Answer:
The rocket's maximum height will be 1424 feet.
It will reach that height in 4 seconds.
It will reach the ground in 8 seconds.
Step-by-step explanation:
One easy way to find the peak is to find the derivative and solve for zero:
h(t) = -16t² + 128t + 1680
To find the derivative of each term in that format, you simply multiply the coefficient by the exponent, and reduce the exponent by one. In the case of terms with no variable, they disappear. That gives us:
h'(t) = -32t + 128
This derivative describes the rate of change of h with respect to t, so to find the peak, we simply need to solve it for zero:
0 = -32t + 128
32t = 128
t = 4
So the maximum height occurs when t = 4. Let's plug it in to the original equation:
h(t) = -16t² + 128t + 1680
h(4) = -256 + 512 + 1680
h(4) = 1424
So the rocket's maxiumum height is 1424 feet.
And we've already answered the second question, it happens at 4 seconds.
Also, the amount of time going up will be the same as the amount of time going down, which means that it will reach the ground in twice that time, or 8 seconds.
NO LINKS WILL MARK BRAINLIEST
Answer:
30.2 sq cm
Step-by-step explanation:
bass times height 10 cm bottom and 3.2 height
Olympia ate lunch at a restaurant. The amount of her check was $6.89. She left $8.00 on the table, which included the amount she owed plus a tip for the waiter. Which equation shows t, the amount of her tip, in dollars? a.6.89 + t = 8.00 b.6.89 - t = 8.00 c.6.89t = 8.00 d.6.89 = 8.00 ÷ t
Answer:
1.11 will be the answer
Step-by-step explanation:
Which pair of angles are complementary? 2 points Option 1 O Option 2 O Option 3 O Option 4
Answer:
option 4, complementary angles total 90°
Step-by-step explanation:
15 Points for this and brainliest pls help I am soooooo desparateeeeeeeeee
Answer:
cant see the words clearly please type the words and answers !!
What type of number is 0?
Select each correct answer.
integer
I rational
irrational
real
O natural
whole
Answer:
0 is a rational number, whole number, integer, and a real number.
Step-by-step explanation:
I need help look in screenshot plzz
Answer:
45
Step-by-step explanation:
3 to the power of 2=9
and 9x5 =45
Answer asp
__% of 75 is 25
33% of 75 is 25... Hope that helps!!
2. A local t-shirt company sold 2000 t-shirts two weeks ago when they charged $10 for each shirt. The following week they sold 1120 t-shirts when they raised the price to $19 per shirt. Assuming that this rate of change continues find the following: a. Find a linear function S(p) that models the number of shirts sold as a function of the price p. b. Explain the meaning of the slope In terms of the problem. c. Predict the number of shirts the store would sell if they charged $25 for each shirt. d. If the store would like to maintain a weekly sales level of 1450 shirts how much should they charge per shirt?
9514 1404 393
Answer:
a) S(p) = -97.78p +2977.78
b) about 98 fewer shirts per week will be sold for each $1 increase in price
c) 533 shirts per week
d) $15.63
Step-by-step explanation:
a) You are given two ordered pairs: (p, s) = (10, 2000) and (19, 1120). The two-point form of the equation for a line can be used.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
s = (1120 -2000)/(19 -10)(p -10) +2000
s = -97.78(p -10) +2000
S(p) = -97.78p +2977.78
__
b) The slope is shirts/dollar, meaning about 98 fewer shirts will be sold for each dollar increase in price.
__
c) S(25) ≈ 533
At a price of $25, the store would sell about 533 shirts per week.
__
d) 1450 = S(p) = -97.78p +2977.78
-1527.78 = -97.78p
15.625 = p ≈ 15.63
The store should charge $15.63 per shirt to maintain sales of 1450 shirts per week.
subject : bible:
What two words summarize Romans 10:9-10?
sacrifice
work
believe
confess
justify
Answer:
confess and believe are the two main words.
Step-by-step explanation:
Just got this right :')
HELP!!! DUE IN 8 MINS!!
Answer:
Step-by-step B. is your answer
explanation:
What is the measure of angle GXI?
Answer:
Step-by-step explanation:
GXI with three points sounds like a triangle and a triangle angle equals 180 degrees.
