Answer:
[tex]20.11\ cm[/tex]
Step-by-step explanation:
we know that
The surface area of the cone is equal to
[tex]SA=\pi r^{2}+\pi rl[/tex]
where
r is the radius
l is the slant height
In this problem we have
[tex]SA=822.78\ cm^{2}[/tex]
[tex]r=18/2=9\ cm[/tex] -----> the radius is half the diameter
substitute and solve for l
[tex]822.78=\pi (9)^{2}+\pi (9)l[/tex]
[tex]822.78=81\pi +9\pi l[/tex]
[tex]l=(822.78-81\pi)/9\pi[/tex]
[tex]l=(822.78-81(3.14))/9(3.14)=20.11\ cm[/tex]
The slant height of the cone is approximately 20.1154 cm.
[tex]\[ \text{Surface Area} = \pi r (l + r) \][/tex]
where r is the radius of the base of the cone, and l is the slant height of the cone.
Given that the diameter of the cone is 18 cm, we can find the radius r by dividing the diameter by 2:
[tex]\[ r = \frac{diameter}{2} = \frac{18 \text{ cm}}{2} = 9 \text{ cm} \][/tex]
Now we can substitute the values we know into the surface area formula:
[tex]\[ 822.78 \text{ cm}^2 = \pi \times 9 \text{ cm} \times (l + 9 \text{ cm}) \][/tex]
To find l, we need to solve for l in the equation:
[tex]\[ 822.78 \text{ cm}^2 = 9 \pi \text{ cm} \times (l + 9 \text{ cm}) \] \[ \frac{822.78 \text{ cm}^2}{9 \pi \text{ cm}} = l + 9 \text{ cm} \] \[ \frac{822.78}{9 \pi} = l + 9 \] \[ l = \frac{822.78}{9 \pi} - 9 \][/tex]
Now we calculate the value of l:
[tex]\[ l = \frac{822.78}{9 \times \pi} - 9 \] \[ l = \frac{822.78}{28.27433388} - 9 \] \[ l \approx 29.1154 - 9 \] \[ l \approx 20.1154 \text{ cm} \][/tex]
How many flowers, spaced every 3 in., are needed to surround a circular garden with a 150-ft radius? Use 3.14 for pi.
Final answer:
To surround a circular garden with a 150-ft radius every 3 inches with flowers, calculate the garden's circumference using the formula C = 2πr, convert it to inches and divide by the spacing. You'd need approximately 3,768 flowers.
Explanation:
To calculate the number of flowers needed to surround a circular garden with a 150-ft radius spaced every 3 inches, you have to find the circumference of the garden and then determine how many 3-inch spaces fit along that circumference.
First, find the circumference (C) of the garden using the formula C = 2πr, where π (pi) is approximately 3.14 and r is the radius. In this case:
C = 2 × 3.14 × 150 ftC = 2 × 3.14 × 150 ft = 942 ftConvert 942 ft into inches because the spacing is in inches:
C = 942 ft × 12 in/ft = 11,304 inNow, divide the circumference in inches by the spacing to get the number of flowers:
Number of flowers = 11,304 in / 3 in per flowerNumber of flowers = 3,768Therefore, you would need 3,768 flowers to surround the garden spaced every 3 inches.
Find the total area of the rectangular prism whose base is 3 feet by 2 feet, and is 5 feet high
Answer:
The total area of the prism is 30 cubic feet
Step-by-step explanation:
To find the area multiply 3 by 2 by 5
The town swimming pool is d feet deep. The width of the pool is 5 feet greater than 5 times its depth. The length of the pool is 50 feet greater than 5 times its depth. Enter a simplified expression to represent the volume of the pool.
Answer:
[tex]V = 25d ^ 3 + 275d ^ 2 + 250d[/tex]
Step-by-step explanation:
If the pool has a rectangular shape then its volume can be written as:
V = Width * Length * Depth
Let's call:
w = width
l = length
d = depth.
So we know from the statement of the problem that:
[tex]d = d[/tex]
[tex]w = 5 + 5d[/tex] (5 feet more than 5 times the depth)
[tex]l = 50 + 5d[/tex] (50 feet more than 5 times the depth)
Then, the volume can be written according to the depth as:
[tex]V = d(5 + 5d)(50 + 5d)[/tex]
[tex]V = d[250 + 25d + 250d + 25d ^ 2][/tex]
[tex]V = 25d ^ 3 + 275d ^ 2 + 250d[/tex]
The volume of the swimming pool is represented by the expression V = (5d + 50)(5d + 5)(d), where d is the depth of the pool.
