If a cone has a surface area of 822.78cm^2 and a diameter of 18cm, find the slant height of the cone
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]
Which of the following is the graph of y= x2 + 2x +1
Answer:
Step-by-step explanation:
you should show the graph
but
simplify it
A point has zero dimension and a line has one
A point has zero dimensions. There's no length, height, width, or volume. Its only property is its location.
One Dimension: Once you connect two points, you get a one-dimensional object — a line segment.
Find the surface area of the rectangular prism.
Answer:
130 ft^2
Step-by-step explanation:
SA= surface area
SA= 2*l*w + 2*l*h + 2*w*h
l= length = 10
w= width =5
h = height = 1
SA= 2*l*w + 2*l*h + 2*w*h
SA= 2*10*5 +2*10*1+2*5*1
SA= 100+20+10
SA= 130 ft^2
Write the equation of a circle givin by (x-3)^2+(y+7)^2=4
Answer:8
Step-by-step explanation:(
x
+
4
)
2
+
(
y
−
7
)
2
=
64
This is the form of a circle. Use this form to determine the center and radius of the circle.
(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
Match the values in this circle to those of the standard form. The variable
r
represents the radius of the circle,
h
represents the x-offset from the origin, and
k
represents the y-offset from origin.
r
=
8
h
=
−
4
k
=
7
The center of the circle is found at
(
h
,
k
)
.
Center:
(
−
4
,
7
)
These values represent the important values for graphing and analyzing a circle.
Center:
(
−
4
,
7
)
Radius:
8
Which equation represents a circle with a center at -3,-5 and a radius of 5
Answer: [tex](x+3)^2+(y+5)^2=25[/tex]
Step-by-step explanation:
The equation of the in center-radius form is the shown below:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where the center is at the point (h,k) and r is the radius of the circle.
Based on the information given in the problem, the center of the circle is at the point (-3,-5) and a radius of the circle is 5, then, you must substitute values into the equation shown above.
Therefore, you obtain the following equation:
[tex](x-(-3))^2+(y-(-5))^2=(5)^2[/tex]
[tex](x+3)^2+(y+5)^2=25[/tex]
DeSean throws a ball up with an initial vertical velocity of 30 ft/s from a platform that is at ground level. How long will the ball be in the air?
Answer:
Time, t = 1.875 seconds
Step-by-step explanation:
It is given that,
Initial velocity of the ball, u = 30 ft/s
DeSean throws a ball from a platform that is at ground level. The equation of motion when an object is thrown vertically upward is given by the following equation as :
[tex]h(t)=-16t^2+vt+h[/tex]
Here, h = 0 since, the ball is thrown up at the ground level. We have to determine the time when the ball be in air. The quadratic equation becomes :
[tex]-16t^2+30t+0=0[/tex]
t = 1.875 seconds
So, the ball be in air for 1.875 seconds. Hence, this is the required solution.
What is the same value as 5/8 2?
The answer is (D) 5/8 x 1/2
!!!!!!!50 POINTS!!!!!!
What jobs use parallel and perpendicular lines? (give examples)!!!
Answer:
Perpindicular ---
construction - the walls need to be build at a perfect shape
interior decorating - things need to be hung on the wall, properly aligned
carpentry - if you want to build a square you need to make a line perpendicular to the first piece of wood, to make a perfect right angle
Step-by-step explanation:
Architects and engineers use parallel and perpendicular lines in technical drawings to ensure accuracy and consistent dimensions, while artists may use these concepts in perspective artwork. Physics calculations involving moments of inertia also apply these principles in determining rotational properties of objects.
Many professions use the concepts of parallel and perpendicular lines. For instance, architects and engineers frequently use parallel and perpendicular lines in their drawings and designs. When architects design buildings with a rectangular plan, they rely on parallel projections, where they scale down a two-dimensional representation of the building while maintaining parallel lines. Engineering drawings, such as those for machine parts, also employ parallel and perpendicular lines to convey the dimensions and orientation of objects accurately.
Artists working in perspective, on the other hand, often employ the concept that parallel lines appear to converge at a vanishing point in the distance, as seen in linear perspective artwork. However, for technical drawings where accuracy and measurement are key, the parallel projection method is crucial as it allows for dimensions to remain consistent.
In physics, moments of inertia calculations for objects like discs and rods often utilize parallel and perpendicular axes theorems to determine rotational properties. And in geometry, constructions frequently involve drawing parallel or perpendicular lines from given points, which is fundamental in defining figures and solving problems.
how much larger is 8,000,000 than 200 ?
Answer:
7,999,800
Step-by-step explanation:
8,000,000 minus 200 = answer
Help anyone please and I need to show the work!
