Answers
The equation of the curve is given by:
[tex]y=5+\cot(x)-2\csc(x)[/tex]Differentiating both sides of the equation with respect to x, we have:
[tex]\frac{dy}{dx}=2\cot(x)\csc(x)-\csc^2(x)[/tex]Therefore, the slope of the tangent is given by the value of dy/dx when x= π / 2
[tex]2\cot(\frac{\pi}{2})\csc(\frac{\pi}{2})-\csc^2(\frac{\pi}{2})=-1[/tex]Using the point slope formula, it follows that:
[tex]\begin{gathered} y-3=-1(x-\frac{\pi}{2}) \\ y=-x+\frac{\pi}{2}+3 \end{gathered}[/tex]Therefore, the equation of the tangent at P is given by:
y = -x + π /2 + 3
Related Questions
a surveyor locating the corners of a four-sided of property started at one corner and walk 200 feet in the direction of N80°E 5o reach the next corner he turned and walked to north 160 feet to the next corner of the property he did turn and walk due west to get to the 4th corner of the property finally he walked in the direction S15°E to get back to the starting point. What is the area of the property is in square feet?
Answers
we have three figures, we must find the area of each one and at the end, add them
lower triangle
we must find x and y to calculate the area, we will use trigonometric ratios
[tex]\begin{gathered} \sin (80)=\frac{x}{200} \\ \\ x=200\sin (80) \\ x=197 \end{gathered}[/tex][tex]\begin{gathered} \sin (10)=\frac{y}{200} \\ \\ y=200\sin (10) \\ y=34.73 \end{gathered}[/tex]now calculate the area
[tex]\begin{gathered} A_{T1}=\frac{b\times h}{2} \\ \\ A_{T1}=\frac{y\times x}{2}=\frac{34.73\times197}{2} \\ \\ A_{T1}_{}=3420.9 \end{gathered}[/tex]the area of the triangle is 3420.9 square feet
Rectangle
we have the height (160ft) and the base we calculate it in the previous step (x=197ft)
the area is
[tex]\begin{gathered} A_R=b\times h \\ A_R=197\times160 \\ A_R=31520 \end{gathered}[/tex]the area of the rectangle is 31520 square feet
Left Triangle
we must use trigonometric ratios to calculate Z
[tex]\begin{gathered} \tan (15)=\frac{Z}{160+34.73} \\ \\ Z=194.73\tan (15) \\ Z=52.18 \end{gathered}[/tex]and the area of the triangle is
[tex]\begin{gathered} A_{T2}=\frac{b\times h}{2} \\ \\ A_{T2}=\frac{Z\times(160+34.73)}{2}=\frac{52.18\times194.73}{2} \\ \\ A_{T2}=5080.5 \end{gathered}[/tex]Total area
[tex]\begin{gathered} A=A_{T1}+A_R+A_{T2} \\ A=3420.9+31520+5080.5 \\ A=40021.4 \end{gathered}[/tex]the total area is 40,021.4 square feet
1. Which of the following pairs of figures are congruenta which are not ? How do you know Be sure to use the following vocabulary words congruent .
Answers
Congruent and similar goes by:
Two figures are congruent if they have the same shape and size.
and,
When two figures are similar, the ratios of the lengths of their corresponding sides are equal.
Now, check the images.
First figure (two houses) are congruent.
Second figures (two triangles) are not congruent.
what is the slope and x and y intercepts on these graphs
Answers
ANSWER:
Slope: -1
Y intercept: (0, -3)
X intercept: (-3, 0)
STEP-BY-STEP EXPLANATION:
The slope of a function is calculated using the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]To calculate the slope we use the indicated points (-4, 1) and (-2, -1), we substitute:
[tex]m=\frac{-1-1}{-2-(-4)}=\frac{-2}{-2+4}=\frac{-2}{2}=-1[/tex]The y-intercept is when it crosses the y-axis and the x-intercept is when it crosses the x-axis.
Therefore:
Y intercept: (0, -3)
X intercept: (-3, 0)
The time required for the stone to hit the ground is ( ) seconds?