The student is asked to find a simplified expression to represent the volume of the swimming pool, with the pool's depth given as d feet. To calculate the volume, we need to find the dimensions for the width and length of the pool. The width is described as 5 feet greater than 5 times its depth, which translates to
5d + 5 feet.
The length is 50 feet greater than 5 times its depth, so it will be
5d + 50 feet. The volume (V) of a rectangular solid is given by the product of its length (L), width (W), and depth (D), so the volume of this swimming pool is
V = LWD = (5d + 50)(5d + 5)(d).
what is an equation of the line that is perpendicular to y-3 =-4(x+2)
Answer:
[tex]y - 3 = \frac{1}{4}(x+2)[/tex] or choose any line with slope 1/4
Step-by-step explanation:
The slope of this line is -4. The slope of the line perpendicular to this line will be the negative reciprocal or 1/4.
Write the equation using the slope m=1/4 and the point slope form.
[tex]y-y_1=m(x-x_1)\\y-3=\frac{1}{4}(x+2)[/tex]
This is the equation of the line that is perpendicular and passes through the same point (-2,3) as the equation listed.
Answer:
[tex]y=\frac{1}{4} x+c[/tex] where [tex]c[/tex] can be any number.
Step-by-step explanation:
First we need to clear for y:
[tex]y-3 =-4(x+2)\\y=-4(x+2)+3\\y=-4x-8+3\\y=-4x-5[/tex]
and now we have an equation of the form:
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept.
in this case [tex]m=-4[/tex] and [tex]b=-5[/tex]
to find and equation perpendicular to this line, the following must be true:[tex]m*m_{1}=-1[/tex]
where m is the slope of the original line that i just mentioned, and [tex]m_{1}[/tex] is the slope of the new line. Substituting [tex]m=-4[/tex]
[tex]-4*m_{1}=-1[/tex]
clearing for [tex]m_{1}[/tex]
[tex]m_{1}=\frac{-1}{-4} \\m_{1}=\frac{1}{4}[/tex]
thus, the new perpendicular line must have the form:
[tex]y=m_{1}x+c\\y=\frac{1}{4}x+c[/tex]
where the y-intecept [tex]c[/tex] can be any number, some examples are:
[tex]y=\frac{1}{4}x+3\\y=\frac{1}{4}x-8[/tex]
and so on, the important thing to be a perpendicular line is that the slopes are related to the equation [tex]m*m_{1}=-1[/tex].
If p=-1, which of the following has the greatest value?
A) 4p^2
B) 6p^2
C) 8p^2
D) 10p^2
Answer:
D)
Step-by-step explanation:
Plz help me with it !
Answer: [tex]\bold{-7+2\sqrt{14}+5\sqrt{7}-10\sqrt{2}}[/tex]
Step-by-step explanation:
[tex]\dfrac{\sqrt7-5}{\sqrt7+\sqrt8}\bigg(\dfrac{\sqrt7-\sqrt8}{\sqrt7-\sqrt8}\bigg)=\dfrac{7-2\sqrt{14}-5\sqrt{7}+10\sqrt2}{7-8}=\dfrac{7-2\sqrt{14}-5\sqrt{7}+10\sqrt2}{-1}\\\\\\=\boxed{-7+2\sqrt{14}+5\sqrt{7}-10\sqrt2}[/tex]
Evaluate cos^2 (n/12)
Answer:
[tex]\frac{2+\sqrt{3} }{4}[/tex]
Step-by-step explanation:
We can use the identity [tex]Cos^2(x)=\frac{1}{2}+\frac{1}{2}Cos(2x)[/tex] to write it as:
[tex]Cos^2(\frac{\pi}{12})=\frac{1}{2}+\frac{1}{2}Cos(2(\frac{\pi}{12}))\\=\frac{1}{2}+\frac{1}{2}Cos(\frac{\pi}{6})\\=\frac{1}{2}+\frac{1}{2}(\frac{\sqrt{3} }{2})\\=\frac{1}{2}+\frac{\sqrt{3} }{4}\\=\frac{2+\sqrt{3} }{4}[/tex]
Note: The value of [tex]Cos(\frac{\pi}{6})[/tex] is [tex]\frac{\sqrt{3} }{2}[/tex]
The answer is the 2nd one, [tex]\frac{2+\sqrt{3} }{4}[/tex]
Plz help me i need it
Answer: [tex]a)\quad f^{-1}(x)=\sqrt[3]{\dfrac{x+5}{3}}[/tex]
Step-by-step explanation:
Inverse is when you swap the x's and y's and solve for y. Note: f(x) is y
[tex]y=3x^3-5\\\\\text{Swap the x's and y's:}\\x=3y^3-5\\\\\text{Add 5 to both sides:}\\x+5=3y^3\\\\\text{Divide both sides by 3:}\\\dfrac{x+5}{3}=y^3\\\\\\\text{Take cubed root of both sides:}\\\sqrt[3]{\dfrac{x+5}{3}}=y[/tex]
What is the mean of the mean of the data set below?
