curved surface area of a cone = Trl, where r is the
radius and is the slant height.
The cone below has a slant height of 23 cm and a
diameter of 6 cm.
Work out the curved surface area of the cone.
Give your answer to the nearest integer and remember
to give the correct units.
6 cm
23 cm
Not drawn accurately
The curved surface area of the cone is 144 cm².
What is the curved surface area?A cone is a three-dimensional object that consists of a circular base and an vertex.
curved surface area = πrl
Where:
r = radius = diameter / 2 = 6/2 = 3 cm l = slant heightπ = 3.143.14 x 3 x 23 = 144 cm²
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A chopstick model of a catapult launches a marshmallow in a classroom. The path of the marshmallow can be modeled by the quadratic y=−0.07x2+x+2.2,
where y represents the height of the marshmallow, in feet,
and x represents the horizontal distance from the point it is launched, in feet.
When the marshmallow hits the ground, what is its horizontal distance from the point where it was launched?
The horizontal distance from the point where it was launched is 7.143.
We have given that,
The path of the marshmallow can be modeled by the quadratic y=−0.07x^2+x+2.2,
x represents the horizontal distance from the point it is launched, in feet.
What is the horizontal distance?Horizontal distance means the distance between two points measured at a zero percent slope.
(1) Put x = 7.143 in given equation
y= -0.07(7.143)^2+7.143+2.2
y= 2.2
y= 5.771
We have to determine the what is its horizontal distance from the point where it was launched.
The value of x is called horizontal distance.
Therefore the horizontal distance from the point where it was launched is 7.143.
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Please create an example using exponential growth and exponential decay
Answer:
f(x)=4^x exponential growth, -6^x exponential decay Step-by-step explanation:
Triangle P Q R is shown. Angle P Q R is a right angle. The length of hypotenuse P R is q, the length of P Q is r, and the length of Q R is p.,
Which cosine ratios are correct for ΔPQR? Check all that apply.
cos (P) = StartFraction r Over q EndFraction
cos (P) = StartFraction p Over q EndFraction
cos (Q) = StartFraction r Over p EndFraction
cos (R) = StartFraction r Over p EndFraction
cos (R) = StartFraction p Over q EndFraction
The cosine ratios which are correct for the ΔPQR are CosineP = r/q and CosineR = p/q.
We have,
Δ PQR,
Length of hypotenuse PR = q
The length of PQ = r,
And the length of QR = p
NOw,
We know that Trigonometric ratios of CosineΘ;
CosineΘ = Base/Hypotenuse
So,
CosineP = r/q
And,
CosineR = p/q
So, from the above find out values we can say that these values are given in option (a) and option (d).
Therefore, the cosine ratios which are correct for the ΔPQR are CosP = r/q and CosR = p/q.
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Help is needed with this math problem!
Answer:
expression for (g + h)([tex]x\\[/tex]) = [tex]2x[/tex] + [tex]3x^2\\[/tex] and for (g - h)([tex]x[/tex]) = [tex]2x[/tex] - [tex]3x^2[/tex]
value of (g .h)(2) = 24
Step-by-step explanation:
function operations: Functions with overlapping domains can be added, subtracted, multiplied and divided. If f(x) and g(x) are two functions, then for all x in the domain of both functions we can find the sum, difference, product and quotient
given :
g([tex]x[/tex]) = [tex]2x[/tex]
h([tex]x[/tex]) = [tex]3x^2[/tex]
we know that ;
(g + h)([tex]x[/tex]) = g([tex]x[/tex]) + h([tex]x[/tex])
= [tex]2x[/tex] + [tex]3x^2[/tex]
similarly;
(g - h)([tex]x[/tex]) = g([tex]x[/tex]) - h([tex]x[/tex])
= [tex]2x[/tex] - [tex]3x^2[/tex]
now,
(g . h)([tex]x[/tex]) = 2([tex]3x^2\\[/tex])
= 6[tex]x^2\\[/tex]
for (g .h)(2) = 6([tex]2^2[/tex])
= 6 × 4
= 24
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GUYS PLEASE HELP WITH THIS PLEASE
Examine how sounds of music are related to trigonometric functions.
What does change of amplitude do? How about frequency?
Using graphs and equations, represent multiple transformations explaining their relevancy to the sound wave
Trigonometry functions is often employed in taking the measurement of the level or the pitch of a sound wave or musical note.