Add picture and I'll try to solve full problem
Please help I will give brainliest
Answer:
The third option 56
Step-by-step explanation:
56 is the middle number but I'm sorry if I'm wrong
the two the numbers -2.6 and -2.1 are shown on the number line what is the distance between the two points
Answer:
0.5Step-by-step explanation:
The distance between the points will be the difference between the points as shown;
Difference = -2.1 - (-2.6)
Difference = -2.1 + 2.6
Difference = 2.6 - 2.1
Difference = 0.5
Hence the difference between the numbers -2.6 and -2.1 on the number line is 0.5
The trinomial 2x2 + 13x + 6 has a linear factor of x + 6.
2x2 + 13x + 6 = (x + 6)(?)
What is the other linear factor?
A. x + 3
B. x + 6
C. 2x + 1
D. 2x + 3
Answer:
C (2x+1)
Step-by-step explanation:
I hope this helps!
Evaluate the expression: 2 ⋅ 6^2 *
Answer:
72
Step-by-step explanation:
First square 6.
6^2=36
Then multiply 26 by 2.
2*36=72
What TWO steps do you take to solve the following equation: 5x - 3 = 12
Answer:
First add 3 to each side
Then divide each side by 5
Step-by-step explanation:
5x - 3 = 12
First add 3 to each side
5x-3+3 = 12+3
5x = 15
Then divide each side by 5
5x/5 = 15/5
x = 3
Answer:
3
Step-by-step explanation:
5x = 12 + 3
x = 15/5
x = 3
Solve triangle ABC. (Round your answers to one decimal place.)
∠A =
13.5
°
∠B =
63.9
°
∠C =
Find the value of x
Please help
Answer:
128 degrees
Step-by-step explanation:
360-90-90-52=128
Angle ABD is 90°
What is the measure of ZABC?
O A 360
O B. 54°
OC. 90°
OD. 126°
O E. 144º
What is equivalent to 0 = 2x2 - 16x – 18 when completing the
square?
Answer:
x = 1
x = -9
Step-by-step explanation:
(2x2 + 16x) - 18 = 0
2x2 + 16x - 18 = 2 • (x2 + 8x - 9)
x2 + 8x - 9
-9 + 1 = -8
-3 + 3 = 0
-1 + 9 = 8
2 • (x + 9) • (x - 1) = 0
2 = 0
x+9 = 0
x = -9
x-1 = 0
x = 1
x2 + 8x - 9 = 0
x2+8x = 9
(x+4) • (x+4) =
(x+4)2
x2+8x+16 = 25 and
x2+8x+16 = (x+4)2
(x+4)2 = 25
x = -4 + √ 25
x2 + 8x - 9 = 0
has two solutions:
x = -4 + √ 25
or
x = -4 - √ 25
- B ± √ B2-4AC
x = ————————
2A
A = 1
B = 8
C = -9
B2 - 4AC =
64 - (-36) =
100
-8 ± √ 100
x = —————
2
x = ( -8 ± 10) / 2
x =(-8+√100)/2=-4+5= 1.000
or:
x =(-8-√100)/2=-4-5= -9.000
Answer: x = 1
x = -9
-4--7=n cual es el valor de n
A large tank is filled to capacity with 400 gallons of pure water. Brine containing 3 pounds of salt per gallon is pumped into the tank at a rate of 4 gal/min. The well-mixed solution is pumped out at a rate of 8 gals/min. Find the number A(t) of pounds of salt in the tank at time t.
Answer:
The number A(t) of pounds of salt in the tank at time t = [tex]\frac{3t(100 - t)}{25}[/tex]
Step-by-step explanation:
Given - A large tank is filled to capacity with 400 gallons of pure water. Brine containing 3 pounds of salt per gallon is pumped into the tank at a rate of 4 gal/min. The well-mixed solution is pumped out at a rate of 8 gals/min.
To find - Find the number A(t) of pounds of salt in the tank at time t.