2 and 2, 15tenths is the corret anwser
What is the sum of -3 2/8 + 1/4
Consider the following geometric sequence -5, 10, -20, 40,..... if the recursive formula for the sequence above expressed in the form a(n)=b*c^n-1, determine the value of b and c.
what asks no questions but must be answered
The riddle 'what asks no questions but must be answered' typically refers to a telephone or a doorbell, both of which signal when someone is attempting to communicate or get attention.
Explanation:The student's question, "what asks no questions but must be answered," is a type of riddle, which is a question or statement intentionally phrased to require ingenuity in ascertaining its answer. In this context, the answer to the riddle is typically the telephone or a doorbell, as both signal when someone is trying to get in contact or gain attention, and generally, one responds to them. Riddles can form part of the teaching in English, particularly when focusing on language play, word definitions, and understanding semantics. They can encourage students to pay attention to wording and to contemplate why certain expressions carry the meanings they do.
Which expressions are equivalent to 8(-10x+3.5y-7) check all that apply
Answer:
-80x + 28y - 424(-20x + 7y - 14)Step-by-step explanation:
Use the distributive property a(b + c) = ab + ac:
8( -10x + 3.5y - 7)
= (8)(-10x) + (8)(3.5y) + (8)(-7)
= -80x + 28y - 42
8(-10x + 3.5y - 7)
= (4)(2)(-10x + 3.5y - 7)
= 4[(2)(-10x) + (2)(3.5y) + (2)(-7)]
= 4(-20x + 7y - 14)
The expression 8(-10x+3.5y-7) equivalent to -80x + 28y - 56.
How to solve an expression?Let the expression be
8(-10x + 3.5y - 7)
Simplifying the above equation as
[tex]$\ 8\left(-10 x+\frac{35}{10} y-7\right)$[/tex]
Multiplying the equation, then we get
[tex]$-80 x+8 \times \frac{35}{10} y-8 \times 7$[/tex]
[tex]$-80 x+4 \times \frac{35}{5} y-56$[/tex]
[tex]$-80 x+4 \times 7 y-56$[/tex]
- 80x + 28y - 56
Therefore, the correct answer is option (b) - 80x + 28y - 56.
To learn more about the expression
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What is the measure of PQR
A.51
B.55
C.74
D.78
Please I really need help
the answer is B maybe
180- 51- 74
=55
Answer:
b
Step-by-step explanation:
what graph shows the solution to the inequality p ≥ -1
The solution to the inequality [tex]\( p \geq -1 \)[/tex] represents all the values of p that are greater than or equal to -1.
To represent this on a graph, you would draw a number line with an open circle at -1 (since it's "greater than or equal to", not just "greater than"), and then shade to the right to indicate all values greater than -1.
The open circle at -1 indicates that -1 is not included in the solution, and the shaded area to the right indicates all values greater than -1.
Please help me!
Write y = x2 + 2x + 5 in vertex form.
y = (x – 1)2 + 5
y = (x + 1)2 + 5
y = (x + 1)2 + 4
y = (x – 1)2 + 4
Answer:
the answer is
y=(x+1)2+4
the sum of three numbers is 125. the second number is 5 less than the first. the third number is 4 times the second. what are the numbers
Answer:
The numbers are 25, 20 and 80
Step-by-step explanation:
125=a+b+c
b=a-5
c=4b
c=4(a-5)
c=4a-20
125=a+a-5+4a-20
125=6a-25
150=6a
25=a
b=a-5
b=25-5
b=20
c=4b
c=4(20)
c=80
✓:
80+20+25=125✓
The function y = -2(x-3)^2+4 shows the daily profit (in hundreds of dollars) of a hot dog stand, where x ist the price of a hot dog (in dollars). Find and interpret the zeros of this function
Answer:
The answer in the procedure
Step-by-step explanation:
we know that
The zeros of the function are the values of x when the value of y is equal to zero
In this problem
The zeros of the function are the price of a hot dog (in dollars) when the daily profit (in hundreds of dollars) of a hot dog stand are zero
we have
[tex]y=-2(x-3)^{2}+4[/tex]
using a graphing tool
The zeros of the function are
x=$1.59, x=$4.41
so
for these prices the daily profit are zero
see the attached figure
Which numbers are irrational?
Select each correct answer.
A. 6.25−−−−√
B. 3√
C. −1√
D. 32−−√
The first one I believe
Answer: A
Step-by-step explanation: rational numbers \can be turned into a fraction so yea.