Answers
we have the equation
[tex]h=-16t^2+144[/tex]Remember that
when the stone hit the ground, the value of h is zero
so
For h=0
[tex]-16t^2+144=0[/tex]solve the quadratic equation
[tex]\begin{gathered} 16t^2=144 \\ t^2=\frac{144}{16} \\ t=\pm\frac{12}{4} \\ t=\pm3 \end{gathered}[/tex]the solution is the positive value
t=3 sec
How to create a table like the following for the following problem:
Answers
We have to graph the function:
[tex]y=-\frac{5}{2}+\cos \lbrack3(x-\frac{\pi}{6})\rbrack[/tex]We can start from known points of the cosine function and then find the values of y.
We know the exact values of cosine for the following angles:
[tex]\begin{gathered} \cos (0)=1 \\ \cos (\frac{\pi}{6})=\frac{\sqrt[]{3}}{2} \\ \cos (\frac{\pi}{4})=\frac{\sqrt[]{2}}{2} \\ \cos (\frac{\pi}{3})=\frac{1}{2} \\ \cos (\frac{\pi}{2})=0 \\ \cos (\frac{2\pi}{3})=-\frac{1}{2} \\ \cos (\frac{3\pi}{4})=\frac{-\sqrt[]{2}}{2} \\ \cos (\frac{5\pi}{6})=\frac{-\sqrt[]{3}}{2} \\ \cos (\pi)=-1 \end{gathered}[/tex]We have half the cycle here. We will complete the values later.
We then can find the value of x that matches the arguments of the known vlaues of the cosine as:
[tex]\begin{gathered} \alpha=3(x-\frac{\pi}{6}) \\ x=\frac{\alpha}{3}+\frac{\pi}{6} \end{gathered}[/tex]where α is the argument of the known values of cosine (0, π/6, π/4, ...).
We then can calculate the values of x for each one as:
[tex]\begin{gathered} x_1=\frac{0}{3}+\frac{\pi}{6}=\frac{\pi}{6} \\ x_2=\frac{1}{3}\cdot\frac{\pi}{6}+\frac{\pi}{6}=\frac{\pi}{18}+\frac{\pi}{6}=\frac{4\pi}{18} \\ x_3=\frac{1}{3}\cdot\frac{\pi}{4}+\frac{\pi}{6}=\frac{\pi}{12}+\frac{\pi}{6}=\frac{3\pi}{12}=\frac{\pi}{4} \\ x_4=\frac{1}{3}\cdot\frac{\pi}{3}+\frac{\pi}{6}=\frac{\pi}{9}+\frac{\pi}{6}=\frac{5\pi}{18} \\ x_5=\frac{1}{3}\cdot\frac{\pi}{2}+\frac{\pi}{6}=\frac{\pi}{6}+\frac{\pi}{6}=\frac{\pi}{3} \\ x_6=\frac{1}{3}\cdot\frac{2\pi}{3}+\frac{\pi}{6}=\frac{2\pi}{9}+\frac{\pi}{6}=\frac{7\pi}{18} \\ x_7=\frac{1}{3}\cdot\frac{3\pi}{4}+\frac{\pi}{6}=\frac{\pi}{4}+\frac{\pi}{6}=\frac{5\pi}{12} \\ x_8=\frac{1}{3}\cdot\frac{5\pi}{6}+\frac{\pi}{6}=\frac{5\pi}{18}+\frac{\pi}{6}=\frac{4\pi}{9} \\ x_9=\frac{1}{3}\pi+\frac{\pi}{6}=\frac{\pi}{2} \end{gathered}[/tex]We then can calculate the value of y for each of this points, using the known values of the cosine, as:
[tex]\begin{gathered} x=\frac{\pi}{6}\Rightarrow y=-\frac{5}{2}+1=-\frac{3}{2} \\ x=\frac{4\pi}{18}\Rightarrow y=-\frac{5}{2}+\frac{\sqrt[]{3}}{2}=\frac{\sqrt[]{3}-5}{2} \\ x=\frac{\pi}{4}\Rightarrow y=-\frac{5}{2}+\frac{\sqrt[]{2}}{2}=\frac{\sqrt[]{2}-5}{2} \\ x=\frac{5\pi}{18}\Rightarrow y=-\frac{5}{2}+\frac{1}{2}=-\frac{4}{2}=-2 \\ x=\frac{\pi}{3}\Rightarrow y=-\frac{5}{2}+0=-\frac{5}{2} \\ x=\frac{7\pi}{18}\Rightarrow y=-\frac{5}{2}-\frac{1}{2}=-\frac{6}{2}=-3 \\ x=\frac{5\pi}{12}\Rightarrow y=-\frac{5}{2}-\frac{\sqrt[]{2}}{2}=\frac{-5-\sqrt[]{2}}{2} \\ x=\frac{4\pi}{9}\Rightarrow y=-\frac{5}{2}-\frac{\sqrt[]{3}}{2}=\frac{-5-\sqrt[]{3}}{2} \\ x=\frac{\pi}{2}\Rightarrow y=-\frac{5}{2}-1=-\frac{7}{2} \end{gathered}[/tex]We can repeat this process for the rest of the cycle, but in this case, we will only graph the mean value (when cosine is 0) and the extreme values (when cosine is -1 or 1).
