The volume of the cylinder with height 6 meters and the radius 18 meters is [tex]6,104.16 m^{3}[/tex].
What is a volume of a cylinder?The volume of a cylinder is the capacity of the cylinder which calculates the amount of material quantity it can hold.
Given that, the height of a cylinder=6 meters and the diameter of a cylinder=6×6=36 meters (A diameter that is 6 times the measure of the height)
Now, radius [tex](r)=\frac{d}{2} =18 meters[/tex]
[tex]\pi =3.14[/tex]
We know that, the volume of the cylinder[tex]=\pi r^{2} h[/tex]
[tex]=3.14\times 18^{2} \times 6 m^{3}[/tex]
[tex]=6,104.16 m^{3}[/tex]
Hence, the volume of the cylinder with height 6 meters and the radius 18 meters is [tex]6,104.16 m^{3}[/tex].
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Use the compound interest formulas A=P1+
r
nnt and A=Pert to solve the problem given. Round answers to the nearest cent.
Find the accumulated value of an investment of $25,000 for 3 years at an interest rate of 7% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously.
The accumulated value of an investment if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously is $30731.4 $ , $30785.98 $30823.14 , 30841.95
What is Interest ?Interest is the amount received by a person as a result of investing certain amount of money for a certain period of time.
It is given that
Principal = $ 25000
Time = 3 years
Interest Rate = 7 %
The amount is given by
[tex]\rm A = P( 1+ \dfrac{r}{n}) ^{nt}[/tex]
Compounded semiannually
n = 2
Compounded Quarterly
n = 4
Compounded Monthly
n =12
Compounded Continuously
P = P₀ [tex]\rm e ^{rt}[/tex]
Therefore the accumulated value for
compounded Semiannually is
[tex]\rm A = 25000( 1+ \dfrac{7}{200}) ^{2*3}[/tex]
A = $30731.4
Compounded Quarterly
[tex]\rm A = 25000( 1+ \dfrac{7}{400}) ^{4*3}[/tex]
A = $30785.98
Compounded Monthly
[tex]\rm A = 25000( 1+ \dfrac{7}{1200}) ^{12*3}[/tex]
A = $30823.14
Compounded Continuously
[tex]\rm P = 25000 e ^{ 7 * 3 }[/tex]
P = $30841.95
Therefore the accumulated value of an investment if the money is
a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously is
$30731.4 $ , $30785.98 $30823.14 , 30841.95
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r=
help me please thank u
Answer:
[tex]\fbox {r = 34}[/tex]
Step-by-step explanation:
Finding IQ and RJ by tangent rule :
⇒ IQ = QK = 10
⇒ KR = RJ = 8
Finding PJ :
⇒ PJ = 32 - 8
⇒ PJ = 24
∴ But PJ = PI (by tangent rule)
⇒ PI = 24
Finding r :
⇒ PI + IQ
⇒ 24 + 10
⇒ r = 34
Make u the subject formula
Please help
X=4uy/M
Answer:
[tex]\frac{XM}{4y}=u[/tex]
Step-by-step explanation:
First, multiply both sides by M.
X M = 4uy
Now, divide both sides by 4y.
[tex]\frac{XM}{4y} =\frac{4uy}{4y}[/tex]
Therefore,
[tex]\frac{XM}{4y}=u[/tex]
On a coordinate plane, solid circles appear at the following points: (negative 2, negative 5), (negative 1, 3), (1, negative 2), (3, 0), (4, negative 2), (4, 4).
Which explains why the graph is not a function?
A boat leaves a dock and goes 240 miles in a direction of 290 degrees. It then turns and goes 50 miles in a direction on 30 degrees. How far is the boat from the dock and in what direction?
By Pythagorean theorem and trigonometric functions, the magnitude and direction of the boat are approximately 284.403 miles and 295.043° with respect to the east.
What is the direction and magnitude of the resulting displacement with respect to the origin
In this problem we assume that the first angle is measured with respect to the east side and that the second angle is counterclockwise and measured with respect to the direction of the first vector. First, we need to determine the resulting vector by using trigonometric and vectorial formulas:
(x, y) = (240 · cos 290°, 240 · sin 290°) + (50 · cos 320°, 50 · sin 320°)
(x, y) = (120.387, - 257.666) [mi]
The magnitude is found by Pythagorean theorem:
[tex]r = \sqrt{(120.387\,mi)^{2}+(-257.666\,mi)^{2}}[/tex]
r ≈ 284.403 mi
The direction of the boat is obtained by inverse trigonometric functions:
θ = tan⁻¹ (- 257.666/120.387)
θ ≈ 295.043°
By Pythagorean theorem and trigonometric functions, the magnitude and direction of the boat are approximately 284.403 miles and 295.043° with respect to the east.
