Step-by-step explanation:
If r and h are the radius and height of the cylinder, then its surface area A is given by :
[tex]A=2\pi r^2+2\pi rh[/tex] ....(1)
We need to find the cylinder's height in terms of its radius and surface area. Subtracting [tex]2\pi rh[/tex] on both sides, we get :
[tex]A-2\pi r^2=2\pi rh+2\pi r^2-2\pi r^2\\\\A-2\pi r^2=2\pi rh[/tex]
Dividing both sides by [tex]2\pi r[/tex]. So,
[tex]\dfrac{A-2\pi r^2}{2\pi r}=\dfrac{2\pi rh}{2\pi r}\\\\h=\dfrac{A-2\pi r^2}{2\pi r}[/tex]
Hence, this is the required solution.
If a wheel has a radius of 5cm
how much is one rotation of the wheel
How many rotations can the wheel do within a distance of 50km
Answer:
circumference = 2*PI*radius
circumference = 2 * PI * 5 cm
circumference = 31.4159265358979 cm
50 km = 500,000 centimeters
rotations = 500,000 / 31.4159 cm
15,915.51 rotations
Step-by-step explanation:
Please help! I don’t get it much
9514 1404 393
Answer:
∠BDC = 46°
Step-by-step explanation:
Angle BDC intercepts arc BC, identified as having a measure of 92°. The angle's vertex, point D, is on the circle, so the angle is called an "inscribed angle." The measure of an inscribed angle is half the measure of the arc it intercepts.
∠BDC = (1/2)arc BC = 1/2(92°)
∠BDC = 46°
G is a transformation of f. What is the formula of g in terms of f?
A. [tex]-\frac{1}{2}f(x)[/tex]
B. -2f(x)
C. f ([tex]-\frac{1}{2}x[/tex])
D. f(-2x)
Answer:
C
Step-by-step explanation:
First, we can see that from f(x) to g(x), the change in x for each change in y is significantly increased. This represents a stretch in the x direction. A stretch/compression in the x direction is represented by
f(cx), with c > 1 representing a compression by c and 0 < c < 1 representing a stretch by a value of 1/c. From the vertex of each, when y changes by 1, in f(x) x changes by 2 (e.g. from x=2 to x=4), whereas in g(x) x changes by 4 (e.g. from x=-4 to x=0). Therefore, g(x) stretches x by 2, so c = 1/2, giving us
f(c(x))
= f(1/2(x))
Let's say f(a) = f(1/2(x))
Then, because the graph stretched by 2, the vertex goes from x=2 to x=4. Our vertex is at x=-4 in g(x), so to make the vertex equal to that, we can flip f(a) around the y axis. To flip this around the y axis, we can plug -a in for a, resulting in
f (-(a))
= f(-(1/2)(x))
= g(x)
Triangle QRP is congruent to triangle YXZ. What is the perimeter of triangle YXZ?
What is the perimeter of triangle YXZ?
Answer:
Perimeter of XYZ = Perimeter of QRP
Step-by-step explanation:
Since congruent then
P of XYZ = P of QRP
Which graph represents the solution to the system of equations? {x+2y=4 2x−y=1/2}
Answer:
Below
Step-by-step explanation:
I graphed the functions here
The graph is shown below:
What is graphing ?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
The graph of a linear equation in one variable x forms a vertical line that is parallel to the y-axis and vice-versa, whereas, the graph of a linear equation in two variables x and y forms a straight line
As, per the given equations
x+2y=4 & 2x−y=1/2.
The document attached with the question shows the fourth graph correct.
The intersecting point of both line is (1, 1.5)
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Consider function f. (-412 + 6.3 + 36, 1 < -2 15, 2 < I 4 Are the statements about the graph of function ftrue or false? true false 2 false The graph crosses the y-axis at (0.–15). The graph has a point of discontinuity at I = The graph is increasing over the interval (4, co) The graph is decreasing over the interval (-12, -2). false The domain of the function is all real numbers. false
Please help
Answer:
Behold.
Step-by-step explanation
The answer to the statement is 1)false 2) false 3) true 4) true and 5) false.
Given functions,f
1) For x ≤ -2: f(x) = -12 + 6x
2) For -2 < x < 1: f(x) = 41 - 15x
3) For x ≥ 1: f(x) = 31 - 4x
1) The graph crosses the y-axis at (0, -15).
This is false because if x = 0, the function value would be -12 + 6 * 0 = -12, not -15.