We can list this as:
[tex]\begin{gathered} \cos (\pi)=-1 \\ \cos (\frac{3\pi}{2})=0 \\ \cos (2\pi)=1 \end{gathered}[/tex]We can relate this values to x using the formula we used before:
[tex]\begin{gathered} x_{10}=\frac{1}{3}(\pi)+\frac{\pi}{6}=\frac{\pi}{3}+\frac{\pi}{6}=\frac{\pi}{2} \\ x_{11}=\frac{1}{3}(\frac{3\pi}{2})+\frac{\pi}{6}=\frac{\pi}{2}+\frac{\pi}{6}=\frac{2\pi}{3} \\ x_{12}=\frac{1}{3}(2\pi)+\frac{\pi}{6}=\frac{2\pi}{3}+\frac{\pi}{6}=\frac{5\pi}{6} \end{gathered}[/tex]Now, we calculate the values of y as:
[tex]\begin{gathered} x=\frac{\pi}{2}\Rightarrow y=-\frac{5}{2}-1=-\frac{7}{2} \\ x=\frac{2\pi}{3}\Rightarrow y=-\frac{5}{2}+0=-\frac{5}{2} \\ x=\frac{5\pi}{6}\Rightarrow y=-\frac{5}{2}+1=-\frac{3}{2} \end{gathered}[/tex]Using this particular values for the complete cycle we can complete the table as:
why is this correct?
Answers
Trapezoid area = (7+3)/2• height = 10/2 •height
Parallelogram area= 5 • height
Then ,Candy is correct ,both areas are EQUAL
The area of parallelogram is 5•H
The area of trapezoid is 10•H divided by 2 ,or. 5•H
Twin brothers, Andy and Brian, can mow their grandparent's lawn together in 60 minutes. Brian could mow the lawn by himself in 22 minutes more than it would take Andy. How long would ittake each person mow the lawn alone?lespleesIt would take Andy minutes to mow the lawn by himself(Simplify your answer.)It would take Brian minutes to mow the lawn by himself(Simplify your answer.)
Answers
STEP - BY - STEP - EXPLANATION
What to find?
The time taken for each person to mow the lawn alone.
Given:
Time take for the two to mow the lawn together = 60 minutes.
Brian could mow himself 22 minutes more than it would take andy.
Let x be the time taken for Andy to mow the lawn.
Let x + 22 be the time taken for Brian to mow the lawn.
Step 1
Form the equation.
[tex](\frac{1}{x}+\frac{1}{x+22})\times60=1[/tex]Step 2
Divide both-side of the equation by 60.
[tex]\frac{1}{x}+\frac{1}{x+22}=\frac{1}{60}[/tex][tex]\frac{x+22+x}{x(x+22)}=\frac{1}{60}[/tex][tex]\frac{2x+22}{x^2+22x}=\frac{1}{60}[/tex]Step 3
Cross-multiply.
[tex]x^2+22x=60(2x+22)[/tex]Step 4
Open the parenthesis.
[tex]x^2+22x=120x+1320[/tex][tex]x^2+22x-120x-1320=0[/tex][tex]x^2-98x-1320=0[/tex]Step 5
Solve the above using factorization method.
[tex]\begin{gathered} x^2-110x+12x-1320=0 \\ \\ x(x-110)+12(x-110)=0 \\ \\ (x-110)(x+12)=0 \end{gathered}[/tex]Either (x-110) = 0 or x+12 =0
x =110 or x =-12
Since there is no negative timing, we will consider only the positive value.