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someone please help me with this question!!
The Answer is in simplest form:-
4/9
=0.4444444444
Answer:
4/9
Step-by-step explanation:
1) since we know that; when a fraction is raised to a negative power, we take reciprocal of the fraction and raise both the numerator and the denominator to a positive power,
(27/8)^-⅔
that's how we write it then
2) we take the reciprocal and multiply with positive power respectively
(8/27)⅔
that is by expanding
8^⅔/27^⅔
enter it in your calculator and you should get
4/9
hope that helps!
Part A Can image 1 be the reflected figure from question 1? Explain your answer.
The resulting reflected image would be congruent to image 1, i.e. have congruent corresponding sides.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and translation.
Reflection is a rigid transformation, hence it does not affect the size and shape of the object or pre-image.
The resulting reflected image would be congruent to image 1, i.e. have congruent corresponding sides.
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Event A: Spinning violet or yellow on the spinner.
Event B: Rolling an even number on a number cube.
What is P(A and B)?
Answer:
[tex]\sf P(A \cap B)=\dfrac{1}{4}[/tex]
Step-by-step explanation:
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
Event A - spinning violet or yellow
Assuming that the spinner has 4 different colors (red, orange, violet and yellow) - see attachment.
[tex]\implies \sf P(A) = \dfrac{2}{4}=\dfrac{1}{2}[/tex]
Event B - rolling an even number
Assuming the number cube has 6 sides numbered 1, 2, 3, 4, 5 and 6. Therefore, the even numbers are 2, 4 and 6.
[tex]\implies \sf P(B)=\dfrac{3}{6}=\dfrac{1}{2}[/tex]
Events A and B are independent events as the outcome of one event does not affect the outcome of the other event.
For independent events A and B:
[tex]\implies \sf P(A \cap B)=P(A)P(B)[/tex]
To find P(A and B), substitute the found values of P(A) and P(B):
[tex]\implies \sf P(A \cap B)=\dfrac{1}{2} \times \dfrac{1}{2}=\dfrac{1}{4}[/tex]
P(A)
2/41/20.5P(B)
3 even nos are 2,4,6
3/61/20.5P(A[tex]\cap[/tex])
0.5²0.25 or 1/4Is this correct? If not then whats the answer?????
(image below)
he given line passes through the points and (4, 1).
On a coordinate plane, a line goes through (negative 4, negative 3) and (4, 1).
What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (, 3)?
The equation of the line that passes through the point (-4 , 3) with slope ₋2 is:
y = ₋2x ₋ 5
Given the points are (₋4 , ₋3) and (4 , 1)
The gradient of the line through the points' locations (x₁ , y₁) and (x₂ , y₂) is: y₂ ₋ y₁/x₂ ₋ x₁
Substitute the given points in the above formula:
=1 ₋(₋3)/4 ₋ (₋4)
=4/8
=1/2
If the product of the slopes of two perpendicular lines is -1, then the slope of the perpendicular line is ₋1/1/2 = ₋2
Therefore the line that passes through the point (-4 , 3) with slope ₋2 has equation:
y ₋ 3 = ₋2(x ₊ 4)
y = ₋2x ₋ 8 ₊ 3
y = ₋2x ₋ 5
Hence we get the expression as y = ₋2x ₋ 5
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what does y=mx+b equal
Answer:
slope intercept form
Step-by-step explanation:
y=mx+b is slope-intercept form
I hope this helps :)
A bag contains 20 identical sweets apart from the colour: 10 are pink, 7 are green and 3 are yellow. Jovian randomly selects wtwo sweets from the bag, one after the other, ans eats them. Find the probability that:
i) she eats two pink sweets,
ii)the first sweet is green and the second sweet is yellow,
iii) she eats exactly one pink sweet,
iv)neither sweet is green
Answer: Relative frequency and probability are similar terms and the answer to both of them are the same. What I mean is that, even if the question asks for probability or relative frequency, the answer will remain the same. The basic difference is that relative frequency is used when probability is being estimated using the outcomes of an experiment or trial, when theoretical probability cannot be used.
We can write the probability in the help of a normal formula,
P(A) is the probability of an event “A” n(B) is the number of favorable outcomes. n(S) is the total number of events in the sample space.
One more thing you might need to know is that, in probability, and means multiplication and or means addition.
And = multiplication
Or = addtion
So from the above equation, n(S) , the total number " 10 + 7 + 3" is 20.
i) 2/20 and in simplified terms, 1/10
ii) 7/20 * 3/20 = 21/400
iii) 1/20
iv) 13/20
∩_∩
(„• ֊ •„)♡
┏━∪∪━━━━┓
hope it helped
┗━━━━━━━┛
Please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!ASAP
The ordered pair of the given equation will be ( 3, 6 ) and ( -3, 18).
