Answer:
h = 80
Step-by-step explanation:
A bullet is fired straight upward with an initial speed of 720 ft/s. It’s path is modeled by the equation h=-16t^2 + 720t, where h is the height of the bullet t seconds after it was fired. When does the bullet reach a height of 4,000 feet?
Answer:
The bullet reaches a height of 4000 feet after 6.49 seconds, and then, coming back down, after 38.5 seconds.
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
The height of the bullet after t seconds is given by:
[tex]h(t) = -16t^2 + 720t[/tex]
When does the bullet reach a height of 4,000 feet?
This is t for which [tex]h(t) = 4000[/tex]. So
[tex]4000 = -16t^2 + 720t[/tex]
[tex]16t^2 - 720t + 4000 = 0[/tex]
Dividing by 16
[tex]t^2 - 45t + 250 = 0[/tex]
So [tex]a = 1, b = -45, c = 250[/tex]
[tex]\bigtriangleup = b^{2} - 4ac = (-45)^2 - 4(1)(250) = 1025[/tex]
[tex]t_{1} = \frac{-(-45) + \sqrt{1025}}{2} = 38.5[/tex]
[tex]t_{2} = \frac{-(-45) - \sqrt{1025}}{2} = 6.49[/tex]
The bullet reaches a height of 4000 feet after 6.49 seconds, and then, coming back down, after 38.5 seconds.
Multiplying by which number is equivalent to a decrease of 8.2%?
Does this expression represent the sum 13.76 + 2.8?
fourteen and four hundredths
Answer:
False
Step-by-step explanation:
ir doesn't add up from what i saw
Please help me, thanks!!!!
Help plz dis is a lil importatnete
Following order of operations:
3^2 = 9
(10-2) = 8
Now you have :
9 + 8 x 5 -4
Multiplication is next:
9 + 40 -4
Now just add and subtract from left to right:
9 + 40 = 49
49-4 = 45
The answer is 45
Step-by-step explanation:
So first you solve whats inside of the parenthesis 10 -2 aand get 8 then you figure 3^2 which is 9 then multiplie 8 times 5 and get 40. 9 + 40 - 4 is what it is so far then add 9 to 40 which is 49 then subtract 4 and get 45!
Round number 245-320
Answer:
300
Step-by-step explanation:
if you mean, 245.320
how much money will she have left after she pays back the money she borrowed from the bank
Step-by-step explanation:
whatever amount her bank account balance is at the same time frame when paying off her loan as only her bank knows
John was adding Rational Numbers. He showed his work below. What was John's error?
Explain to John how to solve it correctly.
Adding Rational Numbers Error.
Answer:
-5 3/5
Step-by-step explanation:
John's error was in adding the whole number and fractional portions separately, the fractions must be converted to improper fractions with common denominators to be added or subtracted properly so
(-7 4/5) + (2 1/5), convert to improper fractions
-39/5 + 11/5, both fractions have common denominator so we can continue
-39 + 11 = -28, so -39/5 + 11/5 = -28/5, convert back to proper fractions
-28/5 = (-25/5) + (-3/5) = -5 3/5
what is the equation
Answer:
n = -7
Step-by-step explanation:
3n-27-2n-8=6n
n-35=6n
-35=5n
n=-7
How do I evaluate this using trigonometric substitution?
