Answer:
D. by multiplying 58 by 0.17
[tex]17\% \: of \: 58 \\ = \frac{17}{100} \times 58 \\ = \frac{986}{100} \\ = 9.86[/tex]
How to solve it?
[tex]\int\limits^a_b {x^2+2x} \, dx[/tex]
Hi there! Assume that this is your question.
[tex] \large{ \int \limits^a_b ( {x}^{2} + 2x)dx}[/tex]
Before we get to Integral, you have to know Differentiation first. If you know how to differentiate a polynomial function then we are good to go in Integral!
We call the function that we are going to integrate as Integrand. Integrand is a function that's differentiated. In Integral, Integrating requires you to turn the function from differentiated to an original function.
For Ex. If the Integrand is x² then the original function is (1/3)x³ because when we differentiate (1/3)x³, we get x²
[tex] \large{f(x) = \frac{1}{3} {x}^{3} \longrightarrow f'(x) = {x}^{2} } \\ \large{f'(x) = 3( \frac{1}{3} ) {x}^{3 - 1} } \\ \large{f'(x) = {x}^{2} }[/tex]
So when we Integrate, make sure to convert Integrand as in original function. From the question, our Integrand is x²+2x. The function is in differentiated form. We know that x² is from (1/3)x³ and 2x comes from x²
[tex] \large{ f(x) = {x}^{2} \longrightarrow f'(x) = 2x} \\ \large{f'(x) = 2 {x}^{2 - 1} } \\ \large{f'(x) = 2x}[/tex]
Thus,
[tex] \large{ \int \limits^a_b ( {x}^{2} + 2x)dx} \\ \large{\int \limits^a_b ( \frac{1}{3} {x}^{3} + {x}^{2}) }[/tex]
Normally, if it's an indefinite Integral then we'd just put + C after (1/3)x³+x² but since we have a and b, it's a definite Integral.
[tex] \large{ \int \limits^b_a f(x)dx = F(b) - F(a)}[/tex]
Define F(x) as our anti-diff
From our problem, substitute x = a in then subtract with the one that substitute x = b
[tex] \large{ (\frac{1}{3}{a}^{3} + {a}^{2} ) - ( \frac{1}{3} {b}^{3} + {b}^{2}) }[/tex]
Simplify as we get:
[tex] \large \boxed{ \frac{1}{3}{a}^{3} + {a}^{2} - \frac{1}{3} {b}^{3} - {b}^{2}}[/tex]
The function h(t)=−16t2+7t+63 represents the height of a t-shirt launched from a t-shirt cannon after t seconds. a. Write an equation that tells us when the t-shirt hits the ground. b. At what time does the t-shirt hit the ground. SHOW ALL WORK. Round to 2 decimal places.
Answer:
[tex](a)\ -16t^2 + 7t + 63=0[/tex]
[tex](b)\ t = 2.215[/tex]
Step-by-step explanation:
Given
[tex]h(t) = -16t^2 + 7t + 63[/tex]
Solving (a): Equation when it hits the ground.
This means that [tex]h(t) = 0[/tex]
So, we have:
[tex]h(t) = -16t^2 + 7t + 63[/tex]
[tex]-16t^2 + 7t + 63=0[/tex]
Solving (b): The value of t in (a)
[tex]-16t^2 + 7t + 63=0[/tex]
Using quadratic formula, we have:
[tex]t = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
This gives:
[tex]t = \frac{-7 \± \sqrt{7^2 - 4*-16*63}}{2*-16}[/tex]
[tex]t = \frac{-7 \± \sqrt{49+ 4032}}{2*-16}[/tex]
[tex]t = \frac{-7 \± \sqrt{4081}}{-32}[/tex]
[tex]t = \frac{-7 \± 63.88}{-32}[/tex]
Split
[tex]t = \frac{-7 + 63.88}{-32}; or\ t = \frac{-7 - 63.88}{-32}[/tex]
[tex]t = \frac{56.88}{-32}; or\ t = \frac{-70.88}{-32}[/tex]
[tex]t = -1.7775; or\ t = 2.215[/tex]
Time can't be negative; So:
[tex]t = 2.215[/tex]
how to graph linear standard 3x−4y=24
Graph the linear equation. 3x-4y= 24
---------------------
Let x = 0, then y = -6
Let y = 0, then x = 8
----------------------------
Plot (0,-6) and (8,0) and draw a line thru them to get:
Translate this sentence into an equation. 59 decreased by Vanessa's score is 7. Use the variable v to represent Vanessa's score.
So, Vanessa's score = v. Let's work from there.
