Answer:
Option D is correct.
as the particle always moves to the right
Step-by-step explanation:
Given the function: [tex]s(t) = \frac{t^3}{3} - \frac{12t^2}{2} + 36t[/tex] , 0<t<15;
where
s(t) represent the distance in feet.
t represents the time in second.
Since, when the particle is moving to the right,
⇒ s(t) is increasing.
so, [tex]v(t) =\frac{ds}{dt} > 0[/tex]
Find the derivative of s(t) with respect to t;
Use derivative formula:
[tex]\frac{dx^n}{dx} = nx^{n-1}[/tex]
[tex]\frac{ds}{dt} = \frac{3t^2}{3}-\frac{24t}{2}+36[/tex]
Simplify:
[tex]\frac{ds}{dt} = t^2-12t+36[/tex]
As [tex]\frac{ds}{dt} > 0[/tex]
⇒[tex] t^2-12t+36 > 0[/tex]
[tex](t-6)^2 >0[/tex] [[tex](a-b)^2 = a^2-2ab+b^2[/tex] ]
⇒ this is always true because square of any number is always positive
Therefore, it means that the particle always moves to the right.
sin(x)/1-cos(x) - 1-cos(x)/sin(x) = 2cot(x)
let's recall the pythagorean identity that sin²(θ) + cos²(θ) = 1.
[tex]\bf \cfrac{sin(x)}{1-cos(x)}-\cfrac{1-cos(x)}{sin(x)}=2cot(x) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{sin(x)}{1-cos(x)}-\cfrac{1-cos(x)}{sin(x)}\implies \cfrac{[sin(x)]^2-[1-cos(x)]^2}{sin[1-cos(x)]} \\\\\\ \cfrac{[sin^2(x)]-[1^2-2cos(x)+cos^2(x)]}{sin[1-cos(x)]}\implies \cfrac{sin^2(x)-1+2cos(x)-cos^2(x)}{sin[1-cos(x)]} \\\\\\ \cfrac{sin^2(x)-[\underline{sin^2(x)+cos^2(x)}]+2cos(x)-cos^2(x)}{sin[1-cos(x)]} \\\\\\ \cfrac{sin^2(x)-sin^2(x)-cos^2(x)+2cos(x)-cos^2(x)}{sin[1-cos(x)]}[/tex]
[tex]\bf \cfrac{-2cos^2(x)+2cos(x)}{sin[1-cos(x)]}\implies \cfrac{2cos(x)[-cos(x)+1]}{sin[1-cos(x)]}\implies \cfrac{2cos(x)[\underline{1-cos(x)}]}{sin[\underline{1-cos(x)}]} \\\\\\ \cfrac{2cos(x)}{sin(x)}\implies 2\cdot \cfrac{cos(x)}{sin(x)}\implies 2cot(x)[/tex]
WILL GIVE BRAINLIEST
Solve for x
Answer:
6x^2 +81x - 17
---------------------
7x-15
Step-by-step explanation:
We cannot solve for x since this is an expression
((6x+9) (x+12) -sqrt(49+76) ^2
--------------------------------------------
(49+7x) -64
Lets simplify the numerator
((6x+9) (x+12) -sqrt(49+76) ^2
Simplify what is inside the last parentheses
((6x+9) (x+12) -sqrt(125) ^2
Squaring a square root leaves the original number
((6x+9) (x+12) -(125)
FOIL the first two terms
First 6x*x = 6x^2
Outer: 6x*12 = 72x
Inner: 9x
Last : 9*12 = 108
Add them together
6x^2 +72x+9x+108 = 6x^2 +81x+108
Subtract the 125
6x^2 +81x+108-125
6x^2 +81x - 17
Now lets simplify the denominator
(49+7x) -64
49+7x-64
7x-15
6x^2 +81x - 17
---------------------
7x-15
A 54-kg jogger is running at a rate of 3 m/s. What is the kinetic energy of the jogger? A. 18 J B. 81 J C. 162 J D. 243 J
[tex]\displaystyle\bf\\\text{\bf kinetic energy}=\frac{mv^2}{2}=\frac{54\times3^2}{2}=27\times9=\boxed{\bf243~J} \\\\\text{\bf Correct answer: D.}[/tex]
Answer:
The answer would be be D.243 j
Step-by-step explanation:
Find the degree of the polynomial: 7.5x^3yz+x^7z^2+2x^3y^3z−x^4z
The degree of this polynomial is 9
Answer:
Answer in image
Step-by-step explanation:
Answer in image
A gardener is planting two types of trees: Type A is 8 feet tall and grows at a rate of 3 inches per year. Type B is 7 feet tall and grows at a rate of 4 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.