∫dx/(81x^2+4)^2
Answer:
[tex]\displaystyle \frac{1}{144}arctan(\frac{9x}{2}) + \frac{x}{8(81x^2 + 4)} + C[/tex]
General Formulas and Concepts:
Alg I
Terms/CoefficientsFactorExponential Rule [Dividing]: [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]Pre-Calc
[Right Triangle Only] Pythagorean Theorem: a² + b² = c²
a is a legb is a legc is hypotenuseTrigonometric Ratio: [tex]\displaystyle sec(\theta) = \frac{1}{cos(\theta)}[/tex]
Trigonometric Identity: [tex]\displaystyle tan^2\theta + 1 = sec^2\theta[/tex]
TI: [tex]\displaystyle sin(2x) = 2sin(x)cos(x)[/tex]
TI: [tex]\displaystyle cos^2(\theta) = \frac{cos(2x) + 1}{2}[/tex]
Calc
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
IP [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
U-Substitution
U-Trig Substitution: x² + a² → x = atanθ
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \int {\frac{dx}{(81x^2 + 4)^2}}[/tex]
Step 2: Identify Sub Variables Pt.1
Rewrite integral [factor expression]:
[tex]\displaystyle \int {\frac{dx}{[(9x)^2 + 4]^2}}[/tex]
Identify u-trig sub:
[tex]\displaystyle x = atan\theta\\9x = 2tan\theta \rightarrow x = \frac{2}{9}tan\theta\\dx = \frac{2}{9}sec^2\theta d\theta[/tex]
Later, back-sub θ (integrate w/ respect to x):
[tex]\displaystyle tan\theta = \frac{9x}{2} \rightarrow \theta = arctan(\frac{9x}{2})[/tex]
Step 3: Integrate Pt.1
[Int] Sub u-trig variables: [tex]\displaystyle \int {\frac{\frac{2}{9}sec^2\theta}{[(2tan\theta)^2 + 4]^2}} \ d\theta[/tex][Int] Rewrite [Int Prop - MC]: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[(2tan\theta)^2 + 4]^2}} \ d\theta[/tex][Int] Evaluate exponents: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4tan^2\theta + 4]^2}} \ d\theta[/tex][Int] Factor: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4(tan^2\theta + 1)]^2}} \ d\theta[/tex][Int] Rewrite [TI]: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4sec^2\theta]^2}} \ d\theta[/tex][Int] Evaluate exponents: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{16sec^4\theta} \ d\theta[/tex][Int] Rewrite [Int Prop - MC]: [tex]\displaystyle \frac{1}{72} \int {\frac{sec^2\theta}{sec^4\theta} \ d\theta[/tex][Int] Divide [ER - D]: [tex]\displaystyle \frac{1}{72} \int {\frac{1}{sec^2\theta} \ d\theta[/tex][Int] Rewrite [TR]: [tex]\displaystyle \frac{1}{72} \int {cos^2\theta} \ d\theta[/tex][Int] Rewrite [TI]: [tex]\displaystyle \frac{1}{72} \int {\frac{cos(2\theta) + 1}{2}} \ d\theta[/tex][Int] Rewrite [Int Prop - MC]: [tex]\displaystyle \frac{1}{144} \int {cos(2\theta) + 1} \ d\theta[/tex][Int] Rewrite [Int Prop - A/S]: [tex]\displaystyle \frac{1}{144} [\int {cos(2\theta) \ d\theta + \int {1} \ d\theta][/tex]Step 4: Identify Sub Variables Pt.2
Determine u-sub for trig int:
u = 2θ
du = 2dθ
Step 5: Integrate Pt.2
[Ints] Rewrite [Int Prop - MC]: [tex]\displaystyle \frac{1}{144} [\frac{1}{2} \int {2cos(2\theta) \ d\theta + \int {1 \theta ^0} \ d\theta][/tex][Int] U-Sub: [tex]\displaystyle \frac{1}{144} [\frac{1}{2} \int {cos(u) \ du + \int {1 \theta ^0} \ d\theta][/tex][Ints] Integrate [Trig/Int Rule - RPR]: [tex]\displaystyle \frac{1}{144} [\frac{1}{2} sin(u) + \theta + C][/tex][Expression] Back Sub: [tex]\displaystyle \frac{1}{144} [\frac{1}{2} sin(2 \theta) + arctan(\frac{9x}{2}) + C][/tex][Exp] Rewrite [TI]: [tex]\displaystyle \frac{1}{144} [\frac{1}{2}(2sin(\theta)cos(\theta)) + arctan(\frac{9x}{2}) + C][/tex][Exp] Multiply: [tex]\displaystyle \frac{1}{144} [sin(\theta)cos(\theta) + arctan(\frac{9x}{2}) + C][/tex][Exp] Back Sub: [tex]\displaystyle \frac{1}{144} [sin(arctan(\frac{9x}{2}))cos(arctan(\frac{9x}{2})) + arctan(\frac{9x}{2}) + C][/tex]Step 6: Triangle
Find trig values:
[tex]\displaystyle tan\theta = \frac{9x}{2}[/tex]
[tex]\displaystyle \theta = arctan(\frac{9x}{2})[/tex]
tanθ = opposite / adjacent; solve hypotenuse of right triangle, determine trig ratios:
sinθ = opposite / hypotenuse
cosθ = adjacent / hypotenuse
Leg a = 2
Leg b = 9x
Leg c = ?
