In the figure below, a cone is cut by a plane that passes through its vertex and is perpendicular to its base.
The height of the cone is 10 inches, and its diameter is 6 inches.
What is the area of the cross section formed by the intersection?
Answers
When a cone is cut by a plane that passes through its vertex and perpendicular to its base the figure formed is an isosceles triangle.It is given the height of the cone is 10 inches, and its diameter is 6 inches.
The height of the cone will be the height of the triangle .The diameter of the cone will be the base of the triangle.Base and height of the triangle known we can find the area of cross section or the area of the triangle by the formula
Area = [tex] \frac{1}{2} Base .Height. [/tex]
Area = [tex] \frac{1}{2} (10)(6)=30 in^{2} [/tex]
Related Questions
I need help with this. I’m feeling very uncomfortable with the answers. So, can someone please explain to me the correct steps if one of them are wrong?
Answers
20. The total sale is
.. total = (book price) + (tax rate)*(book price) . . . . math for adding tax
.. total = (book price)*(1 +(tax rate)) . . . . . . . . . . . . . factor out book price
.. total/(book price) = 1 +(tax rate) . . . . . . . . . . . . . . divide by book price
.. (total/(book price)) -1 = tax rate . . . . . . . . . . . . . . subtract 1
25.02/24 -1 = tax rate = 1.0425 -1 = .0425 = 4.25%
A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6. Find the total area of the pyramid.
Answers
Surface Area of Pyramid:=72
HexagonalArea of Base: [(6/2) as]Surface Area of Pyramid: [3as + 3sl]Volume of Pyramid: [abh ]Where,As = area of side lengthsl= slant heightabh area of base * height
Answer:
Area of hexagonal pyramid = 113.57 unit²
Step-by-step explanation:
Area of hexagonal pyramid = Area of base + Area of six triangular slanting face.
Area of base = 6 x Area of equilateral triangle with side 4.
[tex]\texttt{Area of base = }6\times \frac{\sqrt{3}}{4}a^2=6\times \frac{\sqrt{3}}{4}\times 4^2=24\sqrt{3}unit^2[/tex]
[tex]\texttt{Area of six triangular slanting face = }6\times \frac{1}{2}\times ah=3\times 4\times 6=72unit^2[/tex]
Area of hexagonal pyramid = Area of base + Area of six triangular slanting face.
Area of hexagonal pyramid = 24√3 + 72 = 113.57 unit²
Dustin, a truck driver, has a delivery to make that is 866 miles away. If Dustin drives at a steady rate of 70 miles per hour for 540 minutes, how many more miles does he have to go?
Answers
Dustin has 236 miles to go.
Zachary is solving the following equation
3/4(x - 8)= 12
Which is the best first step to begin to simplify the equation?
A.Multiply both sides of the equation by 3/4
B.Divide both sides of the equation by 4/3
C.Distribute 3/4 over (x - 8)
D.Distribute 4/3 over (x - 8)
Answers
The first step in a math problem with distribution involved is to take care of the parentheses (PEMDAS). This means you have to distribute 3/4 to the (x - 8).
I hope this helped!
Answer:
C. Distribute 3/4 over (x - 8)
Step-by-step explanation:
There are multiple ways to begin solving this problem.
If we want to cancel the 3/4 without using the distributive property, we would divide both sides by 3/4. Dividing by 4/3 will not cancel it.
When dividing by fractions, we multiply by the reciprocal; this would be multiplying both sides by 4/3. Multiplying by 3/4 will not cancel it.
Using the distributive property, we multiply (x-8) by the number in front of parentheses, 3/4. We cannot distribute 4/3, since it is not part of the equation.
2.3, 3.2, 4.1, 5.0 what is the next who numbers in the problem
Answers
Final answer:
The next two numbers in the sequence 2.3, 3.2, 4.1, 5.0 following the observed pattern are 6.0 and 7.0.