Hence, x=110
Therefore,
The time taken Andy to mow = 110 minutes.
The time taken for Brian to mow = x+ 22 = 110+22 = 132
ANSWER
It takes Brian 132 minutes to mow the lawn himself.
It takes Andy 110 minutes to mow the lawn himself.
g(n) = 2n^2 - 4; Find g(-2)
Answers
ANSWER
g(-2) = 4
EXPLANATION
We are given the function g(n) as:
[tex]g(n)=2n^2\text{ - 4}[/tex]To find g(-2), we have to replace n with -2 in g(n) and simplify it.
[tex]\begin{gathered} g(-2)=2(-2)^2\text{ - 4 = 2}\cdot4\text{ - 4} \\ g(-2)\text{ = 8 - 4} \\ g(-2)\text{ = 4} \end{gathered}[/tex]That is the value of g(-2)
combining functionsConsider the following functions. f(-2) = -10 and g(-2) = -11Find (f +g)(-2). (f + g) (-2) =
Answers
f(-2) = -10 and g(-2) = -11
Find (f +g)(-2).
we have that
(f +g)(-2)=f(-2)+g(-2)
substitute the given values
(f +g)(-2)=-10+(-11)=-21
In how many ways can a committee of four Democrats and five Republicans be formed from a group of seven Democrats and eleven Republicans?
Answers
The percentage of majority and minority party members on each committee is also decided by party leaders.
How many Republicans and Democrats are there in each committee?The percentage of majority and minority party members on each committee is also decided by party leaders. Each standing committee (apart from Standards) is required under the Democratic Caucus Rules to have at least three Democrats for every two Republicans.The percentages of Democrats and Republicans in the committees generally correspond to their representation in the House and the Senate overall.In the House, there are now 20 standing committees and 1 permanent select committee. Please visit the Clerk of the House website for the most recent committee information.Individual Senators are typically only allowed to serve on two Class A committees and one Class B committee.To learn more about standing committees refer to:
https://brainly.com/question/2609442
#SPJ1
The percentage of majority and minority party members on each committee is also decided by party leaders.
How many Republicans and Democrats are there in each committee?The percentage of majority and minority party members on each committee is also decided by party leaders. Each standing committee (apart from Standards) is required under the Democratic Caucus Rules to have at least three Democrats for every two Republicans.
The percentages of Democrats and Republicans in the committees generally correspond to their representation in the House and the Senate overall. In the House, there are now 20 standing committees and 1 permanent select committee.
Please visit the Clerk of the House website for the most recent committee information. Individual Senators are typically only allowed to serve on two Class A committees and one Class B committee.
To learn more about standing committees refer to:
brainly.com/question/2609442
#SPJ1
if I can...give me any word problems that have to deal with multiply and dividing rational numbers
Answers
Determine whether the given numbers are rational or irrational.
(a) 1.75 (b) 0.01 (c) 0.5 (d) 0.09 (d) √3
So, rational can be any fraction number, but it can not be in under root form.
Thus the only option (d) is irrational number. all other are rational number.
[tex]\begin{gathered} \text{The product of rational number }\frac{4}{7}\text{ and }\frac{3}{5\text{ }}is? \\ \Rightarrow\frac{4}{7}\times\frac{3}{5} \\ \Rightarrow\frac{12}{35} \end{gathered}[/tex]14) Which of the following is NOT a rational number?a. product of 15 and .25b. sum of 2/5 and 1/2c. the sum of 2+√√4 and 15-√4d. product of 20 and √6
Answers
If we multiply 20 by squareroot 6, the answer would be 20(squareroot6). So it is a rational numbersquare root.
But in a, if we multiply 0.25 that is 1/4, by 15 it will be 15/4, so. itis a rational number
In b:
[tex]\frac{2}{5}+\frac{1}{2}=\frac{4+5}{10}=\frac{9}{10}[/tex]It is rational.
However, let's do the operation.
