PRESLEY
You are curious about the amount of coffee that the giant fountain cup could actually hold.
The dimensions of the fountain cup are as follows:
• Height is 8 feet.
• Diameter of the top is 6 feet.
• Diameter of the base is 4 feet.
Use this formula with height, h, radius of the base, roase, and radius of the top, rtop, to determine the volume
of the cup:
(πh).
V= -((rbase)+ (rbase) (stop) + (top)).
3
There are 7.5 gallons of liquid per cubic foot.
Enter the volume, in gallons, of the fountain cup.
Answers
The volume of the fountain cup in gallons is 4775.2 gallons
Volume of a frustumSince the fountain cup is in the shape of a frustum, its volume is given by
V = πh/3(r² + rr' + r'²) where
h = height of cup = 8 feet, r = radius of base of cup = 4 feet and r' = radius of top of cup = 6 feet.So, substituting the values of the variables into th equation, we have
V = πh/3(r² + rr' + r'²)
V = π × 8 ft/3[(4 ft)² + 4 ft × 6 ft + (6 ft)²]
V = π × 8 ft/3[16 ft² + 24 ft² + 36 ft²]
V = π × 8 ft/3 × (76 ft²)
V = 608π ft³/3
V = 1910.088 ft³/3
V = 636.69 ft³
V ≅ 636.7 ft³
Volume of the fountain cup in gallonsSince there are 7.5 gallons per cubic foot,
The volume of the fountain cup in gallons is V = 636.7 ft³ × 7.5 gallons/ft³ = 4775.2 gallons
So, the volume of the fountain cup in gallons is 4775.2 gallons
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Related Questions
Use the ordered pairs below. (10,20), (11, 21), (12, 22) What patterns are used to create the ordered pairs?
Answers
Answer:
Add 1 unit to the X coordinates and Y coordinates for each new pair.
step-by-step explanation:
X: 10 + 1 = 11 + 1 = 12
Y: 20 + 1 = 21 + 1 = 22
Subway creates a paid promotion featuring a different 6-inch sub of the day each day of the week. The sub of the day is only $3. 50. Subway utilizes the radio to spread the word. Which promotion method is subway using?.
Answers
Based on the information provided, the promotion method subway is using is sales promotion.
What is promotion?It is a marketing tool that involves letting know potential customers about a product that a company wants to sell.
What are the promotion methods?Most common methods include:
Direct selling.Public relations.Sales promotion.What is sales promotion?This involves promoting or advertising products through sales, which means customers are offered special discounts or lower prices. This is the method used by the subway because the sub of the day is a sales.
Learn more about sales in: https://brainly.com/question/15375944
Help!!!!!!! v is a vector of magnitude 4 making an angle of 30° with the positive x-axis. find v in component form .
Answers
Since v is a vector of magnitude 4 and makes angle 30° with the positive x axis, vector v in component form is v = 2√3i + 2j
To find vector v in component form, we need to know what a vector is
What is a vector?A vector is a physical quantity that has both magnitude and direction.
Component of a vectorA vector can be resolved into perpendicular components along the x, y and z axis.
Components of vector vSince vector v has a magnitude of 4 making an angle of 30 with the positive x - axis, its x-component is V = (vcos30°)i
= (4cos30°)i
= (4 × √3/2)i
= 2√3i.
The y-component of v is V' = (vsin30°)j
= (4 × sin30°)j
= (4 × 1/2)j
= 2j
Vector v in component form
So, vector v in component form is v = V + V'
= 2√3i + 2j
So, since v is a vector of magnitude 4 and makes angle 30° with the positive x axis, vector v in component form is v = 2√3i + 2j
Learn more about vectors here:
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Look at these equations.
9 = 7+ a
a + 8 = b + 5
Use both equations to work out the value of B
Answers
Answer:
B=5
Step-by-step explanation:
If 7 plus a equals 9 then a would equal 2.