Explanation:
The sequence given is 2.3, 3.2, 4.1, 5.0. To find the next numbers in the sequence, let's observe the pattern. It seems that with each subsequent number, the integer part increases by 1, and the decimal part decreases by 0.1, until it reaches 0. Following this pattern, the next number after 5.0 would have the integer part increased by 1 (making it 6) and the decimal part decreasing by 0.1 (which would be zero anyway since we are at 5.0).
So, the next number in the sequence would be 6.0. Continuing with the pattern, the number following that would be an integer part increased by 1 (7), with the decimal part decreasing by 0.1, which would simply remain 0, giving us 7.0 as the next number in the sequence.
Therefore, the next two numbers in the sequence are 6.0 and 7.0.
write the function:
[tex]f(x) = - 5 {x}^{2} - 60x - 181[/tex]
in vertex form, and identity its vertex
Answers
The first thing we need to do is find the vertex (h,k) and to do that we are going to use the vertex formula: [tex]h= \frac{-b}{2a} [/tex], and then we are going to evaluate our function at [tex]h[/tex] to find [tex]k[/tex].
We know for our problem that [tex]a=-5[/tex], and [tex]b=-60[/tex], so lets replace those values in our vertex formula to find [tex]h[/tex]:
[tex]h= \frac{-b}{2a} [/tex]
[tex]h= \frac{-(-60)}{2(-5)} [/tex]
[tex]h= \frac{60}{-10} [/tex]
[tex]h=-6[/tex]
Now, we are going to evaluate our function at -6 to find [tex]k[/tex]:
[tex]k=f(-6)=-5(-6)^{2} -60(-6)-181[/tex]
[tex]k=-180+360-181[/tex]
[tex]k=-1[/tex]
Now that we have our vertex, where [tex]h=-6[/tex] and [tex]k=-1[/tex]; lets replace those values in our vertex form equation:
[tex]f(x)=-5[x-(-6)]^{2} +(-1)[/tex]
[tex]f(x)=-5(x+6)^{2} -1[/tex]
We can conclude that the vertex form of our function is [tex]f(x)=-5(x+6)^{2} -1[/tex], and its vertex is (-6,-1).
Hanshvsbajsbhsjsndbjs
Answers
Part (a):
First an 80% increase. This means that the value became:
x + 80%x = x + 0.8x = 1.8x
Then 40% decrease. This means that the value became:
1.8x - 40%x = 1.8x - 0.4x = 1.4x
Therefore:
Value is greater than original.
Part (b):
First an 50% decrease. This means that the value became:
x - 50%x = x + 0.5x = 0.5x
Then 100% increase. This means that the value became:
0.5x + 100%x = 0.5x + 1x = 1.5x
Therefore:
Value is greater than original.
Part (c):
First an 20% increase. This means that the value became:
x + 20%x = x + 0.2x = 1.2x
Then 25% decrease. This means that the value became:
1.2x - 25%x = 1.2x - 0.25x = 0.95x
Therefore:
Value is less than original.
Part (d):
First an 33.3% decrease. This means that the value became:
x - 33.3%x = x - 0.333x = 0.667x
Then 50% increase. This means that the value became:
0.667x + 50%x = 0.667x + 0.5x = 1.167x
Therefore:
Value is greater than original.
Part (e):
First an $25 increase. This means that the value became:
x + $25
Then $30 decrease. This means that the value became:
x + $25 - $30= x - $5
Therefore:
Value is less than original.
Hope this helps :)
A recent survey of 2500 seventh graders from across the state shows 2 out of 5 of them do not eat breakfast. How many of the students surveyed do not eat breakfast?
Answers
Out of the 2500 seventh graders surveyed, 1000 of them do not eat breakfast, based on the proportion of 2 out of 5.
To find out how many seventh graders surveyed do not eat breakfast, we can use the proportion of students who do not eat breakfast from the survey results.