Sub variables [PT]: [tex]\displaystyle 2^2 + (9x)^2 = c^2[/tex]Evaluate exponents: [tex]\displaystyle 4 + 81x^2 = c^2[/tex][Equality Property] Square root both sides: [tex]\displaystyle \sqrt{4 + 81x^2} = c[/tex]Rewrite: [tex]c = \sqrt{81x^2 + 4}[/tex]Substitute into trig ratios:
[tex]\displaystyle sin\theta = \frac{9x}{\sqrt{81x^2 + 4}}[/tex]
[tex]\displaystyle cos\theta = \frac{2}{\sqrt{81x^2 + 4}}[/tex]
Step 7: Integrate Pt.3
[Exp] Sub variables [TR]: [tex]\displaystyle \frac{1}{144} [\frac{9x}{\sqrt{81x^2 + 4}} \cdot \frac{2}{\sqrt{81x^2 + 4}} + arctan(\frac{9x}{2}) + C][/tex][Exp] Multiply: [tex]\displaystyle \frac{1}{144} [\frac{18x}{81x^2 + 4} + arctan(\frac{9x}{2}) + C][/tex][Exp] Distribute: [tex]\displaystyle \frac{1}{144}arctan(\frac{9x}{2}) + \frac{x}{8(81x^2 + 4)} + C[/tex]Estimate The Product of 62.375 and 9 (I Need A Clear Answer, DO NOT PUT "SORRY I DONT KNOW BLAH BLAH BLAH I NEED A NICE AND CLEAR QUESTION )
Which inequality represents the number line below?
x< 2
x > 2
x _< 2
x >_ 2
Answer:
x_<2
Step-by-step explanation:
its shaded in so you have to flip it
Answer:
The answer is
x_<2
The circle is shaded and the arrow is going to the left hand side
Lamar is saving money to buy a game. So far he has saved $6, which is two-thirds of the total cost of the game. How much does the game cost?
Step-by-step explanation:
$9 because 1 third of 3 third would be $3
In a city election, 5,000 people voted for mayor. If the new mayor received 60% of the votes, how many people voted for the new mayor? Show how you know.
Answer:
3000
Step-by-step explanation:
100%-> 5000
60%->3000
Which expression is equivalent to the given expression?
8(34a)−8
34a
6a
8(34a−1)
34a−1
Answer:
8(34a-1)
Step-by-step explanation:
Hope this helps :)
Answer:
8(34a-1)
Step-by-step explanation:
What is the overlap of Team 1 and Team 2?
high
medium
low
none
Two line plots aligned vertically so that their labels match. The first line plot is from 72 to 82, is labeled Team 1, and shows the following values that appear as x marks above the line. One x mark above 73. Two x marks above 74. Two x marks above 75. Three x marks above 76. Two x marks above 77. One x mark above 78. One x mark above 80. The second line plot is also from 72 to 82, is labeled Team 2, and shows the following values that appear as x marks above the line. One x mark above 74. Two x marks above 75. Four x marks above 76. Two x marks above 77. One x marks above 78. One x mark above 79. One x mark above 80.
Answer:
low
Step-by-step explanation:
The dry cleaning fee for three pairs of pants is $18. How much will it cost to clean 11 pairs of pants?
Does the point (4, 0) satisfy the equation y = x2?
Given a point translated from A(1,2) to B(4,4). If a point C at (0,0) is translated in the same way, what will be its new endpoints?
A.(−3,−2)
B.(3,2)
C.(2,2)
D.(3,3)
please help
Answer:
B. (3,2)
Step-by-step explanation:
Step 1) When shifting from A(1,2) to B(4,4), the point shifted 3 units to the right (which means x=3) and 2 units upwards (which means y=2).
Step 2) So when you apply the same movements to point C(0,0), the new point will be (3,2).
See the diagram below. Step 1 is the graph on the left. Step 2 is the graph on the right. The movement is colored in green. Hope this helps!
Please help me......