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
The given functions are:-
F(x) =x²-2x+3
F(x) = -2x + 12
When we plot the graph of the function we will see that the line -2x +12 cut the parabola at points ( -3, 18 ) and ( 3, 6 ) so these are the ordered pairs of the two functions. The graph of the functions is also attached with the answer.
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Pls explain this to me, I don't understand why the answer is a^3 +b^3 and not a^3-b^3
Answer:
[tex](a+b)(a^2-ab+b^2)=a^3+b^3[/tex]
Step-by-step explanation:
Given expression:
[tex](a+b)(a^2-ab+b^2)[/tex]
Using the Distributive Property Law, expand the brackets:
[tex]\implies a(a^2-ab+b^2)+b(a^2-ab+b^2)[/tex]
[tex]\implies a^3-a^2b+ab^2+a^2b-ab^2+b^3[/tex]
Group like terms:
[tex]\implies a^3+b^3-a^2b+a^2b+ab^2-ab^2[/tex]
As -a²b+a²b=0 and ab²-ab²=0 then:
[tex]\implies a^3+b^3[/tex]
What is the measure of
Please help! Consider the following subset of the real number line. How can this set be expressed using inequalities?
Inequalities help us to compare two unequal expressions. The correct option is A.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
The set of numbers that the number line represents is -1, -2,-3, and -4. Thus, The inequalities that can express the given set are -4≤x≤-1.
Hence, the correct option is A.
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Your are designing a rectangular birthday card for a friend. You want the card's length to be 1 inch more than twice the card's width. The area of the card is 88 square inches. What is the width of the card to the nearest tenth of an inch?
The width of the card to the nearest tenth of an inch is 6.15 inches
Area of rectangleWidth = xLength = 2x + 1Area = 88 square inchesArea of a rectangle = Length × Width
88 = (2x + 2) × x
88 = 2x² + 2x
2x² + 2x - 88 = 0
x = -b ± √b² - 4ac / 2a
= -2 ± √2² - 4(2)(-88) / 2(2)
= -2 ± √4 - (-704) / 4
= -2 ± √708 / 4
= -1/2 ± √177/2
x = 6.15 or -7.15 inches
The width of the rectangle can not be negative, so, 6.15 inches is the width.
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find the linear measure of arc vw on circle p, where pv = 32 inches and angle vpw = 84. use 3.14 for pie and estimate your answer to two decimal places.
The linear measure of arc vw as described in the task content is; 46.89in.
What is the linear measure of the arc vw?It follows from the task content that the radius of the circle with center p is given as pv = 32in. and the angle subtended by the arc is; 84.
On this note, the measure of arc vw is;
= (84/360) × 2 × 3.14 × 32
= 46.89 inches.
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Cans of wood varnish come in three sizes.
Small can: A 200 ml can costs £0.88.
Medium can: A 500 ml can costs £1.32.
Large can: A 1 litre can costs £3.60.
Calculate the cost of 1 litre for the small and medium cans.
Give your answer in pounds to 2 dp.
The cost of 1 liter for the small and medium cans is 4.4 and 2.4.
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
As,
Small can: A 200 ml can costs £0.88.
Medium can: A 500 ml can costs £1.32.
Large can: A 1 litre can costs £3.60.
Now, 200 ml = 0.2 l
500 ml = 0.5 l
For 0.2 l = 0.88
For 1 l= 0.88/0.2
For 1 liter = 4.4
For 0.5l medium can = 1.32
For 1 l medium can= 1.32/0.5
For 1 l medium can = 2.4
Hence, cost of 1 liter for the small can is £ 0.88 the cost of 1 liter for the medium can is £ 2.4.
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Y = 3x + 10
Y = 2x - 8
find the substitution
Show your work please ill give brainlyest
Answer:
x = -18, Y = -44
Step-by-step explanation:
Since Y = 2x - 8, we can substitute that into the first equation:
2x - 8 = 3x + 10
3x - 2x = -8 - 10
x = -18
Now we plug x = -18 back into the second equation:
Y = 2(-18) - 8
Y = -36 - 8
Y = -44
f(x) = 4x² + 7x-3
g(x) = 6x³ – 7x² - 5
-
Find (f + g)(x).
Answer:
(f + g)(x) = 6x³ - 3x² + 7x - 8
Step-by-step explanation:
Another way of writing (f + g)(x) is f(x) + g(x). So, this question is asking you to combine both of the functions.
f(x) + g(x)
(4x² + 7x - 3) + (6x³ - 7x² - 5) <----- Insert functions
-3x² + 7x - 3 + 6x³ - 5 <----- Combine 4x² and -7x²
-3x² + 7x - 8 + 6x³ <----- Combine -3 and -5
6x³ - 3x² + 7x - 8 <----- Rearrange
Write a quadratic function f whose zeros are 2 and 7.