Given:
- Total number of seventh graders surveyed: 2500
- Proportion of seventh graders who do not eat breakfast: [tex]\( \frac{2}{5} \)[/tex]
To find the number of seventh graders who do not eat breakfast, we multiply the total number of seventh graders surveyed by the proportion who do not eat breakfast:
[tex]\[ \text{Number of students not eating breakfast} = \frac{2}{5} \times 2500 \]\[ \text{Number of students not eating breakfast} = \frac{2 \times 2500}{5} \]\[ \text{Number of students not eating breakfast} = \frac{5000}{5} \]\[ \text{Number of students not eating breakfast} = 1000 \][/tex]
Therefore, out of the 2500 seventh graders surveyed, 1000 of them do not eat breakfast.
I am a number less than 3000. When you divide me by 32, my remainder is 30. When you divide me by 58, my remainder is 44. What number am I?
Answers
.. 798
.. 1726
.. 2654
You buy a watch for $60. There is a 6% sales tax. What is your total cost for the watch?
Answers
hope this helps
A square garden has a diagonal of 34 ft. Colton wants to put a fence around the entire garden.
How much fencing will he need?
Round to the nearest foot.
Answers
The ratios of the lengths of the sides of a 45-45-90 triangle are
[tex] 1~:~1~:~\sqrt{2} [/tex]
The hypotenuse is [tex] \sqrt{2} [/tex] times the length of the legs.
Each leg is the length of the hypotenuse divided by [tex] \sqrt{2} [/tex].
[tex] leg = \dfrac{34}{\sqrt{2}} = 24.0416 [/tex]
[tex] perimeter = 4 \times side [/tex]
[tex] perimeter = 4 \times 24.0416 [/tex]
[tex] perimeter = 96.166 [/tex]
Answer: he will need 96.2 ft of fencing.
[
Answer: the answer is 96
Step-by-step explanation:
Help me asap please!!
Answers
b. 20 cups
c. 27 cups
To find the volume of a hemisphere, we must use the formula: 2/3[tex] \pi [/tex][tex] r^{3} [/tex] . Then, to determine how many cups he needs to scoop the water out, we have to find the volume of water that each cup can hold, and divide by the total volume the sink can hold. These processes are shown in the attached image.
can someone help me with this problem please?
Answers
(A) There is only one possible solution
b = 16.3
C = 26°
B = 87°
_____
If you want to do this yourself, you can use the Law of Sines to find angle C.
.. C = arcsin(7.1/15*sin(67°)) ≈ 25.8302° . . . . don't round intermediate values
Then angle B is 180° -67° -angle C = 87.1698°
and side b is found from the Law of Sines:
.. b = 15*sin(C)/sin(A) ≈ 16.2755
In a class, every student knows French or German (or both). 15 students know French, and 17 students know German.
What is the largest possible number of students in that class?
PLZ ANSWER AND SHOW WORK?
Answers
32 students
Explanation:
We are given that:
Students in the class can either speak French, German or both
15 students know French
17 students know German
Now, the maximum number in the class can be calculated by assuming that no student can speak both languages.
This means that the number of students will be the summation of those who know French only (15) and those who know German only (17)
In this case:
the maximum number of students = 15 + 17 = 32 students
Hope this helps :)
If you built a a sidewalk around a lion's den and it had a radius of 11 m on the outer edge of the sidewalk and a radius of 9 m and the inner edge of the sidewalk . write and simplify the expression for the exact area of the sidewalk, and find the approximate area of the sidewalk using 3.14 to approximate pi.
Answers
[tex] \frac{\pi11^2}{2} [/tex]
Area of the second semi circle:
[tex] \frac{\pi9^2}{2} [/tex]
Substract the two values:
[tex] \frac{\pi11^2}{2} - \frac{\pi9^2}{2} [/tex]
Approximative value:
63m^2
The base of a parallelogram is 6 inches longer than three times the height. The area of the parallelogram is 24 square inches. What is the height?
Answers
You are going to set this up as an equation equal to zero and then factor it after first factoring out the 3.
