Answer:
The maximum height of the arrow is 125 feet.
Step-by-step explanation:
The pathway of the arrow can be represented by the equation,
[tex]h = -16t^2 +80t + 25[/tex] .....(1)
Where h is height in in feet and t is time in seconds.
It is required to find the maximum height of the arrow. For maximum height, [tex]\dfrac{dh}{dt}=0[/tex].
So,
[tex]\dfrac{d(-16t^2 +80t + 25)}{dt}=0\\\\-32t+80=0\\\\t=\dfrac{80}{32}\\\\t=2.5\ s[/tex]
Put t = 2.5 s in equation (1). So,
[tex]h = -16(2.5)^2 +80(2.5) + 25\\\\h=125\ \text{feet}[/tex]
So, the maximum height of the arrow is 125 feet.
Find the volume of the figure
Answer:
see below
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
We know the diameter so we need the radius
r = d/2 =13/2 = 6.5
V = pi (6.5)^2 (19)
V = 802.75 pi mm^3
We can approximate pi by 3.14
V =2520.635 mm^3
or by using the pi button
V =2521.913503 mm^3
Which of the following scenarios represents an impulse purchase?
1) Tara goes to the pet store for fish food. She visits the pet adoption center and quickly decides to adopt a dog without considering all of the costs in caring for the dog.
2)Tara goes to the pet store for fish food. She visits the pet adoption center and decides to research the costs in caring for a dog before she adopts one.
3) Tara goes to the pet store for fish food. She visits the pet adoption center and decides to make an affordable donation towards the care of the animals waiting to be adopted.
Answer:
1
Step-by-step explanation:
Answer 1 is an impulse purchase. An impulse purchase is when someone does something just because they feel like it. She doesn't give herself time to think about the outcomes, how much it would cost, the type of dog, nada. She just buys it. Therefore, answer 1 is an example of impulse buying.
The width of a swimming pool is 12 feet less than the pool's length. The area of the pool is 540 square feet. What are the dimensions of the pool?
Answer:
30 feet by 18 feet
Step-by-step explanation:
Area = length * width
A = x*w
w = x - 12
A = 540 sq. ft
540 = x * (x -12)
x*x - 12x - 540 = 0
x*x - 12x + 36 - 36 - 540 = 0
(x - 6)^2 - 576 = 0
x - 6 = 24
or x -6 = -24
x = 30 or x = -18
w = 30 - 12 = 18
30 ft by 18 ft
15 / x equals 50 / 4
Answer:
Step-by-step explanation:
Solve for x by cross multiplying.
Exact Form:
x=6/5
Decimal Form:
x=1.2
Mixed Number Form:
x=1 1/5
i hope its correct plz tell me if im wrong
A line plot titled Household T V Ownership has Number of televisions on the x-axis. There is x about 0, 2 above 1, 4 above 2, 7 above 3, 0 above 4, 1 above 5, 1 above 6, and 0 above 7.
The line plot shows the number of televisions students have at home.
students have two televisions at home.
How many televisions do most students have at home?
televisions
Answer
4
3
Step-by-step explanation:
i did the test.
When graphed, which parabola opens downward?
y = –3x2
y = (x – 3)2
y = one-third x squared
y = x2 – 3
The parabola that opens downward when graphed is y = –3x^2, as the negative coefficient of the x^2 term determines the downward opening direction.
The student has asked which parabola opens downward when graphed. The general form of a parabola is y = ax2 + bx + c. The direction in which the parabola opens is determined by the coefficient a of the x2 term. If a is negative, the parabola opens downward, and if a is positive, the parabola opens upward. Looking at the provided equations, we can identify the equation with a negative a value:
y = –3x2 (The coefficient of the x2 term is -3, so this parabola opens downward.)y = (x – 3)2 (The coefficient here is positive after expanding, so this parabola opens upward.)y = one-third x squared (The coefficient is positive 1/3, so this parabola opens upward.)y = x2 – 3 (The coefficient is positive 1, so this parabola opens upward.)Therefore, the equation of the parabola that opens downward when graphed is y = –3x2
Which polynomial function has a leading coefficient of 1, roots -2 and 7 with multiplicity 1, and root 5 with multiplicity 27
O
f(x) = 2(x + 7)(x + 5)(x-2)
Rx) = 2(x - 7)(x - 5)(x + 2)
Rx) = (x + 7)(x + 5)(x + 5)(x - 2)
f(x) = (x - 7)(x - 5)(x - 5)(x + 2)
The polynomial function with a leading coefficient of 1 and the specified roots and multiplicities is f(x) = (x + 2)(x - 7)(x - 5)^27.