12, 15, 10 ,11
Answer:
12
Step-by-step explanation:
12+15+10+11=48
48/4=12
Sum of all the data which is 12+15+10+11=48 then divide by how many data point which is 4
48/4 =12
A die is rolled 3 times. What is the probability of getting 1’s on each roll?
Answer: The answer is around 16.66%
Answer:
Step-by-step explanation
The first step you have to get it into this form
a[tex]x^{2}[/tex] + bx + c
So that would be
3x[tex]x^{2}[/tex] + 1x + c
we do not know what c is
we have to get x by it self from 3x[tex]x^{2}[/tex] so first you have to square it now we are at 9x
9x divided by 9 that would leave us with x
so our finished product is x + 1x + c
we have to get x by itself from 1x so we do exactly what we just did 1x divided by 1x would leave us with x
x + x=[tex]x^{2}[/tex] + x
[tex]x^{2}[/tex] + c is the finished product which is your answer
Use the slope formula to find the missing coordinate. m = -7/2 , T(13, 2), W(_, -5)
A. -11
B. 11
C. 15
Answer:
Option C. [tex]15[/tex]
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]T(13,2)\ W(x2,-5)[/tex]
[tex]m=-\frac{7}{2}[/tex]
Substitute the values and solve for x2
[tex]-\frac{7}{2}=\frac{-5-2}{x2-13}[/tex]
[tex]-\frac{7}{2}=\frac{-7}{x2-13}[/tex]
equate the denominators
[tex]x2-13=2\\x2=2+13\\ x2=15[/tex]
Answer:
The answer is C-15
what is exactly 1/12 of a full rotation
in degrees the answer is 30° since a full rotation is 360°, divide by 12 and 1/12 of a full rotation is 30°
1/12 of a full rotation in mathematics refers to an angle of 30 degrees. This is calculated by dividing the full rotation (360 degrees) by 12. For example, each hour on a clock represents 1/12 of a full rotation.
Explanation:In Mathematics, a full rotation is defined as 360 degrees. Therefore, to find 1/12 of a full rotation, you would divide 360 by 12. This results in 30 degrees. Hence, 1/12 of a full rotation refers to an angle of 30 degrees in a circular motion. This concept is often applied in geometry and other mathematical applications. For instance, imagining a clock, where each hour signifies 1/12 of a full rotation. The difference in the angle from 12 to 1 on the clock is therefore 30 degrees.
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A plate lunch costs $1.35. Bought separately, the items cost: sandwich, $0.95; milk, $0.35; and fruit, $0.20. Which is the less expensive way to buy the items?
Plz explain
Add 0.95 0.35 and 0.20 and if it’s less than 1.35 it’s ur answer but if 1.35 is less, than that’s ur answer
Answer:
Step-by-step explanation:
Cost of items =$0.95+$0.35+$0.20=$1.50
Plate cost=$1.35
Plate is less expensive way to buy items
What is x+8y=-15 7x+8y=-19
Answer:
x = − 15 − 8 y
y=-7/8x-19/8
Step-by-step explanation:
If you are trying to solve for x the answer for first problems is
x = − 15 − 8 y
second problem the slope intercept form is:
y=-7/8x-19/8
I'm not sure exactly what you are looking for but I hope that is it.