The change of amplitude of a sound wave's amplitude is linked to the change in pressure that occurs due to the wave measured at a given location.
Frequency tells the number of waves that pass a fixed location in a specific time frame.
How does sound waves relate to trigonometric functions?Sound engineers uses the basic laws of trigonometry via sine and cosine graphs.
Note that all sounds can be broken down into a lot of sine waves, as sine waves comes together to form sounds.
Therefore, Trigonometry functions is often employed in taking the measurement of the level or the pitch of a sound wave or musical note.
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Group of 5 people can do a piece of work in 6hrs- Calculate the time a group of 8 people working half the rate of first group could take
The time taken by a group of 8 people working half the rate of the first group is 7.5 hours.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
A Group of 5 people can do a piece of work in 6hrs.
5 people, at a rate of 1, and the time taken is 6 hours
Work done is 30
8 people, at a rate of 1/2, and the time taken is x hours
8(1/2)x = 30
x = 60/8 = 7.5 hours
Thus, the time taken by a group of 8 people working half the rate of the first group is 7.5 hours.
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What are the solution(s) to the quadratic equation 50 - x² = 0?
x = +2√5
x = ±6√3
x=+5√2
no real solution
The solutions to the quadratic equation 50 - x² = 0 are x = ±5√2.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .
The solution(s) to the quadratic equation 50 - x² = 0 can be found by setting the equation equal to zero and solving for x.
50 - x² = 0
To solve this equation, we can rearrange it as follows:
x² = 50
Taking the square root of both sides, we have:
x = ±√50
Simplifying the square root of 50, we get:
x = ±√(25 × 2)
x = ±√25 × √2
x = ±5√2
Therefore, the solutions to the quadratic equation 50 - x² = 0 are x = ±5√2.
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What is the product of the reciprocal of 6 and the reciprocal of 7?
Answer:
The answer is 1/42 as you take reciprocal of 6=(1/6) and reciprocal of 7=(1/7) and multiply.
Answer:
[tex]\boxed {\frac{1}{42}}[/tex]
Step-by-step explanation:
Reciprocal of 6 : 1/6
Reciprocal of 7 : 1/7
Their product :
1/6 × 1/71/42Which expression can be used to find the difference of the polynomials?
The expression that can be used to find the difference of the polynomials is (4m - 5) + ( -6m + 7 - 2n). D
How to find the difference
Given the expression:
(4m - 5) - (6m - 7 + 2n)
Note that - * - = +
+ * - = -
So in finding the difference, we have
(4m - 5) - ( 6m + 7 - 2n )
It could as be written as
(4m - 5) + ( -6m + 7 - 2n)
Therefore, the expression that can be used to find the difference of the polynomials is (4m - 5) + ( -6m + 7 - 2n) . D
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Which represents a quadratic function?
f(x) = 2x³ + 2x² - 4
f(x) = -7x²-x+2
f(x)=-3x + 2
f(x) = 0x² + 3x-3
Option B is correct, the function f(x) = -7x² - x + 2 represents a quadratic function
What is quadratic equation?A quadratic function is a polynomial function of the form f(x) = ax² + bx + c, where a, b, and c are constants and a is not equal to zero.
f(x) = -7x² - x + 2 is a quadratic function because it is of the required form.
Specifically, it has a quadratic term (-7x²), a linear term (-x), and a constant term (2).
The other three functions do not have a quadratic term and thus are not quadratic functions.
f(x) = 2x³ + 2x² - 4 is a cubic function because it has a cubic term (2x³).
f(x) = -3x + 2 is a linear function because it has only a linear term (-3x) and a constant term (2).
f(x) = 0x² + 3x - 3 is also a linear function because it has no quadratic term and only a linear term (3x) and a constant term (-3).
Hence, the function f(x) = -7x² - x + 2 represents a quadratic function
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According to the U.S. Census Bureau, the mean of the commute time to work for a resident of CA is 21.5 minutes. Assume that the standard deviation of the commute time is 4.8 minutes to complete parts (a) through (c).
Part 1
(a) What minimum percentage of commuters in has a commute time within standard deviations of the mean?
enter your response here%
(Round to one decimal place as needed.)
Using Chebyshev's Theorem, the minimum percentage of commuters in has a commute time within 2 standard deviations of the mean is of 75%.
