Repost-9 TOTAL QUESTIONS
#19 (LAST PICTURE)
Which of the following shows a graph of a tangent function in the form y = atan(bx − c) + d, such that b = 2? (Two graphs below, I think one of these graphs are correct)
Answers
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1 (#3)
The formula for a regular octagon inscribed in a circle of radius [tex]r[/tex] is [tex]A=2\sqrt{2}r^2[/tex]. Hence, [tex]A=2\sqrt{2}(4)^2=16*2\sqrt{2}=32\sqrt{2}\approx45.255m^2[/tex].
Thus, C is the correct answer
Problem 2 (#4)
Using the co-function identity [tex]\displaystyle \sin\biggr(x+\frac{\pi}{2}\biggr)=\cos(x)[/tex], the equation can be rewritten as [tex]cos(x)=\frac{\sqrt{3}}{2}[/tex]. Using a unit circle, it's easy to see that the answer is [tex]\displaystyle\biggr\{\frac{\pi}{6},\frac{11\pi}{6}\biggr\}[/tex].
Thus, C is the correct answer
Problem 3
[tex]f(x)=g(x)\\\\2\sin^2 x-1=-\cos(x)\\\\2(1-\cos^2 x)-1=-\cos(x)\\\\2-2\cos^2 x-1=-\cos(x)\\\\1-2\cos^2 x=-\cos(x)\\\\2\cos^2x-\cos(x)-1=0[/tex]
Let [tex]u=\cos(x)[/tex], hence:
[tex]2u^2-u-1=0\\\\(2u+1)(u-1)=0[/tex]
[tex]\displaystyle2u+1=0\\\\2u=-1\\\\u=-\frac{1}{2}\\ \\\cos(x)=-\frac{1}{2}\\ \\x=\biggr\{\frac{2\pi}{3},\frac{4\pi}{3}\biggr\}[/tex]
[tex]u-1=0\\\\u=1\\\\\cos(x)=1\\\\x=\{0\}[/tex]
So, the solution set is [tex]\displaystyle\biggr\{0,\frac{2\pi}{3},\frac{4\pi}3}\biggr\}[/tex]
Thus, B is the correct answer
Problem 4 (#8)
If we construct a right triangle in Quadrant I with an opposite leg length of 1 unit and an adjacent leg length of 1 unit, this shows that [tex]\displaystyle\tan\theta=\frac{opposite}{adjacent}=\frac{1}{1}=1[/tex]. Since [tex]\displaystyle \csc\theta=\frac{1}{\sin\theta}[/tex] and [tex]\displaystyle\sin\theta=\frac{opposite}{hypotenuse}[/tex], we must solve for the hypotenuse with the Pythagorean Theorem:
[tex](opposite)^2+(adjacent)^2=(hypotenuse)^2\\1^2+1^2=(hypotenuse)^2\\1+1=(hypotenuse)^2\\2=(hypotenuse)^2\\\sqrt{2}=hypotenuse[/tex]
Therefore, since [tex]\displaystyle \sin\theta=\frac{opposite}{hypotenuse}=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}[/tex], then [tex]\displaystyle \csc\theta=\frac{1}{\sin\theta}=\frac{1}{\frac{\sqrt{2}}{2}}=\frac{2}{\sqrt{2}}=\frac{2\sqrt{2}}{2}=\sqrt{2}[/tex].
Thus, B is the correct answer
Problem 5 (#9)
As no angles are given and only side lengths, we are forced to use the Law of Cosines to solve for the angles:
Side "a" will be the distance from A to B with corresponding angle ASide "b" will be the distance from B to C with corresponding angle BSide "c" will be the distance from C to A with corresponding angle CAngle A:
[tex]a^2=b^2+c^2-2bc\cos(A)\\400^2=500^2+600^2-2(500)(600)\cos(A)\\160000=250000+360000-600000\cos(A)\\160000=610000-600000\cos(A)\\-450000=-600000\cos(A)\\\frac{3}{4}=\cos(A)\\ A\approx41.410^\circ[/tex]
Angle B:
[tex]b^2=a^2+c^2-2ac\cos(B)\\500^2=400^2+600^2-2(400)(600)\cos(B)\\250000=160000+360000-480000\cos(B)\\250000=520000-480000\cos(B)\\-270000=-480000\cos(B)\\\frac{9}{16}=\cos(B)\\B\approx55.771^\circ[/tex]
Angle C:
By the Triangle Angle-Sum Theorem, [tex]C\approx82.819^\circ[/tex]
Hence, we can conclude that angle A is the smallest angle the swimmers must turn between the buoys.
