The surface area of this cylinder will be 80π ft².
What is Total surface area ?
Total surface area is the total area, which includes the curved portion and any bases. It refers to the entire surface area of the thing. The total area will be equal to the sum of the two areas if the shape has a curved base and surface.
Given : height of cylinder = 3 ft
radius of base of cylinder = 5 ft
We know that, Total surface area of cylinder = 2πrh + 2πr²
= 2πr(h+r)
So, The surface area of given cylinder = 2π × 5 ( 3+5)
= 10π (8)
= 80π ft²
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A plane flies horizontally at an altitude of 5 km and passes directly over a tracking telescope on the ground. When the angle of elevation is a/4, this angle is decreasing at a rate of 1/3 rad/min. How fast is the
plane traveling at that time?
Answer:
-csc^2 θ = dθ/dt = 1/5 (dx/dt)
or
3.49 km/min
Step-by-step explanation:
dx/dt
- 5cosec^2 θ * (rate of change of angle of elevation)
- 5 cosec^2 (π/3) * (-π/6)
(5π/6) * (4/3)
= 10π/9 km/min. = 3.49 km/min
Write an equation or proportion. Define the
variable/s. Solve and label the answer/s. The
measure of the smallest angle in a triangle is 40
degrees less than the measure of the largest angle
and 20 degrees less than the measure of the next
smallest angle. What is the measure of each
angle?
Answer:
Step-by-step explanation:
40-20 =20 then times 3 which is 60.
Help (options for the first choose your answer are: bigger, stayed the same, or smaller. And for the second one its 0.5, -0.5, 2, and -2)
We can see that the scale factor is 0.5, which means that the image got smaller, and that the values are:
b' = 4
c = 14.
Which dilation was applied?If k is the scale factor applied, all the sides are modified by the same scale factor, so we know that:
a' = k*a
Here we know that:
a = 6
a' = 3
Then:
3 = k*6
3/6 = k
1/2 = k
now.
If b = 8, then:
b' = (1/2)*8 = 4
if c' = 7, then:
7 = (1/2)*c
2*7 = c
14 = c
Finally, the scale factor is smaller than 1, then the image got smaller, and the scale factor is 1/2 = 0.5
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The question is present in the problem
PLEASE HELP ALGEBRA 2 WORK
The domain of a function is all the possible input values for which the function is defined.
What is function?Function is a block of code that performs a specific task. It is a reusable piece of code that can be called from other parts of the code, reducing the amount of code that needs to be written and making the code easier to read and maintain. Functions can take in parameters and return values, allowing for increased flexibility and reusability. Functions can also be used to break up large programs into smaller, more manageable pieces.
In this case, the reasonable domain for the function f(x) = 4x³-50x²+150x would be all real numbers. This is because the function is a polynomial, which is continuous, meaning that it is defined for all real numbers.
The input of the function is a width, and the output is a volume. Therefore, the domain of the function should include all reasonable widths that could produce a volume. This means that the domain should include all positive real numbers, as any negative value would produce a negative volume, which is not reasonable. Thus, the reasonable domain for the function f(x) = 4x³-50x²+150x is all positive real numbers.
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A beetle is 1/5 inch wide and 2/5 inch long.How much greater is the beetle’s length than it’s width?
Answer: To find how much greater the beetle's length is than its width, we need to subtract the width from the length:
Length - Width
Substituting the given values, we get:
2/5 inch - 1/5 inch
Simplifying the expression by finding the common denominator of 5, we get:
(2/5 - 1/5) inch
= 1/5 inch
Therefore, the beetle's length is 1/5 inch greater than its width.
Step-by-step explanation:
The weather forecast says there is a 75% chance it will rain later today.
Draw a spinner you could use to simulate this probability
A spinner which can be use to simulate this probability is shown in figure.
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Given that;
The weather forecast says there is a 75% chance it will rain later today.