[tex](2+\sqrt{4})+(15\text{ - }\sqrt{4})=(2+2)+(15\text{ - }2)=4+13=17[/tex]Therefore, it is a natural number and not a rational. The answer is c
Mona bought 3 3/8 pounds of cheese. She used 2 3/4 pounds to make sandwiches. Write and solve an equation to find how much cheese is left.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
cheese:
purchased amount = 3 3/8 lb
used amount = 2 3/4
Step 02:
equation:
remaining amount = purchased amount - used amount
[tex]\begin{gathered} \text{remaining amount = 3 3/8 - 2 3/4 }=\text{ (3 + }\frac{3}{8})\text{ - (2 + }\frac{3}{4}) \\ \text{ } \end{gathered}[/tex][tex]\text{remaining amount = }\frac{27}{8}\text{ - }\frac{11}{4}=\frac{5}{8}[/tex]The answer is:
5/8 lb = 0.625 lb
PLEASE HELP ME!!!!
What is the value of this expression when p = 5 and q=−2?
−3(p−q)2
Enter your answer in the box.
Answers
Answer:
-147
Step-by-step explanation:
We can solve this by plugging in p = 5 and q=−2 and then evaluating using PEMDAS which tells us the order we do the math in by operation
Remember,
PEMDAS means
Parenthesis
Exponents
Multiplication and Division ( perform going left to right )
Addition and Subtraction ( perform going left to right )
-3(p-q)²
==> plug in p = 5 and q = -2
-3(5-(-2))²
==> remove parenthesis on -2
-3(5 + 2)²
==> do the operations inside of the parenthesis
-3(7)²
==> do the exponents
-3(49)
==> multiply -3 and 49
=-147
What is the value of x?x = ___ ydRound your answer to the nearest tenth
Answers
We need to use the cosine of the angle, in this case:
Cos(37°) = 30 yd / X
Thus, X = 30 / Cos(37) = 30 / 0.7986 = 37.56
how do I find which coordinate pairs represent vertices of P'Q'R'S after these two transformations?
Answers
We have two transformations.
We will apply them to a generic point P=(x,y), and then we can replace them with any coordinates as inputs.
First transformation: translating 6 units to the right.
This changes the x-coordinate by adding 6 units (x=0 becames x'=6, for example), so we can write:
[tex]P=(x,y)\longrightarrow P^{\prime}=(x+6,y)[/tex]Second transformation: rotate 90 degrees clockwise.
This changes both x and y coordinates. We can look at a drawing to understand the transformation.
The x-coordinate becomes the y-coordinate, and the y-coordinate becomes the negative x-coordinate.
We can then write:
[tex]P^{\prime}=(x+6,y)\longrightarrow P^{\prime}^{\prime}=(y,-x-6)[/tex]So now we know that the final image of a point (x,y) after the two transformations is (y,-x-6).
Then, we can list all four points:
[tex]P=(-3,7)\longrightarrow P^{\prime}^{\prime}=(7,-(-3)-6)=(7,-3)[/tex][tex]Q=(4,12)\longrightarrow Q^{\prime}^{\prime}=(12,-4-6)=(12,-10)[/tex][tex]R=(4,-2)\longrightarrow R^{\prime}^{\prime}=(-2,-4-6)=(-2,-10)[/tex][tex]S=(-3,-7)\longrightarrow S^{\prime}^{\prime}=(-7,-(-3)+6)=(-7,-3)[/tex]Final coordinates: (7,-3), (12,-10), (-2,-10) and (-7,-3).
2x + 9 + 3x + x = __x + __Fill in the empty spaces to make this equation have one solution
Answers
Answer:
2x + 9 + 3x + x = 7x + 5
Explanation:
The expression on the left side is equal to
2x + 9 + 3x + x
Adding the like terms, we get
(2x + 3x + x) + 9
6x + 9
Then, the given equation is
2x + 9 + 3x + x = __x + __
To make this equation have one solution, the coefficient of x on the right side has to be different from 6, which is the coefficient of 6x + 9.
Therefore, we can fill the empty spaces as
2x + 9 + 3x + x = 7x + 5
Solving this equation, we get:
(2x + 3x + x) + 9 = 7x + 5
6x + 9 = 7x + 5
6x + 9 - 5 = 7x + 5 - 5
6x + 4 = 7x
6x + 4 - 6x = 7x - 6x
4 = x
Therefore, the only solution is x = 4.
Check for Understanding 1eteofLook at the function table below and select the correct equation rule.tly510714918Select one:Of(0) =Of(0) = 21 +1Of(1) = 20Of(1) = 21 - 1Check
Answers
C) y= 2x
1) Examining that table, we can notice that the value of y is precisely twice the value of x
x | y
5 10
7 14
9 18
2) Hence, we can state since y is twice x that the function can be written as:
y=2x
3) So the answer is C) y= 2x
Nicole can run 4
laps in 2/5 hour.
How long will it
Hake her to run 5
laps?
Answers
Answer:
1/2 hour
Step-by-step explanation:
Each lap is 1/10 hours times that by 5 and you get 5/10 and simplified is 1/2
3. Are the triangles congruent? If so, how? b. yes, AAS ves, SSS yes, SAS + d
Answers
Yes are congruent , SSS because the graph shows us two equal sides, if they are equal, then the upper and lower sides of the quadrilateral will be equal, for this reason we already have two equal sides, and since the triangles share the diagonal we can say that their three sides are equal
red and green sides are equal one by one,the red ones are the same because the drawing says so, and the green ones are the same because in a parallelogram the opposite sides have the same measure.
we already have that two of the three sides of each triangle are equal,and we can conclude that the third side is also the same, since the triangles share it
then the triangles are equivalent since their three sides are equal SSS
Tim bought a new computer for his office for $1200. He read that thecomputer depreciates (loses value) at a rate of $200 per year. What will bethe value of the computer after 3 years? *
Answers
If each year the computer loses $200 of it's value, in 3 years it'll have lost 3 times that amount i.e. $600.
So, after 3 years the computer will have $600 less the value than when Tim bought it:
[tex]1200-600=600[/tex]After 3 years, the value of the computer will be $600
The loss of the computer's value can be model as:
[tex]y=-200x+1200[/tex]Where 1200 is the initial value, 200 is how much it's devalued per year. 'x' represents the years since Tim bought the computer and 'y' represents it's value after 'x' years.
How is seeing the parts of a partitioned number line the same as seeing the parts of a partitioned rectangle? How is it different?
Answers
Partitioning a number line:
If you have a number line, you can partition into fractions. This is done by dividing the number lines into equal portions and summing up the portions to give the total part that you need.
For example, to partition a number line into 3/4 portion of a number line, you can partition the number line into 4 portions of 1/4 each and take 3 portions out of the four to get 3/4.
The same strategy is used for a rectangle:
To divide a rectangle into two portions of 3/4 and 1/4, you can use similar method as above:
Difference:The difference is that in a number line, you only have the length and you can partition only across the length
In a rectangle you can partition both the length and the width of the shape
2. Which graph represents the solution set to the following system of inequalities?y +6 > (x + 1)^2 + 2-x+2<= -1/2y+3
Answers
Solution:
The inequalities are given below as
[tex]\begin{gathered} y+6>(x+1)^2+2 \\ -x+2\leq-\frac{1}{2}y+3 \end{gathered}[/tex]Using a graphing calculator, we will have the graph be
Let Z be a standard normal random variable. Calculate the following probabilities using the ALEKS calculator. Round your responses to at least three decimal places.
Answers
(a)
P (Z > -1.62 ) = 0.94738
(b)
P (Z ≤ 1.72) = 0.95728
(c)
P (-058 < Z < 1.91 ) = 0.69097
Z<1.91 = 0.97193
Z<-0.58 = 0.28096
0.97193 - 0.28096 = 0.69097
Find dy/dx by implicit differention.1) x^4 + x^2y^2 + y^3 = 5(2) Sin (x+y) = cosx + casy
Answers
The given equation is:
[tex]x^4+x^2y^2+y^3=5[/tex]The differential is given as:
[tex]4x^3+2xy^2+2yx^2\frac{dy}{dx}+3y^2\frac{dy}{dx}=0[/tex]Make dy/dx the subject of the formula:
[tex]\begin{gathered} 2yx^2\frac{dy}{dx}+3y^2\frac{dy}{dx}=-(4x^3+2xy^2) \\ \\ \frac{dy}{dx}(2x^2y+3y^2)=-(4x^3+2xy^2) \\ \\ \frac{dy}{dx}=\frac{-(4x^3+2xy^2)}{2x^2y+3y^2} \end{gathered}[/tex]Find the volume of this object.Use 3 for T.Volume of a CylinderV=Tir2h6 in8 in10 in] 2 in V ~ [?]in3
Answers
Solution:
Given:
Two cylinders on each other;
[tex]\begin{gathered} \text{For the cylinder at the top, the following were given;} \\ d=6in \\ \text{radius is half of a diameter,} \\ \text{Hence,} \\ r=\frac{d}{2}=\frac{6}{2} \\ r=3in \\ h=8in \\ \pi=3 \end{gathered}[/tex]Using the formula of the volume of a cylinder;
[tex]\begin{gathered} V=\pi r^2h \\ V=3\times3^2\times8 \\ V=216in^3 \end{gathered}[/tex]For the cylinder at the bottom, the following were given;
[tex]\begin{gathered} \\ d=10in \\ \text{radius is half of a diameter,} \\ \text{Hence,} \\ r=\frac{d}{2}=\frac{10}{2} \\ r=5in \\ h=2in \\ \pi=3 \end{gathered}[/tex]Using the formula of the volume of a cylinder;
[tex]\begin{gathered} V=\pi r^2h \\ V=3\times5^2\times2 \\ V=150in^3 \end{gathered}[/tex]Hence, the volume of the object is the total volume of both cylinders.
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Therefore, the volume of the object is 366 cubic inches.
These tables represent an exponential function. Find the average rate ofchange for the interval from x = 8 to x = 9.хyInterval0110 to 13291 to 2Average rateof change2]x36]x318]*3543x3162]*34863272 to 34813 to 44 to 5524367295 to 6O A. 13,122O B. 3O C. 19,683D. 6561
Answers
Average rate can be calculated like the slope
[tex]\frac{y2-y1}{x2-x1}[/tex]where (x2,y2) is a right point yo (x1,y1)
But we need the values of x=8 and x=9
we realize the change between values of y is the last value by 3 then if
[tex]\begin{gathered} 6\longrightarrow729 \\ 7\longrightarrow729\times3=2187 \\ 8\longrightarrow2187\times3=6561 \\ 9\longrightarrow6561\times3=19683 \end{gathered}[/tex]we have the corresponding values for x=8 and x=9
now replace on the formula of the slope using the points (8 , 6561) and (9 , 19683)
where (9 , 19683) is (x2,y2) and (8 , 6561) is (x1,y1)
[tex]\begin{gathered} \frac{19683-6561}{9-8} \\ \\ \frac{13122}{1}=13122 \end{gathered}[/tex]the avreage rate of change for the interval 8 to 9 is 13122
We realize the values of the average are multiplied by 3 too, then we can fi
Find the measure in degrees of the smallest angle in the triangle.
Answers
Answer:
Explanation:
The sum of the angles in a triangle is 180 degrees. The angles in the given triangle are 2x, 6x + 4 and 2x + 6
Thus,
2x + 6x + 4 + 2x + 6 = 180
By collecting like terms, we have
2x + 6x + 2x + 4 + 6 = 180
10x + 10 = 180
10x = 180 - 10 = 170
x = 170/10
x = 17
The smallest angle in the triangle is 2x. Thus,
Smallest angle = 2 * 17
Smallest angle = 34 degrees
Select the correct choices to complete the sentence.
AIR SHOW At a flight demonstration, two planes are flying in a synchronized pattern. The planes start their demonstration at (−20,−15) and (5, −15) . Select the transformation that represents the planes’ flight pattern to their final destinations at (−30, 20) and (0, 20) .
Options:
A. (-2, 7)
B. (-10, 35)
C. (-12, 48)
Answers
Answer:
The coorect option is letter C
12. A local poll finds that 0.35 of all citizens approve of the mayor's policies. What fraction of citizens approve? Write the answer in lowest terms. O 3/5 035/100 O 7/20 O 35/50
Answers
Explanation:
Writing 0.35 as a fraction we have:
[tex]\frac{35}{100}[/tex]And we can simplify dividing both numerator and denominator by 5:
[tex]\frac{\frac{35}{5}}{\frac{100}{5}}=\frac{7}{20}[/tex]Answer:
7/20