Thus, C) 41.410° is the correct answer
Problem 6 (#unknown)
As we are given two angles and a side length, we can use the Law of Sines to find side length "b". Firstly, we need angle C so we can set up the proportion to find "b". By the Triangle Angle-Sum Theorem, [tex]m\angle C=60^\circ[/tex].
[tex]\frac{\sin(B)}{b}=\frac{\sin(C)}{c}\\\\\frac{\sin(64^\circ)}{b}=\frac{\sin(60^\circ)}{8}\\\\8\sin(64^\circ)=b\sin(60^\circ)\\\\b=\frac{8\sin(64^\circ)}{\sin(60^\circ)}\\ \\b\approx8.303[/tex]
Thus, B is the correct answer (how ironic lol)
Problem 7 (#13)
[tex]\displaystyle\sqrt{2}\cos2x=\sin^2x+\cos^2x\\\\\sqrt{2}\cos2x=1\\\\\cos2x=\frac{1}{\sqrt{2}}\\\\\cos2x=\frac{\sqrt{2}}{2}\\ \\2x=\frac{\pi}{4},\frac{7\pi}{4}\\ \\x=\frac{\pi}{8},\frac{7\pi}{8}[/tex]
Hence, B is the correct answer
Problem 8 (#14)
[tex]\displaystyle \sec\theta=2\\\\\frac{1}{\cos\theta}=2\\ \\\cos\theta=\frac{1}{2}\\ \\\theta=\frac{\pi}{3}+2\pi n,\frac{5\pi}{3}+2\pi n[/tex]
Thus, D is the correct answer
Problem 9 (#19)
The bottom graph looks correct as the period of the tangent function is [tex]\frac{\pi}{|b|}=\frac{\pi}{2}[/tex].
Related Questions
A fictional country has a population of 5 million people and a net immigration rate of 1 person per 1000 people. The population is increasing only due to migration and not biological replacement. How long will it take the country’s population to double?
Group of answer choices
300 years
1,000 years
5,000 years
700 years
Answers
Answer:
1,000
Step-by-step explanation:
just took the quiz
can someone please help? :((
if you want another 50 points or more you could maybe help with one of the previous unanswered questions on my profile
Answers
Just find the vertex and then compare with graph
#a
y=2x²-8y=2(x-0)²-8Parabola opening upwards
Vertex at (0,-8)Graph 3
#2
y=(x+3)²+0Vertex at (-3,0)
Graph IV
#3
y=-2(x-4)²+8Parabola opening downwards as a is -ve
Graph I
#4
One graph is left
Graph IiAnswer:
a) graph iii)
b) graph iv)
c) graph i)
d) graph ii)
Step-by-step explanation:
Vertex form of a quadratic equation: [tex]y = a(x - h)^2 + k[/tex]
where [tex](h, k)[/tex] is the vertex (turning point)
First, determine the vertices of the parabolas by inspection of the graphs:
Graph i) → vertex = (4, 8)Graph ii) → vertex = (3, -8)Graph iii) → vertex = (0, -8)Graph iv) → vertex = (-3, 0)Next, write each given equation in vertex form and compare to the vertices above.
