Answer:
Period=6
Step-by-step explanation:
Given:
t=1cos(1.05h)+37
Using acos(bx-c)+d to find the period of the given function
amplitude= a
period= 2π/Bb
phase shift=c (positive is to the left)
vertical shift=d
comparing with t=1cos(1.05h)+37, we get
a=1
b=1.05
c=0
d=37
period= 2π/b
=2π/1.05
=5.983
=6
Period of function is 6, after every 6 hours the refrigerator sensor will reach its maximum temperature and the cycle will move towards reducing temperature i.e it'll reach the minimum temperature then again the cycle will move upwards raising the temperature to maximum and so one period will be completed!
Answer:
6
Step-by-step explanation:
Felicity set the thermostat of her refrigerator to 37°F. The refrigerator temperature t in degrees Fahrenheit h hours after the temperature sensor in the refrigerator is activated satisfies t=1cos(1.05h)+37. Therefore, the period of the function is 6.
What is the volume of the following triangular prism?
288 ft3
480 ft3
96 ft3
576 ft3
The base is a right triangle with side lengths of 6 and 8 ft.
The area of a triangle is 1/2 x base x height = 1/2 x 6 x 8 = 24 square feet.
Now to find the volume, multiply the area by the height:
24 square ft x 12 ft = 288 ft^3
Answer:
i think it is 288 ft^3
Step-by-step explanation:
If a baseball player hits a baseball from 4 feet off the ground with an initial velocity of 64 feet per second, how long will it take the baseball to hit the ground? Use the equation h = −16t2 + 4t + 4. Round your answer to the nearest hundredth.
please answer asap
Answer:
t = 4.06 sec
Step-by-step explanation:
First of all, if the initial velocity is 64 feet per second, then the parabola should actually look like this:
[tex]h(t)=-16t^2+64t+4[/tex]
The initial velocity is in the place of our linear term, so it should be 64 not just 4.
Anyways, the h(t) value represents the height of the object after a certain number of seconds, t, it was launched from the initial height. We are looking for the length of time it takes the object to hit the ground. The height of something on the ground is 0. So we replace h(t) with a 0 and factor to solve for the values of t:
[tex]0=-16t^2+64t+4[/tex]
If you plug that into the quadratic formula to factor it, you will get that the values of t are
t = -.06 seconds and
t = 4.06 seconds
We all know that the 2 things in math that will never EVER be negative are time and distance/measures, so we can safely disregard the negative value of time.
It takes the ball 4.06 seconds to hit the ground when it is launched from an initial height of 4 feet.
Dirt cut 2 ft deep from a section of land 33 ft by 65 ft is used to fill a section 23 ft by 22ft to a depth of 4 how many cubic yards of dirt are left after the fill
Answer:
83 25/27 yd³
Step-by-step explanation:
Assuming a 4 ft depth of fill, the cut volume is ...
(2 ft)(33 ft)(65 ft) = 4290 ft³
The fill volume is ...
(23 ft)(22 ft)(4 ft) = 2024 ft³
The left over dirt occupies a volume of ...
4290 ft³ -2024 ft³ = 2266 ft³ = (2266 ft³)(1 yd³)/(27 ft³) = 83 25/27 yd³
HELP ME!!!
Select the correct answer from the drop-down menu.
The value of x that satisfies the equation is °.
Answer:
210 is the only choice I see listed that works.
Step-by-step explanation:
I don't know if you know this but you can apply a co-function identity here giving you the equation:
[tex]cos(x)=-\frac{\sqrt{3}}{2}[/tex].
If you are unsure of the identity sin(90-x)=cos(x) then I can show you another identity that leads to this one.
The difference identity for sine is sin(a-b)=sin(a)cos(b)-sin(b)cos(a).
Applying this to sin(90-x) gives you sin(90)cos(x)-sin(x)cos(90).
Let's simplify that using that sin(90)=1 while cos(90)=0:
sin(90-x)=sin(90)cos(x)-sin(x)cos(90)
sin(90-x)=1cos(x)-sin(x)(0)
sin(90-x)=cos(x)
You can also prove this identity using a right triangle like the one in this picture:
That missing angle is 90-x since we need the angles in this triangle to add up to 180 which it does:
(x)+(90)+(90-x)
x+90+90-x
x-x+90+90
0+180
180
Anyways you should see that sin(90-x)=b/c while cos(x)=b/c.