Now, We can simplify the number is,
⇒ 75%
⇒ 75/100
⇒ 3/4
Thus, We can draw A spinner which can be use to simulate this probability as shown in figure.
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Using the grouping method use this equation to put it in factored form
10. Given that xy = a², show that + a+x a+y
Employing the identity (a+b)² = a² + 2ab + b², where a and b are any real numbers.
Substituting a and b with a and x/y, respectively:
(a + x/y)² = a² + 2a(x/y) + (x/y)²
(a + x/y)² = (a + x/y)(a + x/y)
= a² + ax/y + ax/y + x²/y²
= a² + 2ax/y + x²/y²
add a² to both sides of the equation:
a² + (a + x/y)² = a² + 2ax/y + x²/y² + a²
a² + (a + x/y)² = (a² + x²/y²) + 2ax/y + a²
xy = a² substitute a² for xy in the last term:
a² + (a + x/y)² = (a² + x²/y²) + 2axy/xy + a²
a² + (a + x/y)² = (a² + x²/y²) + 2a + a²
We have that x²/y² = (xy)/(y²) = a/y, and substituting this back into the equation:
a² + (a + x/y)² = (a² + a/y + a/y) + 2a + a²
= 2a² + (2a/x) + (2a/y)
What are real numbers?A real number is described as a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.
Therefore from the mathematical expression shown above, we have shown that:
a² + (a + x/y)² = 2a² + (2a/x) + (2a/y)
This is the mathematical expression we wanted to prove.
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What is the measure of the three missing angles in the rhombus below?
Answer:
[tex]x[/tex] = 100 , [tex]y[/tex] = 100 , [tex]z[/tex] = 80
Step-by-step explanation:
Information we need to know:
Opposite angles in a rhombus are equal
Angles in a quadrilateral equal to 360
1) Find any angles that we can
We already know that opposite angles are 80. This means that we can easily see that [tex]z[/tex] is 80.
The total we have at the moment is 160
2) Find the remaining angles
If we know that all angles in a quad add up to 360, we can easily find [tex]x[/tex] and [tex]y[/tex] by taking 160 from 360 and the dividing by 2!
360 - 160 = 200200 ÷ 2 = 100[tex]x[/tex] = 100[tex]y[/tex] = 100TOP TIP:
To make sure our answer is correct we can add all our answers up and check that they add up to 360
100 + 100 + 80 + 80 = 360Our answer is correct!
Hope this helps, have a great day! :)
Answer:
x = 100
y = 100
z = 80
Step-by-step explanation:
The properties of a rhombus are:
All sides are equal in length.The opposite sides are equal and parallel.Opposite angles are congruent.Adjacent angles are supplementary (sum to 180°).Two angles are said to be adjacent when they share a common vertex.
Therefore, both angle x and angle y are adjacent to the angle that measures 80°.
Since adjacent angles in a rhombus are supplementary:
⇒ x° + 80° = 180°
⇒ x° = 100°
⇒ x = 100
Similarly:
⇒ y° + 80° = 180°
⇒ y° = 100°
⇒ y = 100
As opposite angles in a rhombus are equal:
⇒ z° = 80°
⇒ z = 80
Write a quadratic function in standard form to represent the data in the table.
X=2,4,6,8,10
Y=3,1,3,9,18
The quadratic functiοn in standard fοrm that wοuld represent the data in the table is y = 2x² + x - 9.
What is quadratic functiοn?A quadratic functiοn is a type οf pοlynοmial functiοn that can be written in the fοrm οf f(x) = ax² + bx + c, where a, b, and c are cοnstants, and x is an unknοwn variable. The graph οf a quadratic functiοn is a parabοla, and the rοοts οf the equatiοn (the x-intercepts) are the pοints where the parabοla crοsses the x-axis. Quadratic functiοns are used tο mοdel a variety οf natural phenοmena, such as the trajectοry οf a prοjectile οr the grοwth οf a pοpulatiοn οver time.
