Answer:
Step-by-step explanation:
a) The height of the springboard above the water should be h(0) : Read, the height at t = 0
h(0) = -5(0) + 10(0) + 3
h(0) = 0 + 0 + 3
h(0) = 3
a) 3 meters
b) The time it takes the diver to hit water should be, the positive 0 solution for t. Remember, in a quadratic equation, there are two values for t where a parabola crosses the horizontal axis, which in this case would be t. Just by looking at the function, h(t) = -5t2 + 10t + 3 , one should be able to see that it cannot be factored easily, so it requires the Quadratic Formula to find the zeros ; x = -b ±√(b2-4ac) / 2a
Substitute t for x, and use the coefficients for a, b, c:
t = (-10 ± √((102 - 4(-5)(3)))/2(-5)
t = (-10 ±√(100 + 60))/-10
t = (-10 ±√160)/-10) ; Now factor the 160 to simplify:
t = (-10 ±√(10*16))/-10
t = (-10 ±4√10)/-10 ; Factor out leading coefficient of -2 from the numerator:
t = -2(5 ± 2√10)/-10
t = (5 ± 2√10)/5
Using a calculator to find the zeros, and disregarding the negative zero (because t starts at 0):
t ≈ 2.265
b) approx. 2.265 seconds for diver to hit water.
c) To find this, set the function equal to 3 to find what other value for t would be equal to 3 (we know one is 0).
-5tt + 10t + 3 = 3
-5t2 + 10t = 0 ; factor out t
t(-5t + 10) = 0
We know t = 0:
We also know that -5t + 10 = 0
-5t = -10
t = 2
c) 2 seconds. This is the time that diver would equal height of t=0 which is where he started, and where he equals the height of the springboard.
d and e) The peak of the dive (parabola), is determined using the formula h = -b/2a (Derived from the Quadratic Formula) to find the y value (in this case, the h value, answering e) and then using that result in the function to find the x value (in this case, the t value answering d) of the point where the parabola (dive path) reaches a maximum(height), or minimum(in upward opening parabolas).
h = -10/2(-5)
h = -10/-10
h = 1
h(1) = -5(1)2 + 10(1) + 3
h(1) = -5 + 10 + 3
h(1) = 8
d) At t = 1 second, diver will have reached peak of dive.
e) At t = 1 second, diver will have reached a maximum height of 8 meters.
need help with these two math problems
Answer:
y = (x - 1)(x - 3)
y = (x + 2)^2
Step-by-step explanation:
3)
Has roots at x = {1, 3}
y = (x - 1)(x - 3)
4)
Has double root at x = -2
y = (x + 2)^2
A board 120 inches long is divided into 2 sections. If the ratio of the 2 sections is 3:5, what are the lengths of the sections?
15 inches, 105 inches
A
B
24 inches, 96 inches
C 40 inches, 80 inches
D 45 inches, 75 inches
Answer:
D 45 inches, 75 inches
Step-by-step explanation:
3:5 is 3 + 5 = 8 parts
one section is 3/8 of 120 = 45 inches
other section is 5/8 of 120 = 75 inches
D 45 inches, 75 inches
There are 550 calories in 100 g of bacon. There are 196 calories in a fried egg. Philip has 60 g of bacon and two fried eggs for breakfast. Work out the total number of calories in this breakfast.
Answer:
509.6 calories
Step-by-step explanation:
196+196=392 calories
10g of bacon=19.6 calories
60g of bacon=19.6×6=117.6 calories
392+117.6=509.6 calories
pls help the will mean the world
Answer:
A: the area of the walls that are being painted
C: the cost per gallon of different paints
F: the number of square feet that can be painted per gallon of paint
Step-by-step explanation:
Need help!! Answer asap!! No links! What is the most likely reason that nonmetals are electrical insulators?
A. Since valence shells are mostly empty in nonmetal atoms, the atoms attract and hold any electrons they can in order to fill their valence shells.
B. Since valence shells in nonmetal atoms are almost full, the atoms attract electrons and hold them tightly to fill their valence shells.
C. Since all nonmetals have valence shells that are full, they hold electrons tightly to avoid changing.
D. Since all nonmetals have valence shells that are completely empty, they do not attract or release any electrons.
Answer:
B. because it just isssssssss I'm typing things to let me answerrr
What is the slope of the line that has a y-intercept of (0, 6) and passes through the point (2, 8)?
m= ?
Answer:
m=1
Step-by-step explanation:
[tex]m=\frac{8-6}{2-0} =\frac{2}{2} =1[/tex]
I hope this help you
Solve for X. 22 = 10x Simplify your answer as much as possible. x = 음. 6 08 ?
Answer:
x=11/5
Step-by-step explanation:
isolate x
22/10 = 10x/10
22/10 = x
simplify
11/5 = x
If a certian perosn has a mass of 250kg on earth, would that person's mass be on the moon, if the moon's gravity is 1.62m/s2? *
10 points
245kg x 1.62m/s2
245 x 1.62m/s2
It remains the same
The person would be weightless
Answer:
Weight On the Moon: 41.34 kilograms
Step-by-step explanation:
1.