Since they are equal to the same ratio, then you can say sin(90-x)=cos(x).
There are other co-function identities you can get from using this idea.
Anyways back to the problem.
We are solving:
[tex]cos(x)=-\frac{\sqrt{3}}{2}[/tex].
It looks like you have a drop-down menu with answers ranging from 0 to 360.
So I'm going to answer in degrees using the unit circle.
cosine value refers to the x-coordinate.
We are looking for when the x-coordinate is [tex]-\frac{\sqrt{3}}{2}[/tex] which is at [tex]\theta=150^\circ , 210^\circ[/tex].
Milford Company uses the percent-of-sales method to estimate uncollectibles. Net credit sales for the current year amount to $ 140 comma 000, and management estimates 2% will be uncollectible. The Allowance for Uncollectible Accounts prior to adjustment has a credit balance of $ 3 comma 000. The amount of expense to report on the income statement will be?
Amount of expenditure to be shown on the income statement = 0 and Income from the reversal of additional balance = $200
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
Given that the Allowance for Uncollected Accounts is at 2% based on the percentage of sales method, the closing amount for the current year must be 2% of credit sales.
Current year credit sales = $140,000
Allowance for Uncollected Accounts = $140,000 × 2% = $2,800
the current amount of Allowance for Uncollected Accounts is $3,000, it is already $200 in excess of the threshold ($3000 - $2800), hence it must be reversed by $200.
Amount of expenditure to be shown on the income statement = 0.
Income from the reversal of additional balance = $200
Learn more about Arithmetic operations here:
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Final answer:
To calculate the expense for uncollectibles using the percent-of-sales method, multiply the net credit sales by the estimated percentage of uncollectibles. For Millford Company, this calculation is $140,000 * 2%, resulting in an expense of $2,800, ignoring the existing allowance balance.
Explanation:
The student has asked how to calculate the expense to report on the income statement for uncollectibles using the percent-of-sales method. Millford Company estimates that 2% of their net credit sales of $140,000 will be uncollectible. To find the uncollectible expense, you multiply the total net credit sales by the estimated percentage, which is $140,000 * 2% = $2,800. Since the Allowance for Uncollectible Accounts has a prior credit balance of $3,000, the current period's expense recognized in the income statement is calculated by adjusting for this existing balance. However, if the question simply asks for the expense amount based on current sales, it ignores the pre-adjustment balance and focuses solely on the estimated uncollectibles from current sales, which is $2,800.
If (x-2)^2=49 then x could be
-9
-7
2
5
9
Answer:
9
Step-by-step explanation:
Plug the numbers in
The result for each number when plugged in order is:
121
81
0
9
49
So 9 would be the answer
Answer:
9
Step-by-step explanation:
If (x-2)^2=49 then x could be 9.
(x-2)^2 = 49
x or 9 - 2 = 7
7^2 = 49
Write an equation in point-slope form of the line having the given slope that contains the given point.
m = 5/6, (30, 12)
A) y = 5/6 x - 37
B) y - 30 = 5/6 (x - 12)
C) y + 12 = 5/6 (x - 30)
D) y - 12 = 5/6 (x - 30)
Answer:
c
Step-by-step explanation:
It would be c because you would add subtract 30 - x which equals 30x then you would divided 5 / 6 which equals 0.12 then you would add y plus some number which equals 12y then you would add 12y+12=24y=24y / 2=12 thenyou have 30x,12y.
Answer:
D
Step-by-step explanation:
A might be right for the wrong linear equation type. It could be describing a y intercept slope line. So even if it is right, it is not the answer. Actually the answer to A should be y = (5/6)x - 13
The general formula for the answer you want is
Givens
y -y1 = m(x - x1)
x1 = 30
y1 = 12
m = 5/6
Solution
y - 12 = (5/6)(x - 30)
That makes the answer D
In? 2008, a country used ?twenty-five percent or 100 million tons of all the grain grown that year to produce ethanol. How much grain was grown in the country in? 2008?