This can be determined by putting the given values intο the standard fοrm equatiοn: y = ax² + bx + c and sοlving fοr a, b and c.
When x = 2, y = 3. Therefοre, 3 = 2a + b - 9, which gives b = 11.
When x = 4, y = 1. Therefοre, 1 = 8a + 11 - 9, which gives a = -1/4.
When x = 6, y = 3. Therefοre, 3 = 18a - 1/4 + 11 - 9, which gives c = -5/4.
The quadratic equatiοn in standard fοrm, y = 2x² + x - 9, can then be written using the values οf a, b and c fοund.
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cos x = 0.4505 find angle x
We can calculate the value of {x} as 63.2°.
What are trigonometric functions?There are six major trigonometric functions as -
Sine(x) Cosine(x)Tangent(x) Cotangent(x)Secant(x) Cosecant(x)We can write the relation between them as -
Sine = 1/cosecantCosine = 1/secantTangent = 1/CotangentAlso the following trigonometry relations hold true -
sin²Ф + cos²Ф = 11 + tan²Ф = sec²Ф1 + cot²Ф = cosec²ФGiven is that -
cos{x} = 0.4505
We have -
cos{x} = 0.4505
{x} = cos⁻¹(0.4505)
{x} = cos⁻¹{cos(63.2)}
{x} = 63.2°
Therefore, we can calculate the value of {x} as 63.2°.
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In △STU , t = 1.3 inches, u = 3.5 inches and ∠S=159° . Find the length of s, to the nearest tenth of an inch. Responses 2.7
Find the exact value of tan G in simplest radical form.
2
F
√58
√54
E
Answer:
[tex] \tan G = \dfrac{3\sqrt{6}}{2} [/tex]
Step-by-step explanation:
tan G = opp/adj
[tex] \tan G = \dfrac{\sqrt{54}}{2} [/tex]
[tex] \tan G = \dfrac{\sqrt{9 \times 6}}{2} [/tex]
[tex] \tan G = \dfrac{3\sqrt{6}}{2} [/tex]
Show that cos θ/2 (1-cosθ) = sin θ/2 sinθ
can anyone write the steps please? many Thanks!
Answer:
[tex]\cos \dfrac{\theta}{2}(1-\cos \theta)=\sin \dfrac{\theta}{2} \sin \theta[/tex]
Step-by-step explanation:
[tex]\textsf{To show that}\;\;\cos \dfrac{\theta}{2}(1-\cos \theta)=\sin \dfrac{\theta}{2} \sin \theta:[/tex]
[tex]\textsf{Let}\;\;u=\dfrac{\theta}{2} \implies 2u=\theta[/tex]
Therefore:
[tex]\implies \cos \dfrac{\theta}{2}(1-\cos \theta)=\cos u(1-\cos 2u)[/tex]
Cosine Double Angle Identitiescos(A±B) = cosA cosB ∓ sinA sinB
cos(2θ) = cos²θ - sin²θ
cos(2θ) = 2cos²θ - 1
cos(2θ) = 1 - 2sin²θ
Use the cos double angle identity cos(2θ) = 1 - 2sin²θ to rewrite cos(2u) in terms of sin:
[tex]\begin{aligned}\implies \cos \dfrac{\theta}{2}(1-\cos \theta)&=\cos u(1-\cos 2u)\\&=\cos u(1-(1-2 \sin^2 u))\end{aligned}[/tex]
Simplify:
[tex]\begin{aligned}\implies \cos \dfrac{\theta}{2}(1- \cos \theta)&=\cos u(1- \cos 2u)\\&=\cos u(1-(1-2 \sin^2 u))\\&=\cos u(1-1+2 \sin^2 u)\\&= \cos u(2 \sin^2 u)\\&=2 \sin u \cos u \sin u\end{aligned}[/tex]
Sine Double Angle Identitiessin(A±B) = sinAcosB ± cosAsinB
sin(2θ) = 2sinθcosθ
Using the sine double angle identity to rewrite 2sin(u)cos(u) as sin(2u):
[tex]\begin{aligned}\implies \cos \dfrac{\theta}{2}(1-\cos \theta)&=\cos u(1- \cos 2u)\\&=\cos u(1-(1-2 \sin^2 u))\\&= \cos u(1-1+2 \sin^2 u)\\&= \cos u(2 \sin^2 u)\\&=2 \sin u \cos u \sin u\\&= \sin(2u) \sin u\end{aligned}[/tex]