Answer:
<BAC=1/2 <BOC=1/2 X=X/2(INSCRIBED ANGLE IS HALF OF CENTRAL ANGLE)
HELP ASAP NEED ANSWER
Answer:
2
Step-by-step explanation:
hope this helps
please give brainliest. Thanks! :)
1/3 divided by what equals 1/12
Answer:
You cannot get a positive answer for this, nor can you divide. You could however divide 1/12 by 1/4 to get 1/3.
Step-by-step explanation
The number whose 1/3 is 1/12 is 4.
What is Division?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
let 1/3 divided by x equals 1/12.
So, 1/3 ÷ x = 1/12
and, 1/3 (1/x) = 1/12
1/x = 3/12
1/x = 1/4
x = 4
So, the required number is 4.
Learn more about Fraction here:
https://brainly.com/question/10354322
#SPJ2
I will give brainly Brett has a box that has edges 2.5 meters long. He plans to paint the
outside of all sides, including the top and bottom, of this box. Before
buying the paint, he needs to know the area of the surface he plans to
paint. What is the outside surface area of this box?
Answer:37.5
Step-by-step explanation:
Answer:
37.5
Step-by-step explanation:
What is the common difference for this arithmetic sequence?
31, 48, 65, 82, ...
Answer:
d = 17
Step-by-step explanation:
The given arithmetic sequence is :
31, 48, 65, 82, ...
We need to find the common difference for this sequence.
First term, a₁ = 31
Second term, a₂ = 48
Common difference = a₂-a₁
= 48-31
= 17
So, the common difference for this arithmetic sequence is equal to 17.
Find the next three terms: −14,−17,−20,−23,...
Answer:
-26, -29, -32
Have a great day!
Step-by-step explanation:
Explain 5 different ways you use Math in your everyday life.
Answer:
Buying Groceries, paying for a house, maybe in your job, doing schoolwork of course, and counting money.
Step-by-step explanation:
Answer:
1. you use it to calculate time (managing your day)
2. you use it while driving (use in angles and degrees)
3. you use it while drawing (again, use in angles and degrees)
4. you use it while cooking
5. you use it while banking (financial help)
Step-by-step explanation:
hope this helps:) please mark brainliest
GO ON
Page 4
Book 1
o
Which sentence from the article best explains why stunt performers are willing to do
such a dangerous job?
Answer:
for stunt performers and this is lady's work ( paragraph 6)
The period between two numerals is identified as a decimal point. true or false?
Answer: TRUE!
Step-by-step explanation: Hope this helps!
Answer: True
Step-by-step explanation:
1-Un balón de fútbol tiene un precio de $125 + IVA
1. ¿Cuánto es el IVA del balón?
A) 125 b) 200 c) 245
Answer:
b) 200
Step-by-step explanation:
The correct answer is b) 200
1) El IVA del balón es de $ 20.
2) El precio final del balón es $ 145.
1) El Impuesto al Valor Agregado (IVA) es un impuesto indirecto que se aplica sobre el precio de compra del artículo comprado, es decir, se trata de un impuesto indirecto al consumo.
El porcentaje por concepto del impuesto varía de país en país. No obstante, el valor más común en países hispanoparlantes se ubica en torno al 16 % del precio de compra del artículo.
El IVA del balón se determina mediante la siguiente operación aritmética:
[tex]\Delta C = 0.16\cdot (125)[/tex]
[tex]\Delta C = 20[/tex]
El IVA del balón es de $ 20.
2) El precio final del producto es la suma del precio de compra y el IVA, es decir:
[tex]C = 125 + 20[/tex]
[tex]C = 145[/tex]
El precio final del balón es $ 145.
Para aprender más sobre impuestos, invitamos cordialmente a ver esta pregunta verificada: https://brainly.com/question/24907444
Nota - El enunciado reporta numerosos errores tipográficos y está incompleto, el enunciado correcto y completo es el siguiente:
Un balón de fútbol tiene un precio de $ 125 + IVA.
1) ¿Cuánto es el IVA del balón? a) 20, b) 145, c) 325
2) ¿Cuál es el precio final con IVA del balón? a) 125, b) 200, c) 145
11
A blue dress is marked down 15%. What is the sale price of the dress if the
regular price is $150?
Type your answer...
Answer:
45 dollar's ezzzzzzzzzzzzz