Answer:
400,000,000 tons
Step-by-step explanation:
You could reword this sentence to ask the question, "100,000,000 is 25% of how much?"
The word "is" means equals, the percent will be .25 in decimal form, the word "of" means to multiply, and "how much" is x, our unknown. In equation form, then, this looks like
100,000,000 = .25 × x
We will divide both sides by .25 to get that
x = 400,000,000
That's how much grain was grown in 2008
Answer: 400 million tons
Step-by-step explanation:
100 millions is 1/4 of 400 million
A mouse traveled a total distance of 3/24 of a mile in a maze over the past three hours the mouse travel the same distance each hour to determine the distance that the mouse traveled age our map reformed the calculations below he concluded that the mouse travel 3/8 of a mile each hour what is Matt's error
i was a
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
At the movie theatre, child admission is $5.20 and adult admission is $9.80
. On Tuesday, 147 tickets were sold for a total sales of $1054.20. How many child tickets were sold that day?
Answer:
84 child tickets were sold
Step-by-step explanation:
Had they all been adult tickets, revenue would have been ...
$9.80 × 147 = $1440.60
It was less by ...
$1440.60 -1054.20 = $386.40
The child's ticket costs less by ...
$9.80 -5.20 = $4.60
so there must have been $386.40/$4.60 = 84 child tickets sold.
__
Replacing an adult ticket with a child ticket reduces the revenue by $4.60 without changing the number of tickets sold.
_____
You can let c represent the number of child tickets sold. Then (147 -c) is the number of adult tickets sold, and total revenue is ...
5.20c + 9.80(147 -c) = 1054.20
-4.60c +1440.60 = 1054.20 . . . . simplify
-4.60c = -386.40 . . . . . . . . . . . . . subtract 1440.60
c = 386.40/4.60 = 84
A nontoxic furniture polish can be made by combining vinegar and olive oil. The amount of oil should be five times the amount of vinegar. How much of each ingredient is needed in order to make 57 oz of furniture polish?
To make 57 oz of furniture polish, ____ oz of vinegar and
________ oz of olive oil are needed.
(Simplify your answers. Type mixed numerals, if possible. Otherwise, type integers or fractions.)
Answer:
See below in bold.
Step-by-step explanation:
The ratio of oil to vinegar is 5 : 1. That means that 5/6 of the mixture is oil and 1/6 is vinegar.
So to make 57 oz of the polish, 57/ 6 = 9 1/2 oz is vinegar and 5/6 * 57 =
47 1/2 oz is olive oil.
Please solve the following complex number system ASAP, show work and please simplify fully.
[tex]x^{2}[/tex]-16x+80=0
Answer:
x= 16±√-64 over 2
Step-by-step explanation:
x= -(-16)±√(-16)²-4×1×80 over 2×1
x= 16±√256-320 over 2
x= 16±√-64 over 2
can also be represented with all real numbers.
A person died leaving property worth rs.4000.40. His widow get 0.125 of the property and his son got 0.4 of the remainder. What did his widow and his son get
Answer:
Widow's Share = Rs 500.05
Son's share = Rs 1400.14
Step-by-step explanation:
Property = 4000.40
Widow get share = 0.125
So, Share of Widow = 0.125 * 4000.40
Widow's Share = Rs 500.05
Remaining Property = 4000.40 - 500.05
Remaining Property = 3500.35
Son's share = 0.4 * 3500.35
Son's share = Rs 1400.14
To solve this problem, we will follow these steps:
1. Calculate the widow's share of the property.
2. Determine the remainder of the property after the widow has received her share.
3. Calculate the son's share of the remainder of the property.
Step 1: Calculate the widow's share.
The widow gets 0.125 (or 12.5%) of the total property. The total property is valued at 4000.40 units (where the unit could be in rupees, dollars, etc.).
Widow's share = Total property * Widow's share percentage
= 4000.40 * 0.125
Let's calculate that:
Widow's share = 4000.40 * 0.125
= 500.05
So, the widow gets 500.05 units.
Step 2: Determine the remainder of the property.
Now, subtract the widow's share from the total property to find out how much is left for the son to receive his share from.
