Answer: See below
Step-by-step explanation:
Answer (1)
We must break down the expressions into factors. That is:
[tex]\begin{align} \log 12&=\log 4\times 3=\log 2^2\times 3\\ \log 12&=\log 2^2+\log 3=2\log 2+\log 3=2x+y\\ \end{align}[/tex][tex]\log \frac{14}{3}&=\log 14-\log 3 \\ =\log 2\times 7-\log 3\\ \\\log \frac{14}{3}& =\log 2+\log 7-\log 3 \\ =x+z-y\\[/tex]
Answer (2)
[tex]\log 0.3 &=\log \frac{3}{10} \\ \\ =\log 3-\log 10 \\=y-1[/tex]
Answer (3)
[tex]\log 10.5& \\ =\log \frac{21}{2} \\=\log 21-\log 2\\ \\ \log 10.5& \\ =\log 3\times 7-\log 2\\=\log 3+\log 7-\log 2\\=y+z-x[/tex]
Which expression is equivalent to -8(x+2)-(x+4)
Answer:
-8x+-16-(-8x)+(-32)
Step-by-step explanation:
Evaluate this:
[tex]\displaystyle\rm\int_0^\frac{\pi}{2}\sqrt{\sin x}\ dx \times \int_0^\frac{\pi}{2}\frac{1}{\sqrt{\sin x}}\ dx[/tex]
Only elementary methods are allowed.
The first integral has a well-known beta function representation, so the second one should too. The beta function itself is defined as
[tex]B(x,y) = \displaystyle \int_0^1 t^{x-1} (1-t)^{y-1} \, dt[/tex]
and satisfies the identity
[tex]\displaystyle B(x,y) = \frac{\Gamma(x) \Gamma(y)}{\Gamma(x+y)}[/tex]
Later on, we'll also use the so-called reflection formula for the gamma function; for non-integer z,
[tex]\Gamma(z) \Gamma(1-z) = \dfrac{\pi}{\sin(\pi z)}[/tex]
as well as the identity
[tex]\dfrac{\Gamma(z+1)}{\Gamma(z)} = z[/tex]
Replace [tex]x\to\sin^{-1}(x)[/tex] in both integrals, so that
[tex]\displaystyle \int_0^{\frac\pi2} \sqrt{\sin(x)} \, dx = \int_0^1 \frac{\sqrt x}{\sqrt{1-x^2}} \, dx[/tex]
[tex]\displaystyle \int_0^{\frac\pi2} \frac{dx}{\sqrt{\sin(x)}} = \int_0^1 \frac{dx}{\sqrt x \sqrt{1-x^2}}[/tex]
Now replace [tex]x\to\sqrt x[/tex] :
[tex]\displaystyle \int_0^1 \frac{\sqrt x}{\sqrt{1-x^2}} \, dx = \frac12 \int_0^1 x^{-\frac14} (1-x)^{-\frac12} \, dx = \frac12 B\left(\frac34, \frac12\right) [/tex]
[tex]\displaystyle \int_0^1 \frac{dx}{\sqrt x \sqrt{1-x^2}} = \frac12 \int_0^1 x^{-\frac34} (1-x)^{-\frac12} \, dx = \frac12 B\left(\frac14, \frac12\right)[/tex]
So, the original integral (which I condense here to a double integral) is
[tex]\displaystyle \int_0^{\frac\pi2} \int_0^{\frac\pi2} \sqrt{\frac{\sin(x)}{\sin(y)}} \, dx \, dy = \frac14 B\left(\frac34, \frac12\right) B\left(\frac14, \frac12\right)[/tex]
[tex]\displaystyle = \frac14 \frac{\Gamma\left(\frac14\right) \Gamma\left(\frac34\right) \Gamma\left(\frac12\right)^2}{\Gamma\left(\frac54\right) \Gamma\left(\frac34\right)}[/tex]
[tex]\displaystyle = \frac14 \frac{\Gamma\left(\frac14\right) \Gamma\left(\frac34\right) \Gamma\left(\frac12\right)^2}{\frac14 \Gamma\left(\frac14\right) \Gamma\left(\frac34\right)}[/tex]
[tex]\displaystyle = \Gamma\left(\frac12\right)^2 = \frac{\pi}{\sin\left(\frac\pi2\right)} = \boxed{\pi}[/tex]
A ball is thrown from an initial height of 2 meters with an initial upward velocity of 15 m/s. The ball's height h (in meters) after t seconds is given by the following.
Real world inequalities:
You must be 4 feet or taller to ride the roller coaster
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
The required inequality that represent the given scenario is :
[tex]\qquad \tt \dashrightarrow \:x \geqslant 4[/tex]
where, x is height in feet.