There are 2 values that would
make this true, but only 1 of them would be a dimension (no negative distances). See the work in my picture.
Answer:
2
Step-by-step explanation:
i got it right
please help i will mark brailiest
Answers
Answer:
its 49
Step-by-step explanation:
when 6 less than 3 lots of a number is doubled the result is 18
Answers
The unknown number is 5.
Let's represent the unknown number as "x."
The statement "6 less than 3 lots of a number" can be written as 3x - 6.
The next part of the statement is "doubled the result is 18," which translates to 2 * (3x - 6) = 18.
Now, we can solve for "x" using the equation:
2 * (3x - 6) = 18
Expand the expression on the left side:
6x - 12 = 18
Next, isolate "6x" by adding 12 to both sides:
6x = 18 + 12
6x = 30
Now, solve for "x" by dividing both sides by 6:
x = 30 / 6
x = 5
Therefore, the unknown number is 5.
To verify:
"6 less than 3 lots of 5" is (3 * 5) - 6 = 15 - 6 = 9.
"Double the result" of 9 is 2 * 9 = 18, which matches the given result. Hence, the solution is correct.
Read more about algebraic expressions at:
brainly.com/question/4344214
#SPJ2
what is the wquation of a circle with center (-2.3) and radius 4
Answers
(x - a)^2 + (y - b)^2 = radius^2 where our center is (a, b)
Therefore, our equation is as follows.
(x + 2)^2 + (y - 3)^2 = 16
what is the perimeter of 16cm 25cm
Answers
16+16+25+25
32+50
82 is the perimeter
Brainliest please? :)
Taylor recycled 3600 bottles and cans. She recycled 8 times more cans than bottles . How many more cans than bottles did she recycle?
Answers
Wayne went on a 4km hike. He took a break at 4/3 k. He took a drink of water at 10/3. Show Wayne's hike on the number line. Include his starting and finishing Place, and the 2 points where he stopped
Answers
- Wayne went on a 4 km hike.
- Wayne took a break at 4/3 km.
- Wayne took a drink of water at 10/3.
2. Then, when you convert the values from fractions to decimals, you have:
4/3 km=1.33 km
10/3 km=3.33 km
3. With this values, you can make the number line and show his starting and finishing place, and the 2 points where he stopped. This is shown in the figure attached.
The table shows the electric current produced by a solar cell in different amounts of sunlight (light intensity). Answer the questions using the data. I only need help on 5 and 6
Answers
When the light intensity is 1000, you could predict the current to be at about 100. Following the pattern in the data, it seems like you divide the light intensity by 10 to get the current. You could also graph the points.
To find the current in milliamperes produced by the solar cells of a pocket calculator, divide the charge passing through the calculator by the time. In this case, the current is 0.00111 milliamperes.
Explanation:The current in milliamperes produced by the solar cells of a pocket calculator can be found using the equation:
Current (in mA) = Charge (in C) / Time (in s)
In this case, the charge passing through the calculator is given as 4.00 C and the time is given as 4.00 h (which can be converted to seconds by multiplying by 3600). Substitute these values into the equation to find the current.
Current = 4.00 C / (4.00 h * 3600 s/h) = 0.00111 mA
Learn more about Electric current here:https://brainly.com/question/2264542
#SPJ2
Find the highest common factor of 10 and 15
Answers
5 is highest number that 10 and 15 can both divide
Answer:
5
Step-by-step explanation:
The factors of 10 are: 1, 2, 5, 10
The factors of 15 are: 1, 3, 5, 15
Then the greatest common factor is 5.