2+8=b+5
10=b+5
Ask yourself what number plus 5 equals 10
B is 5 because 5 plus 5 is 10
Y^2+8y+2 y=-5 evaluate the expression
Answers
Answer:
the correct answer is shown below
Step-by-step explanation:
hope this helps
have an awesome day -TJ
pls mark brainliest if this helps :)
A 60 cm high cylinder with 14 cm its diameter is cut vertically into two equal halves. what is the volume of a half part
Answers
The volume of the half part of a cylinder of 60 cm high and 14 cm in diameter is 1470π cm³.
Volume of a cylindervolume of a cylinder = πr²h
where
r = radiush = heightTherefore,
r = 14 / 2 = 7 cm
h = 60 cm
volume of the cylinder = π × 7² × 60
volume of the cylinder = π × 49 × 60
volume of the cylinder = 2940π cm³
The volume of the half part = 2940π / 2 = 1470π cm³
learn more on volume here: https://brainly.com/question/13267675
Use the definition of continuity and the properties of limits to show that the function k(x)= √8−x2 2x2−5 is continuous at x = -2
Answers
12. A grocery store collects donated canned
food for a food bank. The cans are packed
in boxes that hold 24 cans. The store has
collected 744 cans.
a) Draw a graph to show this situation. Put
the number of boxes on the horizontal
axis and the number of cans on the
vertical axis. 2
b) Use your graph to estimate the number
of boxes needed to hold 744 cans.
c) Write an equation that relates the
number of boxes needed to the number
of cans.
d) Solve your equation to determine the
number of boxes needed.
e) Compare your solution in part (d) with
your estimate in part (b). Do you think
)
your solution is correct? Explain.
Answers
Answer:
For the last three years, the National Post has greeted the yuletide season by publishing the video above. With a simple message of maximizing charitable giving by donating money to the food bank instead of canned goods, it is one of our most popular videos of all time, reaching virtually every corner of the English-speaking world.
Step-by-step explanation:
A triangle has two sides of length 19 and 15. What is the largest possible whole-number length for the third side?
Answers
Answer:
34? Idek
Step-by-step explanation:
Answer:
33
Step-by-step explanation:
To maximize the length of the third side, which I'll call x, it needs to be the longest side.
So by the triangle inequality theorem, 19+15>x, meaning the maximum whole number value of x is 33.
There are exactly 4 parts to this question so if u can please answer thanks
Part A
Dilate Triangle OPQ with a scale factor of 1/2.
Provide the coordinates of each new vertex.
Part B
How does the size Triangle O'P'Q' compare to the size of Triangle OPQ?
Explain how this relates to the scale factor.
Part C
Are
Part D
If the length of segment OQ measures 9.8 units, what is the length of segment O'Q'? Explain in terms of similarity.
Answers
Answer:
see my question and come there now I want to talk with you
Step-by-step explanation:
Goal: illustrates radius, diameter, chord, center, arc, central angle, and
inscribed angle.
Role: Garden Designer/Landscape Architect
Audience: Math Teacher
Situation: A certified plantita and backyard owner plans to have a unique
garden. As a Landscape Architect, you are asked to make a sample layout of
a circular garden. She asks you to include the following on her garden:
● well
● pond
● bridge
● fountain
● walkways
● benches or chairs
● entrance and exit gates.
● trees, ornamental plants, and herbs
Procedure:
1. Draw a circle.
2. Conceptualize a circular garden and layout using the specified
items mentioned above.
What I Can Do
9
DISCIPLINE • GOOD TASTE • EXCELLENCE
3. Label the parts of circle formed on the garden layout
Please I'm looking for a serious answer. I need to pass this on monday. Thank you.
Point c is the center of dilation. line segment b a is dilated to create line segment b prime a prime. the length of c a is 4. the length of a a prime is 16. what is the scale factor of the dilation of line segment ba? one-fifth one-fourth 4 5
Answers
The scale factor of the dilation of line segment ba for which the center of dilation is C, is 5.
What is the dilation of the figure?Dilation of a figure, means the transformation of the figure. The factor by which the given figure dilated, called the scale factor of dilation.
Point c is the center of dilation. Line segment BA is dilated to create line segment b prime, a prime. The image of the given problem is attached below. The length of CA is 4.
[tex]CA=4[/tex]
The length of a prime is 16.