Let's interpret the information given:
4 feet or taller ⇒ the person can be 4 feet or above 4 feetLet's set 'x' as the hypothetical height of a person
Therefore the inequality should be x ≥ 4
⇒ we put x as greater than 4 since the person must be taller than 4
feet to ride the roller coaster
⇒ we also put the '_' under the inequality to signify that the person
can equal 4 feet in height and still be eligible to ride the roller
coaster
Hope that helps!
Find the arc length of the partial circle.
Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal.
Explanation:
A full circle of radius r has a circumference of 2pi*r which is the perimeter aka distance around the circle's edge.
We divide that by 4 to get the arc length of the quarter circle and we'd get to (2pi*r)/4 = 0.5pi*r
Plug in r = 1 and pi = 3.14
0.5*pi*r = 0.5*3.14*1 = 1.57
if two angles at the base of an isosceles triangle are 50, the other angle is _____because_____________________________________________.
please helpp
A garden table and a bench cost $984 combined. The garden table costs $84 more than the bench. What is the cost of the bench?
Answer:
$450
Step-by-step explanation:
a garden table costs $84 more than the bench,
therfore, $900-84 = $900
$900/2 = cost of bench
$450 = cost of bench
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Given a trapezoid with a height of 4.3m and bases of 9.2 m and 3.2m, what is the area of the trapezoid? Do not include units in your answer.
For a height of 4.3m and bases of 9.2 m and 3.2m, the area of the trapezoid is mathematically given as
A=26.7
What is the area of the trapezoid?Generally, the equation for the trapezoid is mathematically given as
A=0.5*(a+b)*h
Therefore
A=0.5*(3.2+9.2)*4.3
A=26.7
In conclusion,area of the trapezoid
A=26.7
Read more about Arithmetic
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Can someone please help me with this? I'm not sure how to do it.
Looking for the best answer
Answer:
4x - 5 - 3
Step-by-step explanation:
the 3rd is the best answer i think
Which number best represents thirty-one feet below sea level?
A. 31
B. +31
C. −31
D. 31−
Answer:
c
Step-by-step explanation:
Ellie left her house and drove to the store. She stopped and went inside. From
there, she drove in the same direction until she got to the bank. She stopped
and went inside the bank. Then she drove home. The graph below shows the
number of blocks away from home Ellie is x minutes after she left her house,
until she got back home.
Answer:
Ellie spent 21 minutes after she left her house until she got back home
1. There were 4,504,227 people who came to see soccer matches last year. What digit is in the millions place?
2. If Gary's ruler is 12 inches, and Perl’s ruler is 36 inches, what is the length difference between the two rulers? Which number operation will be used to
1. A million has 7 digits. The number shown has 7 digits so the first number is in the millions place. Answer: 4
2. use subtraction
36-12 = 24
50 PTS PLS HELP! Michael works at a furniture store. He makes a commission for every piece of furniture he sells. He sold a couch for $1245 he got a check for $62.25. What was the % of the commission he made?
Answer:
11% yan po answer hehehe tama yan
3,6,4,10, x; the mean is 6
Answer:
x=7
Step-by-step explanation:
You can find the complete solution in the given attachment
I hope it helped you
Lucas bought a package of baseball cards for $0.70. His friend bought 3 times as many packages. How much did his friend spend?
$2.10
$2.50
$2.80
$3.10
Answer: $2.10
Step-by-step explanation:
PLEASE HELP PLEASE HELP
Answer:
B
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
The Square Pyramid Has 5 Vertices.
:)
Solve for 2. Round to the nearest tenth, if necessary.
B
U
67
T
x
142°
Tan(angle) = opposite/ adjacent
tan(42) = 67/x
x =67/tan(42)
X = 74.411
rounded to nearest tenth : x = 74.4
1
C
2
3
✓4
5
7
8
✓ 10
A car travels at an average speed of 56 miles per hour. How many miles does it travel in 4 hours and 45 minutes?
mites
x
5
?
I
Answer:
266 miles
Step-by-step explanation:
Given statement
4 hours and 45 minutesClearly, 45 is 3/4th of an hour. Thus, this statement can also be written as:
⇒ 4 hours and 3(Hour)/4 minutes⇒ 4 hours + 3(Hour)/4 minutes⇒ 4 hours + 0.75(Hour)⇒ 4.75 hoursWe are given that:
56 miles per hourWhen we convert this statement into an equation, we get:
⇒ 56 miles = 1 hourMultiply both sides by 4.75 to obtain the distance in 4.75 hours.