2) The graph has a point of discontinuity at x = 1.
This is false because the function is defined at x = 1 there is no space, so there is no point of discontinuity at x = 1.
3) The graph is increasing over the interval (4, ∞).
This is true because the coefficient of x in the function's expression is negative, showing that it is decreasing. Therefore, as x increases, the function values decrease.
4) The graph is decreasing over the interval (-12, -2).
This is true because the coefficient of x in the first piece of the function (-12 + 6x) is positive, showing an increasing trend. Therefore, as x decreases from -12 to -2, the function values increase.
Statement 5: The domain of the function is all real numbers.
This is false because the domain of the function is limited by the intervals in its definition. The function is defined differently for different intervals of x.
So, the answer to the statement is
1) false
2) false
3) true
4) true
5) false
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plz help me this will be appreciated
Answer:
1. h
2. b
3. a
4. d
5. c
Step-by-step explanation:
all answers are straight forward. only the last (5) is phrased a bit strangely. I would have said "reflect across a horizontal line".
Find the quotient and remainder when p (x) divides with g (x) question (i) P (x) = x raise to 4 - 3 x square +4x + 5, g (x) = x square +5
Answer: [tex]x^2-8+\dfrac{4x+5}{x^4-3x^2+4x+5}[/tex]
Step-by-step explanation:
P(x) = x⁴ - 3x² + 4x + 5
g(x) = x² + 5
_x²_- 8
x² + 5) x⁴ + 0x³ - 3x² + 4x + 5
-(x⁴ + 0x³ + 5x²) ↓ ↓
-8x² + 4x + 5
-(-8x² + 0x - 40)
4x + 45
[tex]\dfrac{x^4-3x^2+4x+5}{x^2+5}=\large\boxed{x^2-8+\dfrac{4x+5}{x^4-3x^2+4x+5}}[/tex]
6. Alex and Brian park their bikes side-by-side. Alex leaves to visit friends, and Brian leaves 30 minutes later,
headed for the same destination. Alex pedals 5 miles per hour slower than Brian. After 1 hour, Brian passes Alex. At
what speed are they each pedaling?
Answer:
See below.
Step-by-step explanation:
When Brian passes Alex they both have travelled the same distance.
Call this distance d.
Let the speed that Brian passes = x miles/hour.
Distance = speed * time so:
For Alex:
d = (x - 5) * 1.5 ( Alex cycles for 1 + 30 minutes = 1.5 hours)
For Brian:
d = x * 1
So substituting d = x in Alex's equation:
x = 1.5(x - 5)
x = 1.5x - 7.5
7.5 = 0.5x
7/5 / 0.5 = x
15 = x.
ANSWER:
Brian's speed is 15 miles/hour.
Alex's speed is 15 - 5 = 10 miles/hour.
at old oak farm, there are chicken and horses. there are 120 legs and 48 heads altogether. how many horses and how many chickens are there?
Answer:
Step-by-step explanation:
We must use system of equations:
horses = h chickens = c
horses have 4 legs & chickens have 2 and there are 120 legs total so to set up the first part of the equation...
4h + 2c = 120
They both have only 1 head each and there are 48 heads total so to set up the second part of the equation...
h + c = 48
Now we combine the equations and solve:
4h + 2c = 120
h + c = 48
Now we solve...
4h + 2c = 120
h = 48 - c (subtract c on both sides to single out h)
--------------------
4(48 - c) + 2c = 120
192 - 4c + 2c = 120
-192 -192
----------------------------
-2c = -72 (divide both sides by -2)
c = 36
Now we go back and find the value of h...
h = 48 - c
h = 48 - 36
h = 12
So there are 36 chickens & 12 horses!
0,2,4,0,2,3,2,8,6
What is the mean?
What is the median?!
What is the first quartile (Q1)?!
What is the third quartile (Q3)?
What is the minimum?
What is the maximum?
What is the interquartile range of the data?!
Answer:
LOOK BELOW
Step-by-step explanation:
Mean= add all of the numbers together and divide by total amount of
numbers
aka=3
Median= put all the numbers in order and find the number in the middle
aka=2.5
Minimum=0
Maximum=8
This data can only be found using a Box and Whisker Plot....
I can't really explain a box and whisker plot so you have to look that up to understand that.. SRY!!!