[tex]AA'=16[/tex]
The new dimension will be,
[tex]CA'=CA+AA'\\CA'=4+16\\CA'=20[/tex]
Now, the scale factor is the ratio of the new dimension to the original dimension. Thus, the scale factor of the dilation is,
[tex]r=\dfrac{20}{4}\\r=5[/tex]
This will be the same for the line segment BA. Thus, the scale factor of the dilation of line segment ba for which the center of dilation is C, is 5.
Learn more about the dilation of the figure here;
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Answer:
the answer is 5
Step-by-step explanation:
D
Trigonometry, how would I find the area of this triangle?
Answers
Answer:
Step-by-step explanation:
Area of triangle = 1/2 * base * height
Use the side of length 5.6cm as base, the height will be a perpendicular line from the base to the tip of the triangle.
From the right-angle triangle formed by the height and the side of length 3.9cm,
sin(56°45') = height / 3.9
height = 3.9*sin(56°45')
Substituting back into the area equation:
Area = 1/2*5.6*3.9*sin(56°45')
= 9.0cm^2
= 9cm^2
Use sine rule for Area
[tex]\\ \rm\rightarrowtail Area=\dfrac{1}{2}absinC[/tex]
[tex]\\ \rm\rightarrowtail Area=\dfrac{1}{2}(3.9)(5.6)sin56°45'[/tex]
[tex]\\ \rm\rightarrowtail Area=10.92(0.836)[/tex]
[tex]\\ \rm\rightarrowtail Area=10.22cm^2[/tex]
An aluminum bar 3 feet long weighs 12 pounds. What is the weight of a similar bar that is 3 feet 4 inches long?
Answers
Answer: 13 [tex]\frac{1}{3}[/tex] pounds
Step-by-step explanation:
We will set up a proportion. I will have the weight, in pounds, on the top (numerator) and the length, in inches, on the bottom (denominator).
[tex]\frac{12}{36} =\frac{x}{40}[/tex]
Cross-multiply:
36 * x = 12 * 40
36x = 480
Divide both sides of the equation by 36:
x = 13 [tex]\frac{1}{3}[/tex] pounds
Answer:
Step-by-step explanation:
First find unit weight.
1 foot = 12 inches
3 ft = 3*12 = 36 inches
3ft 4 inches = 36 + 4 = 40inches
Weight of 36 inches long bar = 12 pounds
Weight of 1 inch bar = 12/36
[tex]\text{Weight of 40 inches long bar = $\dfrac{12}{36}*40$}[/tex]
= 13.3 pounds
Natoshia's den is 4 feet longer than it is wide. If the den's area is 320 square feet, what are the dimensions of the room?
Answers
Dimensions : 16 x 20
Let the width be xthen the length: x + 4 area of rectangle = Length * Widthsolving steps:
(x+4)(x) = 320x² + 4x = 320x² + 4x - 320 = 0x² +20x -16x -320 = 0x(x + 20) -16(x+20) = 0(x-16)(x+20) = 0x = 16, -20x = 16 [ As length or width can never be negative ]So we found Width = 16 feet
Length:
16 + 420 feetAnswer:
width = 16 ft
length = 20 ft
Step-by-step explanation:
Let width = x
If the length is 4 ft longer than the width, then
⇒ length = x + 4
Area of a rectangle = width × length
Given:
area = 320width = xlength = x + 4Substituting these values into the equation for the area of a rectangle and solving for x:
⇒ 320 = x(x + 4)
⇒ 320 = x² + 4x
⇒ x² + 4x - 320 = 0
⇒ (x - 16)(x + 20) = 0
⇒ x = 16, -20
As distance is positive, then x = 16 only.
Therefore, width = 16 ft and length = 20 ft
How do solve this
h(x)=1/2x-14; h(4)
Answers
Answer:
-12
Step-by-step explanation:
h(x) = ½x - 14 where x = 4:
h(4) = ½(4) - 14
= 2 - 14
= -12
Please Help this is due soon
The table below represents an exponential function.
table represents an exponential function.
What is the interval between neighboring
x-values shown in the table?
1
What is the ratio between neighboring y-values?
4
What is the equation for this pattern?
y = _^x
I only need the last one answered
Answers
Answer:
[tex]y = {4}^{x} [/tex]
is the answer
If and , which expression is equivalent to ?
