How could i find the base?What is the volume of the cylinder?Approximate volume of cylinder in 3 decimals.
Answers
Given:
Here a cylinder is given with radius is 2 unit and height is 6 unit.
Required:
Find the base and volume.
Explanation:
The base of cylinder is circle and the area of circle is
[tex]A=\pi r^2=3.14*2*2=12.56\text{ unit}^2[/tex]Now we have to find the volume of cylinder
[tex]V=\pi r^2h=2*2*6*\pi=24\pi\text{ unit}^3[/tex]now put the value of
[tex]\pi=3.14[/tex]so now volume of cylinder is
[tex]V=24*3.14=75.398\text{ unit}^3[/tex]Final answer:
The base of cylinder is circle and the value of base is 12.56 square unit
Exact volume of cylinder is 24pi cubic unit and approximate volume of cylinder is 75.398 cubic unit
Related Questions
Consider the function f(θ)=4sin(2θ)+2.What is the amplitude of f?What is the period of f?Graph of the function f below.
Answers
Given data:
The given function is f(θ)=4sin(2θ)+2.
Amplitude is the maximum vertical distance, amplitude of the given function is,
A=6
The period of the given function is,
[tex]\begin{gathered} P=\frac{2\pi}{2} \\ =\pi \end{gathered}[/tex]The graph of the given function is shown below.
Thus, amplitude of the function is 6, and period is π.
Write an equation that passes through (5,-1) and is perpendicular to y=5/2x-5
Answers
Answer:
[tex]y=-\frac{2}{5}x+1[/tex]Step-by-step explanation:
The equation of a line is represented by the following equation:
[tex]\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{ slope} \\ b=y-\text{intercept} \end{gathered}[/tex]If the given line is perpendicular to the one we want to find, the slope of the missing line would be the negative reciprocal of the given slope:
[tex]\begin{gathered} m=-(\frac{2}{5}) \\ m=-\frac{2}{5} \end{gathered}[/tex]Use the slope-point form of the line equation to determine the equation in slope-intercept form:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-1)=-\frac{2}{5}(x-5) \\ y+1=-\frac{2}{5}x+2 \\ y=-\frac{2}{5}x+2-1 \\ y=-\frac{2}{5}x+1 \end{gathered}[/tex]A car travels 87 miles north and
then 114 miles west.
What is the magnitude of the
car's resultant vector?
Hint: Draw a vector diagram.
[?] miles
Round your answer to the nearest tenth.
Answers
Answer:
143.4 miles
Step-by-step explanation:
To find the magnitude of the resultant vector, we have to use the Pythagorean theorem. The Pythagorean theorem is [tex]a^{2} +b^{2} =c^{2}[/tex].
What is given: (Look at the attached photo)
a = 86 miles (north)
b = 114 miles (west)
c = ?
-
Now let us substitute and solve:
1) [tex]87^{2} + 114^{2} = c^{2}[/tex]
2) [tex]7569 + 12996 = c^{2}[/tex]
3) [tex]c^{2} =20565[/tex]
4) [tex]c= \sqrt{20565}[/tex]
5) [tex]c = 143.4[/tex]
The magnitude of the car's resultant vector is approximately 143.4 miles, rounded to the nearest tenth.
Given that a car travels 87 miles north and then 114 miles west, we need to find the magnitude of the car's resultant vector.
To find the magnitude of the car's resultant vector, we can use the Pythagorean theorem since the car traveled north and west, forming a right-angled triangle.
Let's label the distance traveled north as "A" and the distance traveled west as "B."
Then the magnitude of the resultant vector "R" can be calculated using the formula:
R = √(A² + B²)
Given that the car travels 87 miles north (A = 87 miles) and 114 miles west (B = 114 miles), we can plug these values into the formula:
R = √(87² + 114²)
R = √(7569 + 12996)
R = √20565
R ≈ 143.4 miles
So, the magnitude of the car's resultant vector is approximately 143.4 miles, rounded to the nearest tenth.
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I need a quick and easy Explanation for this answer I have been waiting for this and I do not get it
Answers
Answer
Explanation
Given:
mm
A.
To determine the measure of [tex]\begin{gathered} m\angle TRQ+m\angle QRS=180 \\ 145+m\angle QRS=180 \\ \text{Simplify and rearrange} \\ m\angle QRS=180-145 \\ m\angle QRS=35\degree \end{gathered}[/tex]
Therefore, m
B.
To determine the measure of [tex]\begin{gathered} m\angle QRS+\angle S+\angle Q=180 \\ 35+y+4y=180 \\ \text{Simplify and rearrange} \\ 35+5y=180 \\ 5y=180-35 \\ 5y=145 \\ y=\frac{145}{5} \\ y=29\degree \end{gathered}[/tex]Now, we plug in y=29 into m[tex]\begin{gathered} m\angle Q=4y \\ m\angle Q=4(29) \\ m\angle Q=116\degree \end{gathered}[/tex]Therefore, m
I would like somebody to verify my solution for this particular problem!
Answers
Step 1
Given;
[tex]\begin{gathered} x(t)=t-2 \\ y(t)=2t^2+4 \\ t\text{ is on the interval \lbrack-3,1\rbrack} \end{gathered}[/tex]Required; To write in standard form.
Step 2
[tex]\begin{gathered} x=t-2 \\ t=x+2 \end{gathered}[/tex][tex]\begin{gathered} y(t)=2(x+2)^2+4 \\ y(t)=2x^2+8x+12 \\ \end{gathered}[/tex]The answer will be;
[tex]y=2x^2+8x+12\text{ where x is on the interval \lbrack}[/tex]Rewrite the following polynomial in standard form.1+ 10x − 2x³ + x5-x^2-9
Answers
Hello!
We have the following polynomial:
[tex]1+10x-2x^3+x^5-x^2-9[/tex]To put it in the standard form, we have to start with the highest exponent on the left and then write in decreasing order. Look:
[tex]\begin{gathered} x^5-2x^3-x^2+10x-9+1 \\ \end{gathered}[/tex]We can simplify it by solving -9 +1, look:
[tex]x^5-2x^3-x^2+10x-8[/tex]book: $39, 7.5% markupWhat is the DISCOUNT dollar amount?What is the SELLING PRICE dollar amount?
Answers
The original price of the book is $39
Mark up is 7.5% . This means there is an increase in price
7.5% increase is 100 + 7.5
= 100 + 7.5
107.5%
To calculate the discount dollar
The mark up price is
107.5/100 x $39
= 1.075 x 39
= $ 41.925
The discount dollar amount = Marked up price - Original price
= $41.925 - $39
= $2.925
The discount dollar amount is $2.925
The selling price is $41.925
The table gives some information
about the heights of 60 boys.
a) Complete the boxplot for this information.
b) Work out an estimate for the number of these boys with a height between
149 cm and 181 cm.
Answers
Considering the information of the distribution given in the table, it is found that:
a) The box plot is given at the end of the answer.
b) The estimate for the number of these boys with a height between 149 cm and 181 cm is of 45.
What does a box-and-whisker plot shows?A box and whisker plot shows five things of a distribution, listed as follows:
The minimum value of the data-set.The first quartile, which is the median of the bottom 50% of measures in the data-set, hence it is the value that 75% of the measures are greater than.The median, which is the middle-value of the data-set, meaning that 50% of the data-set is less than the median and 50% is greater.The thid quartile, which is the median of the upper 50% of the measures in the data-set, hence it is the value that 75% of the measures are lesser than.The maximum value of the data-set.For the data-set of the heights, these measures are given as follows:
Minimum: 142 cm.First quartile: 149 cm.Median: 156 cm.Third quartile: 160 cm.Maximum: 181 cm.The box plot showing these information is given by the image at the end of the answer.
The proportion of students with a height between 149 cm and 181 cm is of 75% = 0.75, as:
149 cm is the first quartile of the distribution.181 cm is the maximum value of the distribution.75% of the values are greater than the first quartile, hence the number of students is:
Number = 0.75 x 60 = 45 students.
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Given vectors u =<4, -1> and v= <-5, 11>find the followingto 1 decimal):||u||=
Answers
Answer:
[tex]\lvert u\rvert=17[/tex]Step-by-step explanation:
Given the vector, u =<4, -1>, determine the magnitude.
The magnitude of a vector is represented as:
[tex]\begin{gathered} \lvert{v}\rvert=\sqrt{v1^2+v2^2} \\ where, \\ v=\langle v1,v2\rangle \end{gathered}[/tex]Therefore, for the given vector:
[tex]\begin{gathered} \lvert{u}\rvert=\sqrt{4^2+(-1)^2} \\ \lvert{u}\rvert=\sqrt{16+1} \\ \lvert{u}\rvert=\sqrt{17} \end{gathered}[/tex]Which of the following are true of bar graphs? 1.Bars must be in order from least to greatest. 2.Data is displayed in intervals. 3. Specific data is shown. 4. There are gaps between bars.
Answers
1.Bars must be in order from least to greatest. → correct
2.Data is displayed in intervals. → not necesarly, this depends on wether the variable is discrete or continuous
3. Specific data is shown. → No, the observed frequency for the determined range of the variable is observed.
4. There are gaps between bars. →No, only if there are no observations for a determined value of the variable.
If she pays $10.00 to join, she will get 10% off on all the grocerie must she buy before her savings equal her membership fee?
Answers
Answer:
rat
Step-by-step explanation:
The sum of one-fifth of a number and three is equal to half of the number. What is the number?
Answers
Answer:
Step-by-step explanation:
(1/5)(x)+3=(1/2)(x)
3=(1/2)x-(1/5)x
3=(5/10)x-(2/10)x
3=(3/10)x
3=0.3x
30=3x
x=30/3
x=10
Solving a percent make sure problem using a system of linear equations
Answers
We have to make a 170 gallons mixture of antifreeze with a 40% antifreeze percentage.
We have to made it mixing products from two brands:
• First brand (F): 35% pure antifreeze
,• Second brand (S): 85% pure antifreeze.
NOTE: To work with percentage and perform calculations, it is better to express the percentages in decimal form. We can do this by dividing the percentage by 100. Then, for example, 35% will become 0.35.
We will call F to the volume for the first brand and S to the volume of the second brand.
We know that the total mixture volume is 170 gallons. The volume is made of the mixture fo the volume of the first brand and the volume of the second brand. Then, this total volume is equal to the sum of F and S, so we can write:
[tex]F+S=170[/tex]We need another equation to have a complete system of equations (two equations for two unknowns).
We can use the antifreeze content to write one.
We know the the mixture has to have 40% pure antifreeze. Then, the volume of antifreeze will be 40% of the total volume of 170 gallons.
This volume of antifreeze will come from 35% of the volume of the first brand and 85% of the volume of the second brand.
Then, we can write:
[tex]\begin{gathered} 0.35*F+0.85*S=0.40*170 \\ 0.35F+0.85S=68 \end{gathered}[/tex]We now have can use the first equation to express S in function of F:
[tex]\begin{gathered} F+S=170 \\ S=170-F \end{gathered}[/tex]We can now replace S in the second equation and solve for F:
[tex]\begin{gathered} 0.35F+0.85S=68 \\ 0.35F+0.85(170-F)=68 \\ 0.35F+144.5-0.85F=68 \\ 0.35F-0.85F=68-144.5 \\ -0.5F=-76.5 \\ F=\frac{76.5}{0.5} \\ F=153 \end{gathered}[/tex]We have found that the first brand will have a volume in the mixture of 153 gallons.
We can now calculate S as:
[tex]\begin{gathered} S=170-F \\ S=170-153 \\ S=17 \end{gathered}[/tex]The second brand volume in the mix is 17 gallons.
Answer:
First brand: 153 gallons
Second brand: 17 gallons.
AB, CD and EF are straight lines
AB is parallel to CD
work out the size of angle y
Answers
The required value of y is 117°
Given AB and CD are parallel lines;
and EF is the transversal
Thus 2x + 16 = 3x - 12 { because they are corresponding angles }
On solving the above mentioned linear equation
we get,
x = 25
Thus the required angles are 2x + 16 = 50 + 16 = 66 degrees
and 3x - 12 = 75 - 12 = 63 degrees
And to find the value of y
we can use linear pair property
Thus y + 63 = 180
y = 180 - 63
y = 117 °
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Which equation shows the distributive property? A 4(3+6)=12+24 B (4+3)+6=6+(4+3) C (12+4)+0=12+4 (12+4)+6=12+(4+6) D
Answers
To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
so the correct answer is A.
A 4(3+6)=12+24
B (4+3)+6=6+(4+3)
C (12+4)+0=12+4
D (12+4)+6=12+(4+6)
What is the scale factor of the dilation (with center at the origin) shown below?A) 1/2B) -2C.)2D) -1/2
Answers
The graph is shown having two triangle with different coordinates.
The one triangle is of larger size and othe triangle is of smaller size.
To determine the scale factor of the dilation we need to find the coordinates of the triangle.
The larger triangle coordinate are,
[tex]A^{\prime}=(-4,-4)\text{ ,B'}=(-2,4)\text{ , C'}=(4,2)[/tex]The smaller triangle coordinates are,
[tex]A=(-2,-2),B=(-1,2),C=(2,1)[/tex]The coordinate A is formed by multiply with
[tex]\frac{1}{2}[/tex]in A' coordinate.
Similarly other coordinates is also determined by multiply with 1/2 in the corrdinates with B' and C'.
Therefore, the scale factor for dilation obtained is,
[tex]\frac{1}{2}[/tex]Hence the correct option is A.
Helppppppppppppppppppp
Answers
If the y value of the coordinate was flipped, then the opposite axis would be where it was flipped over. Think of it on a coordinate plane; (8,-7) is below the x-axis, while (8,7) is above the x-axis. If the point went from below the x-axis to above the x-axis, then the x axis is what it was reflected over.
what is 11/12 ÷ 1/3 0 2 1/4 0 2 3/40 3 1/3 0 3 2/3
Answers
Identify the terminal point for a 45° angle in a unit circle.O A. (24)O B. (1.)Oc. (1,1)O D. (2,3)
Answers
(x, y) = ( cos 45, sin 45) =
[tex]=\text{ (}\frac{\sqrt[]{2}}{2}\text{ , }\frac{\sqrt[]{2}}{2}\text{ )}[/tex]The correct option is A
Please HELP me on my ASSESSMENT practice its URGENT Find the ZEROS of each quadratic function by factoring
Answers
13.
[tex]x^2+x-20=(x+5)(x-4)[/tex]Then, the zeros are x=-5 and x=4.
14.
[tex]x^2-4x-60=(x+6)(x-10)[/tex]Then, the zeros are x=-6 and x=10.
15.
[tex]x^2-15x+50=(x-5)(x-10)[/tex]Then the zeros are x=5 and x=10.
16.
[tex]x^2-x-72=(x+8)(x-7)[/tex]Then the zeros are x=-8 and x=7.
17.
[tex]x^2+2x-48=(x+8)(x-6)[/tex]Then the zeros are x=-8 and x=6.
18.
[tex]x^2-12x+36=(x-6)^2[/tex]Then there is only one zero at x=6.
19.
[tex]x^2+32x+60=(x+30)(x+2)[/tex]Then the zeros are x=-30 and x=-2.
20.
[tex]x^2-21x-100=(x+4)(x-25)[/tex]Then the zeros are x=-4 and x=25.
hello so this is a area model with two multiplication
Answers
We have the following:
Now,
[tex]1000+20+200+4=1224[/tex]Need help with question 8 Only Part B C and D
Answers
Answer:
Explanation:
Given:
[tex]g(x)=3x^2+12x+9[/tex]B.)
To find the vertex, we use the following formula:
[tex]\begin{gathered} x=-\frac{b}{2a} \\ \text{From the Form:} \\ y=ax^2+bx+c \end{gathered}[/tex]So based on the given equation, the values of a and b are:
a=3
b=12
We plug in what we know:
[tex]\begin{gathered} x=-\frac{b}{2a} \\ =-\frac{12}{2(3)} \\ x=-2 \end{gathered}[/tex]Next, we plug in x=-2 into g(x)=3x^2+12x+9:
[tex]\begin{gathered} g(x)=3x^2+12x+9 \\ =3(-2)^2+12(-2)+9 \\ \text{Calculate} \\ g(x)=-3 \end{gathered}[/tex]Therefore, the vertex is (-2,-3).
C.
Now, to find the axis of symmetry, we also use the formula x=-b/2a since it is the vertical line that goes through the vertex.
Therefore, the Axis of Symmetry for the given equation is x = -2.
D.
We let g(x)=0 to find the x-intercept:
[tex]\begin{gathered} 3x^2+12x+9=0 \\ \text{Simplify} \\ =3(x^2+4x+3) \\ =3(x+1)(x+3) \end{gathered}[/tex]Based on the factors, the values for x are:
x=-1
x=-3
Therefore, the x intercept points are:
(-1,0),(-3,0)
To get the y-intercept, we let x=0 and plug in into g(x)=3x^2+12x+9. So,
[tex]\begin{gathered} g(x)=3x^2+12x+9 \\ g(0)=3(0)^2+12(0)+9 \\ g(0)=9 \end{gathered}[/tex]Therefore, the y intercept point is (0,9).
Sandwiches cost $5, French friescost $3, and drinks cost $2. Theexpression 5n + 3n + 2n gives the totalfor cost, in dollars, for buying a sandwich,French fries, and a drink for n people.Which is another way to write thisexpression?A. 10nB. 10nC. 30nD. 30n3
Answers
Given 5n+3n+2n, we need to combine like terms
By combining like terms, we get 5n+3n+2n=1
Give the appropriate similarity criteria that can be used the trianglessimilar.a. AAb. SASc. SSSd. Not Similar
Answers
Since DEC and DAB share the angle D, and the lines EC and AB are parallel, then we can also see that the angles CED and BAD are congruent. Then, we can prove the similarity between those two triangles thanks to the AA criterion.
Therefore, the answer is:
[tex]AA[/tex]there are 20, 000 owls in the wild. Every year the owl population decrease 8%.identify the state. the starting amount the rate change this growth or decay justify .write the equation that represents the owl population after a number of years. how many owls will there be after six years
Answers
Given:
Number of owls in the wils is 20,000.
The rate of decrease is 8%.
From the given data the starting amount of owls is 20000.
The rate of change is -8%.
The general exponential equation of population growth is,
[tex]P=P_0(1+\frac{r}{100})^t[/tex]Here t represents the number of years.
Substitute the given values in the above equation,
[tex]\begin{gathered} P=20000(1+(-\frac{8}{100}))^t \\ P=20000(1+(-0.08))^t \\ P=20000(1-0.08)^t \\ P=20000(0.92)^t \end{gathered}[/tex]Hence, the required equation that represents the owl population after a number of years is obtained.
The number of owls after 6 years can be calculated by substituting t = 6 in the above equation.
[tex]\begin{gathered} P=20000(0.92)^6 \\ P=20000(0.606355) \\ P=12127 \end{gathered}[/tex]Hence, the population of owls in the wild is 12,127 after 6 years. And the population is decreasing.
I don't quite understand the second question, so I hope to answer the second question.
Answers
The relation is a function because it passes the vertical line test. This means, if we draw a vertical line anywhere in the graph, it will only intersect the graph at one point.
The domain of this relation or the possible values of x in this relation is from negative infinity to positive infinity (-∞, ∞).
The range of this relation is from -1 to infinity [-1, ∞). As we can see in the graph, the vertex of the parabola is at the minimum point located at (-3, -1). Therefore, the possible value of y starts from -1 and runs to infinity.
Evaluate the following equation if x=-2 and y=3[x to the 2nd power+5]-y
Answers
Given the expression;
[tex]\lbrack x^2+5\rbrack-y[/tex]If x = -2 and y =3, we are to substitute the values into the expression and get the result as shown:
[tex]\begin{gathered} =\lbrack(-2)^2+5\rbrack-3 \\ =(4+5)-3 \\ =\text{ 9 -3} \\ =\text{ 6} \end{gathered}[/tex]Hence the coorect answer is 6
In ARST, the measure of ZT=90°, the measure of ZR=6°, and RS = 3.6 feet. Find thelength of ST to the nearest tenth of a foot.S3.6XN60T70
Answers
we have taht
sin(R)=ST/SR -----> by opposite side divided by the hypotenuse
substitute given values
sin(6)=x/3.6
solve for x
x=3.6*sin(6)
x=0.4 ftif x= 2y-4 and x=6y+16 find the value for both x and y
Answers
In order to find the values of x and y, let's compare both values of x given:
[tex]\begin{gathered} x=2y-4 \\ x=6y+16 \\ \\ 2y-4=6y+16 \\ 6y-2y=-4-16 \\ 4y=-20 \\ y=-\frac{20}{4} \\ y=-5 \\ \\ x=2y-4 \\ x=2\cdot(-5)-4 \\ x=-10-4 \\ x=-14 \end{gathered}[/tex]So we have that x = -14 and y = -5.
Which of the following expressions can be used to find PQ?
Answers
Answer:
C
[tex]\frac{30}{\cos25}[/tex]Explanation:
Given the image of the right angle, to find PQ, we have to take the cosine of angle 25 degrees as shown below;
[tex]\cos 25=\frac{30}{PQ}[/tex]Let's go ahead and make PQ the subject of formula;
[tex]\begin{gathered} PQ\cos 25=30 \\ PQ=\frac{30}{\cos25} \end{gathered}[/tex]