Convert 6 pounds, 4 oz. to ounces.
64 oz.
76 oz.
95 oz.
100 oz.
Answer:
The answer is 100 oz
Step-by-step explanation:
HOPE THIS HELPS YOU
Help me solve plz. Use substitution to check. y - 4 = 36
Answer:
y = 40
Step-by-step explanation:
Isolate the variable (y). Note the equal sign, what you do to one side, you do to the other. Add 4 to both sides.
y - 4 = 36
y - 4 (+4) = 36 (+4)
y = 36 + 4
y = 40
Check. Substitute 40 for y.
Plug in 40 for y.
y - 4 = 36
(40) - 4 = 36
36 = 36 (True).
~
-5/2 x 5/7
help me i bad at math
Answer:
Step-by-step explanation:
assuming that the X is a multiplication symbol and not a variable, because the multiplication symbol is * not x, 5*5/2*7=25/14=1 and 11/14
Use substitution to solve the system of equations
y=x+1.75
substitute for y in equation 2.
4x-2(x+1.75)=4
4x-2x-3.5=4
2x=7.5
x=3.75
y=3.75+1.75
y=5.5
The solution of the system as an ordered pair is (3.75, 5.5).
The correct option is first box.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
System of equations,
y = x + 1.75 {equation 1}
4x - 2y = 4 {equation 2}.
Substituting the value of y top the equation 2,
4x - 2(x + 1.75) = 4
4x - 2x - 3.5 = 4
2x = 7.5
x = 3.75
And y = 5.5
Therefore, the solution is x = 3.75 and y = 5.5.
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picking a blue shirt from a drawer with 8 blue shirts and 2 white shirts
Answer:
you have 10 shirts in all to choose from
Step-by-step explanation:
if ur picking a shirt then you will have 10 all together.
♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫
➷The answer is 8/10, 4/5, or 80%.
Since there are 8 blue shirts out of 10 shirts, you have a 8/10 chance to pick a blue shirt. Since this is probability, it is best to show it in percent and decimal form too.
8/10=80%=0.8 chance
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
DOGE
How many 2/3 's make up 4 1/5
Answer:
6³/₁₀
Step-by-step explanation:
Number of bits = Total amount/Size of each bit
= (4⅕)/(⅔)
Convert the mixed number to an improper fraction
No. = (²¹/₅)/(⅔)
Invert the denominator and change division to multiplication
No. = ²¹/₅ × ³/₂
Multiply numerators and denominators.
No. = ⁶³/₁₀
Convert the improper fraction to a mixed number.
No. = 6³/₁₀
It takes 6³/₁₀ ⅔s to make up 4⅕.
Bob is thinking about leasing a car the lease comes with an interest rate of 8% determine the money factor that will be used to calculate bonus payment
Answer:
0.00333
Hope that helps.
PLEASE GIVE ME A VALID ANSWER IM GIVING ALOT OF POINTS!
Wanatobe walked to the moot at 4 mph and then rode back home in bus at 24 mph. If her total traveling time was 14 hours, how far was it to the moot?
Answer:
Step-by-step explanation: It is 1/2 of 14 = 7 hours to the moot
And plug in 7 hours to the equation 4*7+14*7=126 divide that by 2 and the distance is 63
A construction company plans to invest in a building project. There is a 30% chance that the company will lose $30,000, a 40% chance of a break even, and a 30% chance of a $60,000 profit. Based ONLY on this information, what should the company do?
30% chance of losing money.
40% chance of breaking even
Added together = 70% of not making any money or losing money.
Only a 30% chance of making money.
The company should not invest, since they only have a 30% chance of making money.
What is the surface area of this cylinder to the nearest integer?
57 in2
75 in2
132 in2
250 in2
Answer:
131.95in^2
Step-by-step explanation:
The formula for surface area in a cylinder is A = 2pi*r*h + 2pi*r^2
The radius in this cylinder is half the diameter in the cylinder which is 6, so the radius is 3.
The height is 4 since it is given.
Then we just plug the values into the equation and we get a surface area around 131.95in^2
Answer:
The answer is C. 132 [tex]in^{2}[/tex]
Step-by-step explanation:
Remember: If the answer is not there, check your work or round up! :)
Patrick 8
Jeffery 12
Robin 7
Sally 15
Manuel 4
Ming 10
Jesse 12
Mark 17
Jenna 16
The owner of a car dealership keeps track of the monthly car sales for the salespeople at the dealership. What is the range for the number of cars sold?
