at equal powers of x. So kind of like what you might do when adding two numbers with more than 1 digit each.
For example, the sum 123 + 456 can be computed by adding digits in the same digits place:
… 1 2 3
+ 4 5 6
… 5 7 9
Then for this sum, you have
… - 3x ² - 6x + 8
+ 8x ² + 7x - 14
… 5x ² + x - 6
n 1990, the mean height of women 20 years of age or older was 63.7 inches based on data obtained from theCDC. Suppose that a random sample of 45 women who are 20 years of age or older in 2015 results in a meanheight of 63.9 inches with a standard deviation of 0.5 inch. Does your sample provide sufficient evidencethat women today are taller than in 1990
Answer:
The sample does not provide sufficient evidence that women today are taller than women in 1990.
The difference in mean height is not significant to arrive at such a conclusion.
Step-by-step explanation:
Mean height of women 20 year of age or older in 1990 = 63.7 inches
Mean height of women 20 years of age or older in 2015 = 63.9 inches
The standard deviation of the mean height in 2015 = 0.5 inch
The difference between the two years' mean height is 0.2 (63.9 - 63.7) inch.
This difference is less than the standard deviation of the mean height in 2015.
Therefore, the difference does not provide sufficient evidence that women today are taller than women in 1990.
40 points help me please
Answer:
x=60
Step-by-step explanation:
(1/6)(x+6)=11
Multiply both sides by six:
(6)(1/6)(x+6)=11(6)
x+6=66
Take six from both sides:
x+6-6=66-6
x=60
Some researchers have conjectured that stem-pitting disease in peach-tree seedlings might be controlled with weed and soil treatment. An experiment is conducted to compare peach-tree seedling growth when the soil and weeds are treated with one of two herbicides. In a field containing 20 seedlings, 10 are randomly selected throughout the field and assigned to receive herbicide A. The remainder of the seedlings is assigned to receive herbicide B. Soil and weeds for each seedling are treated with the appropriate herbicide, and at the end of the study period, the height in centimeters is recorded for each seedling. The following results are obtained: Herbicide A = 94.5 cm s1 = 10 cm Herbicide B = 109.1 cm s2 = 9 cm
Required:
1. What is a 90% confidence interval (use the conservative value for the degrees of freedom) for μ2 – μ1? a. 14.6 ± 7.00 b. 14.6 ± 7.38 c. 14.6 ± 7.80 d. 14.6 ± 9.62
2. Suppose we wish to determine if there tends to be a difference in height for the seedlings treated with the different herbicides. To answer this question, we decide to test the hypotheses H0: μ2 – μ1 = 0, Ha: μ2 – μ1 ≠0. What is the value of the two-sample t statistic?
a. 14.6
b. 3.43
c. 2.54
d. 7.80
3. What can we say about the value of the P-value?
a. P-value < 0.01
b. 0.01 < P-value < 0.05
c. 0.05 < P-value < 0.10
d. P-value > 0.10
4. If you use the 0.05 level of significance, what conclusion would you reach?
a. The evidence is not sufficiently strong to reject the null hypothesis.
b. There is sufficient evidence to reject the null hypothesis.
c. Cannot be determined by the information given.
Answer:
1. b. 14.6 ± 7.38
2. b. 3.43
3. b. 0.01 < P-value < 0.05
4. b. There is sufficient evidence to reject the null hypothesis.
Step-by-step explanation:
The hypothesis test is used to test the null hypothesis against the alternative hypothesis. The p value of the test determines whether to accept or reject the null hypothesis. In the given scenario the p value is less than 0.05 so there is sufficient evidence against the null hypothesis in favor of alternative hypothesis.
How to show work on this one topic is angles formed by 2 chords and secants
Answer:
Step-by-step explanation:
VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.
Answer:
I would believe 90* clockwise.
Step-by-step explanation:
It rotated 90* to be located on its side.