What does Chebyshev’s Theorem state?When we have no information about the population distribution, Chebyshev's Theorem is used. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.At least 89% of the measures are within 3 standard deviations of the mean.An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].Hence, the minimum percentage of commuters in has a commute time within 2 standard deviations of the mean is of 75%.
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What is the product?
- 6(x²-1)-8(x+1)
O 6(x-1)²
O 6(x²-1)
O(x + 1)(6x-1)
O(x-1)(6x - 1)
Answer: C
Explanation:i got it right on my test
Drag each tile to the correect location on the table. Not all tiles will be used. Maych each quadratic function with the attributes of its graph.
Answer:
I believe you forgot to add a picture
Please help me answer this question
Answer:
Z = sin(xy)
[tex]\frac{1}{y} \times \frac{\partial Z}{\partial x} =\cos \left( xy\right) =\frac{1}{x} \times \frac{\partial Z}{\partial y}[/tex]
North
A
72°
80m
115m
B
NOT TO
SCALE
The diagram shows the positions of three points A, B and C in a field.
(a)
Show that BC is 118.1 m, correct to 1 decimal place.
Using the cosine rule, BC = √(115² + 80² - 2(115)(80)(cos 72) ≈ 118.1 m (1 decimal place).
How to Use the Cosine Rule?If we are given a triangle with two known sides and an included angle, the cosine rule that can be used to find the side opposite to the given angle is: a = √(b² + c² - 2bc(cos A)
We are given the following:
a = BCA = 72°b = 115 mc = 80 mPlug in the values
BC = √(115² + 80² - 2(115)(80)(cos 72)
BC ≈ 118.1 m (1 decimal place)
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Which of these correctly explains the solution of the system of equations shown below?
2 x + 3 y = 6
x + 3 y = 12
using elimination method
2x + 3y = 6 -----(1)
-
x + 3y = 12-------(2)
———————
x = 12
substitute x as 12 into equation (1) or (2), let's choose equation (1)
2(12) + 3y = 6
24 + 3y = 6
collect like terms
3y = 6 - 24
3y = 18
divide both sides by 3 ( to make y the subject of formula )
3y = 18
— —
3 3
y = 6
therefore X = 12 and y = 6
Hope this helps eh
Good luck ✅.
I REQUIRE HELP IMMEDIATELY
All the equations have been solved
What is a Quadratic Equation ?A quadratic equation is what can be represented by
ax² +bx+c = f(x)
It is given to solve the given quadratic equations
1. x² = 25
x = ± 5
2. 16x² = 25
x² = 25/16
x = ± 5/4
3. (3x+2)²= 25
9x² +4+12x = 25
9x² +12x -21 = 0
3x(3x+7) -3(3x+7) = 0
x =1
x = -7/3
4. x² = 11x
x² -11x = 0
x (x-11) = 0
x = 0, 11
5. 3x²= 14x
3x² -14x = 0
x (3x - 14) = 0
x = 0 , 14/3
6. x²+2x = 3
x²+2x -3 = 0
x (x+3) -1(x+3) = 0
x = 1 ,-3
7.x²+2x -5 = 0
determined from the formula for the roots
x=−1±√6
x=1.44949
x=−3.44949
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9. The regular admission price at a museum is
$4.50 per adult and $2.75 per child. This week,
there is a special offer that allows 1 child to get
in for half price with each paying adult. How
much would the total admission price be for
3 children and 2 adults?
Answer:
$14.4
Step-by-step explanation:
there are 2 adults so 2 children will get the discount
4.50 + 4.50 + 1.375 + 1.375 + 2.75 = $14.5
Answer:
Step-by-step explanation:
Use the property of real numbers to write the expression 2/5 x (-7)x 5/2
The simplified form of the expression 2/5 x (-7)x 5/2 would be -7.
How to solve the expression?When two fractions are multiplying each other, the numerator of both fractions multiplies each other, likewise the denominator of both fractions respectively.
Use the property of real numbers to write the expression
[tex]\dfrac{2}{5} \times (-7) \times \dfrac{ 5}{2}\\\\\dfrac{10}{10} \times (-7) \\\\-7 \times 1\\\\= -7[/tex]
Therefore, The simplified form of the expression would be -7.
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What is the period of this graph?
Answer:
Look at the pic for answer.