A.
B.
C.
D.
Answers
The normal price of a television is £1200
It is reduced to £970
Work out the percentage reduction.
Give your answer to 1 decimal place
Answers
Answer:80.8%
Step-by-step explanation:
£1200=100%
£970=
£970*100%/£1200=80.8333333
80.8%
Answer:
19.2%.
Step-by-step explanation:
Reduction = 1200-970 = £230,
% reduction = 230*100/ 1200
= 19,2%
An object is attached by a string to the end of a spring. Fang throws the object upwards and starts a stopwatch at t=0t=0t, equals, 0 seconds. The object starts oscillating vertically in a periodic way that can be modeled by a trigonometric function.
The object's average height is -20\text{ cm}−20 cmminus, 20, start text, space, c, m, end text (measured from the top of the spring). It first achieves that average height on the way up at t=0.2t=0.2t, equals, 0, point, 2 seconds, and then again every 222 seconds. The object's maximum and minimum heights are each 5\text{ cm}5 cm5, start text, space, c, m, end text from its average height.
Find the formula of the trigonometric function that models the height HHH of the weight ttt seconds after Fang started the stopwatch. Define the function using radians.
\qquad H(t) =H(t)=H, left parenthesis, t, right parenthesis, equals
What is the height of the object after 0.60.60, point, 6 seconds? Round your answer, if necessary, to two decimal places.
Answers
The object attached to a string illustrates a sinusoidal trigonometric function
The trigonometric function is H(t) = 5sin(π/2(t-0.2))-20, and the object's height after 0.6 seconds is -17.06 cm
How to determine the trigonometry function model?The trigonometry model of the object is a sine function represented by:
H(t) = Asin(B(t - c)) + D
The maximum height is 5 cm.
So, we have:
Amplitude, A = 5
The average height is - 20 cm.
So, we have
Vertical shift, D = -20
Its first average height is at t = 0.2.
So, we have:
Horizontal shift, C = 0.2
The period B is then calculated as:
B = π/t
The object reaches the maximum height every 2 seconds.
So, we have:
B = π/2
Substitute these values in H(t) = Asin(B(t - c)) + D
H(t) = 5sin(π/2(t-0.2))-20
Hence, the trigonometric function is H(t) = 5sin(π/2(t-0.2))-20
The height of the object after 0.6 secondsSubstitute 0.6 for t in H(t)
H(0.6) = 5sin(π/2(0.6-0.2))-20
Evaluate
H(0.6) = -17.06
Hence, the object's height after 0.6 seconds is -17.06 cm
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Answer:
What is the importance of biology laboratory?
Biological Science Laboratory Apparatus is essential for meeting our basic needs of food, clothing, shelter, health, energy, clean air, water and soil. Biological Science Laboratory Apparatus enrich the quality of life in numerous ways by providing new solutions to problems in health and materials and energy usage.
Consider the quadratic function.
f(x)=x^(2)+2x-15
If the line of symmetry of the function is located at x=N, what is the value of N?
HELP ASAP
Answers
Answer:
N = -1
explanation:
x = N
solving steps:
[tex]\sf f(x)=x^2+2x-15[/tex]
To find symmetry of a quadratic function.
vertex formula : [tex]\sf x=\dfrac{-b}{2a}[/tex]
[tex]a=1,\:b=2[/tex]
[tex]\sf x=\dfrac{-2}{2\cdot \:1}[/tex]
[tex]\sf x = -1[/tex]
Then,
N = -1
What is the value of X?
A) 17
B) 16
C) 16.5
D) 15
Answers
Answer:
answer is 16.5
Step-by-step explanation:
answer is 16.5
Angle 1 and Angle _____________ are supplementary angles.
Answers
Answer: number 2
Step-by-step explanation: so a supplementary Angle adds up to a 180 angle so it would be number 2 I think.
If the hypotenuse of a 30°-60°-90° Triangle is 10√2, find the length of the other two sides.
Answers
Let us consider a 30°-60°-90°△ABC right angled at B in which ∠C = 30⁰ and ∠A = 60⁰ with hypotenuse AC = 10√2 units.