[tex]\textsf{a)}\quad y=2x^2-8[/tex]
[tex]\textsf{Vertex form}: \quad y=2(x-0)^2-8[/tex]
⇒ Vertex = (0, -8)
Therefore, graph iii)
[tex]\textsf{b)} \quad y=(x+3)^2[/tex]
[tex]\textsf{Vertex form}: \quad y=(x+3)^2+0[/tex]
⇒ Vertex = (-3, 0)
Therefore, graph iv)
[tex]\textsf{c)} \quad y=-2|x-4|^2+8[/tex]
[tex]\textsf{Vertex form}: \quad y=-2|x-4|^2+8[/tex]
⇒ Vertex = (4, 8)
Therefore, graph i)
[tex]\textsf{d)} \quad y=(x-3)^2-8[/tex]
[tex]\textsf{Vertex form}: \quad y=(x-3)^2-8[/tex]
⇒ Vertex = (3, -8)
Therefore, graph ii)
a sphere is inscribed in a cube with a volume of 125 cubic inches what is the volume of the sphere
Answers
Answer:
using [tex]\pi[/tex]: 65.45 in³ (nearest hundredth)
using [tex]\pi =3.14[/tex]: 65.42 in³ (nearest hundredth)
Step-by-step explanation:
The radius of the sphere is half the side length of the cube (see attached diagram). Therefore, the side length of the cube = 2r
Given:
volume of the cube = 125 in³side length of cube = 2r[tex]\textsf{Volume of a cube}=x^3\quad \textsf{(where}\:x\:\textsf{is the side length)}[/tex]
[tex]\implies 125=(2r)^3[/tex]
[tex]\implies \sqrt[3]{125}=2r[/tex]
[tex]\implies 5=2r[/tex]
[tex]\implies r=\dfrac52[/tex]
Substitute the found value of r into the volume of a sphere equation:
[tex]\begin{aligned}\textsf{Volume of a sphere} & =\dfrac43 \pi r^3\\\\ & =\dfrac43 \pi \left(\dfrac52\right)^3\\\\ & =\dfrac43 \pi \left(\dfrac{125}{8}\right)\\\\ & =\dfrac{500}{24} \pi\\\\ & =\dfrac{125}{6} \pi\\\\ & =65.45\:\sf in^3\:(nearest\:hundredth) \end{aligned}[/tex]
Find the area of the triangle.
Answers
Answer:
40m^2 :)
Step-by-step explanation:
Area of a triange = (h·b)/2
Now lets solve :)
4 + 6 = 10
(8·10)/2
80/2
40
Have an amazing day!!
Please rate and mark brainliest!!
Helpppppp pleaseeeee ):
Answers
Answer:
Smily face=5 lightning=8
Step-by-step explanation:
5+5=10 8x3=24 24+10=34
8x5=40 5x8=40
Find all solutions in the interval [0,2π)
Answers
Answer:
Its B
Step-by-step explanation:
Hello can u guys help me please
Answers
Answer:
[tex]\displaystyle \frac{1}{4}[/tex]
Step-by-step explanation:
Given:
[tex]\displaystyle\frac{4^{6} }{4^{7}}[/tex]
Expand:
[tex]\displaystyle\frac{4*4*4*4*4*4 }{4*4*4*4*4*4*4}[/tex]
Simplify ones, in this case [tex]\frac{4}{4}[/tex]:
[tex]\displaystyle \frac{1}{4}[/tex]
If you raise 4 to the power of 6, to the power of 7, and then simplify the fraction, you will get the same result. This method is much quicker when you have numbers with the same bases (here the base is 4) so I used this way.
4th question!!! Can anyone help me ?
Answers
Cost=66*2*4=176//
Answer:
₹528Step-by-step explanation:
Length of Fence
Circumference = 2πr or πdπd22/7 x 21 m22 x 3 m66 m2 rounds = 66 x 2 = 132 mCost
₹4 x 132₹528What negative impact can interdependence have on a country?
A. Threat to political interference
B. Threat to security
C. Threat to industrialization
D. Increased progress and industrialization
Answers
When two countries are interdependent both countries can economically grow
i would like the answer to 1/4 minus 1/3 is it 12
Answers
Answer:
-1/12
Step-by-step explanation:
1/4 - 1/3 = 3/12 - 4/12 = - 1/12
Can someone please go into detail on how they simplified this expression? Thanks!
: 4a - (4a-3)=4a 1(4a 3) Identity property
4a -4a + 3 Distributive property
0 -3 Combine like terms.
3 simplify
I really don't get how they got plus 3
Thanks again!
Answers
Answer:
Step-by-step explanation:
4a - (4a-3)
= 4a -1(4a - 3)
= 4a - 4a + 3 <--- Distributing the -1 over the parenthes
= 3 <---- ( as 4a - 4a = 0)
What is the area, in square centimeters, of the parallelogram?
(20 points)
Answers
Answer:
30
Step-by-step explanation:
10 x 3 = 30
Answer:
30 centimeters squared
Step-by-step explanation:
The area of a parallelogram can be found by using the formula base x height. The base of this parallelogram is 10, and the height is 3. Therefore the area is 30 square centimeters.
It is estimated that 0.54 percent of the callers to the Customer Service department of Dell Inc. will receive a busy signal. What is the probability that of today's 1,300 callers at least 5 received a busy signal?