Helpppp!BASIC MATHhhh
How much we need for start-up supplies . . . . . $25
AFTER start-up supplies we want to have . . . $70
Total amount we need to get started . . . (25 + 70) = $95
Number of people contributing . . . (me + 4) = 5
Amount each person needs to kick in . . . (95/5) = $19
As your preliminary Accountant, please reserve me one dozen (13) bagels from the first batch you produce !
A bakery has 63 donuts and 36 muffins for sale. What is the ratio of muffins to donuts?
A.
4 to 1
B.
7 to 4
C.
1 to 4
D.
4 to 7
Answer:
D.) is the answer
Step-by-step explanation:
I know this because the ratio of muffins to donuts is 36:63 but simplified is 4:7
The ratio of muffins to donuts is 4:7 if the bakery has 63 donuts and 36 muffins for sale, option (D) 4 to 7 is correct.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We have:
Number of donuts = 63
Number of muffins = 36
The ratio of muffins to donuts:
36:63
4:7
Ratio is 4 to 7
Thus, the ratio of muffins to donuts is 4:7 if the bakery has 63 donuts and 36 muffins for sale option (D) 4 to 7 is correct.
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When you don’t know the answer on a multiple choice questions, it is generally best to:
APEX
When you don’t know the answer on a multiple choice questions, it is generally best to use the process of elimination, make an educated guess, or use prior knowledge to increase your chances of getting the right answer.
Explanation:When you don’t know the answer on a multiple choice questions, it is generally best to:When you encounter a multiple choice question and you don't know the answer, there are a few strategies you can use to increase your chances of getting it right:
Process of elimination: Go through each answer choice and eliminate the ones that you know are incorrect. This reduces the options and increases your chances of guessing correctly.Guess strategically: If you can eliminate a few answer choices, make an educated guess based on the remaining options. For example, if you know that two answer choices are incorrect, your guess will have a 50% chance of being correct.Use prior knowledge: Sometimes, even if you don't know the answer, you can make an educated guess based on what you already know about the subject. Use any clues or information from the question stem to help guide your guess.Remember, when guessing on multiple choice questions, it's important to consider the context of the question and eliminate obvious incorrect choices before making your guess.
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x/2 + 3/2 < 5/2 give solution
Start with
[tex]\dfrac{x}{2}+\dfrac{3}{2}<\dfrac{5}{2}[/tex]
Multiply the whole equation by 2. Since 2 is positive, we don't need to switch the inequality sign:
[tex]x+3<5[/tex]
Subtract 3 from both sides:
[tex]x<2[/tex]
the pair of variables x=–3, y=8 is the solution to the equation 5x+by=17. Find the coefficient b.
Answer:
Step-by-step explanation:
I think I have helped you before with this problem, substitute x and y with -3 and 8 respectively, so 5*(-3)+8b=17, -15+8b=17, 8b=32, divide both sides by 8 and you get b=4
Erin earned $25 last week for 5 hours of baby-sitting. This week she earned $40 for 8 hours of baby-sitting. What was her hourly rate in whole dollars?
Answer:
5 dollars
Step-by-step explanation:
25/5 = 5 (25 dollars for 5 hours. Divide 25 and 5 to get how many dollars she earned for one hour)40/8 = 5 (Each hour she earned $5 since 40/8=5 and 25/5=5~Jax
Complete the series. 9 = 4, 21 = 9, 22 = 9, 24 = 10, 8 = 5, 7 = 5, 99 = 10, 100 = 7, 16 = ?, 17 =?
just simply count the number of letters in each number, that is to say:
NINE= 4 letters
TWENTY-ONE= 9 letters
so 16=7 since
SIXTEEN is 7 letters
and 17=9 since
SEVENTEEN is 9 letters
Which of these is an example of an employer using benefits to encourage employees to stay with their company
Answer:
maybe convince them for a higher pay rate
Step-by-step explanation:
The number of painters, p, employed to paint a building is inversely proportional to the time taken to paint the building, b. Which equation best models the number of painters required to finish the painting?
Answer:
Option B. [tex]p=k/b[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]
Let
p-----> the number of painters
b----> the time taken to paint the building
we know that
[tex]p*b=k[/tex]
so
[tex]p=k/b[/tex]
Answer:
B. [tex]p=\frac{k}{b}[/tex]
Step-by-step explanation:
Given,
The number of painters, p, employed to paint a building is inversely proportional to the time taken to paint the building, b
[tex]\implies p\propto \frac{1}{b}[/tex]
[tex]\implies p=\frac{k}{b}[/tex]
Where, k is the constant of proportionality,
Hence, the required equation that models the relation between p and b is,
[tex]p=\frac{k}{b}[/tex]
Option 'B' is correct.