Remainder of property = Total property - Widow's share
= 4000.40 - 500.05
Let's calculate that:
Remainder of property = 4000.40 - 500.05
= 3500.35
Now we have 3500.35 units remaining after the widow has received her share.
Step 3: Calculate the son's share.
The son gets 0.4 (or 40%) of the remainder of the property.
Son's share = Remainder of property * Son's share percentage
= 3500.35 * 0.4
Let's calculate that:
Son's share = 3500.35 * 0.4
= 1400.14
So, the son gets 1400.14 units.
To summarize, the widow receives 500.05 units of the property, and the son receives 1400.14 units of the property after the widow has received her share.
Can u guys PLEASE do this question 31
Answer:
see below
Step-by-step explanation:
The attached printable graph paper is a scale drawing. The 1 : 100 scale means each meter will be represented by 1 cm.
You put the names of all the students in your class in a paper bag. There are 16 boys and 18 girls. If you draw a name at random, what is P(boy’s name)?
Answer:
Step-by-step explanation:
The probability of drawing a boy's name is found in:
number of boys/total number of students
Our ratio then is
16/16+18 which is
16/34 which reduces to
8/17
As a percentage, it would be about 47%
Total students = 16 + 18 = 34
16 boys
Probability of picking boy = 16/34
Which reduces to 8/17
Which products result in a perfect square trinomial? Check all that apply. (x + 9)(x 9) (xy + x)(xy + x) (2x 3)(3 + 2x) (16 x2)(x2 16) (4y2 + 25)(25 + 4y2)
Answer:
(xy + x)(xy + x)(16 x2)(x2 16) (4y2 + 25)(25 + 4y2)Step-by-step explanation:
The product of two identical binomial factors will be a perfect square trinomial. The appropriate answer choices are those having both factors the same.
Answer:
2nd 3rd5thStep-by-step explanation:
(xy + x)(xy + x)
(16 x2)(x2 16)
(4y2 + 25)(25 + 4y2)
Of what numbers does the binary system consist of
Answer:
0 and 1
Step-by-step explanation:
binary
The solution generated by the calculator is 5.779E–8. Describe how to interpret the solution.
Answer:
5.779 x 10^-8 =0.00000005779
Step-by-step explanation:
The E-8 at the end means the number is multiplied by 10^-8.
So 5.779E-8=5.779 x 10^-8
A negative power means move the decimal place that many places to the left
So 5.779 x 10^-8 =0.00000005779
Answer:
Sample response: The E indicates scientific notation. The first number is the coefficient of the number in scientific notation. This number is multiplied by a power of 10. The number following the E, which is –8, is the exponent, and the base is 10.
Step-by-step explanation:
2020
one x-intercept for a parabola is at the point (3.22,0) find the other x-intercept for the parabola defined by this equation y=2x^2-8x+5 round to the nearest hundredth if necessary
Answer:
(0.78,0)
Step-by-step explanation:
I would use the quadratic formula.
[tex]a=3[/tex]
[tex]b=-8[/tex]
[tex]c=5[/tex]
[tex]\text{ The quadratic formula is } x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{ Let's find } b^2-4ac \text{ first}\\(-8)^2-4(2)(5)\\64-8(5)\\64-40\\24\\\\\text{ Now let's find } -b\\-b=8\\\text{ And } 2a\\2(2)=4\\\\\text{ Let's plug in this information }\\x=\frac{8 \pm \sqrt{24}}{4}\\\\\text{ We are now going to simplify }\\x=\frac{8}{4} \pm \frac{\sqrt{24}}{4} \\x=2 \pm \frac{\sqrt{4 \cdot 6}}{4}\\x=2 \pm \frac{\sqrt{4} \sqrt{6}}{4} \\x=2 \pm \frac{2 \sqrt{6}}{4}\\[/tex]
[tex] x=2 \pm \frac{\sqrt{6}}{2}[/tex]
So let's put both of these into out calculator
2 + sqrt(6)/2 and 2-sqrt(6)/2
One of them should be approximately 3.22 as the question suggests.
3.22 0.78
So the other x-intercept is approximately (0.78,0)
Identify each line or segment that intersects ⊙ S.