Answers
Using the binomial distribution, it is found that there is a 0.8295 = 82.95% probability that at least 5 received a busy signal.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
0.54% of the calls receive a busy signal, hence p = 0.0054.A sample of 1300 callers is taken, hence n = 1300.The probability that at least 5 received a busy signal is given by:
[tex]P(X \geq 5) = 1 - P(X < 5)[/tex]
In which:
P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{1300,0}.(0.0054)^{0}.(0.9946)^{1300} = 0.0009[/tex]
[tex]P(X = 1) = C_{1300,1}.(0.0054)^{1}.(0.9946)^{1299} = 0.0062[/tex]
[tex]P(X = 2) = C_{1300,2}.(0.0054)^{2}.(0.9946)^{1298} = 0.0218[/tex]
[tex]P(X = 3) = C_{1300,3}.(0.0054)^{3}.(0.9946)^{1297} = 0.0513[/tex]
[tex]P(X = 4) = C_{1300,4}.(0.0054)^{4}.(0.9946)^{1296} = 0.0903[/tex]
Then:
P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0009 + 0.0062 + 0.0218 + 0.0513 + 0.0903 = 0.1705.
[tex]P(X \geq 5) = 1 - P(X < 5) = 1 - 0.1705 = 0.8295[/tex]
0.8295 = 82.95% probability that at least 5 received a busy signal.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
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Test the claim that LeBron James and Steph Curry average the same amount of points per game, on average.
Be sure to include the claim, critical values, test statistic and the conclusion.
For 70 games Lebron James averaged 30.1 points with a standard deviation of 9.112
For 70 games Steph Curry averaged 25.5 points with a standard deviation of 12.602
Answers
When the variances are known and the sample size is high, a z-test is used to assess if two population means vary. The mean of the two players is not the same.
What is a Z-test?When the variances are known and the sample size is high, a z-test is used to assess if two population means vary.
In order to execute an appropriate z-test, the test statistic is expected to have a normal distribution, and nuisance factors such as standard deviation should be known.
(1) Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
[tex]\begin{array}{ccl} H_0: \mu_1 & = & \mu_2 \\\\ H_a: \mu_1 & \ne & \mu_2 \end{array}[/tex]
This corresponds to a two-tailed test, and a z-test for two means, with known population standard deviations, will be used.
(2) Rejection Region
Based on the information provided, the significance level is α=0.05, and the critical value for a two-tailed test is [tex]z_c = 1.96[/tex]
The rejection region for this two-tailed test is R={z:∣z∣>1.96}
(3) Test Statistics
The z-statistic is computed as follows:
[tex]\begin{array}{ccl} z & = & \displaystyle \frac{\bar X_1 - \bar X_2}{\sqrt{ {\sigma_1^2/n_1} + {\sigma_2^2/n_2} }} \\\\ & = & \displaystyle \frac{ 30.1 - 25.5}{\sqrt{ {9.112^2/70} + {12.602^2/70} }} \\\\ & = & 2.475 \end{array}[/tex]
[tex]\begin{array}{ccl} z & = & \displaystyle \frac{\bar X_1 - \bar X_2}{\sqrt{ {\sigma_1^2/n_1} + {\sigma_2^2/n_2} }} \\\\ & = & \displaystyle \frac{ 30.1 - 25.5}{\sqrt{ {9.112^2/70} + {12.602^2/70} }} \\\\ & = & 2.475 \end{array}[/tex]
(4.) The decision about the null hypothesis
Since it is observed that |z| = 2.475 > z_c = 1.96, it is then concluded that the null hypothesis is rejected.
Using the P-value approach: The p-value is p = 0.0133p=0.0133, and since p = 0.0133 < 0.05p=0.0133<0.05, it is concluded that the null hypothesis is rejected.
(5.) As it is concluded that the null hypothesis H₀ is rejected. Therefore, there is enough evidence to claim that the population mean μ1 is different than μ2.
Hence, the mean of the two players is not the same.
Learn more about Z-test:
https://brainly.com/question/15683598
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I am playing a number game, there are 2 tiles for each number from 0 thru 9. One tile is chosen at random, can you list the possible outcomes ?
Answers
Answer:
If each tile has a number from 0 thru 9 then the possible outcomes for each tile are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
A rectangular field is 30 yards in length and 81 feet in width.
What is the area of the field in square feet?
Answers
Answer:
7290in ^2
Step-by-step explanation:
covert 30yd to feet which equals too 90ft.
Then multiple 90 x 81 = 7290
A property's value is $400,000 and its land value is $75,000. Assuming a depreciation term of 39 years, what is the amount of annual depreciation?