------------------------------------
First Quartile=1
Third Quartile=5
Interquartile Range=4
Answer:
Mean= add all of the numbers together and divide by total amount of
numbers
aka=3
Median= put all the numbers in order and find the number in the middle
aka=2.5
Minimum=0
Maximum=8
This data can only be found using a Box and Whisker Plot....
I can't really explain a box and whisker plot so you have to look that up to understand that.. SRY!!!
------------------------------------
First Quartile=1
Third Quartile=5
Interquartile Range=4
Step-by-step explanation:
Point E is on line segment DF. Given DE
EF.
6 and DF =9, determine the length EF
Answer:
3Step-by-step explanation:
IF point E lies on the line segment DF, this means that all the points DEF are collinear and DE+EF = DF.
Given parameter
DE = 6
DF = 9
Required
EF
Substituting the given parameter into the expression above to get the required will be;
DE+EF = DF.
EF = DF-DE
EF = 9-6
EF = 3
Hence the length of EF is equivalent to 3
Which of the following statements is false?
Answer:
c
Step-by-step explanation:
AB and CD are opposite sides of quadrilateral.
If AC = 40, find the length of JK.
Answer:
JK = 24
Step-by-step explanation:
Δ BKJ and Δ BCA are similar triangles and ratios of corresponding sides are equal, that is
[tex]\frac{JK}{AC}[/tex] = [tex]\frac{BK}{BC}[/tex] , substitute values
[tex]\frac{JK}{40}[/tex] = [tex]\frac{3}{5}[/tex] ( cross- multiply )
5JK = 120 ( divide both sides by 5 )
JK = 24
the triangles are all similar, because they have proportional sides and equal angles.
if you assume the smallest, equal part of side to be x
the biggest triangle has "5 parts" so BC=5x and BK has 3 parts so BK=3x .
since they're similar, ratio of their corresponding sides is constant or equal.
[tex] {BK\over BC}={JK \over AC}[/tex]
BK/BC=3/5
and AC=40
so JK = 40*3/5=24
PLEASE HELP!!!! I’m about to rip my hair out over this.
1. A ball is thrown into the air at an initial velocity of 18 meters per second from an initial height of 10 meters. The equation that models the path of the ball is given by h=-4.9t^2+18t+10. When does the ball reach its Maximum height?
2. A ball is thrown into the air at an initial velocity of 18 meters per second from an initial height of 10 meters. The equation that models the path of the ball is given by h=-4.9t^2+18t+10. When does the ball hit the ground?
3. A ball is thrown into the air at an initial velocity of 18 meters per second from an initial height of 10 meters. The equation that models the path of the ball is given by h=-4.9t^2+18t+10. How high is the ball at 3 seconds?
4. Logan is doing a handstand dive from a 12 meter platform. The equation that models the path of her dive is given by h=-4.9t^2+12, where t is seconds. At what height will she be after 1 second?
I absolutely hate math with all of my heart.
Step-by-step explanation:
1. The equation graph is a parabola, so the maximum height will be the vertex of the parabola. You can find the vertex coordinate t using the formula:
t = -b/2a
t = -18/2•(-4.9)
t = -18/-9.8
t = 1.84 seconds
2. The height of the ground is 0, so the balls hit the ground when the equation result is 0:
0 = -4.9t²+18t+10
Now you solve it using Bhaskara:
Δ = b² -4ac
Δ = 18² -4•(-4.9)•10
Δ = 520
t = (-b ±√Δ)/2a
t = (-18 ± √520)/2•(-4.9)
t1 = (-18 - 20.8)/-9.8
t1 = 3.96 seconds
t2 = (-18 +20.8)/-9.8
t2 = -0.28
Doesn't exist negative time, so we pick the first value found, t = 3.96 seconds
3. Now you just need to put 3 in place of t to find the result:
h = -4.9•3² +18•3 +10
h = -4.9•9 + 54 + 10
h = -44.1 + 64
h = 19.9 meters
4. You just need to put 1 in place of t to find the height:
h = -4.9•1²+12
h = -4.9+12
h = 7.1 meters
find the value of a and b in each of the following diagrams.
Answer:
a=122
b=115
Step-by-step explanation:
We have a hexagon inscribed of a Circle. Let use some obvious properties to solve some of the angles.
The upper triangle that includes 112 and 30, have a missing angle. We can use triangle interior Theorem to find the missing third angle.
The missing angle is 38.
The upper trapezoid is a cyclic quadrilateral. It 4 vertices touched the circle circumference. This means the opposite angles of the trapezoids are supplementary.