Answer:
Exactly 12 years it will take for these trees to be the same height
Step-by-step explanation:
Slope intercept form: An equation of line is in the form of [tex]y = mx+b[/tex] where m is the slope or unit rate and b is the y-intercepts.
Let x represents the time in years and y represents the height of the tree.
Use conversion:
1 ft = 12 inches
As per the given statement:
Type A is 8 feet tall and grows at a rate of 3 inches per year.
⇒unit rate per year = 3 inches = [tex]\frac{1}{4}[/tex] ft
Then, we have;
[tex]y =\frac{1}{4}x + 8[/tex] ......[1]
Similarly for;
Type B is 7 feet tall and grows at a rate of 4 inches per year.
⇒unit rate per year = 4 inches = [tex]\frac{1}{3}[/tex] ft
then;
[tex]y =\frac{1}{3}x + 7[/tex] .....[2]
To find after how many years it will take for these trees to be the same height.
Since, trees to be the same height;
⇒equate [1] and [2], to solve for x;
[tex]\frac{1}{4}x + 8 = \frac{1}{3}x +7[/tex]
Subtract 7 from both sides we get;
[tex]\frac{1}{4}x + 8-7= \frac{1}{3}x +7-7[/tex]
Simplify:
[tex]\frac{1}{4}x + 1= \frac{1}{3}x[/tex]
Subtract [tex]\frac{1}{4}x[/tex] from both sides we get;
[tex]1= \frac{1}{3}x-\frac{1}{4}x[/tex]
Simplify:
[tex]1 = \frac{x}{12}[/tex]
Multiply both sides by 12 we get;
x = 12
Therefore, exactly it will take for these trees to be the same height is, 12 years
The taxpayer had a qualifying child who is not disabled and who turned 13 on may 31, 2017. They paid a child care provider to care for the child for the entire year while they worked. How many months of child care expenses can they deduct on their tax return?
Answer:
5 months
Step-by-step explanation:
The taxpayer can only deduct the first five months of the qualifying child. May is the fifth month. On June 1st, the qualifying child is going to be 14 years old. Therefore he cannot be included in work-related expenses as specified in the Publication 503 - Main Content from the IRS. Please see the Working-Related Expenses, Indent (b) which is as follows:
(b) The parent of your qualifying person if your qualifying person is your child and under age 13.
Solve the quadratic equation by completing the square.
2x² - 20x + 48 = 0
So firstly, we need to isolate the x terms onto one side. To do this, subtract 48 on both sides of the equation:
[tex]2x^2-20x=-48[/tex]
Next, divide both sides by 2:
[tex]x^2-10x=-24[/tex]
Next, we are gonna make the left side of the equation a perfect square. To find the constant of this soon-to-be perfect square, divide the x coefficient by 2 and then square the quotient. Add the result onto both sides of the equation:
[tex]-10 \div 2=-5\\(-5)^2=25\\\\x^2-10x+25=1[/tex]
Now, factor the left side:
[tex](x-5)^2=1[/tex]
Next, square root both sides of the equation:
[tex]x-5=\pm 1[/tex]
Next, add 5 to both sides of the equation:
[tex]x=5\pm 1[/tex]
Lastly, solve the left side twice -- once with the plus sign and once with the minus sign.