Explanation:The polynomial function you are looking for, which has a leading coefficient of 1, roots at -2 and 7 each with a multiplicity of 1, and a root at 5 with multiplicity 27, is given by the expression:
f(x) = (x + 2)(x - 7)(x - 5)^27
The given roots indicate the factors of the polynomial, and the multiplicity of each root shows how many times that factor is repeated. Hence, the root -2 becomes (x + 2), the root 7 becomes (x - 7), and the root 5 with multiplicity 27 becomes (x - 5)^27. The leading coefficient is 1, which means these factors are not multiplied by any other constant.
Learn more about Polynomial Function here:https://brainly.com/question/30474881
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what is the general solution to the differential equation dy/dx= cos(8x)/cos(4y) ?
A. sin =(4y) - sin(8x) = C
B. sin (4y) - 2 sin(8x) = C
C. 2 sin(4y) - sin(8x) = C
D. 2 tan(4y) - sin(8x) = C
Answer:
2sin4y - sin8x = K (C)
Step-by-step explanation:
Given the differential equation
dy/dx= cos(8x)/cos(4y)
This can be solved by using the variable separable method.
Step 1;
Separate the variables
Cos4ydy = cos 8xdx
step 2:
Integrate both sides of the equation
∫cos4y dy = ∫cos8x dx
sin4y/4 = sin8x/8
Step 3:
Add constant of integration to the side containing x variable
sin4y/4 = sin8x/8+ C
Taking sin8x to the other side we have:
sin4y/4-sin8x/8 = C
Multiplying through by 8:
2sin4y - sin8x = 8C
2sin4y - sin8x = K (where K = 8C )
To solve the given differential equation we have apply variable separation method.
The correct option is (c) 2 sin(4y) - sin(8x) = C.
Variable separation:In mathematics, variable separation method used to calculate the partially and ordinary differential function in which we rewrite the equation so that two variable occurs on two side.
Given:
The given differential equation is as follows,
[tex]\dfrac{dy}{dx}=\dfrac{\cos(8x)}{\cos(4y)}[/tex]
How to calculate the Separate the variable?Separate the variable.
[tex]\cos 4y \:dy =\cos 8x\:dx\\[/tex]
Integrate both side of the equation.
[tex]\int \cos4y dy = \int \cos8x dx\dfrac {1}{4}\sin4y = \dfrac {1}{8}\sin8x\\\dfrac {1}{4}\sin4y-\dfrac {1}{8}\sin8x=C\\2\sin4y - \sin8x = 8C[/tex]
Thus, the correct option is (c) 2 sin(4y) - sin(8x) = C.
Learn more about variable separation here:
https://brainly.com/question/18651211
A wooden door contains a rectangular window. The width of the window is (x - 2) feet. The area of the window can be represented by x ^ 2 - 3x + 2 .
a. Write a binomial that represents the height of the window.
b. The height of the door is 5 feet more than the height of the window. Write a polynomial that represents the height of the door.
c. The area of the door can be represented by x ^ 2 + 4x . The area is 32 square feet . Find the width and the height of the window.
Answer: height of the door is x+4
Step-by-step explanation:
What is answer 6x+7-5x=10
Answer:
i think the answer is going to be 3
Step-by-step explanation:
a) 15/20
b) 20/25
c) 20/25
d) 20/15
Answer:
a 15/20
Step-by-step explanation:
A=25in
B15in
C20in
Answer:
15/20
Step-by-step explanation:
lol
brainiest rate 5 stars , thank me : )
Determine the longest side in ΔDEF.