Answer:
f(x) = (x - 2)(x - 7)
Step-by-step explanation:
an easy way to write a quadratic function who has zeroes of certain numbers is to use this format- f(x) = a(x - p)(x - q)
in this format
the p and the q are both zeroes
it does not matter what the a value is
an example for when the zeroes are 2 and 7 could be
f(x) = (x - 2)(x - 7)
The point (-6, 4) is reflected over the x-axis. Find the point of reflection.
Answer:
-6, -4
Step-by-step explanation:
Instruction: draw a line perpendicular to line AB at point C.
I have followed the steps, please tell me what have I done wrong? :)
(picture included of my answer)
Answer:
it’s correct
Step-by-step explanation:
Answer:
[tex]\fbox {See below} \downarrow[/tex]
Step-by-step explanation:
When taking the perpendicular of the line, it should be done at the midpoint of the line. Hence, by taking arcs from both endpoints, it should be done. This is why this is incorrect.
Square measures 8 m on each side if each side is written by 1/4 of eight originally the premiere of the new square will be blank meters and its area blank square meters
Step-by-step explanation:
so, if I understand this correctly, the original square had a side length of 8 m.
now we transform this square into one with side length 1/4×8 = 8/4 = 2 m.
and the questions are what are the perimeter and the area of that new (smaller) square ?
the perimeter of a square is
4× side length = 4×2 = 8 m
the area of a square is
side length ² = 2² = 4 m²
Aiden has a smart phone data plan that costs $25 per month that includes 2 GB of data, but will charge an extra $10 per GB over the included amount. How much would Aiden have to pay in a month where he used 2 GB over the limit? How much would Aiden have to pay in a month where he used went over by xx GB?
Total cost when over by 2 GB:
Total cost when over by xx GB:
need answer quick
Answer:
45 dollars for going over 2GB
Step-by-step explanation:
If he pays 25 dollars every month and he goes over 2 GB then he’ll have to pay 20 dollars extra since every GB over cost 10 dollars. The equation is 25+10+10 which equals 45.
An expression is a mixture of terms that are combined by using operations such as subtraction, addition, multiplication, and division.
The amount when 2 GB is used over the limit in a month is $45.
What is an expression?An expression is a mixture of terms that are combined by using operations such as subtraction, addition, multiplication, and division.
Example: 2x + 3x2 is an expression.
We have,
Cost of data plan with 2 GB = $25
Cost of one GB = $10
The equation that can be used to find the amount to pay when using x GB over the limit in a month:
= 25 + 10x
The amount when 2 GB is used over the limit in a month:
= 25 + 10 x 2
= 25 + 20
= $45
Thus,
The amount when 2 GB is used over the limit in a month is $45.
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which equation represents the line through (4,5) and (0,-3)
A. y = 2x + 3
B. y = 2x - 3
C. y = -2x - 3
D. y = -2x + 3
The linear equation that represents the line that passes through the points (4,5) and (0,-3) is given by:
B. y = 2x - 3
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The line passes through (0,-3), that is, when x = 0, y = -3, hence the y-intercept is of b = -3.
The slope is given by the change in y divided by the change in x, hence:
m = (5 - (-3))/(4 - 0) = 2
Hence the equation is:
y = 2x - 3.
Which means that option B is correct.
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128 (4 + 2) = (128 ÷ 4) + 2
A. True
B. False
Answer:
B. False
Step-by-step explanation:
Just like last time, solve it first to check.
128(4+2)=(128/4)+2
Remember PEMDAS, parenthesis first.
128(6)=(32)+2
Now multiply the left side and add the right side.
128*6=768. The star sign is just another way to write a multiplication sign.
32+2=34
768≠34
This is a false statement. 768 does not equal 34.
Hope this helps!
If not, I am sorry.
Lucy is knitting a blanket and needs to buy some more yarn. at her local craft store, 2 skeins of yarn cost $7 and 8 skeins of yarn cost $28. what is the constant of proportionality in this direct variation?
Answer:
4
Step-by-step explanation:
Proportionality between skein values
8:2=4:1
Proportionality between cost values
28:7=4:1
The variation(both the skein values and cost values) has the constant of 4 ie the 1st skein value × 4= the last skein value & the 1st cost value × 4=the last cost value
Combine the radicals 4√7 + 3√28
Answer:
10√7
Step-by-step explanation:
you can simplify the second radical and break it up into
√4 * √7 which then simplifies to 2√7 which you then multiply by 3. 4√7 + 3(2√7) which becomes 4√7 + 6√7 and then you just add the numbers Infront to get 10√7