[tex]x=6,4[/tex]
AnswerIn short, x = 6 and 4
Answer: x = 4 x = 6
Step-by-step explanation:
2x² - 20x + 48 = 0
2x² - 20 x + _____ = -48 + ______ subtracted 48 from both sides
2(x² - 10x + _____ ) = 2(-24 + _____ ) factored out 2 from both sides
x² - 10x + _____ = -24 + _____ divided both sides by 2
x² - 10x + 25 = -24 +25 added 25 to both sides
↓ ↑ ↑
[tex]\dfrac{-10}{2}=(-5)^2[/tex] [tex]\bigg(\dfrac{b}{2}\bigg)^2[/tex] makes a perfect square
(x - 5)² = 1 simplified
[tex]\sqrt{(x-5)^2} =\sqrt{1}[/tex] took square root of both sides
x - 5 = ± 1 simplified
x - 5 = 1 x - 5 = -1 split into two separate equations
x = 6 x = 4 solved for x
what is -2 sqrt20 - sqrt125
Answer:
-9sqrt(5)
Step-by-step explanation:
-2 sqrt20 - sqrt125
Lets simplify the square roots
sqrt(ab) = sqrt(a)sqrt(b)
-2 sqrt(4) sqrt(5) - sqrt(25) sqrt(5)
-2 *2sqrt(5) - 5sqrt(5)
-4sqrt(5) -5sqrt(5)
-9sqrt(5)
The expression 24(1−x) gives the discounted price of a pair of shorts, where x is the percent of the discount written in decimal form.
What does 1−x represent in the expression?
percent of original price being paid
original price of shorts
discount price of the shorts
percent of discount
Answer:
1-x represents the percent of the original price being paid.
Step-by-step explanation:
The expression 24(1−x) gives the discounted price of a pair of shorts, where x is the percent of the discount written in decimal form.
For example , 10% is the discount percentage
1 - 10% = 90% will be the percentage of original price to be paid
Here x represents the percent of the discount
so 1-x represents the percent of the original price being paid.
Answer:
percent of original price being paid
Step-by-step explanation:
Please help! Urgent! Will mark brainliest!
Lamar wanted to explain why the measure of angle 5 is equal to the sum of the measures of angles 1 and 3.
Which geometry concepts should be used in Lamar’s work?
A) supplementary angles and the sum of the measures of interior angles of a triangle
B) complementary angles and the sum of the measures of interior angles of a triangle
C) supplementary angles and vertical angles
D) the sum of the measures of interior angles of a triangle and vertical angles
Answer:
B
Step-by-step explanation:
Because the angles make up the interior parts of the triangle without the extra endings
Answer: The answer would be B
An elephant can run 1/4 of a mile in 36 seconds. At this rate, which expression can be used to determine how fast an elephant runs in miles per hour?
A) 36seconds/1/4 mile = 25 miles per hour
B) 1/4 mile/36 seconds=144 miles per hour
C) 1/4 mile/36 seconds= 25miles per hour
D) 36 seconds/1/4 mile= 144 miles per hour
Answer:
an elephant can run 25 miles per hour
Step-by-step explanation:
60 minutes x 60 seconds = 3,600 seconds in an hour
3600 / 36 = 100
100 x .25 = 25 miles an hour
The time a basketball player spends in the air when shooting a basket is called the "hang time." the vertical leap l measured in feet is related to the hang time t measured in seconds by the equation equals=4t squared 4t2. suppose that a basketball player has a vertical leap of 44 feet 1111 inches. find the hang time for this leap.
Answer: 1.1 seconds
Step-by-step explanation:
leap = 4t² ; leap = 4 ft 11 inches, find t
[tex]4\frac{11}{12} = 4t^2[/tex]
[tex]\frac{59}{12} = 4t^2[/tex]
[tex]\frac{59}{48} = t^2[/tex]
[tex]\sqrt{\frac{59}{12}} = \sqrt{t^2}[/tex]
[tex]\sqrt{1.23} = t[/tex]
1.1 = t
Which number sentence correctly solves this problem? There were 52,165 people at the soccer game on Friday. There were 49,872 people at the game on Saturday. What is the total attendance for the two days? A. 52,165 – 49,872 = 2,293 B. 52,165 – 49,872 = 17,713 C. 52,165 + 49,872 = 92,037 D. 52,165 + 49,872 = 102,037
Answer: D.