A) segment EF
B) segment DE
C) segment FE
D) segment DF
1000^m / 100^n can be written in the form of 10^z express z in terms of m and n
Answer:
z = 3m - 2n
Step-by-step explanation:
[tex] \frac{ {1000}^{m} }{ {100}^{n} } = {10}^{z} \\ \\ \frac{ {10}^{3m} }{ {10}^{2n} } = {10}^{z} \\ \\ {10}^{3m - 2n} = {10}^{z} \\ \\ 3m - 2n = z \\ \\ \huge \red{ \boxed{z = 3m - 2n}}[/tex]
The circumference of a circle measures 11.27π ft.What is the measure of the diameter of this Circle?
PLZ HELP ON THIS QUESTION ASAP PLZ THANKS AND 5 STARS AND WHEN THERES OPTION FOR BRAINLEST ILL GIVE YOU BRAINLEST ASAP WITH ANSWER PLZ 15 POINTS
Answer:
£114
Let me know if it is incorrect so that I can review my answer and fix it! :)
Step-by-step explanation:
20% * £1200 = £240
£1200 + £240 = £1440
£1440 - £300 = £1140
£1140 / 10 = £114
Answer:
£114
Step-by-step explanation:
Total to be paid:
[1200 + (20% of 1200)] - 300
[1200 + (20/100 × 1200)] - 300
1200 + 240 - 300
1140
10 installments
Each:
1140/1
114
Write one digit on each side of 92 to make a four digit multiple of 45. How many different solutions does this problem have?
Answer:
Two solutions:
Adding 7 to the left and 0 to the right: 7920
Adding 2 to the left and 5 to the right: 2925
Step-by-step explanation:
The multiples of 45 always have as last digit 0 or 5, so the digit to the right of 92 has to be 0 or 5.
If we use 0 as the last digit, our options of multiples will be just 7920 (7920 = 45 * 176)
If we use 5 as the last digit, our option of multiples will be just 2925 (2925 = 45 * 65)
So we have just two solutions for this problem:
Adding 7 to the left and 0 to the right: 7920
Adding 2 to the left and 5 to the right: 2925
18,300 divided by 19.7%
Answer:
13,300 divided by 19.7 % is 92893.4010152
Step-by-step explanation:
Find the HCF of 168 and 196.
Answer:
The HCF of 168 & 196 is 28
Step-by-step explanation:
The factors of 168 are: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
The factors of 196 are: 1, 2, 4, 7, 14, 28, 49, 98, 196
The highest factor that both 168 and 196 share is 28
Hope this helps :D
Answer:
28
Step-by-step explanation:
168 = 2³ × 3 × 7
196 = 2² × 7²
HCF(168 ; 196) = 2² × 7 = 4 × 7 = 28
Andrea has a credit score of 895 and Ashley has a credit score of 768. Stutts National Bank has determined that both will receive a credit card; however, the borrower with the lower credit score will be charged a $50.00 fee the first time she makes a purchase. If both receive a credit card with $1,500.00 available credit, what will Ashley's remaining available credit be after she purchases a $425.00 Coach bag?
Answer:
Ashley's remaining available credit after her first purchase is $1025.00
Step-by-step explanation:
Here we are told that the borrower with the lower credit score will be charged $50.00 fee after the first purchase
Therefore, we have
Credit score Andrea = 895
Credit score for Ashley = 768
Therefore, Ashley has the lower credit score hence after her first purchase of a $425.00 Coach bag, we have
Available credit = Initial balance - Purchase - Charges
∴ Available credit = $1,500.00 - ($425.00 + $50.00) = $1025.00
Therefore, Ashley's remaining available credit after she purchases the $425.00 Coach bag = $1025.00.
A line passes through the points (-1, 4) and (2, -2). What is the equation of this line?
Write your answer in the form y=mx+b.
I don't get it please help!
Answer:
y = -2x+2
Step-by-step explanation:
First we find the slope
m = (y2-y1)/(x2-x1)
= (-2-4)/(2--1)
= (-2-4)/(2+1)
-6/3
-2
We have the slope =-2
We can substitute it into the equation
y = mx+b where m is the slope and b is the y intercept
y =-2x+b
Use a point for x and y to solve for b
4 = -2(-1) +b
4 = 2+b
Subtract 2 from each side
4 -2 = -2+2+b
2 = b
We know m and b
y = -2x+2
Answer:
y = -2x + 2
Step-by-step explanation:
Slope: (-2-4)/(2--1) = -6/3 = -2
y - 4 = -2(x - -1)
y = -2x - 2 + 4
y = -2x + 2
(11+i)^2
please help!