Answer:
AC, CE, AB, and AS
I belive those are your answers
Answer:
chords: CE and AB; secant: CE; tangent:t; diameter AB; radii: AS and SB
Step-by-step explanation:
Use the discriminant to determine how many and what kind of solutions the quadratic equation x^2−x=−1/4 has
Select one:
a. two real solutions
b. no real or complex solutions
c. one real solution
d. two complex (nonreal) solutions
its c
Using the discriminant to know about the nature of the solution of the quadratic equation x² -x = -1/4 tells us the fact as given by: Option c. one real solution
How to use discriminant to find the property of solutions of given quadratic equation?Let the quadratic equation given be of the form [tex]ax^2 + bx + c = 0[/tex], then
The quantity [tex]b^2 - 4ac[/tex] is called its discriminant.
The solution contains the term [tex]\sqrt{b^2 - 4ac}[/tex] which will be:
Real and distinct if the discriminant is positiveReal and equal if the discriminant is 0Non-real and distinct roots if the discriminant is negativeThere are two roots of a quadratic equations always(assuming existence of complex numbers). We say that the considered quadratic equation has 2 solution if roots are distinct, and have 1 solutions when both roots are same.
For this case, the given equation is:
[tex]x^2 - x = -1/4[/tex]
Converting this to the form [tex]ax^2 + bx + c = 0[/tex], we get:
[tex]x^2 - x + 1/4= 0\\or\\4x^2 -4x + 1 = 0[/tex]
Thus, we get:
a = 4, b = -4, c = 1
Putting these values in the expression for discriminant, we get:
[tex]D = b^2 - 4ac =(-4)^2 - 4(4)(1) = 16 - 16 = 0[/tex]
The discriminant is 0, so the considered quadratic equation is going to have both roots real and equal. Or in terms of distinct solutions, it is going to have one real solution (distinct).
Thus, using the discriminant to know about the nature of the solution of the quadratic equation x² -x = -1/4 tells us the fact as given by: Option c. one real solution
Learn more about discriminant of a quadratic equation here:
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Solve the system of equations. 4x - 4y = 10 3x + 2y = 5
ANSWER CHOICES
(2, -1/2)
(1, 1)
(3, -2)
(3,1/2 )
Answer:
A) (2, -1/2)
Step-by-step explanation:
Start with one equation and isolate a variable:
4x - 4y = 10
4x - 4x - 4y = 10 - 4x
-4y = 10 - 4x
-4y/-4 = 10/-4 - 4x/-4
y = -2 1/2 + x
Now plug this in for y in the other equation:
3x + 2(-2 1/2 + x) = 5
3x - 5 + 2x = 5
5x - 5 = 5
5x - 5 + 5 = 5 + 5
5x = 10
5x/5 = 10/5
x = 2
Right here we can tell your answer is A since it is the only one with 2 as the x-value
Please help me with this problem.
Answer:
b. 9/5
Step-by-step explanation:
Cotangent is the inverse of tangent.
tan θ = y/x
cot θ = x/y
cot θ = (-9)/(-5)
cot θ = 9/5
just to add to that great reply by @MathPhys above
[tex]\bf (\stackrel{adjacent}{-9},\stackrel{opposite}{-5})~\hfill cot(\theta )=\cfrac{\stackrel{adjacent}{-9}}{\stackrel{opposite}{-5}}\implies cot(\theta )=\cfrac{9}{5}[/tex]
bear in mind that, the value coordinate pairs we get is the (x,y) coordinates, and x = adjacent side of the triangle whilst y = opposite side of it.
Can someone please help me, I need to know the missing side length (x) using trigonometric ratios.
Answer:
x = 5.34
Step-by-step explanation:
The reference angle is 24 degrees. I'm sure you are aware from the square at the other base angle that is a right triangle. Right triangles have ratios by which we can determine missing side and angle measures. The sin of a reference angle has a ratio that is side opposite/hypotenuse. The cos of a reference angle has a ratio that is side adjacent/hypotenyse. The tan of a reference angle has a ratio that is side opposite/side adjacent.
