Match each solid cone to it’s surface area. Answers are rounded to the nearest square unit
Answers
The surface area of a cone is given by the formula below:
[tex]S=\pi r^2+\pi rs[/tex]Where r is the base radius and s is the slant height.
So, calculating the surface area of first cone, we have:
[tex]\begin{gathered} s^2=21^2+6^2\\ \\ s^2=441+36\\ \\ s^2=477\\ \\ s=21.84\\ \\ S=\pi\cdot6^2+\pi\cdot6\cdot21.84\\ \\ S=525 \end{gathered}[/tex]The surface area of the second cone is:
[tex]\begin{gathered} s^2=8^2+12^2\\ \\ s^2=64+144\\ \\ s^2=208\\ \\ s=14.42\\ \\ S=\pi\cdot12^2+\pi\cdot12\cdot14.42\\ \\ S=996 \end{gathered}[/tex]The surface area of the third cone is:
[tex]\begin{gathered} s^2=15^2+8^2\\ \\ s^2=225+64\\ \\ s^2=289\\ \\ s=17\\ \\ S=\pi\cdot8^2+\pi\cdot8\cdot17\\ \\ S=628 \end{gathered}[/tex]And the surface area of the fourth cone is:
[tex]\begin{gathered} s^2=10^2+10^2\\ \\ s^2=100+100\\ \\ s^2=200\\ \\ s=14.14\\ \\ S=\pi\cdot10^2+\pi\cdot10\cdot14.14\\ \\ S=758 \end{gathered}[/tex]Related Questions
Simplify the inequality. Graph it, write it in interval notation, and then inequality notation. Write your answer in interval notation.3x+2<−4 or 3x+3>27Clear All Draw: Line segments interval inequality
Answers
given the inequality
[tex]3x+2<−4\text{ }or\text{ }3x+3>27[/tex]then
[tex]3x<−4-2\text{ }or\text{ }3x>27-3[/tex][tex]3x<−6\text{ }or\text{ }3x>24[/tex][tex]x<−2\text{ }or\text{ }x>8[/tex]Graph:
notice the empty circle because the ineqaulity does not have equal symbol
interval:
[tex]\left(-\infty \:,\:-2\right)\cup \left(8,\:\infty \:\right)[/tex]inequality:
[tex]x<-2\text{ }or\text{ }x>8[/tex]You have a combination lock with 3 secret digits. Find the 3 correct digits using the following clues and enter your answer below.
Answers
The first clue only tells us that there is one digit that is in the right place, so it could be any one of the following.
The second one tells us that one of the digits is right but in the wrong place, we still cannot confirm if 5 is the number we are talking about.
The fourth clue says that all the numbers are incorrect, so the digits are 2, 5, 0 or 1, now we must find out the correct order.
From clues 3 and 5 we can assume that 0 is one of the digits and that it comes first.
We will discard the number 5 because in clue 3 they talk about 2 correct digits, we already know that 0 is one and we choose 2 instead of the number five because of clues 1 and 2, which talk about only one digit in the correct place but in both of them the 5 remains in the same place.
The 3 digists are: 1, 0 and 2
The correct order is 012
SLV is a 45°-45°-90° triangle with leg SV. If SV = m, determine the length ofthe other leg and the hypotenuse.
Answers
Since angles S and L are congruent, the triangle SLV is isosceles with base SL, that means SV = LV.