Proof -
Given that,
Capacity of water = 400 gallons
rate in flow = 4 gal/min
rate out flow = 8 gal/min
Concentration in = 3 lbs/gal
Concentration out = (Amount of salt at time t )/ (Solution in tank at time t)
Now,
Let
A(t) = Amount of salt in the tank at time t
Now,
Initially tank has 400 gallons of water, So
A(0) = 0 ................(1)
Now,
Rate of change in the amount of salt = [tex]\frac{d}{dt} A(t)[/tex]
= (Rate in flow )( Concentration In) - (Rate out flow )( Concentration out)
= (4) (3) - (8) ([tex]\frac{A(t)}{400 - 4t)}[/tex]
= 12 - [tex]\frac{2A(t)}{100 - t)}[/tex]
⇒[tex]\frac{d}{dt} A(t)[/tex] + [tex]\frac{2A(t)}{100 - t)}[/tex] = 12
Now,
Integrating Factor, I.F = [tex]e^{\int {\frac{2}{100 - t} } \, dt }[/tex]
= [tex]e^{-2ln(100 - t)}[/tex]
= (100 - t)⁻²
⇒I.F = (100 - t)⁻²
The solution becomes
A (I.F) = ∫ (I.F)(12) dt + C
⇒A (100 - t)⁻² = ∫12(100 - t)⁻² dt + C
⇒A (100 - t)⁻² = -12(100 - t)⁻¹ (-1) + C
⇒A(t) = [tex]12(100 - t)+ C(100 - t)^{2}[/tex]
Now,
We have A(0) = 0
⇒C = -12/100
∴ we get
A(t) = 12(100 - t) - [tex]\frac{12}{100}[/tex] (100 - t)²
= 12(100 - t) [ 1 - [tex]\frac{100 - t}{100}[/tex] ]
= 12(100 - t) ([tex]\frac{t}{100}[/tex])
= [tex]\frac{3t(100 - t)}{25}[/tex]
⇒A(t) = [tex]\frac{3t(100 - t)}{25}[/tex]
∴ we get
The number A(t) of pounds of salt in the tank at time t = [tex]\frac{3t(100 - t)}{25}[/tex]
which statement is true.
7. Below are the steps taken to simplify the expression. Which justification matches Step c of the simplified expression? *
7x+8y+5x+3(y+1)
a. 7x + 8y + 5x + 3y + 3
b. 7x + 5x + 8y + 3y + 3
c. (7x + 5x) + (8y + 3y) + 3
d. 12x + 11y+ 3
A. Associative Property of Addition
B. Commutative Property of Addition
C. Combine Like Terms
D. Distributive Property
Answer:
A. Associative property of addition
Step-by-step explanation:
The associative property is about the grouping of terms/numbers in parentheses in an equation.
Will give brainlest, find the area
Find the unit rate: $1.98 for 3 pounds
Answer:
$0.66 or 66 cents
Step-by-step explanation:
[tex]\frac{1.98}{3} =0.66[/tex]
What is the median of the data set?
9
8.5
8
10
Answer:
8.5
Step-by-step explanation:
When you write out the data set, it looks like this:
5, 8, 8, 8, 8, 9, 9, 9, 10, 10
The median means the exact middle of the data set. In this case, it falls between the 8 and the 9, so the middle would be 8.5, so that's the median of the set. I hope this helps :)
Answer:
The median is 8.5
Step-by-step explanation:
The median is the middle number in a data set. For example, if you had a data set:
2, 2, 3, 4, 4
You would go forwards and backwards in the set until you found the middle number, which is 3. 3 would be the median.
However, if there is no middle number (there are an even number of points in the set), you add the two remaining numbers and divide it by two.
For example, if the final two numbers were:
2, 6
You would add 2 and 6 to get 8, and divide by 2, and you get the median 4.
In this set, we have
5, 8, 8, 8, 8, 9, 9, 9, 10, 10.
The final two numbers are 8 and 9, so you add 8+9=17, divided by 2 = 8.5.
find the value of x
Answer:
x=6,1,5 is your answer look it once
Solve for X in the diagram below.
Answer:
X = 56
Step-by-step explanation:
4.
What is the error in this equation for a trigonometric ratio? Explain the error in full sentences and give a corrected ratio. (5 points)
Answer:
[tex]\cos\ A = \frac{2}{4.5}[/tex]
Step-by-step explanation:
Given
[tex]sin\ A = \frac{2}{4.5}[/tex]
See attachment
Required
Explain and correct the error
The error in the equation is that: the formula of cosine of angle A is used to calculate the sine of angle A.
The ratio can be corrected as by using:
[tex]\cos\ A = \frac{Adjacent}{Hypotenuse}[/tex]
[tex]\cos\ A = \frac{AC}{AB}[/tex]
[tex]\cos\ A = \frac{2}{4.5}[/tex]