We need to decide which of these fits our needs according to the angle and sides we are given and need to find. We have the reference angle as 24 degrees, we have the side adjacent to this angle as 12. We are looking for x, which is the side opposite the reference angle. Looking to what our definitions are for each ratio, the sides opposite and adjacent are defining the tan of the reference angle. Setting up the ratio then looks like this:
[tex]tan(24)=\frac{x}{12}[/tex]
Multiply both sides by 12 to get
12 tan(24) = x
Do this on your calculator in DEGREE mode to get that
x = 5.342744224
Not sure what your teacher has you round to, but I usually have my students give me 2 decimal places
When a boy pulls his sled with a rope, the rope makes an angle of 35° with the horizontal. If a pull of 16 pounds on the rope is needed to move the sled, what is the horizontal component force?
9 lb
13 lb
19 lb
22 lb
Answer:
13 lb
Step-by-step explanation:
The horizontal component of the force is the magnitude of the force multiplied by the cosine of the angle with the horizontal.
(16 lb)·cos(35°) ≈ 13.1 lb ≈ 13 lb
Answer:
b.13 lb
Step-by-step explanation:
We are given that a boy pulls his sled with a rope .
The rope makes an angle with horizontal =[tex]35^{\circ}[/tex]
If a pull on the rope is needed to move the sled=16 pounds
We have to find the horizontal component of force
We know that horizontal component force=[tex]fcos\alpha[/tex]
Therefore, we have f=16 pound
Then, horizontal component of force=[tex]16cos 35^{\circ}[/tex]
Horizontal component of force=[tex]16\times 0.819=13.1lb[/tex]
Hence, horizontal component of force=13 lb
Answer:b.13 lb
Paul and Tom both commute to work. Paul's commute on the train takes 15 minutes more than one third as many minutes as Tom's commute by car. It takes Paul 45 minutes to get to work. Write an equation to determine how many minutes it takes Tom to get to work.
45 = one thirdx − 15
45 = one thirdx + 15
45 = 3x − 15
45 = 3x + 15
Answer:
45 = (one third)x + 15
Step-by-step explanation:
If x represents the number of minutes Tom commutes, then (1/3)x is "one-third as many minutes as Tom's commute." 15 minutes more than that is ...
(1/3)x + 15
We are told this is the length of Paul's commute, and that it is 45 minutes. So, the appropriate equation is ...
45 = (1/3)x +15
Answer: 45 = (one third)x + 15
Step-by-step explanation:
Determine the scale factor for Δ ABC to Δ A¹B¹C¹.
Answer:
Answer B
Step-by-step explanation:
The triangle has side lengths that are dilated by 2x in the second triangle
Answer:
2
Step-by-step explanation:
A P E X
Which statement wether Shannon is correct ?
Answer:
Option B A rectangular prism in which BA=30 and h=5 has a volume of 150 units³, therefore, Shannon is correct
Step-by-step explanation:
step 1
Find the area of the base of the rectangular pyramid
The volume of the rectangular pyramid is equal to
[tex]V=\frac{1}{3}BH[/tex]
where
B is the area of the base and H is the height of the pyramid
we have
[tex]V=50\ units^{3}[/tex]
[tex]H=5\ units[/tex]
substitute and solve for B
[tex]50=\frac{1}{3}B(5)[/tex]
[tex]B=30\ units^{2}[/tex]
step 2
Find the volume of the rectangular prism with the same base area and height than the rectangular pyramid
The volume of the rectangular prism is equal to
[tex]V=BH[/tex]
where
B is the area of the base and H is the height of the pyramid
we have
[tex]B=30\ units^{2}[/tex]
[tex]H=5\ units[/tex]
substitute
[tex]V=(30)(5)=150\ units^{3}[/tex]
step 3
Compare the volumes
Volume of the rectangular pyramid -------> [tex]50\ units^{3}[/tex]
Volume of the rectangular prism -------> [tex]150\ units^{3}[/tex]
therefore
The volume of the rectangular prism is three times the volume of the rectangular pyramid
Shannon is correct
Find the longer leg of the triangle.
A. 3
B. [tex]\sqrt{3}[/tex]
C. 9
D. [tex]\sqrt{6}[/tex]
Answer:
Choice A. 3.
Step-by-step explanation:
The triangle in question is a right triangle.