Since SV = m, we have LV = m
Now, to calculate the hypotenuse, we can use Pythagorean theorem:
[tex]\begin{gathered} SL^2=SV^2+LV^2 \\ SL^2=m^2+m^2 \\ SL^2=2m^2 \\ SL=m\cdot\sqrt[]{2} \end{gathered}[/tex]2) write the equation of a line that passes through the point ( 4, 5) and is perpendicular to a line that passes through the points ( 6 8) and (10 0)
Answers
We have the following:
First we calculate the slope of the line where we are given two points (6,8) and (10,0)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]repplacing:
[tex]m=\frac{0-8}{10-6}=\frac{-8}{4}=-2[/tex]now, when two lines are perpendicular:
[tex]\begin{gathered} m_1=-\frac{1}{m_2} \\ -2=-\frac{1}{m_2} \\ 2=\frac{1}{m_2} \\ m_2=\frac{1}{2} \end{gathered}[/tex]now,
[tex]y=mx+b[/tex]with the point (4,5), replacing:
[tex]\begin{gathered} 5=\frac{1}{2}\cdot4+b \\ 5=2+b \\ b=5-2 \\ b=3 \end{gathered}[/tex]Therefore, the equation is:
[tex]\begin{gathered} y=\frac{1}{2}x+3 \\ y=\frac{x}{2}+3 \end{gathered}[/tex]check:
[tex]\begin{gathered} y=\frac{4}{2}+3 \\ y=2+3 \\ y=5 \end{gathered}[/tex]Therefore, the answer is y = x/2 + 3
What is the product of 2 1/2 and 1 1/4
Answers
First, we transform the mixed fractions into improper fractions:
[tex]\begin{gathered} 2\frac{1}{2}=\frac{2\cdot2+1}{2}=\frac{5}{2}, \\ 1\frac{1}{4}=\frac{1\cdot4+1}{4}=\frac{5}{4}. \end{gathered}[/tex]Then, we multiply the improper fractions:
[tex]\frac{5}{2}\cdot\frac{5}{4}=\frac{5\cdot5}{2\cdot4}=\frac{25}{8}\text{.}[/tex]Finally, we transform the improper fraction into a mixed fraction:
[tex]\frac{25}{8}=\frac{24+1}{8}=\frac{3\cdot8+1}{8}=3\frac{1}{8}\text{.}[/tex]Answer:
[tex]3\frac{1}{8}\text{.}[/tex]Suppose you invest $2200 at an annual interest rate of 5.3% compounded continuously. How much will you have after 7 years?
Answers
Answer:
$3188.20
Explanation:
From the information given:
• Principal, P = $2200
,• Interest Rate, r=5.3% = 0.053
,• Time, t=7 years
For a principal compounded continuously, we use the formula to determine the amount in the account:
[tex]A(t)=Pe^{rt}[/tex]Substituting the given values, we have:
[tex]\begin{gathered} A(t)=2200\times e^{0.053\times7} \\ =\$3188.20 \end{gathered}[/tex]You will have $3188.20 after 7 years.
Question 4 (5 points)
In Brock's class of 24 students, 10 students report that math is their favorite class, 25% of the students report that science is
their favorite, and 1/3 prefer reading.. Show your work and/or explain your answer: Which subject is favored by the greatest
number of students? (5 points)
Answers
Mathi is favored by the greatest i.e 10 students, using percentage
What is percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. Percentage refers to one in a hundred. The % sign is used to denote it.
There are 24 students in Brock's class
10 students say math is their favorite class , 25% say that science is their favorite class and 1/3 prefer reading.
Now you have to find out if more students prefer math or science. Well since the information tells you that 10 students prefer math, you need to find out that 25% of students prefer science and 1/3 prefer reading.
For 1st case, math favorite have 10 students,
For 2nd case, 25% of 24 is 24*25/100
=24*1/4
=6
And for 3rd case, who prefer reading is 1/3rd of students which is 24*1/3
=8
So Most students like math.
Hence, Mathi is favored by the greatest i.e 10 students.
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I need some help on finding the surface area. i don't know how to solve with a triangular base?
Answers
The surface area(A) of a triangular pyramid can be found using the formula:
[tex]A\text{ = }\frac{1}{2}\text{ }\times\text{ a }\times\text{ b + }\frac{3}{2}\text{ }\times b\text{ }\times\text{ s}[/tex]Given the triangular prism:
Hence, we have:
a = 3.5 m
b = 4m
s = 11.1 m
Substituting the values into the formula:
[tex]\begin{gathered} A\text{ = }\frac{1}{2}\times3.5\text{ }\times4\text{ + }\frac{3}{2}\text{ }\times\text{ 4 }\times\text{ 11.1} \\ =\text{ 7 + 66.6} \\ =\text{ 73.6 m}^2 \end{gathered}[/tex]Hence, the surface area of the pyramid is 73.6 square meter
I narrowly answered the first question on my homework but for some reason EF really confuses me.
Answers
Solution
Part 1
For this case we can find DF with the following proportion formula:
[tex]\frac{AC}{AB}=\frac{DF}{DE}[/tex]And replacing we got:
[tex]\frac{4}{2}=\frac{DF}{1.34},DF=2.68[/tex]Part 2
[tex]\frac{BC}{AB}=\frac{EF}{DE}[/tex]And solving for EF we got:
[tex]EF=1.34\cdot\frac{3}{2}=2.01[/tex]Four different stores have the same digital camera on sale. The original price and discounts offered by each store are listed below. Rank the stores from the cheapest to most expensive sale price of the camera.