Solution:-In △ABC,
[tex]\longrightarrow[/tex]sin ∠C = [tex]\sf \dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\longrightarrow[/tex]sin ∠C = [tex]\sf \dfrac{AB}{AC}[/tex]
[tex]\longrightarrow[/tex]sin 30⁰ = [tex]\sf \dfrac{AB}{10\sqrt{2}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf \dfrac{1}{2}= \dfrac{AB}{10\sqrt{2}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf AB = \dfrac{10\sqrt{2}}{2}[/tex]
[tex]\longrightarrow[/tex][tex]\sf AB = 5\sqrt{2}\:units[/tex]
[tex]\\[/tex]
In △ABC,
[tex]\longrightarrow[/tex]cos ∠C = [tex]\sf \dfrac{Base}{Hypotenuse}[/tex]
[tex]\longrightarrow[/tex]cos ∠C = [tex]\sf \dfrac{BC}{AC}[/tex]
[tex]\longrightarrow[/tex]cos 30⁰ = [tex]\sf \dfrac{BC}{10\sqrt{2}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf \dfrac{\sqrt{3}}{2}= \dfrac{BC}{10\sqrt{2}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf BC = \dfrac{10\sqrt{2}\times \sqrt{3}}{2}[/tex]
[tex]\longrightarrow[/tex][tex]\sf BC = \dfrac{10\sqrt{2\times 3}}{2}[/tex]
[tex]\longrightarrow[/tex][tex]\sf BC = \dfrac{10\sqrt{6}}{2}[/tex]
[tex]\longrightarrow[/tex][tex]\sf BC = 5\sqrt{6}\: units[/tex]
Thus , the length of other two sides of triangles are 5√2 and 5√6 units.
Can someone help me out with this?
What is the value of x?
Enter your answer in the box.
Answers
Answer:
x = 4Step-by-step explanation:
x has the same value as RT since they are equal sides of the isosceles triangle.
RT is also the hypotenuse of ΔRST - 30°×60°×90° right triangle.
Acoording to the property of such triangles, the ratio of sides is:
a : b : c = 1 : √3 : 2We have:
b = 2√3 and c = RTUse the ratio to find the lenght of RT
2√3 : RT = √3 : 2RT = 2*2√3/√3RT = 4So the value of x is 4 units
Find RT
sin60=2√3/RT√3/2=2√3/RTRT=4√3/√3RT=4Now
tan45=x/4x=4Find the area. What type of triangle is triangle ABC?
Answers
Answer:
Isosceles right triangles are half squares, and if the length of one side is 6cm, that is the length of the other side since both segments are equal. Take the formula to find the area of a square (base times height), apply the side measurement of the triangle (6cm) and divide it in half to find the area of half of it (therefore, finding the area of the isosceles triangle.) (6x6) / 26x6 = 3636 / 2 = 18 The area of the isosceles triangle is 18 square centimeters.
Step-by-step explanation:
Elaine sold twice as many T-shirts as Kim
How many did each girl sell if the total
number of T-shirts sold was 27?
(no links no files) I need equation
Answers
is 48,200 in scientific notation?
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \:48200[/tex]
[tex]\qquad \sf \dashrightarrow \:4.82 \times 10 {}^{4} [/tex]
determine if the expressions
are
7. 2 - 2 + 5x; 5x
Answers
help pls first correct answer gets brainleist
Answers
n²= 7²+3²
=49+9
=58
n= V58
=7.62m
What is the value of k?
Answers
Answer:
10°
Step-by-step explanation:
According remote interior angles, 4k + 5 + 6k + 10 = 115.
10k + 15 = 115
10k = 100
k = 10
Hope this helps :)
Have a nice day!
Answer:
k = 10°
Step-by-step explanation:
According to the exterior angle theorem, the exterior angle will be equal to the two opposite inside angles added together. It will look like the following, and we solve for k from there.
115° = (4k + 5)° + (6k + 10)°
115° = 4k° + 5° + 6k° + 10°
115° = 6k° + 4k° + 10° + 5°
115° = 10k° + 15°
100° = 10k°
10° = k
k = 10°