⇒ 56 × 4.75 miles = 1 hour × 4.75⇒ 266 miles = 4.75 hoursa prism is completely filled with 96 cubes that have edge lengths of 1/2 cm.
what is the volume of the prism?
Enter your answer in the box.
Answer:
12 cm^3
Step-by-step explanation:
Volume of one cube is 1/2 * 1/2 * 1/2 = 1/8 cm^3Volume of prism is 1/8 * 96 = 12 cm^3
What are the greatest common factors of 21 and 32?
Answer:
1
Step-by-step explanation:
The biggest common factor number is the GCF number. So the greatest common factor 21 and 32 is 1. Also check out the Least Common Multiple of 21 and 32
The greatest common factor of 21 and 32 is 1.
What is Greatest Common Factor?Greatest common factor or GCF of two numbers is defined as the one common factor of the two given numbers which is the greatest of all the common factors.
GCF is also usually known as Highest Common Factor (HCF).
We have to find the greatest common factors of 21 and 32.
One of the method to find GCF is by prime factorization.
First prime factorize the two numbers. The product of the commonly shared prime factors will be the GCF.
If they don't share any common prime factors, then the GCF will be 1.
21 = 3 × 7
32 = 2 × 2 × 2 × 2 × 2
There are no common prime factors, GCF will be 1.
Hence, the greatest common factor of 21 and 32 is 1 since there are no common prime factors.
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Complete the probability model. Don’t forget to write each answer as a percentage.
Answer:
The answer is the first one
Step-by-step explanation:
The first one is correct because the probaility of you getting some biyatches is zero.
Help help help help help
Answer:
[tex]\sf 5x+6y=12[/tex]
Step-by-step explanation:
[tex]\sf y=-\dfrac{5x}{6}+2[/tex]
Multiply both sides by 6:
[tex]\implies \sf 6 \cdot y=6(-\dfrac{5x}{6}+2)[/tex]
Expand:
[tex]\implies \sf 6y=-5x+12[/tex]
Add 5x to both sides:
[tex]\implies \sf 5x+6y=-5x+12+5x[/tex]
[tex]\implies \sf 5x+6y=12[/tex]
A college student takes the same number of credits each semester. She had 8 credits when she started, and after 7 semesters, she had 92 credits.
Which of these expresses the rate at which she is earning credits
Answer:
12 credits per semester
Step-by-step explanation:
she has 92 in the end but she started off with 8 so your first step is to subtract 8 from 92 which gives you 84 once you get 84 you divide that by 12 you get 7 which means she got 12 credits in each of her 7 semeters
what is the inverse of f(x)=2(3^x)
If [tex]f^{-1}(x)[/tex] is the inverse of [tex]f(x)[/tex], then by definition
[tex]f\left(f^{-1}(x)\right) = x[/tex]
so that
[tex]2 \times 3^{f^{-1}(x)} = x[/tex]
Solve for [tex]f^{-1}(x)[/tex] :
[tex]3^{f^{-1}(x)} = \dfrac x2[/tex]
[tex]\log_3\left(3^{f^{-1}(x)}\right) = \log_3\left(\dfrac x2\right)[/tex]
[tex]f^{-1}(x) \log_3(3) = \log_3\left(\dfrac x2\right)[/tex]
[tex]\boxed{f^{-1}(x) = \log_3\left(\dfrac x2\right)}[/tex]
It took Theo 18 minutes to count his cards and he finished at 4:45
p.m. What time did Theo start counting?
4:27
Step-by-step explanation:
just subtract 45 and 18. common sense
what is the product of 653 and 87
Answer:
56811
Step-by-step explanation:
This is the answer as when you do the math it checks out
Find the mean of the data in the dot plot below. Make sure to show your work and explain the steps you took in solving the problem. please help I took a picture I just need the problem to be explained
Answer: 6.
Step-by-step explanation: To find the mean, the first step is to add all the data together. Here's how it should look:
2 + 3 + 6 + 6 + 7 + 8 + 8 + 8 = 48.
Next, you need to divide whatever you get after adding the data by how many numbers there are for your data. In this case, 48 was the answer when we added all the data. In total, you have 8 numbers in your data, so you need to divide 8 from 48. It should look like this:
48 / 8 = 6.
Therefore, the mean for this data set is 6.
Have a great day! :)
I will give you 100 points and a Brainliest if you can help me with this question.
Complete the calculations so that each shows the correct difference.
Answer:
0.671
0.985
0.137
Step-by-step explanation:
ABove is answer
Answer:
0.671
0.985
0.137
Step-by-step explanation:
Now you could give the person above me brainliest
Simplify
2 × (3 – 1) + 3
Answer:
If you put this in the calculator, the answer would be 7