Store A: price $99.99 and discount of 15%
Store B: price $95.99 and discount of 12%
Store C: price $90.99 and discount of 10%
Store D: price $89.99 and successive discounts of 5% and 5%
Answers
D<C<B<A; This is the correct ranking of the given stores in the order of cheapest to most expensive sale price of the camera as the definition of ascending order says, "Ascending order means to arrange numbers in increasing order, that is, from smallest to largest."
What is ascending order?The arrangement of numbers or other things in increasing order from smallest to largest is known as ascending order. Ascending order is demonstrated by numbers on a number line, which are listed from left to right. Usual representations include using commas or the "less-than symbol (<)" between numbers. For instance, 1, 2, 3, 4, or 5; or 1<2 <3 <4 <5.
Here,
Store A:
Price=$99.99
Discount=15%
Discount in dollar=$14.9985
Discounted price=$84.9915
Store B:
Price=$95.99
Discount=12%
Discount in dollar=$11.5188
Discounted price=$84.4712
Store C:
Price=$90.99
Discount=10%
Discount in dollar=$9.099
Discounted price=$81.891
Store D:
Price=$89.99
Discount=5% and after that 5%
net price after discount=$81.215
The price of store D is minimum that is $81.215.
According to the definition of ascending order, "Ascending order means to arrange numbers in increasing order, that is, from smallest to largest," this ranking of the given stores in order of cheapest to most expensive sale price of the camera is correct; D<C<B<A.
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Find the Midpoint of AB*round to the nearest tenth if necessaryA6,-3), B(2,9)
Answers
the radius of a circle is 15 what is the length of an arc that subtends an angle of Pi radians
Answers
The arc length of a circle is calculated by the formula
[tex]s=\theta\cdot r[/tex]replace the values of the angle and the radius into the formula
[tex]\begin{gathered} s=\pi\cdot15 \\ s=15\pi \end{gathered}[/tex]the arc length of the arc that subtends an angle of pi is 15pi.
Mr. Abraham, a married man, works a 40 hour work week, 48 wooks each yoor, His hourly rate of pay is $36.60 por hour. Aftor tax deductions for his two exemptions, his bl-wookly taxablo wagos were 12,410.77. How much is deducted from each paycheck for fodoral income tax? Noto: Porcontage mothod for calculation: For taxablo bi-wooklywages over 5066, but not over $2,698 - 366,40, plus 18% of excess over $068.$200,00$278.56$283.32$294.70None of these choices are correct.
Answers
We know that the biweekly tax is equal to $65.40 plus 15% of excess over $958. In this case the excess is:
[tex]2410.77-958=1452.77[/tex]Then for this excess the tax is:
[tex]0.15\cdot1452.77=217.92[/tex]Hence the total tax is:
[tex]217.92+65.40=283.32[/tex]Therefore the answer is the third option.
x+4/-2=-1how to solve this problem
Answers
Solve;
[tex]\begin{gathered} \frac{x+4}{-2}=-1 \\ \text{Cross multiply and you have;} \\ x+4=-2\times-1 \\ x+4=2 \\ \text{Subtract 4 from both sides of the equation} \\ x+4-4=2-4 \\ x=-2 \end{gathered}[/tex]Fallington Fair charges an entrance fee of $10 and $1.00 per ticket for the rides. Levittown Fair charges $5 entrance fee and $2 per ticket. Write an equation/inequality to show when Fallington Fair and Levittown Fair will cost the same.
Answers
Information given
Fallington Fair charges an entrance fee of $10 and $1.00 per ticket for the rides. Levittown Fair charges $5 entrance fee and $2 per ticket. Write an equation/inequality to show when Fallington Fair and Levittown Fair will cost the same.
Solution
Let's put some notation for this case, let x the number of rides and we can set up the following equation:
[tex]\text{Fallington}=\text{Levitown}[/tex][tex]10+x=5+2x[/tex]And now we can solve for x on the following way:
10-5= 2x-x
5=x
So then Fallington Fair and Levittown Fair will cost the same at 5 rides
In ∆OPQ, q =1.7cm, o=3.8 cm and < P=96°. Find < Q, to the nearest 10th of a degree.