Step-by-step explanation:
Angles A and B are complementary. If sin A = 4x + 10 and cos B = 2x + 16, what is the value of x? (1 point) 3 4 13 22
Answer: 3
Step-by-step explanation:
The sine of an angle is equal to the cosine of its complement, so
[tex]4x+10=2x+16\\\\2x+10=16\\\\2x=6\\ \\ x=3[/tex]
the volume of a cube depends on the length of its sides.this can be written in function notation as v(s). what is the best interpretation of v(4) =64
Answer:
Interpretation: A cube with sides of 4 units each has a volume of 64 units³.
Explanation:
As v(s) represents the volume of the cube, s represents the length of the sides.
∴ v(4) represents the volume of a cube with sides of units, and the volume is 64 units³
Factor
4m^2+16m+16.
Answer:
4(m+2)²
Step-by-step explanation:
Hope this help!!
Select the correct answer. Which number best represents the slope of the graphed line? A linear function on a coordinate plane passes through (minus 6, minus 7), and (4, minus 2) also intercepts the x-axis at 8 units and the y-axis at minus 4 units. A. B. C. D.
The number best represents the slope of the graphed line is 1/2.
We have given the two points,
(-6,-7) and (4,-2) and slope-intercept is 8 units
What is the slope-intercept form of a line?
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
y = y coordinate of the second point
[tex]y_1[/tex] = y coordinate of point one
m = slope
x = x coordinate of the second point
[tex]x_{1}[/tex]= x coordinate of point one
Therefore the
[tex]slope=\frac{y_2-y_1}{x_2-x_!}[/tex]
[tex]=\frac{-2-(-7)}{4-(-6)} \\=\frac{5}{10}\\ =\frac{1}{2}[/tex]
Therefore the correct option is 1/2.
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41. Which of the following pairs of groups
shows the greatest percent difference?
A. 12 and College
B. 9-11 and 12
C. 8 and 9-11
D. 6-7 and 8
42. If 33.1 million people are 14% of the
population, what is the total population?
A. 4.6 million
B. 42.3 million
C 236.4 million
D. 463.4 million
43. What percent of the population is at or
above the poverty level?
A. 86%
B. 66.9%
C. 33.1%
D. 14%
Answer:
C
C
B
8 abd 9-11
236.4 million
66.9%
What is the approximate value of x in the diagram below? (Hint: You will need to use one of the trigonometric ratios given in the table.) sin 40° cos 40° 50° 0.643 0.766 0.839 tan 40° 90°
Answer:
x is approximately 20.89
Step-by-step explanation:
cos(40°) = 16/x
x cos(40°) = 16
x = 16 / cos(40°) = 16/.766 = 20.89
The approximate value of x in the diagram is,
⇒ x = 20.77
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Now, We can formulate by the given figure;
⇒ sin 50° = 16 / x
⇒ 0.77 = 16 / x
⇒ x = 16 / 0.77
⇒ x = 20.77
Thus, The approximate value of x in the diagram is,
⇒ x = 20.77
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Question 5 of 10
Which function is shown in the graph?
Answer:
A
Step-by-step explanation:
By looking at the graph you can eliminate B as a choice since the denominator is 1+x which means it would have a vertical asymptote as x=-1 which doesn't correspond with the graph shown. You can also eliminate C since the function doesn't have a vertical asymptote as x=3 since the denominator of the function is 3-x meaning it would be undefined at x=3. It should be A since it appears to approaching 1 with a vertical asymptote at x=1 which corresponds with the denominator 1-x. If you plug in the value 0 as x you get 3 which is what is shown on the graph when x equals 0
Which expression is equivalent to...
Answer: the fourth one
Step-by-step explanation:
Answer:
D.) 8x¹²y³
Step-by-step explanation:
When an expression is raised to a power, you have to raise everything in the expression to the power when simplifying. This includes the coefficients and variables. When a variable already raised to a power is raised to another power, the powers are multiplied.
Therefore,
2³ = 8
(x⁴)³ = x⁴*³ = x¹²
(y)³ = y³
Combined, the final answer is 8x¹²y³.
Find m angle angle KML
Answer:
52
Step-by-step explanation:
this is a triangle whose 2 sides are equalfirst take 180 which is the sum of interior angle minus 76 which is the angle givenyou will get 104 which is the other 2 anglesdivide by 2 since they are equal to get 52