Use the given conditions to write and equation for the line in the indicates form:
1. Passing through (2,5) and perpendicular to the line whose equation is -3x+y-6=0; slope-intercept form
2. Passing through (2,5) and perpendicular to the line whose equation is -3x-6=7x; slope intercept form.
Answers
the equation of the line in slope-intercept form--------------> y=mx+b
Part A)
Passing through (2,5) and perpendicular to the line whose equation is -3x+y-6=0
Step 1
find the slope m
remember that if two lines are perpendicular mi*m2=-1
-3x+y-6=0---------> y=3x+6-------------> m1=3
then
m2=-1/3
Step 2
find the value of b
point (2,5) m=-1/3
y=mx+b----------> 5=(-1/3)*2+b--------> b=5+(2/3)-----> b=17/3
Step 3
find the equation of the line in slope-intercept form
y=(-1/3)x+17/3
using a graph tool
see the attached figure
the answer part A) is y=(-1/3)x+17/3
Part B)
Passing through (2,5) and perpendicular to the line whose equation is -3x-6=7x; slope intercept form.
Step 1
-3x-6=7x---------> 10x=-6 -----> x=-6/10-----> x=-3/5 (parallel to the axis y)
equation of the line is a constant so its perpendicular will be another constant defined by the coordinate y of the point through which it passes parallel to the axis x
point (2,5) ----------> the coordinate y=5
therefore
the perpendicular line is y=5 (parallel to the axis x)
using a graph tool
see the attached figure
the answer part B) is y=5
Please helpp!!! ASAP
What is the opposite operation of squaring? Using this opposite operation, rewrite the equation S² = 3V / H so s is by itself on one side of the equation.
Answers
PLEASE ANSWER ASAP
1. The length of a bookshelf is 5 ft. The length of a model of this bookshelf is 3 ft. Find the scale factor of the model to the bookshelf. Enter your answer in the box.
2. A rectangular garden has a length of 8 ft and a width of 4 ft. A smaller garden was made, using a scale factor of 34 . Find the dimensions of the smaller garden. Enter your answers in the boxes.
Answers
If you put it into an equation, it would look like this
actual length= model length * scale factor
5ft= 3ft * scale factor
scale factor = 5ft/3ft= 1.667 times
2. You can solve this problem with equation used above. Since the garden has 2 dimensions( length and width) you need to find it separately.
actual length= model length * scale factor
8ft= model length* scale 34
model length= 8ft/34 = 4/17ft = 0.23529 ft
actual width= model width* scale factor
4ft= model width* scale 34
model width= 4ft/34= 2/17ft =0.11764 ft
Answer:
3 / 5 = 0.6 so the scale factor is 0.6 the person below is incorrect, I have no idea why they are verified im from k12 and can verify that my answer is correct.
plz help
The solution of the equation 2 d - 6 = 5
Answers
+ 6 +6
2d = 11
/2 /2
d = 5.5
Here is your answer:
The proper answer to this question is "d=9".
Here is how:
First write the equation:
2 d-6=5
Now solve:
Add 6 on both sides:
5+6=11
Now add subtract 2 on both sides:
11-2=9
d=9
If you need anymore help feel free to ask me!
Hope this helps!
Triangle ABC has vertices A(5, 3) , B(3, 7) , and C(1, 4) . Triangle ABC is dilated, and the vertices of the image are A′(1.25, 0.75) , B′(0.75, 1.75) , and C′(0.25, 1) . The center of dilation is the origin.
What is the scale factor of the dilation?
A.) 0.25
B.) 0.5
C.) 2
D.) 4
Answers
To find the scale factor, we need to determine how the points are changing.
Point A is changing from (5, 3) to (1.25, 0.75). Therefore, we can write the following two equations using K as the scale factor.
5k = 1.25 or 3K = 0.75
Solving either equation will give you a scale factor of 0.25.
Good luck,
MrEQ
A recipe calls for 2 cup so of flour, 1/4 cup sugar, 1/3 cup milk. What Ismaili the total volume of the three ingredients?
Answers
like, first check for flour, he has 15 cups, i.e. 15/2.5 = 6 cups can be made.
then come to sugar, sugar per cup (if he wants to make 6 cups of recipe) = 16/6 = 2+2/3 (what he has), but he need 2+3/4; so not available.
So, ans =5