Step-by-step explanation:
52,165 + 49,872 = 102,037
is 2i a real or complex root?
By definition, i = sqrt(-1) because it is used to solve the equation x^2+1 = 0 or x^2 = -1, which has no real number solutions.
Since i is imaginary or complex, then so is 2i
You can express it as 2i = 0+2i to be in the form a+bi with a = 0 as the real part and b = 2 as the imaginary component.
An object moves according to the law s = t2 + 5t - 8. what is the exact rate of change of s with respect to t when t = 1.5 seconds?
Answer:
ds/dt =8 when t =1.5
Step-by-step explanation:
s = t^2 + 5t - 8
We want to find ds/dt
ds/dt = 2t +5
evaluated when t=1.5
ds/dt = 2(1.5) +5
ds/dt = 3+5
ds/dt =8 when t =1.5
Replace t with 1.5 seconds and solve for s:
s = 1.5^2 + 5(1.5) -8
s = 2.25+7.5-8
s= 9.75 -8
s = 1.75
Rate of change is S/t
Rate of change = 1.75 / 1.5
Rate of change of s = 1.17
Please help this is so confusing to me
First multiply C by F by multiplying each row in C by each column in F:
12 * -2 + 0*0 + 1.5*2 12*0 + 0*8 + 1.5*1
1*-2 -6*0 +7.2 1*0-6*8 +7*1
to get a matrix of:
-21 1.5
12 -41
Now subtract that matrix from B:
2- -21 = 2+21 = 23
8 - 1.5 = 6.5
0.6 - 12 = -11.4
3 - -41 = 3+41 = 44
So you have:
23 6.5
-11.4 44
Which makes C the correct answer.
Who does this describe? The country was in chaos, but this scholar helped bring order to society through his teachings about family and government relationships, and the Golden Rule.
A. Siddhartha Gautama
B. Ramayana
C. Asoka
D. Confucius
Answer:
The correct answer is D. This statement describes Confucius.
Step-by-step explanation:
Confucius was a Chinese philosopher, whose teachings had a great influence in China, Korea, Japan and Vietnam. According to tradition, he was born in the city of Qufu, in the Kingdom of Lu, now part of Shandong Province. He is said to have become Minister of Justice in Lu's kingdom. After being forced to resign, he toured the small kingdoms of northeast and central China, explaining his ideas about governance.
He emphasizes his philosophy of morality, right social relationships, justice and honesty, both in personal life and in government. During the Han Dynasty period in China, his teachings became the official philosophy of the state. His teachings were introduced to Europe by the Jesuit Matteo Ricci, the first to Latinize his name as "Confucius."
Is abc def name the postulates that applies
Answer:
The answer is C. AAA is not a congruency postulate because the side lengths may be different sizes although the angles are the same.
triangles ABC and DEF are congruent by the Side-Side-Side (SSS) postulate.
In other words, if two triangles have all three corresponding sides equal, then the triangles are congruent.
So the answer to the question is B. Congruent - SSS.
If triangles ABC and DEF are congruent, and if so, to name the postulate that applies.
The triangles are congruent because they have the same side lengths and angles. This can be seen from the following:
AD = BE (given)
∠ADB=∠BED (vertical angles)
AB = EF (given)
∠ABD=∠EBD (corresponding angles when AD ∥ EF )
BC = DF (given)
Therefore, triangles ABC and DEF are congruent by the Side-Side-Side (SSS) postulate
Use the substitution method to solve the system of equations
You solve the substitution method to solve a system of equality by expressing one variable in terms of the other using one equation, and then plugging this expression in the other(s).
In this case, the first equation gives us a way to express n in terms of m. So, we can replace every occurrence of n in the second equation with the given formula.