Finally, substitute u = θ/2 back in:
[tex]\begin{aligned}\implies \cos \dfrac{\theta}{2}(1-\cos \theta)&=\cos u(1-\cos 2u)\\&=\cos u(1-(1-2 \sin^2 u))\\&=\cos u(1-1+2 \sin^2 u)\\&= \cos u(2\sin^2 u)\\&=2\sin u\cos u \sin u\\&=\sin(2u) \sin u\\&=\sin\left(2 \cdot \dfrac{\theta}{2}\right) \sin \dfrac{\theta}{2}\\&=\sin \theta \sin \dfrac{\theta}{2}\\&=\sin \dfrac{\theta}{2} \sin \theta \end{aligned}[/tex]
If you don't want to substitute u = θ/2, the full calculation using the same double angle identities is:
[tex]\begin{aligned}\implies\cos\dfrac{\theta}{2}(1-\cos\theta)&=\cos\dfrac{\theta}{2}\left(1-\left(1-2\sin^2\dfrac{\theta}{2}\right)\right)\\\\&=\cos\dfrac{\theta}{2}\left(1-1+2\sin^2\dfrac{\theta}{2}\right)\\\\&=\cos\dfrac{\theta}{2}\left(2\sin^2\dfrac{\theta}{2}\right)\\\\&=2\sin \dfrac{\theta}{2}\cos \dfrac{\theta}{2} \sin \dfrac{\theta}{2}\\\\&=\sin\left(2\cdot\dfrac{\theta}{2}\right)\sin\dfrac{\theta}{2}\\\\&=\sin\theta\sin\dfrac{\theta}{2}\\\\&=\sin\dfrac{\theta}{2}\sin\theta \end{aligned}[/tex]
What would the missing length be?
Answer:
B
Step-by-step explanation:
step by step you will learn
A water balloon is dropped at 144 feet.
A) After how many seconds does the water balloon touch the ground.
B) Suppose the initial height is adjusted by k feet. How does this affect part (a)?
when k _ 0, the water balloon will take more than _ seconds to hit the ground when k _ 0, the water balloon will take less than _ seconds to hit the ground
Answer: I dont understand the answer that much but off of what i understand i think the answer is A
Step-by-step explanation: I am not sure but i think so
Write an equation in slope-intercept form for the line with y-intercept -7 and slope 1/4
Answer:
Step-by-step explanation:
So your slope intercept is on the y line to you will go to your y line and find the -7
Once you find your -7 you rise 1 and run 4 which mean go up by 1 and right by 4
Hope this helps!!
What the tape diagram and how to find the equation true.
Answer:
20=2g
g=10
20/2=10
g=10
Melissa has a savings account. She deposited $1,000 into the account the first year. For each year after the first, she plans to deposit an amount that is 2 percent greater than the amount deposited the preceding year. If she makes no other deposits, the total amount of the deposited money in years is the sum Sn
of a geometric series of n terms.
The formula for Sn
can be expressed as (1000(1−rn)1−r)
.
Melissa will have deposited approximately how much by year 30?
Responses
A.$30,000
B.$35,729
C.$40,568
D.$87,453
Answer:
Step-by-step explanation:
The formula for Sn of a geometric series with first term a and common ratio r is:
Sn = a((1-r^n)/(1-r))
In this case, the first term a is $1,000, the common ratio r is 1.02 (since she's depositing 2% more each year), and n is 30 (since we're looking for the amount deposited after 30 years).