Solve this question for brainlest
please help me fast thanks
Answer:
if I am not wrong I think the anwser will be 2.3
Answer:
It's 3
Step-by-step explanation:
7 can't be divided by 3 so you leave it as a fraction
The arch support of a bridge can be modeled by y=−0.0012x2, where x and y are measured in feet. Find the height and width of the arch.
Answer:
it will be 300 feet tall and 1000 feet wide
Step-by-step explanation:
The height and width of the arch which support of a bridge and modeled by the provided function is 1000 ft and 300 ft long respectively.
What is an exponential function?Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.
The exponential function with dependent variable y and independent variable x can be written as,
[tex]y=ba^x+c[/tex]
Here, a,b and c are the real numbers.
The arch support of a bridge can be modeled by the following function,
[tex]y=-0.0012x^2+300[/tex]
Here, x and y are measured in feet.
The height and width of the arch has to be found out. First, find the x intercept of the function. As at the x intercept, the y equal to zero. Therefore,
[tex]0=-0.0012x^2+300\\0.0012x^2=300\\x=\sqrt{25000}\\x=500[/tex]
As, the graph is symmetric around the y-axis. Thus, the -500 can also be a solution. Now, the width of the arch can be given as,
[tex]w=500-(-500)\\w=1000\rm ft[/tex]
Now similarly at x equal to zero, the function will be,
[tex]y=300[/tex]
Hence, the height and width of the arch which support of a bridge and modeled by the provided function is 1000 ft and 300 ft long respectively.
Learn more about the exponential function here;
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What is the mode of the set of data points given below? 1 15 12 6 12 9 12 3 6 12 15 9 15 12 15
Answer:
the mode is 12
Step-by-step explanation:
Arrange the numbers in order : 1 , 3, 6, 6, 9, 9, 12, 12, 12, 12, 12, 15, 15, 15, 15
Then count how many numbers that appears the most, so the number that appears the most is 12, therefore, the mode in the data set is 12 .
I need help with this question please
9514 1404 393
Answer:
y = -x -2
Step-by-step explanation:
The line crosses the y-axis at y = -2, so that is the y-intercept.
The slope is the ratio of "rise" to "run." The points on the graph show a "rise" of -3 for a "run" of 3.
m = rise/run = -3/3 = -1
Then the slope-intercept equation is ...
y = mx +b . . . . . slope m, y-intercept b
y = -x -2 . . . . . . . using m=-1, b=-2
Can someone help me with this please ?
A chemist mixed two samples together: a gray liquid that boils at 103°C and a colorless gas that boils at 19°C. She analyzed the results and found two ending substances. One of the ending substances was a pink liquid. This ending substance is made up of the repeating group of atoms shown above. Which of the diagrams to the left shows the repeating groups of atoms that make up the samples the chemist mixed together?
Answer:
Its C
Step-by-step explanation:
Diagram c to the left shows the repeating groups of atoms that make up the samples the chemist mixed together.
What is atoms?Atoms are the smallest unit of matter that make up all physical objects. Atoms are composed of three main components: protons, neutrons, and electrons. Protons and neutrons are found in the nucleus of the atom and have a positive charge, while electrons orbit the nucleus and have a negative charge.
here, we have,
we know that,
Atoms can join together to form molecules, which are the building blocks of all matter. Atoms of different elements can join together in different ways to form compounds and these compounds are the basis of all substances. Atoms are also the basis of all chemical reactions and can exist in different physical states, such as solid, liquid, or gas. Atoms can also be combined to form isotopes, which are atoms of the same element with different numbers of neutrons.
To learn more about atoms
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complete question:
11. A chemist mixed two samples together: a brown solid that melts at about 1,300°C and a colorless liquid that melts at about 20°C. She analyzed the results and found two ending substances. One of the ending substances melts at about 250°C. This ending substance is made up of the repeating group of atoms shown above. Which of the diagrams to the left shows the repeating groups of atoms that make up the samples the chemist mixed together?