The result is
[tex] 14m+2n=-8 \iff 14m+2(-7m-4)=-8 \iff 14m-14m-8=-8 \iff -8=-8 [/tex]
So, the second equation turned to be an equality, i.e. an equation where both sides are the same.
This implies that the system has infinitely many solutions, because every couple [tex] (n,m) [/tex] such that [tex] n=-7m-4 [/tex] is a solution to the system, because it satisfies both equations: the first is trivially satisfied, whereas the second is an identity, and as such is satisfied by any value of the variable.
Convert Fahrenheit to Celsius is C=5/9(F-32) convert 18c to Fahrenheit
Answer:
-7.77778
If you use google it will help u
Becki put some stamps into her stamp collection book she put 14 stamps on each page if she completely filled 16 pages how many stamps did she put in the book?
Answer:
224 stamps.
Step-by-step explanation:
We have been given that Becki put 14 stamps on each page.
To find the total number of stamps that Becki put in the book we will multiply the number of stamps put on each page by the number of completely filled pages.
[tex]\text{The total number of stamps in the book}=14\times 16[/tex]
[tex]\text{The total number of stamps in the book}=224[/tex]
Therefore, Becki put 224 stamps in the book.
To find out how many stamps Becki added to her collection, we multiply the number of stamps per page, which is 14, by the number of filled pages, which is 16, resulting in a total of 224 stamps.
To determine how many stamps Becki put into her stamp collection book, we need to calculate the total number of stamps populated over the completely filled pages. She placed 14 stamps on each page and filled 16 pages. The total number of stamps is the product of the number of stamps on each page and the number of pages filled.
The formula we will use is:
Total stamps = Number of stamps per page x Number of filled pages
Substituting the given values:
Total stamps = 14 stamps/page x 16 pages = 224 stamps
Therefore, Becki put 224 stamps in her stamp collection book.
PLEASE HELP!!
Given: e || f and g is a transversal
Prove: 1 8
Given that e || f and g is a transversal, we know that 4 5 by the alternate interior angles theorem. We also know that 1 4 and 8 5 by the . Therefore, 1 8 by the transitive property.
Answer:
Vertical angle property
Step-by-step explanation:
We are given that e is parallel to f and g is a transversal. Using the alternate interior angles property, ∠4=∠5 which is given.
Since, g is a transversal of the two parallel lines e and f, then ∠1=∠4 and ∠8=∠5 by the vertical opposite angle property.
Hence, ∠1≅∠8 by the transitive angle property.
Answer:
verticle angles theorem
Step-by-step explanation:
hope this helps :)
Drag one model next to each situation. The correct model for each group represents that situation
The question involves creating and analyzing scientific models, collaborating in groups to build and refine these models based on experimental evidence, and engaging in critical thinking about their accuracy and limitations.
Explanation:The question involves students creating and analyzing models that represent certain scientific situations. Creating a model is a fundamental part of scientific inquiry as it helps in visualizing and understanding complex concepts. Students are tasked with exchanging and labeling pictures or drawings of their models, which aids in the development of the communication of scientific ideas. They then apply their models to specific situations, test these models, and note the outcomes to assess the accuracy and limitations of the models they have built. This process involves critical thinking, collaboration, and application of scientific knowledge.
Moreover, students are required to modify their models based on experimental evidence and discussions about the limitations of their models. When building models of atoms, for example, students must consider basic ratios, an understanding of atomic structure, and the unique characteristics of the element they are representing.
The complete question is:Drag one model next to each situation. The correct model for each group represents that situation
What's the product of 42⁄3 and 111⁄4 ?
A. 83⁄7
B. 56⁄135
C. 442⁄12
D. 521⁄2
Change the mixed numbers to the impropert fractions:
[tex]4\dfrac{2}{3}=\dfrac{4\cdot3+2}{3}=\dfrac{14}{3}\\\\11\dfrac{1}{4}=\dfrac{11\cdot4+1}{4}=\dfrac{45}{4}[/tex]
[tex]4\dfrac{2}{3}\cdot11\dfrac{1}{4}=\dfrac{14}{3}\cdot\dfrac{45}{4}=\dfrac{7}{1}\cdot\dfrac{15}{2}=\dfrac{105}{2}=52\dfrac{1}{2}\to\boxed{D.}[/tex]
In ?ABC, the measure of ?C=90°, the measure of ?A=30°, and CA = 68 feet. Find the length of BC to the nearest foot
Answer:
39 feet
Step-by-step explanation:
Since the triangle is right we can use the tan ratio to find BC
tan 30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{68}[/tex]
multiply both sides by 68
68 tan 30° = BC ⇒ BC ≈ 39 feet ( to nearest foot )
Verify the identity.
cotangent of x divided by quantity one plus cosecant of x equals quantity cosecant of x minus one divided by cotangent of x
Identity to verify:
[tex]\dfrac{\cot x}{1+\csc x}=\dfrac{\csc x-1}{\cot x}[/tex]
Recall that
[tex]\cos^2x+\sin^2x=1[/tex]
Divide both sides by [tex]\sin^2x[/tex] and we get
[tex]\cot^2x+1=\csc^2x[/tex]
or
[tex]\cot^2x=\csc^2x-1=(\csc x-1)(\csc x+1)[/tex]
So if we multiply the numerator and denominator of
[tex]\dfrac{\cot x}{1+\csc x}[/tex]
by [tex]\csc x-1[/tex], we get
[tex]\dfrac{\cot x(\csc x-1)}{(1+\csc x)(\csc x-1)}=\dfrac{\cot x(\csc x-1)}{\csc^2x-1}=\dfrac{\cot x(\csc x-1)}{\cot^2x}[/tex]
Then as long as [tex]\cot x\neq0[/tex], we can cancel terms to end up with
[tex]\dfrac{\csc x-1}{\cot x}[/tex]
and establish the identity.
The manufacturer ID number for Proctor and Gamble is (037000) and the item number for a box of Bounce Fabric Softener is (80049). What is the valid UPC?
A) 0-37000-80049-9
B) 0-37000-80049-1
Eliminate
C) 1-37000-80049-1
D) 1-80049-37000-0
Answer:
A) 0-37000-80049-9
Step-by-step explanation:
For a standard bar code, it consists of a five digit manufacturer number and a five digit product number. Check digits are a single digit computed from the other characters in the string of numbers. Check digits are on the far right.
Add the odd number digits: 0+7+0+8+0+9 = 24.
Multiply the result by 3: 24 × 3 = 72.
Add the even number digits: 3+0+0+0+4 =7.
Add the two results together: 72 + 07 = 79.
The last digit is 9
Answer:b
Step-by-step explanation: USA test prep
ughhhh please help me i don’t wanna fail again
Answer:
Step-by-step explanation:
Start with (1,2) . One of the pairs has to begin with a 1. Look around to see which set of points has a 1 for the x value.
B and C do. So all you have gotten rid of is A and D. D looks like it might work, but it really does not. It has - 1 as it's starting point. The point must start with 1.
The next step is to find the distance between the 2 given points. The y value for the two points already on the graph is the same so they do not contribute anything to the distance. -3 and 1 are 4 units apart.
1 and ? must also be 4 units apart. Only D does. 1 and -3 are the x values 2 and 6 are the y values. The answer is B
The pie store is having a 20\%20% off sale on all of its pies. If the pie you want regularly costs \$18$18, how much would you save with the discount? \$
Answer:
$3.6
Step-by-step explanation:
We are told that the pie store is having a 20% off sale on all of its pies. The pie you want regularly costs $18.
To find the amount saved with the discount let us find 20% of 18.
[tex]\text{The amount saved with discount}=\frac{20}{100}\times 18[/tex]
[tex]\text{The amount saved with discount}=0.20\times 18[/tex]
[tex]\text{The amount saved with discount}=3.6[/tex]
Therefore, the amount saved with the discount is $3.6.
A store had 88 diet sodas.The ratio of diet sodas to regular sodas was 8:4.How many regular sodas were there?
Answer:
44
Step-by-step explanation:
diet : regular = 8:4
=> 88:44