Write the equation of the parabola in vertex form.
A. y = –(x – 1)2 + 3
B. y = –x2 – 4
C. y = –x2 + 3
D. y = –x2 + 4
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{o pens~\cap}\qquad \stackrel{"a"~is~positive}{o pens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\begin{cases} h= 0\\ k = 4 \end{cases}\implies y=a(x-0)^2+4~\hfill \textit{we also know that} \begin{cases} x = 1\\ y = 3 \end{cases} \\\\\\ 3=a(1-0)^2+4\implies 3=1a+4\implies \boxed{-1=a} \\\\\\ y=-1(x-0)^2+4\implies \blacktriangleright y = -x^2+4\blacktriangleleft[/tex]
Answer:
A. y = –(x – 1)2 + 3 = Rewrite in vertex form and use this form to find the vertex (h,k). (1,3)= Already in vertex form. y=−(x−1)2+3
OR
D. y = –x^2 + 4 = Rewrite in vertex form and use this form to find the vertex (h,k). (0,4)= Find the vertex form. y=−(x+0)2+4
Step-by-step explanation:
A. y = –(x – 1)2 + 3 = Rewrite in vertex form and use this form to find the vertex (h,k). (1,3)= Already in vertex form. y=−(x−1)2+3
B. y = –x^2 – 4 = Rewrite in vertex form and use this form to find the vertex (h,k). (0,−4)= Find the vertex form. y=−(x+0)2−4
C. y = –x^2 + 3 = Rewrite in vertex form and use this form to find the vertex (h,k). (0,3)= Find the vertex form. y=−(x+0)2+3
D. y = –x^2 + 4 = Rewrite in vertex form and use this form to find the vertex (h,k). (0,4)= Find the vertex form. y=−(x+0)2+4
Seventy-nine ÷ nine and five
Answer:
13.77777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777
What's the negative reciprocal of 5? Question 12 options: A) 1∕5 B) –5 C) –1∕5 D) 5
Answer:
[tex]\huge\boxed{C)\ -\dfrac{1}{5}}[/tex]
Step-by-step explanation:
The reciprocal of 5: [tex]\dfrac{1}{5}[/tex]
The negative reciprocal of 5: [tex]-\dfrac{1}{5}[/tex]
what are the mean variacne and standard deviatioon of the values? round to the nerates tenth. 11,11,3,1,11
Answer:
Mean = 8
Variance = 22
Standard deviation = 4.6904
Step-by-step explanation:
To find out Mean the formula is : total sum of data set / number of values
(11 + 11 + 3 + 1 + 11 + 11) / 6 = 48 / 6 = 8
Mean = 8
Now for variance we will form a table
x 11 11 3 1 11 11
(x - Mean) 3 3 -5 -7 3 3
(x - Mean)² 9 9 25 49 9 9
Now we the formula of variance =
Variance = (9+9+25+49+9+9)/(6-1) = 110/5 = 22
Variance = 22
Now we know Standard deviation = √(variance)
Therefore standard deviation = √22 = 4.6904
Hope this helps!<3
Answer: Mean = 8
Step-by-step explanation:
10. The ordered pairs (1, 2), (2, 8), (3, 18), and (4, 32) represent a function. What is a rule that represents this function?
It also gives me these numbers:
a. 2x
b. 2x + 2
c. x^2
d. 2x^2
Answer:
d. 2x^2
Step-by-step explanation
Dora opens a savings account and puts in $ 290 at the start. Every week, she deposits $ 30 in the account. Which type of function would you use to model the relationship between the number of weeks since Dora opened the account, and the amount of money in the account
Answer:
f(x)=290+30x
Step-by-step explanation:
the 290 is for the money initially put in, the 30 is for the thirty dollars, and the x represents the number of weeks.
How many eggs are 5dozens
Answer:
60
Step-by-step explanation:
1 dozen=12 eggs. 12 ×5=60
Answer:
60
Step-by-step explanation:
dozen=12
5x12=60
True or false? The point (−5, 0) lies on the y-axis.
\well the answrnist that brcause if u think it guys up
-(b-z)-(-2b+z)-(-3b-z)
Step-by-step explanation:
4b + z I think lol I honestly looked it up
what is 5 sixths of a full rotation
Answer:
300°
Step-by-step explanation:
what is 5/6 of a full rotation?
A full rotation is 360°
360 * 5/6 = 300°
Find the first partial derivatives of the function.
z = (6x + 2y)^9
dz/dx=
dz/dy=
If z = (6x + 2y)⁹, then the partial derivatives of z are
• with respect to x :
∂z/∂x = 9 (6x + 2y)⁹⁻¹ • ∂(6x + 2y)/∂x
∂z/∂x = 9 (6x + 2y)⁸ • 6
∂z/∂x = 54 (6x + 2y)⁸
• with respect to y :
∂z/∂y = 9 (6x + 2y)⁹⁻¹ • ∂(6x + 2y)/∂y
∂z/∂y = 9 (6x + 2y)⁸ • 2
∂z/∂y = 18 (6x + 2y)⁸
Write the first five terms for the following recursive rule.
f(1)=7
f(n)=f(n-1)+12
Answer:
PLEASE MARK ME AS BRANLIEST!!!!!
Step-by-step explanation:
a1 = first term; an= an-1 + d a1 = the first term in the sequence an = the nth term in the sequence an-1 = the term before the nth term n = the term number d = the common difference.
{10, 15, 20, 25, 30, 35, } first term = 10, common difference = 5 recursive formula: a1= 10; an= an-1 + 5
f(n) = f(n-1) + 12
f(1) = 7
f(2) = (7-1) + 12 = 18
f(3) = (18-1) + 12 = 29
f(4) = (29-1) + 12 = 40
f(5) = (40-1) + 12 = 51
7, 18, 29, 40, 51
Solve each of the following equations. Show its solution set on a number line. Check your answers. 2|2-x|=-5
Answer:
Use the distributive property to multiply 2 by x−1.
l2x-2I=11
2x-2=-11
Add 2 to both sides of the equation.
2x=-9
Divide both sides by 2.
x=13/2
That's the final answer
Hope u have a great day!!
please help me i’ll give brainlist and points
Answer:
Area solution
Step-by-step explanation:
A=(16+10)×12/2= 156 m^2
evaluate (2/3)6 power
evaluate 2/3 evaluate 2/3 6th power
Answer:
64/729
Step-by-step explanation:
(2/3)^6 = (2^6)/(3^6) = 64/729
-8-8-6-2 4 12 22
What is the nth term rule of the quadratic sequence
Answer:
[tex]n^2 -3n - 6[/tex]
Step-by-step explanation:
Looking at the image attached, you must first work out the difference between each term. This is +0, +2, +4, +6, +8, +10 (shown in orange).
Because you now have a linear sequence, the difference is now the same each time. This is +2 (shown in blue).
Because the original sequence is a quadratic, you have to halve the second difference (the +2). This means that the value of [tex]n^2[/tex] is 1, so 1[tex]n^2[/tex] or just [tex]n^2[/tex] .
If you write out the values of [tex]n^2[/tex], you can work out how much more you need to add or take away. For example, take the first three terms in the sequence.
n = 1, 2, 3
x = -8, -8, -6
[tex]n^2[/tex] = 1, 4, 9
Work out the difference between [tex]n^2[/tex] and x:
1 - -8 = 9
4 - -8 = 12
9 - -6 = 15
This gives you yet another linear sequence, 9, 12, 15.
Working out the formula for this, the difference is 3 each time, so it is 3n. The first value of n is 1, so 3n is 1. The difference is 6, so the formula for this linear sequence is 3n + 6.
Because [tex]n^2[/tex] is greater than x, you need to take 3n + 6 away from [tex]n^2[/tex].
This gives [tex]n^2[/tex] - (3n+6), so the final answer is:
[tex]n^2[/tex] - 3n - 6.
This table represents the number of pounds, p, a puppy grows after w, weeks.
When graphed, all of the points in the table lie on the same line.
What is the slope and y-intercept of the line?
slope=−94, y-intercept=−0.8
slope=−49, y-intercept = 2
slope=49, y-intercept=−0.8
slope=94, y-intercept = 2
Weeks, w Weight in pounds, p
0 2
2 6.5
4 11
6 15.5 help plz
Answer:
the answer is slope=94, y-intercept = 2
Step-by-step explanation:
i took the test
HELP PLS!! no links !!!
Answer:
the correct answer is b
Step-by-step explanation:
Like and give 5 star rating
a line with slope -2 passes through the point (-2,3). What is the equation of the line?
Which set of side lengths will form a triangle
A: 16ft, 4ft, 21ft
B: 30ft, 30ft, 60ft
C: 12ft, 12ft, 20ft
D: 3ft, 5ft, 10ft
PLS HELP
Answer:
the set of side lengths will be d
How does insurance reduce social burden?
A. Insurance ensures that people don't have to pay high deductibles.
B. Insurance ensures that losses are not passed on to society.
C. Insurance ensures that lenders publicize rates and treat all
customers equally.
D. Insurance ensures that people are treated fairly in hiring and
employment decisions.
Answer:
c po is the correct aswer
Step-by-step explanation:
correct me if im wrong hope it's help
thanks
Answer:
B. Insurance ensures that losses are not passed on to society
Hope this helps :)
If xcos(x)= 2, find (-x) • cos(-x)
[tex](-x) \cos(-x)\\\\=-x \cos x \\\\=-(x \cos x)\\\\=-2[/tex]