Plugging in these values, we get:
Sn = 1000((1-1.02^30)/(1-1.02))
Sn ≈ $87,453
Therefore, the answer is D. $87,453.
Help! Factoring Bottoms up method:
1. 2x²-9x-18=0
2. 8x²+2x-3=0
3. 5x²-11x+2=0
In response to the query, we have that Hence, the following are the answers to this equation: 5x - 2 = 0 or x - 1 = 0 Thus, x = 2/5 or x = 1.
What is quadratic equation?A quadratic equation in a single variable is x ax2+bx+c=0, a form of quadratic equation. a 0. The fact that this polynomial is of second sample guarantees that it comprises at least one solution according to the Basic Theorem of Algebra. Solutions might be straightforward or difficult. A quadratic equation is one that has four variables. This suggests that at least single word in it has to be rounded. The formula "ax2 + bx + c = 0" constitutes one of the widely used solutions for complex numbers. where the undefined variable "X" is represented by the numerical values or constants a, b, and c.
2x² - 9x - 18 = 0
Secondly, we must identify two integers whose total is -9 and whose product is 2(-18)=-36. These are the numbers -12 and +3. Hence, we may say:
2x² - 9x - 18 = (2x + 3)(x - 6) = 0
Hence, the following are the answers to this equation:
2x + 3 = 0 or x - 6 = 0
Thus, x = -3/2 or 6.
8x² + 2x - 3 = 0
8x² + 2x - 3 = (4x - 3) (4x - 3)
(2x + 1) = 0
Hence, the following are the answers to this equation:
4x - 3 = 0 or 2x + 1 = 0
Thus, either x = 3/4 or x = -1/2.
5x² - 11x + 2 = 0
5x² - 11x + 2 = (5x - 2)(x - 1) = 0
Hence, the following are the answers to this equation:
5x - 2 = 0 or x - 1 = 0
Thus, x = 2/5 or x = 1.
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A student has a container with a volume of 1.5 liters. She estimates the volume to be 2.1 liters. By what percent is the student's estimate off?
Answer:
40% (high)
Step-by-step explanation:
You want to know the percentage error when an actual value of 1.5 L is estimated to be 2.1 L.
ErrorThe percentage error is given by ...
(percent error) = (estimate/actual - 1) × 100%
percent error = (2.1/1.5 -1) × 100%
= (1.40 -1.00) × 100% = 0.40 × 100%
= 40%
The student's estimate is 40% too high.
Please help with this problem
On the number line, the points that represent the values of x in - 1 < x < 3 are:
012What are the values of x ?The expression given is - 1 < x < 3 which means that x is any whole number that is greater than - 1 but less than 3. This means that on the number line given, the value of x would be any number that is more than - 1 but less than 3.
These numbers will include 0, 1, and 2. The line should therefore begin at -1 and go to 3 to show the values of x in - 1 < x < 3 . The line to use should be the open circle which shows greater than or less than
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What is the value of the following function when x = 0?
-5-4-3-
y=-5
(1
5
-4
3-
-2
1
2 3 4
351
X
Answer:
3.3.1 Approximations for trigonometric functions. 3.3.2 ... 7.2.1 Consistency for three simultaneous linear equations in two unknowns ... x : y : z =5:4:3;.
A. x > 19
B. x _> 19
C. x < 19
D. x_< 19
Answer:
C) x < 19
Step-by-step explanation:
It is an open circle pointing in the negative direction starting at 19.
Which equations represent a proportional relationship?
A) y = 5 + x
B) y = 4x
C) y = 7x²
D) y = 2 - x
The equation which represents a proportional relationship from the given set of equations is y = 4x.
What is meant by a proportional relationship?
Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportional relationship, one variable is consistently equal to the other's constant value. y= k x, where k is the proportionality constant, is the equation that depicts a directly proportional relationship, or a line. y = k(1/x) or xy = k, where k is the proportionality constant, is the equation that depicts an indirectly proportional relationship, or a line. One can argue that two variables are in a proportional relationship if one variable is always equal to a constant multiplied by the other variable.