Answer:
121 + 22i - 1
Step-by-step explanation:
Expand:
(11 + i)² = (11 + i)(11 + i)
Note that:
i² = -1
Use FOIL method. Multiply first terms, outside terms, inside terms, then the last two terms:
(11)(11) = 121
(11)(i) = 11i
(i)(11) = 11i
(i)(i) = -1
Combine like terms:
121 + 11i + 11i - 1
121 + (11i + 11i) - 1
121 + 22i - 1
121 + 22i - 1 is your answer.
~
HELP WITH MY MATHS HOMEWORK, ITS A YEAR 7 QUESTION
Is 2 equal to 2 • 7? Explain.
Answer:
No, 2 is not 14
Step-by-step explanation:
Evaluate 2*7 you get 2*7 = 14
but 14 is not 2 so no.
Answer:
no
Step-by-step explanation:
No because, 2 times 7 is 14.
what does it take to get brailiest like no one marks it these days
Answer:
you really just have to tell them to and if they are nice they will
Step-by-step explanation:
Answer: A competent person with correct answers
A line with a slope of 4 passes through the point (2, 1). What is the equation of this line?
Write your answer using the form y=mx+b.
Please i need help ASAP
Answer:
y = 4x-7
Step-by-step explanation:
We have a slope and a point
m = 4 (2,1)
Using the slope intercept form of the equation
y = mx+b
y = 4x+b
From the point x=2 and y =1
1 = 4(2)+b
1 = 8+b
Subtract 8 from each side
1-8 =8-8+b
-7 = b
We can write the equation by using m=4 and b = -7
y = 4x-7
Answer:
A
Step-by-step explanation:
Z
What is the distance from (-6, 2) to the origin?
1. Complete the inequality below to describe the
domain of the graph shown.
Domain
2. Complete the inequality below to describe the
range of the graph shown.
Range: <_y <5
Domain is the entire span left to right (on the x-axis) that the graph is on. Since the graph goes from x=-4 and ends at x=4, the domain would be from -4 to 4. The circle at -4 is open, so it does not include the point at -4, just everything leading up to it. So, the domain would be
[tex] - 4 < x \leqslant 4[/tex]
The range is similar, it is the entire span that the graph goes up and down (on the y-axis). The graph starts at the bottom at y=-2, and ends at y=5. The bottom point (4,-2) is closed, so the graph includes that point, and the top point (-4,5) is open and doesn't include the point. Therefore, the range would be
[tex] - 2 \leqslant x < 5[/tex]
Answer:
1) -4 2) -2
Step-by-step explanation:
i got it right
what is the distance between the points (1,5) and (5,-4)?
Answer:
[tex]\sqrt{97}[/tex]
Step-by-step explanation:
Using the pythagorean theorem, you can find that the distance between the two points is [tex]\sqrt{(5-1)^2+(5-(-4))^2}=\sqrt{4^2+9^2}=\sqrt{97}[/tex]. Hope this helps!
Answer:
it 95 good luck
Step-by-step explanation:
A fast food restaurant wants to know what types of toys to put in their kids meals, so they will survey their customers. What would be the BEST way to do this?
personally i would ask every one who orders a kids meal.
hope this helps
Answer:
the answer is c) Ask anyone who orders a kid's meals
Step-by-step explanation:
Suppose vanilla beans cost $600 per kilogram. Julie bought 9 grams of vanilla beans. Jacques bought 70 grams of vanilla beans. How much more did Jacques pay for his vanilla beans? A.$5.40 B.$12.00 c.$36.60 D.$42.00
Answer:
The correct option is c,$36.60
Step-by-step explanation:
The key to solving this question lies around measurement conversion,specifically converting grams into its equivalence in kilograms.
1000 grams equal one kilogram
9 grams=9/1000 kg
9 grams=0.009 kg
70 grams=70/1000 kg
70 grams=0.07 kg
Julie pays=$600*0.009=$5.4
Jacques pays=$600*0.07=$42
Jacques pays $36.60 more ($42-$5.4) than Julie paid
Option is wrong because that was what Julie paid
Option D is wrong because that was what Jacques paid
Option B is obviously wrong