Answers
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill &75000\\ P=\textit{initial amount}\dotfill &400000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &39\\ \end{cases} \\\\\\ 75000=400000(1 - \frac{r}{100})^{39}\implies \cfrac{75000}{400000}=\left( \cfrac{100-r}{100} \right)^{39}[/tex]
[tex]\cfrac{3}{16}=\left( \cfrac{100-r}{100} \right)^{39}\implies \sqrt[39]{\cfrac{3}{16}}=\cfrac{100-r}{100}\implies 100\sqrt[39]{\cfrac{3}{16}}=100-r \\\\\\ r=100-100\sqrt[39]{\cfrac{3}{16}}\implies r\approx 4.2[/tex]
what is the volume of this prism ?
Answers
Answer:
576cm³
Step-by-step explanation:
8×6=48
48×12=576
What is the surface area?
2 ft
5 ft
3 ft
square feet
Submit
Answers
Because
2*5*3=30ft
The area of a rectangular patio is 24 3/8
square meters. The width of the patio is 3 3/4
meters. What is the length? Enter your answer as a mixed number in simplest form.
The length of the patio is ___ meters.
Answers
Answer:
6 1/2
Step-by-step explanation:
Use the area formula: A=LengthxWidth
Plug in what we know: 24 3/8= 3 3/4x Width
We need to isolate the width; get it by itself.
Do this by (24 3/8)/(3 3/4). The best way is to enter this into a calculator.
Your answer is 6 1/2
A triangle has perimeter 38 cm.
Two sides of the shapes are put
together to make a pentagon
A square has perimeter 48 cm.
What is the perimeter
of the pentagon?
cm
Answers
Answer:
62cm
Step-by-step explanation:
You were told the perimeter of the triangle is 38
but two sides are added to make a Pentagon. and that Pentagon is made up of a triangle and a square.
so if we find the side of the square, we can equally get the other two sides of the triangle.
hint: (because it's a square, we would be getting an isosceles triangle, meaning two sides are equal)
because one side of the pentagon added to the other two sides of the triangles gives us the perimeter of the triangle.
we first find the sides of the square with all sides equal by diving by 2
[tex] \frac{48}{2} = 12[/tex]
the sides of the square making the perimeter of the square 12cm.
now we subtract 12 from the perimeter of the triangle 38
[tex]38 - 12 = 26[/tex]
now that we have gotten one side we can get the other two by dividing the result by 2
[tex] \frac{26}{2} = 13[/tex]
so the other two sides of the triangle are 13cm.
now since we have the sides of the square and the triangle, we can find the perimeter of the pentagon by adding.
all the sides of the triangle without the base which is also the top of the square.
so instead of adding 4 times of 12, we add 3 times of 12 and 2 times of 13.
3(12)+2(13) = 62
or
12 + 12 + 12 + 13 + 13 = 62cm
For each of the following prisms,find (I) its volume (ii) its total surface area
Answers
NO LINKS!! Please help me with this problem
Answers
FGHIJ ≅ STUQR
Solve for HI
[tex]\sf \dfrac{HI}{GH} = \dfrac{UQ}{UT}[/tex]
[tex]\rightarrow \sf \dfrac{HI}{56} = \dfrac{25}{35}[/tex]
[tex]\rightarrow \sf HI = 40[/tex]
Solve for QR
[tex]\sf \dfrac{IJ}{GH} = \dfrac{QR}{UT}[/tex]
[tex]\rightarrow \sf \dfrac{72}{56} = \dfrac{QR}{35}[/tex]
[tex]\rightarrow \sf QR = 45[/tex]
Solve for ST
[tex]\sf \dfrac{FG}{GH} = \dfrac{ST}{UT}[/tex]
[tex]\rightarrow \sf \dfrac{48}{56} = \dfrac{ST}{35}[/tex]
[tex]\rightarrow \sf ST =30[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{GH}{HI}=\dfrac{UT}{UQ}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{56}{HI}=\dfrac{35}{25}=\dfrac{7}{5}[/tex]
[tex]\\ \rm\Rrightarrow HI=56(5)/7=8(5)=40[/tex]
#QR
[tex]\\ \rm\Rrightarrow \dfrac{GH}{JI}=\dfrac{UT}{RQ}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{56}{72}=\dfrac{35}{RQ}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{7}{9}=\dfrac{35}{RQ}[/tex]
[tex]\\ \rm\Rrightarrow RQ=35(9)/7=5(9)=45[/tex]
#ST
[tex]\\ \rm\Rrightarrow \dfrac{GH}{FG}=\dfrac{UT}{ST}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{56}{48}=\dfrac{7}{6}=\dfrac{35}{ST}[/tex]
[tex]\\ \rm\Rrightarrow ST=6(35)/7=6(5)=30[/tex]
Find center and radius of this circle:
[tex](x-2)^2+(x+12)^2=81[/tex]
Answers
Answer:
center: (2,-12)
radius: 9
Step-by-step explanation:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
[tex]h=2\\k=-12\\r=9[/tex]
get r by getting square root of 81
center = (h,k)
Answer:
center: (2,-12)
radius: 9
Step-by-step explanation:
(x-h)^2+(y-k)^2=r^2
h=2
k=-12
r=9
I NEED HEEEEELP WITH THIS QUESTIOOOON, maybe for some people it is very easy but not for me
Answers
Answer:
the 1.5 goes between -1 and 0 and -3/2 too and -4/3 between the-2 and the 3/2 between the 0 and 1
Step-by-step explanation:
1 box of blue counters from which 25 counters have been removed and then the remaining number has been doubled
Answers
25-1
24
So remaining there are 24 boxes
And then if the remaining is doubled then
24*2
48 boxes is the answer
The graph shows the function f(x) = 3* What is the value of f-1(x) at x = 3?
Answers
Answer:
1
I've attached a screenshot from my graphing calculator of [tex]f(x)[/tex] in blue and [tex]f^{-1}(x)[/tex] in red. Notice how the red line (inverse function) has (3, 1)
Step-by-step explanation:
[tex]f(x) = 3^x\\f^{-1}(x) =\ ?\\[/tex]
We must first figure out the inverse function of [tex]f(x)[/tex] which is [tex]f^{-1}(x)[/tex]
[tex]y = f(x) = 3^x\\y = 3^x\\log\ y = log\ 3^x\\log\ y = x \times log\ 3\\x = \frac{log\ y}{log\ 3}\\[/tex]
We say y = f(x) to begin with, but after find x = ...
we must 'swap' x and y
[tex]x = \frac{log\ y}{log\ 3}\\y = \frac{log\ x}{log\ 3}\\[/tex]
[tex]f^{-1}(x) = \frac{log\ x}{log\ 3}[/tex]
[tex]f^{-1}(3) = \frac{log\ 3}{log\ 3} = 1[/tex]
Jennifer jones has an idea. Join the bbq parties together . She thinks they can rope off more total area if the tie two ropes together to make one giant bbq than the families could have separately. Is this true?
Answers
Jennifer idea of roping off more total area if the tie two ropes together to make one giant BBQ is a true statement.
What is total surface area?The total surface area is known to be the addition of all the sum of any given area of surfaces of a solid together.
Conclusively, Note that by joining together the 2 parties, one can cut off some activities that will be be doubled if it were two separate event and as such, the use of space is been maximize and then the area of the space they will use for the event will be reduced.
Learn more about total surface area from
https://brainly.com/question/26638955
cosx(tanx+cotx)=
Pls Help
Answers
Step-by-step explanation:
Tangent is equal to sine over cosine. Cotangent is equal to cosine over sine. Therefore:
[tex]cos(x)( \frac{sin(x)}{cos(x)} + \frac{cos(x)}{sin(x)} )[/tex]
Distribute the cos(x) into the sum to get:
[tex]sin(x) + \frac{ {cos(x)}^{2} }{sin(x)} [/tex]
Get a common denominator by multiplying the first term by sine over sine to get:
[tex] \frac{ {sin(x)}^{2} }{sin(x)} + \frac{ {cos(x)}^{2} }{sin(x)} [/tex]
The numerator adds to equal 1 due to a common trigonometric identity. Therefore the only remaining term is:
[tex] \frac{1}{sin(x)} [/tex]
What solution value does not satisfy the compound inequality X - 7 < 17 or -6x >
36?
O A) x = -1
OB) x=0
O C) x= - 10
C
O D) x=25
Dx = 25
Answers
Inequalities are expressions not separated by an equal sign. The solution of the compound inequality will be -6 < x < 24
Compound inequalityInequalities are expressions not separated by an equal sign.
Given the compound inequalities
X - 7 < 17 or -6x >36
For the inequality
x - 7 < 17
x < 17 + 7
x < 24
Similarly for -6x >36
x < -36/6
x < -6
The solution of the compound inequality will be -6 < x < 24
Learn more on inequality here: https://brainly.com/question/11613554