My Answer:
The range is from 4 to 17.
When you are identifying a range you need to identify the highest and lowest number. This is your range because all of the other numbers are between the identified two.
Answer:
Step-by-step explanation:
4 to 17.. that is the answer to ur question love.
what decimal is equivalent to -7 / 8
That decimal would be -.875
Hey there!
In order to find the decimal divide the numerator (top number) from the denominator (bottom number)
~ -7 ÷ 8 = 0.875 (as a decimal)
~ Thus your answer will most likely be, -0.875
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
The point slope form of the eqaution of the line that passes through (-5,-1) and (10, -7) is y+7= -2/5 (x - 10) what is the standard form of the equation for this line 2x-5y=-15 2x-5y= -17 2x+5y=-15 2x+5y=-17
Answer:
2x + 5y = -15Step-by-step explanation:
The standard form of an equation of a line:
[tex]Ax+By=C[/tex]
We have the equation in point-slope form:
[tex]y+7=-\dfrac{2}{5}(x-10)[/tex]
Convert it to the standard form:
[tex]y+7=-\dfrac{2}{5}(x-10)[/tex] multiply both sides by 5
[tex]5y+35=-2(x-10)[/tex] use the distributive property a(b + c) = ab + ac
[tex]5y+35=(-2)(x)+(-2)(-10)[/tex]
[tex]5y+35=-2x+20[/tex] subtract 35 from both sides
[tex]5y=-2x-15[/tex] add 2x to both sides
[tex]2x+5y=-15[/tex]
The equation for the circle below is x^2+y^2=64 what is the length of the circle’s radius
Answer:
r = 8Step-by-step explanation:
The standard form of an equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the equation:
[tex]x^2+y^2=64\\\\(x-0)^2+(y-0)^2=8^2[/tex]
Therefore the center is (0, 0) and the radius r = 8
Answer:
The circles radius is 8
Step-by-step explanation:
It is 8 because that's what they say it is
18........................
Answer:
D
Step-by-step explanation:
We will use the radical property [tex]\sqrt{a*b} =\sqrt{a} \sqrt{b}[/tex] to simplify this.
The problem is [tex]\sqrt{169*x^5}[/tex]
We can simplify this as:
[tex]\sqrt{169*x^5} \\=\sqrt{169} \sqrt{x^5}[/tex]
Now we can use the property of radicals, [tex]\sqrt[n]{x^a} =x^{\frac{a}{n}}[/tex] , to write as:
[tex]\sqrt{169} \sqrt{x^5} \\13*x^{\frac{5}{2}}[/tex]
D is right answer.
Answer:
d. [tex]13x^{\frac{5}{2}}[/tex]
Step-by-step explanation:
The given expression is
[tex]\sqrt{169x^5}[/tex]
We can rewrite this as
[tex]\sqrt{169}\times \sqrt{x^5}[/tex]
We rewrite as a rational exponent to obtain;
[tex](13^2)^{\frac{1}{2}}\times (x^5)^{\frac{1}{2}}[/tex]
Recall that;
[tex](a^m)^n=a^{mn}[/tex]
[tex]13^{(2\times \frac{1}{2})}\times (x)^{5\times \frac{1}{2}}[/tex]
[tex]13^1 (x)^{\frac{5}{2}}[/tex]
The correct choice is D
[tex]13x^{\frac{5}{2}}[/tex]
according to the rational root theorem, what are all the potential rational roots of f(x)=5x^3-7x+11
Answer:
[tex]\pm11,\pm1,\pm\frac{11}{5},\pm\frac{1}{5}[/tex]
Step-by-step explanation:
The given polynomial function is
[tex]f(x)=5x^3-7x+11[/tex]
According to the Rational Roots Theorem, the ratio of all factors of the constant term expressed over the factors of the leading coefficient.
The potential rational roots are
[tex]\pm\frac{11}{1}=\pm11[/tex]
[tex]\pm\frac{1}{1}=\pm1[/tex]
[tex]\pm\frac{11}{5}[/tex]
[tex]\pm\frac{1}{5}[/tex]