So according to the above explanation, we can say that the equation y = 4x is an example of a proportional relationship.
This is because the ratio y/x is always a constant 4.
Therefore the equation which represents a proportional relationship is y = 4x.
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Which of the following are solutions to the system of inequalities y<−x+5 and y≥3x+1? Select all that apply.
The only solution to the system of inequalities y < −x+5 and y ≥ 3x+1 is (1,3).
What are the inequalities?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
For the inequality y < -x + 5, any point below the line y = -x + 5 will satisfy the inequality. For the inequality y ≥ 3x + 1, any point on or above the line y = 3x + 1 will satisfy the inequality.
To find the solutions that satisfy both inequalities, we can shade the region that is below the line y = -x + 5 and also on or above the line y = 3x + 1. This region is the shaded triangle bounded by the lines y = -x + 5, y = 3x + 1, and the x-axis.
Therefore, the solutions to the system of inequalities are the points in this shaded triangle. To check which options are solutions, we can substitute the values of x and y given in each option into both inequalities and check if they satisfy both.
(0,2): y < -x + 5 is true because 2 < -0 + 5. y ≥ 3x + 1 is false because 2 < 3(0) + 1. Therefore, (0,2) is not a solution.(1,3): y < -x + 5 is true because 3 < -1 + 5. y ≥ 3x + 1 is true because 3 ≥ 3(1) + 1. Therefore, (1,3) is a solution.(2,1): y < -x + 5 is true because 1 < -2 + 5. y ≥ 3x + 1 is false because 1 < 3(2) + 1. Therefore, (2,1) is not a solution.(3,6): y < -x + 5 is false because 6 ≥ -3 + 5. y ≥ 3x + 1 is true because 6 ≥ 3(3) + 1. Therefore, (3,6) is not a solution.Hence, the only solution is (1,3).
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Complete question:
Which of the following are solutions to the system of inequalities y < −x+5 and y ≥ 3x+1?
Select all that apply.
a. (0,2)
b. (1,3)
c. (2,1)
d. (3,6)
Gwen has $800 in a savings account that earns 10% annually. The interest is not compounded .How much interest will she earn in 1 year?
Need help ASAP!!!!!!!!!
ΔQRS ≅ ΔTUV and ΔTUV ≅ ΔXYZ then ΔXYZ ≅ ΔQRS by Transitive Property.
ΔEFG ≅ ΔJKL then ΔJKL ≅ ΔEFG using Symmetric Property.
What is Transitive Property?The transitive property of congruence states that “ if two shapes are congruent to the third shape, then all the shapes are congruent to each other.
This is the transitive property at work: if a=b and b=c, then a=c.
First, ΔQRS ≅ ΔTUV and ΔTUV ≅ ΔXYZ
The property of Transitivity shows for any angle <A, <B and <C.
So, <A = <B and <B = <C then <A = <C
Second, The property of Symmetry shows or any angle <A, <B
if <A≅ <B then <B≅ <A
So, ΔEFG ≅ ΔJKL then ΔJKL ≅ ΔEFG using Symmetric Property.
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g(n)=−50−15n. complete the recursive formula of g(n).
Answer: To complete the recursive formula for g(n) = -50 - 15n, we need to find an expression for g(n) in terms of previous terms of the sequence.
One way to do this is to notice that g(n) can be obtained by subtracting 15 from the previous term, g(n-1):
g(n) = -50 - 15n
= -50 - 15(n-1) - 15 (adding and subtracting 15)
= g(n-1) - 15
Therefore, the recursive formula for g(n) is:
g(0) = -50 (base case)
g(n) = g(n-1) - 15 (recursive step)
This means that to find g(n), we need to first find g(n-1) and then subtract 15 from it. We can use this recursive formula to generate any term in the sequence of g(n).
Step-by-step explanation: