Given:
Consider the height of the rocket, in feet after x seconds of launch is
[tex]y=-16x^2+152x+74[/tex]
To find:
The time at which the rocket will reach its max, to the nearest 100th of a second.
Solution:
We have,
[tex]y=-16x^2+152x+74[/tex]
It is a quadratic polynomial with negative leading coefficient. So, it is a downward parabola.
Vertex of a downward parabola is the point of maxima.
To find the time at which the rocket will reach its max, we need to find the x-coordinate of the vertex.
If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex], then the vertex is
[tex]Vertex=\left(-\dfrac{b}{2a},f\left(-\dfrac{b}{2a}\right)\right)[/tex]
Here, [tex]a=-16,b=152,c=74[/tex].
So,
[tex]-\dfrac{b}{2a}=-\dfrac{152}{2(-16)}[/tex]
[tex]-\dfrac{b}{2a}=-\dfrac{152}{-32}[/tex]
[tex]-\dfrac{b}{2a}=4.75[/tex]
So, x-coordinate of the vertex is 4.75.
Therefore, the rocket will reach its max at 4.75 second.
Plz help me quickly
what is the product of 9⋅(−4)⋅(−4)⋅(−7)
A. −1008
B. −252
C. 252
D. 1008
Answer:
A. -1008
Step-by-step explanation:
9x-4=-36
-36x-4=-144
-144x-7=-1008
Answer:
just go on playstore and search for photomath
A ladder is leaning against a house so that the top of the ladder is 12 feet above the ground. The angle the ladder makes with the ground is 51°. How long is the ladder?
12•sin51°
12/cos51°
12•cos51°
12/sin51°
None of these
Answer:
12/sin5°
Step-by-step explanation:
This angle can be calculated using the law of sine:
sin(angle)=opposite cathete/hypothenuse
sin(angle)=wall/ladder
In this exercise we want to calculate the length of the hypotenuse (ladder), so the equation is changed afterwards.
sin(angle)=wall/ladder
sin(angle)*ladder=wall
ladder=wall/sin(angle)
Now the given values are used:
ladder=wall/sin(angle)
ladder=12ft/cos(51°)
Find the distance between the two points in simplest radical form.
(3,9)and (0,2)
Answer:
7.62
Step-by-step explanation:
use distance formula
All copper has a density of 8.83g/cm3. True Or False.
please help
Answer:
False
Step-by-step explanation:
Copper actually has about 8.96 g/cm3
Answer: No
Step-by-step explanation:
I really need help with the last one if you could help it would be awesome! Tysm.
it’s the second one..................
Write the equation of a line that is perpendicular to y= 3x-2 and that passes through the point (-9,5)
Answer:
Ans: y = (-1/3)x + 2
Step-by-step explanation:
Perpendicular lines have slopes whose product is -1. The slope given in
y = 3x - 2
is -3.
The slope of the perpendicular line will be m, and m needs to satisfy the equation
3 * m = -1
Hence m = -1/3.
Our perpendicular line is thus
y = (-1/3)x + b
for some constant b.
We are told that the perpendicular line goes through the point (-9,5). If so, then the following must hold:
5 = (-1/3)(-9) + b
= 3 + b
b = 2
Ans: y = (-1/3)x + 2
Please HELP!!!!!!!!!
20 POINTS!
FIND MEASURE 1 AND 3
PLS HELP ME
geometry
Answer:
1 = 45
3 = 45
Step-by-step explanation:
[tex]\angle {1}[/tex] and [tex]\angle {3}[/tex] is 45 degrees since the unmarked angle is 90 degrees, meaning that BOTH [tex]\angle {1} and \angle {3}[/tex] are equal.
Q.3] Formula of (a - b)3 is
This is confusing I need help .
Answer:
x = 54angle ACD = 124°Step-by-step explanation:
The rule is that the exterior angle (ACD) is equal to the sum of the remote interior angles (the two marked angles on the right).
You are expected to use this relation to write and solve an equation.
exterior angle = angle D + angle B
(2x +16) = 58 + (x+12)
2x +16 = x +70
x + 16 = 70
x = 54
Then angle ACD is ...
angle ACD = (2x +16)° = (2·54 +16)°
angle ACD = 124°
Find the percent of decrease. Round to the nearest whole percent.
old: 374 boxes; new: 130 boxes
Answer:
B
Step-by-step explanation:
what is 1/10 of 4.8
Answer:
0.48
Step-by-step explanation:
Just move back one decimal point of 4.8
Answer: I just did this one lol
Step-by-step explanation:
10 percent *4.8 =
(10:100)*4.8 =
(10*4.8):100 =
48:100 = 0.48
Now we have: 10 percent of 4.8 = 0.48
Question: What is 10 percent of 4.8?
Percentage solution with steps:
Step 1: Our output value is 4.8.
Step 2: We represent the unknown value with $x$.
Step 3: From step 1 above,$4.8=100\%$.
Step 4: Similarly, $x=10\%$.
Step 5: This results in a pair of simple equations:
$4.8=100\%(1)$.
$x=10\%(2)$.
Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both
equations have the same unit (%); we have
$\frac{4.8}{x}=\frac{100\%}{10\%}$
Step 7: Again, the reciprocal of both sides gives
$\frac{x}{4.8}=\frac{10}{100}$
$ x=0.48$
Xander needs to collect at least 120 cans for a food drive to earn community service credit. He has already collected 64 items.
Choose the inequality and solution to represent the number of cans, x, that Xander must still collect.
Answer:
Step-by-step explanation:
x + 64 > = 120 (thats a greater then or equal sign)
x > = 120 - 64
x > = 56...he needs to collect at least 56 more
BRAINLIEST PLEASEEEE HELP DUE IN 3hrs Can someone help me with this
Answer:
Step-by-step explanation:
14: k^-3/k^4= 1/k^7
15: answer : 1/3²
16: n^-4
17: f-g^4 = 3-(-5)^4 = -622
18: (x^5-y^2)²+x³ =
(2^5-8^2)²+2³ =1032
19: m²-n³
6²-2³ = 36-8=28
20 : 2²×3²×5³= 4500
4500/10 = 450 islands
plz help ASAP matswatch
Answer:
Step-by-step explanation:
Divide £506 in the ratio 2:4:5
•£92, £184 and £230
•£92, £184 and £240
•£92 , £180, £234
Answer:
2x+4x+5x=506
11x=506
x=46
92:184:230
3 multiplied by what equals 4.5
Answer:
3 multiplied by 1.5 equals 4.5
Step-by-step explanation:
3*x= 4.5 We can do division
3x/3 = 4.5/3
x = 1.5
3 multiplied by 1.5 equals 4.5
Hope this helps!
Simplify: 45÷3+2×8-12+42
Show working
PLEASE ANSWER I MARK AS BRAINLIST PLEASEEE
Answer:
Answer B because $15 for 180 lbs is way more than 300 lbs for $24 dollars.
Step-by-step explanation:
Pls help I’m being timed.
Answer:
x=5
Step-by-step explanation:
trust me its right
An item has a listed price of $70. if the sales tax sales is 8% , how much is the sales tax ( in dollars ) ?
Answer:
$5.60
Step-by-step explanation:
$70 ⋅ 0.08 = $5.60
(I could be wrong. Sorry if I am. Don't get mad at me)
Hope I help :)
Please consider Brainliest :)
[tex]\frac{3}{5} /8[/tex]
Answer:
[tex]\huge\boxed{\frac{\frac{3}{5}}{8}=\dfrac{3}{40}}[/tex]
Step-by-step explanation:
[tex]\dfrac{a}{b}=a:b\\\\a:b=a\cdot\dfrac{1}{b}\\\\========================\\\\\dfrac{\frac{3}{5}}{8}=\dfrac{3}{5}:8=\dfrac{3}{5}\cdot\dfrac{1}{8}=\dfrac{3\cdot1}{5\cdot8}=\dfrac{3}{40}[/tex]
Four times Theo’s number added 20 is 10. what is theo’s number ?