Answers
To solve the exercise you can use the law of cosine, which applies to any triangle:
[tex]b^2=a^2+c^2-2ac\cdot\cos (B)[/tex]Where
So, in this case, you have
[tex]\begin{gathered} p^2=o^2+q^2-2oq\cdot\cos (P) \\ p^2=(3.8cm)^2+(1.7cm)^2-2(3.8cm)(1.7cm)\cdot\cos (96\text{\degree)} \\ p^2=14.44cm^2+2.89cm^2-12.92cm^2\cdot\cos (96\text{\degree)} \\ p^2=17.33\operatorname{cm}^2-(-1.35cm^2) \\ p^2=17.33\operatorname{cm}+1.35cm^2 \\ p^2=18.68\operatorname{cm}^2 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{p^2}=\sqrt[]{18.68\operatorname{cm}^2} \\ p=4.32\operatorname{cm} \end{gathered}[/tex]Now, you can use the law of sine, which applies to any triangle:
[tex]\frac{a}{\sin (A)}=\frac{b}{\sin (B)}=\frac{c}{\sin (C)}[/tex]In this case, you have
[tex]\begin{gathered} \frac{q}{\sin(Q)}=\frac{p}{\sin(P)} \\ \frac{1.7\operatorname{cm}}{\sin(Q)}=\frac{4.32\operatorname{cm}}{\sin(96\text{\degree})} \\ \text{ Apply cross product} \\ 1.7\operatorname{cm}\cdot\sin (96\text{\degree})=\sin (Q)\cdot4.32\operatorname{cm} \\ \text{ Divide by 4.32 cm from both sides of the equation} \\ \frac{1.7\operatorname{cm}\cdot\sin(96\text{\degree})}{4.32\operatorname{cm}}=\frac{\sin(Q)\cdot4.32\operatorname{cm}}{4.32\operatorname{cm}} \\ \frac{1.7\operatorname{cm}\cdot\sin(96\text{\degree})}{4.32\operatorname{cm}}=\sin (Q) \\ 0.39=\sin (Q) \\ \text{ Apply the inverse function }\sin ^{-1}(\theta)\text{ both sides of the equation} \\ \sin ^{-1}(0.39)=\sin ^{-1}(\sin (Q)) \\ 23.0\text{\degree}=Q \end{gathered}[/tex]Therefore, the measure of angle Q is 23 degrees.
6). A movie theater sold twenty-five tickets on Saturday and five tickets on Thursday. They soldhow many times as many tickets on Saturday as they sold on Thursday?
Answers
A movie theater sold 25 tickets on Saturday and 5 tickets on Thursday.
If we compare 25 and 5, we can see that,
[tex]25=5\cdot5[/tex]In other words, they sold 5 more times on Saturday than on Thursday
can someone help me find the valu of X &Y?
Answers
Given that the triangle ABC and DEF are similar, therefore its corresponding sides must be proportional,
[tex]\begin{gathered} \frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF} \\ \frac{4}{6}=\frac{10}{y}=\frac{x}{12} \end{gathered}[/tex]Comparing the first and third terms,
[tex]\begin{gathered} \frac{4}{6}=\frac{x}{12} \\ x=\frac{4}{6}\times12 \\ x=4\times2 \\ x=8 \end{gathered}[/tex]Comparing the first and second terms,
[tex]\begin{gathered} \frac{4}{6}=\frac{10}{y} \\ y=\frac{6}{4}\times10 \\ y=3\times5 \\ y=15 \end{gathered}[/tex]Thus, the values of 'x' and 'y' are 8 and 15, respectively.
1 1/3 divided by 40 using the algorithm
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the given expression is,
1 1/3 = 4/3
[tex]\frac{\frac{4}{3}}{40}=\frac{4}{120}[/tex]Find a linear inequality for the graph.y ≥ 3y > 3x ≤ 3x < 3
Answers
Given:
A graph is given
Required:
To tell whose inequality is this.
Explanation:
[tex]\begin{gathered} This\text{ graph shows the inequality of } \\ y\ge3 \end{gathered}[/tex]Required answer:
Option A is correct.
A person riding a ferris wheel takes 10 minutes to make one complete trip around thewheel. A function in the form y = A cos (Bt) + C can be used to model thissituation. Based on the information given, determine the values of B.
Answers
ANSWER
[tex]\frac{\pi}{300}[/tex]EXPLANATION
The function given is a cosine function:
[tex]A\cos (Bt)+C[/tex]From the function, B can be found as:
[tex]B=\frac{2\pi}{P}[/tex]where P represents the period of the function.
The period is given as 10 minutes (600 seconds), which means that we can find B:
[tex]\begin{gathered} B=\frac{2\pi}{600} \\ B=\frac{\pi}{300} \end{gathered}[/tex]That is the value of B.
List the sides of ABC from shortest to longest.CB AB ACАВ, СВ, АСАВ, АС, СВCB AC AB
Answers
First we need to calculated the missing angle
the intern angles of a triangle must be 180°
angle +63+60=180
angle=57
the shortest side is AB
the next side is AC
and the longest side is CB
t
Solve the equation 3=4-5^3sqrtx^8
Answers
The solution of the equation is x =3.33.