The lower left angle of the upper trapezoid measure is 65. Part of that angle is 38 so the other part is
[tex]65 - 38 = 27[/tex]
Angle b forms a linear pair with the lower left angle so
[tex]b + 65 = 180[/tex]
[tex]b = 115[/tex]
Angle a is also a cyclic quadrilateral so
Angle a and 58 are supplementary
[tex]58 + a = 180[/tex]
[tex]a = 122[/tex]
please solve this fast.
Answer:
- 24 - 70i
Step-by-step explanation:
Given
([tex]\sqrt{5}[/tex] - 7i)²
= ([tex]\sqrt{5}[/tex] - 7i)([tex]\sqrt{5}[/tex] - 7i)
= 5 - 7[tex]\sqrt{5}[/tex] i - 7[tex]\sqrt{5}[/tex] i + 49i² ( note that i² = - 1 )
= 5 - 14[tex]\sqrt{5}[/tex] i - 49
= - 44 - 14[tex]\sqrt{5}[/tex] i
Answer:
Step-by-step explanation:
(a - b)² = a² - 2ab + b²
[tex][\sqrt{5} - 7i]^{2}= (\sqrt{5})^{2} - 2*\sqrt{5}*7i + (7i)^{2}\\\\\\= 5 - 14i\sqrt{5}+7^{2}*i^{2}]]= 5 -14i\sqrt{5} +49 * -1\\\\= 5 -14i\sqrt{5} - 49\\\\= -44 - 14i\sqrt{5}[/tex]
The equations y=x22−8 and y=2x−2 are graphed below. What are the solutions to the equation x22−8=2x−2?
A
x=−8 and x=−2
B
x=−6 and x=10
C
x=−4 and x=4
D
x=−2 and x=6
Answer:
x= -2 and x = 6
Step-by-step explanation:
The solutions are where the two graphs intersect
x=6, y= 10 is one point
x=-2 and y = -6 is the other point
The intersection points of both the equations are the solutions
From the graph the points are
(6,10)(-2,-6)Hence
x=-2 and x=6 are the solutions
Option D
Which inequality is graphed on the coordinate plane shown?
A
y≥2x−6
B
y<2x−6
C
y>2x−6
D
y≤2x−6
Answer:
y ≤ 2x-6
Step-by-step explanation:
First find the equation of the line
The y intercept is -6
The slope is 2
y = 2x-6
The line graphed is solid so we know that there is an equal sign
We are graphing below the line
y ≤ 2x-6
I NEED HELP PLEASE FIRST ONE TO ANSWER THIS RIGHT GETS 5 STARS !
Answer:
The answer is 2Step-by-step explanation:
[tex] {32}^{ \frac{1}{5} } [/tex]To solve the question first write 32 in exponential form
That's
[tex]32 = {2}^{5} [/tex]Multiply the exponent by 1/5
That's
[tex] {2}^{5 \times \frac{1}{5} } [/tex]We have the final answer as
2Hope this helps you
Answer:
2
Step-by-step explanation:
32 ^ (1/5)
Rewriting 32 as 2^5
2^5 ^ 1/5
We know that a^b^c = a^ ( b*c)
2^ ( 5*1/5)
2^1
2
simplify 3/7
into a whole number
Answer:
You can't because it's not a "full fraction" like 7/7. The best you can do is turn that into a decimal like 0.43
Step-by-step explanation:
what is the range of the function on the graph (1,2),
Answer:
gu is the answer of range of function on graph
Given the function g(x) = x^2 + 5x + 14, determine the average rate of change
of the function over the interval 1 < x < 7.
Answer:
13
Step-by-step explanation:
The average rate of change is
f(7) - f(1)
---------------
7-1
f(7) = 7^2 + 5*7 +14 = 49 +35 +14=98
f(1) = 1^2 +5(1)+14 = 1+5+14=20
98-20
--------
7-1
78/6
13
Review what you know about products and sums represented by rectangular area models. [5 points] Use algebra tiles to multiply (x-1)(3x+2).
3x^2 - x - 2
What are some ways to solve an equation?
Different ways to solve equations. We have 4 ways of solving one-step equations: Adding, Substracting, multiplication, and division. If we add the same number to both sides of an equation, both sides will remain equal.
How do you evaluate an equation?