The length of the hypotenuse (the side opposite to the right angle) is given. The measure of one of the acute angle is also given.As a result, the length of both legs can be found directly using the sine function and the cosine function.
Let [tex]\text{Opposite}[/tex] denotes the length of the side opposite to the [tex]30^{\circ}[/tex] acute angle, and [tex]\text{Adjacent}[/tex] be the length of the side next to this [tex]30^{\circ}[/tex] acute angle.
[tex]\displaystyle \begin{aligned}\text{Opposite} &= \text{Hypotenuse} \times \sin{30^{\circ}}\\ &=2\sqrt{3}\times \frac{1}{2} \\&= \sqrt{3}\end{aligned}[/tex].
Similarly,
[tex]\displaystyle \begin{aligned}\text{Adjacent} &= \text{Hypotenuse} \times \cos{30^{\circ}}\\ &=2\sqrt{3}\times \frac{\sqrt{3}}{2} \\&= 3\end{aligned}[/tex].
The longer leg in this case is the one adjacent to the [tex]30^{\circ}[/tex] acute angle. The answer will be [tex]3[/tex].
There's a shortcut to the answer. Notice that [tex]\sin{30^{\circ}} < \cos{30^{\circ}}[/tex]. The cosine of an acute angle is directly related to the adjacent leg. In other words, the leg adjacent to the [tex]30^{\circ}[/tex] angle will be the longer leg. There will be no need to find the length of the opposite leg.
Does this relationship [tex]\sin{\theta} < \cos{\theta}[/tex] holds for all acute angles? (That is, [tex]0^{\circ} < \theta <90^{\circ}[/tex]?) It turns out that:
[tex]\sin{\theta} < \cos{\theta}[/tex] if [tex]0^{\circ} < \theta <45^{\circ}[/tex];[tex]\sin{\theta} > \cos{\theta}[/tex] if [tex]45^{\circ} < \theta <90^{\circ}[/tex];[tex]\sin{\theta} = \cos{\theta}[/tex] if [tex]\theta = 45^{\circ}[/tex].Answer:
A
Step-by-step explanation:
Since the triangle is right use the cosine ratio
cos30° = [tex]\frac{adjacent }{hypotenuse}[/tex] = [tex]\frac{adj}{2\sqrt{3} }[/tex], so
[tex]\frac{\sqrt{3} }{2}[/tex] = [tex]\frac{adj}{2\sqrt{3} }[/tex]
Multiply both sides by 2[tex]\sqrt{3}[/tex]
adj = [tex]\frac{\sqrt{3} }{2}[/tex] × 2[tex]\sqrt{3}[/tex] = 3
What is the volume of the oblique cone? Round to the nearest tenth. 142.4 cubic units 142.4 square units 196.0 cubic units 196.0 square units
Answer:
142.4 cubic units
Step-by-step explanation:
Formula: π * r²
Radius = 4
Height = 8.5
Volume = 1/3 x 3.14 x (4)^2 x 8.5 =
142.4 cubic unitsThe volume of an oblique cone is given in cubic units. The two options presented as cubic units are 142.4 and 196.0. Without additional measurements, we cannot calculate the exact volume, but we know that the volume must be one of these two options.
Explanation:The question is asking to determine which of the provided values represents the volume of an oblique cone. Volume is the measure of space occupied by a three-dimensional object and is expressed in cubic units. In general, the volume of a cone can be calculated using the formula V = (1/3)πr²h, where 'r' is the radius of the base, 'h' is the height, and π is Pi, approximately 3.14159. Since an oblique cone has a circular base but is tilted, the formula for its volume is the same as that of a right cone.
Looking at the options provided, we need to determine which value most likely represents the volume of a cone. Since volume is expressed in cubic units, the correct answer will be in cubic units, not square units. Therefore, we can immediately eliminate the options with 'square units' as they represent an area measure instead of volume.
Thus the potential answers could either be 142.4 cubic units or 196.0 cubic units. Without additional information, such as the dimensions of the base and the height, we cannot perform the calculation to further refine the answer. However, the question might be simplifying the process by providing the answer directly, and it is up to the student to choose between the given cubic unit options based on an understanding of volumes rounding procedures, if applicable.