What is a solution?A solution is a value assignment to an unknown variable that makes the equality of the equation true. In other words, a solution is a value or set of values (one for each unknown) that becomes an equation when the equation is replaced by the unknown. In mathematics, solving an equation means finding its solution, which is a value (number, function, set, etc.) that satisfies the conditions specified by the equation, usually two equations separated by an equal sign. Connected. When looking for a solution, one or more variables are called unknowns. A solution is a value assignment to an unknown variable that makes the equality of the equation true.In other words, a solution is a value or set of values (one for each unknown) that becomes an equation when the equation is replaced by the unknown.Solutions of equations are often called roots of equations and are not specifically limited to polynomial equations. The set of all solutions of an equation is the solution set.3 = 4 - 5³ × √x⁸
3 = 4 - 125 × x⁴
124 = x⁴
x = 3.33
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The solution of the equation is x =3.33.
What is a solution?A solution is a value assigned to an unknown variable that makes the equality of the equation true.In other words, a solution is a value or set of values (one for each unknown) that becomes an equation when the equation is replaced by the unknown.In mathematics, solving an equation means finding its solution, which is a value (number, function, set, etc.) that satisfies the conditions specified by the equation, usually two equations separated by an equal sign.A solution is a value assigned to an unknown variable that makes the equality of the equation true.Solutions of equations are often called roots of equations and are not specifically limited to polynomial equations.The set of all solutions of an equation is the solution set:
3 = 4 - 5³ × √x⁸3 = 4 - 125 × x⁴124 = x⁴x = 3.33Therefore, the solution of the equation is x =3.33.
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write the slope intercept form:through: (-2, 3), perp. to x=0
Answers
write the slope intercept form:
through: (-2, 3), perp. to x=0
we know that
If the line is perpendicular to x=0 (y-axis), then we have a horizontal line
and the equation of a horizontal line (slope is equal to zero) is
y=3Find the value of 3127°B5xАC с3x + 6D127°c
Answers
From the diagram,
The angles, 127 degrees at arc AB and arc CD shows that the Chords AB and CD are equal
[tex]\begin{gathered} \text{chord AB = chord CD} \\ \text{that is} \\ 5x\text{ = 3x + 6} \\ \text{collect like terms} \\ 5x\text{ - 3x = 6} \\ 2x\text{ = 6} \\ \text{divide both sides by 2} \\ x\text{ = }\frac{6}{2} \\ x\text{ = 3} \end{gathered}[/tex]Therefore, the value of x = 3
9 divided by 2765 that’s what I’m am asking for
Answers
Answer: 307.22222222222 ......
Step-by-step explanation: use the bus stop method to help you
7+8=15 how do you decompose 10?I'm doing this for my granddaughter she's in the first grade and the teacher wants to know her dude examples 7 + 8 equals 15 and they want her to decompose it to make 10 then and use the number bond to show how you took two
Answers
To decompose 10 on basis of 8 it becomes 10 -2 =8
so 8 + 2 =10
Let f(x)=x^2 and g(x)=x-3. Find (f o g)(-5)
Answers
Solution
Given that
[tex]\begin{gathered} f(x)=x^2 \\ \\ g(x)=x-3 \\ \\ \Rightarrow(f\circ g)(-5)=f(g(-5)) \\ \\ g(-5)=-5-3=-8 \\ \\ \Rightarrow f(g(-5))=f(-8) \\ \\ f(-8)=(-8)^2=64 \\ \\ \Rightarrow(f\circ g)(-5)=64 \end{gathered}[/tex]Provide the correct reason for the statement in line 4.
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We have to prove x = -16/3.
The steps are:
[tex]1)3(x+5)=-1\longrightarrow\text{Reason: Given}[/tex][tex]2)3x+15=-1\longrightarrow\text{Reason: Distributive property}[/tex][tex]3)3x=-16\longrightarrow\text{ Reason: substracting 15 from both sides}[/tex][tex]4)x=-\frac{16}{3}\longrightarrow\text{ Reason: divide both sides of the equation by 3}[/tex]The bookstore is selling 4 books for $10 in a clearance sale. If Regina has $28 to spend, how many books can she purchase in the clearance sale?
Answers
The bookstore is selling 4 books for $10 in a clearance sale. If Regina has $28 to spend, how many books can she purchase in the clearance sale?
In this problem
Applying proportion
we have
4/10=x/28
solve for x
x=(4/10)*28
x=11.2
therefore
answer is 11 books