Answer:
ur mom
Step-by-step explanation:
genehrrddjdhxxhdhdi hope this didnt help
Difference between (-7x+7) - (-8x-9)
Answer:
x + 16
Step-by-step explanation:
= (-7x +7) - (-8x-9)
= -7x+7+8x+9
*[positive because negative (outside the bracket) multiplied by negative (inside the bracket) will be positive.]
= -7x+8x+7+9 (rearranging like terms together)
= x + 16
If B is the midpoint of AC, AB = 8x + 2 and BC = 5x + 14, then what is the length of AB?
Answer:
The length of AB: 34
Step-by-step explanation:
What are we given?
B = Midpoint of AC
AB = 8x + 2
BC = 5x + 14
|--------------|--------------|
A B C
(This is what your line would look like)
Our equation would be:
AB + BC = AC
(8x + 2) = (5x + 14)
(AB) = (BC)
(Assuming that our line and points are evenly spread out, we can say that they can equal each other)
8x + 2 = 5x +14
- 5x- 2 = -5x -2
---------------------
3x = 12
[tex]\frac{3x}{3}=\frac{12}{3}[/tex]
---------------------
x = 4
1) Substitute
(8x + 2) + (5x + 14) = AC
(AB) + ( BC) = AC
AB = 8(4) + 2
32 + 2
= 34
BC = 5(4) + 14 =
20 + 14
= 34
(We may be able to assume that since the length of the line is possible the same for AB and BC this is considered correct)
The length of the line segment AB is 34 units.
Given that, B is the midpoint of AC, AB = 8x + 2 and BC = 5x + 14.
What is the midpoint of line segment?A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments. The midpoint of a line segment is the point on a segment that is at the same distance or halfway between the two ending points.
Since, B is the midpoint of AC
AB=BC
8x + 2=5x+14
Subtract 5x on both sides of the equation, that is
8x+2-5x=5x+14-5x
⇒ 3x+2 = 14
Transpose 2 to other side of the equation, we get
3x = 14 - 2
⇒ 3x=12
Transpose 3 to other side of the equation, we get
x=4
So, AB=8x+2
=8×4+2
=32+2=34 units
Therefore, the length of the line segment AB is 34 units.
To learn more about the line segment visit:
https://brainly.com/question/25727583.
#SPJ5
Quick help!!!!!!!!Consider the polynomial expression below
X^3 -3x^2 +81x-243
Rewrite the polynomial in the form (x-d) (x-e) (x+f) where D is a real number and E and F are complex numbers of the form BI
x³-3x²+81x-243
x³-3x²+81x-243
Answer : (x-3)(x²+81)
OMG I need halp and this is 8th grade math can someone help me I would really appreiate it.☺
Answer:
Eliana saves at a greater rate because her unit rate of $42 per week is greater than Lana's unit rate of $40 per week
hope this helps =3
sorry if im wrong
5 less than triple the quotient of a number x and 7
Answer:
5 less than triple the quotient of a number x and 7 is 3(x ÷ 7) - 5
-6 + 14 - 9 - (-3) + 8
Please help
Answer:
10
Step-by-step explanation:
−6+14−9−(−3)+8
=8−9−(−3)+8
=−1−(−3)+8
=2+8
=10
-6 + 14 - 9 - (-3) + 8
8 - 9 - (-3) +8
-1 + 3 + 8
2 + 8
10
___ student(s) for every 8 computers.
45 students for every __ computer(s).
Answer:
_18__ student(s) for every 8 computers.
45 students for every _20_ computer(s).
Step-by-step explanation:
18 students for every 8 computers 45 students for every 20 computers