∫ y2+y−2dy ∫ y 2 + y − 2 d y∫ 2 1 y2 +y−2dy ∫ 1 2 y 2 + y − 2 d y∫ 2 −1 y2 +y−2dy ∫ − 1 2 y 2 + y − 2 d y= (x - 1)(3x + 2)
= 3x^2 + 2x - 3x - 2
= 3x^2 - x - 2
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30 POINTS!! Quadratic function F(x) =2x^2- 4x- 6 is shown below. Which describes the domain of this function.
A. All real numbers greater than or equal to -8
B. All real number less than or equal to -8
C. All real number greater than 10
D. All real numbers
Answer:
D. All real numbers
Step-by-step explanation:
The domain is the set of values that can be used for x. There is no restriction on x, so the domain is all real numbers.
Answer:
all real numbers
Step-by-step explanation:
The domain is the possible input values
Since x can be any value, the domain is all real numbers
Given triangle ABC is similar to triangle DEF , calculate the value of BC. Picture is below
Hello! :)
Answer:
[tex]\huge\boxed{BC = 6.4 }[/tex]
Given ΔABC ~ ΔDEF, we can set up a proportion to solve for BC, where:
[tex]\frac{AC}{DF} = \frac{BC}{EF}[/tex]
Let BC = x:
[tex]\frac{8}{15} = \frac{x}{12}[/tex]
Cross multiply:
[tex]8 * 12 = 15 * x[/tex]
[tex]96 = 15x[/tex]
[tex]x = 6.4[/tex]
Therefore, BC = 6.4 units.
Hope this helped you!
1.
The Springfield Meteorological Center wanted to determine the accuracy of their weather forecasts. They
searched their records for those days when the forecaster had reported a 70% chance of rain. They
compared these forecasts to records of whether or not it actually rained on those particular days. The
forecast of 70% chance of rain can be considered very accurate if it rained on:
A. 95% to 100% of those days.
B. 85% to 94% of those days.
C. 75% to 84% of those days.
D. 65% to 74% of those days.
E
55% to 64% of those days.
Answer:
The correct option is;
D. 65% to 74%
Step-by-step explanation:
The accuracy of a forecast given based on a percentage or proportion or likelihood is determined by the based on the prevalence of the forecast in a similar proportion over the range of data points in which the forecast is made
Therefore, if it actually rained on 70% of those days for which the forecast was made, the forecast can be said to be very accurate.
Which is to say that the forecast of 70% chance of rain can be considered very accurate if it rained on 65 to 74% of those days which is in the range of the forecasted 70%.
Find the slope of the line passing through the points -4,-3 and 8,-9
Answer:
-3/4
Step-by-step explanation:
Slope = Rise/Run
Between -4 and 8, the line runs 12 units. Between -3 and -9, the line rises -9 units.
-9/12 = -3/4
Answer:
-3/4
Step-by-step explanation:
36. What is the solution to x+3 = -6?
HELP! answer if you can!
Answer:
x = -9
Step-by-step explanation:
subtract 3 from both sides
x = -9
Answer:
x = -9
Step-by-step explanation:
x + 3 = -6
Subtract 3 from both sides.
x + 3 - 3 = -6 - 3
x = -9
whats the squareroot of 144 needs to be simplified
Answer:
12
Step-by-step explanation:
The square root of any number is basically asking "what number multiplied by itself will equal this number?"
Usually you memorize these, but there's also a quick way to do it.
We know that [tex]10\cdot10=100[/tex], so the square root must be greater than 10.
We also know that [tex]15\cdot15=225[/tex], so the square root must be less than 15.
A good mid point between these numbers is 13. Let's see what 13 squared is:
[tex]13\cdot13=169[/tex]
So it's a bit less than 13. Let's try 12.
[tex]12\cdot12=144[/tex]
So 12 is the square root of 144.
Hope this helped!
Answer:
[tex]\huge\boxed{\sqrt{144}=12}[/tex]
Step-by-step explanation:
[tex]\begin{array}{c|c}144&2\\72&2\\36&2\\18&2\\9&3\\3&3\\1\end{array}\\\\144=2\cdot2\cdot2\cdot2\cdot3\cdot3=2^2\cdot2^2\cdot3^2\\\\\sqrt{144}=\sqrt{2^2\cdot2^2\cdot3^2}=\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt{3^2}=2\cdot2\cdot3=12\\\\\text{Used}\\\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\sqrt{a^2}=a\\\\\text{for}\ a\ge0,\ b\geq0[/tex]