We know that 59 is decreased by Vanessa's score, which is subtraction, and thus: 59 - v
Then, we're told that that quantity is 7. "Is" can be used in place of an equals sign: = 7
Therefore, our equation is as follows: 59 - v = 7
Hope this helps!! :)
the function h=-16t^2+48t represents the height h (in feet) of a kickball t seconds after it is kicked from the ground
Answer:
36 feet
Step-by-step explanation:
Given
[tex]h(t) = -16t^2 + 48t[/tex]
Required
Determine the maximum height attained
First, calculate the time to reach maximum height;
In a quadratic equation;
[tex]y = ax^2 + bx + c[/tex]
The maximum is:
[tex]x = -\frac{b}{2a}[/tex]
So, we have:
[tex]t = -\frac{b}{2a}[/tex]
Where
[tex]a = -16; b = 48[/tex]
So:
[tex]t = -\frac{b}{2a}[/tex]
[tex]t = -\frac{48}{2 * -16}[/tex]
[tex]t = -\frac{48}{-32}[/tex]
[tex]t = \frac{48}{32}[/tex]
[tex]t = 1.5[/tex]
The maximum height is at: [tex]t = 1.5[/tex]
So, we have:
[tex]h(t) = -16t^2 + 48t[/tex]
[tex]h_{max}=-16 * 1.5^2 + 48 * 1.5[/tex]
[tex]h_{max}=36[/tex]
[tex] \sqrt[3]{( - 64)} [/tex]
Answer:
[tex]-4[/tex]
Step-by-step explanation:
Step 1: Apply the rule
[tex]\left(-64\right)=-64\\\\=\sqrt[3]{-64}[/tex]
Step 2: Apply the radical rule
[tex]\sqrt[3]{-64}=-\sqrt[3]{64}\\\\=-\sqrt[3]{64}[/tex]
Step 3: Factor the number
[tex]\:64=4^3\\\\=-\sqrt[3]{4^3}[/tex]
Step 4: Apply the radical rule
[tex]\sqrt[3]{4^3}=4\\\\=-4[/tex]
Therefore, [tex]\:\sqrt[3]{\left(\:-\:64\right)}\:=\:-4[/tex]
Answer:
-4
Step-by-step explanation:
If f (x) = StartRoot x EndRoot + 12 and g (x) = 2 StartRoot x EndRoot, what is the value of (f – g)(144)?
–84
Answer:
hmm very diffecult.
Step-by-step explanation:
if f (x) = StartRoot
A population of beetles is modeled by the equation b(t) = 3,000 (2)t where t represents the number of weeks since the population was first measured?
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]b(t) = 3000 * 2^t[/tex]
The question is incomplete;
A possible question could be to calculate the initial amount of beetle
An exponential function is represented as:
[tex]f(x) = ab^x[/tex]
Where
[tex]a \to Initial\ amount[/tex]
By comparison:
[tex]a = 3000[/tex] --- The initial number of beetles
Another question could be to solve for f(t), after a certain number of weeks (say 3)
Substitute 3 for t in: [tex]b(t) = 3000 * 2^t[/tex]
[tex]b(3) = 3000 * 2^3[/tex]
[tex]b(3) = 3000 * 8[/tex]
[tex]b(3) = 24000[/tex]
Erin has 5 cans of juice and drinks 13 of a can daily. In how many days will she empty all the cans she has?
Answer:
15 days
Step-by-step explanation:
Don't you mean 1/3? If so,
5 cans
-------------------- = 15 days
1/3 can/daily
A 10-foot ladder is leaning against a wall. If the ladder reaches 8 feet up the wall, how fare is thr base of the ladder from the wall?
Answer:
6ft
Step-by-step explanation:
The answer is 6 feet
Have a good day:)
A thin wire inform of an equilateral triangle of side 11 cm find the area of a circle whose circumference is equal to the length of the wire
Answer:
86.70 cm^2
Step-by-step explanation:
circumference = 11 x 3 = 33
circumference of a circle = nD
33 = 3.14 X D
D = 10.51
r = 10.51 / 2 = 5.25
Area = nr^2
3.14 x 5.25^2 = 86.70 cm^2
What is 2000% as a fraction
Answer:
20000/10
Step-by-step explanation:
Answer:
Step-by-step explanation:
2000%=2000/100=20/1
Please help me solve this ;-;
9514 1404 393
Answer:
C log3(√((x -4)/x)
Step-by-step explanation:
The applicable rules of logarithms are ...
log(a/b) = log(a) -log(b)
log(a^n) = n·log(a)
The base is irrelevant, as long as all logs are to the same base.
__
[tex]\dfrac{1}{2}(\log_3{(x-4)}-\log_3{(x)})=\dfrac{1}{2}\log_3(\dfrac{x-4}{x})=\boxed{\log_3\left(\sqrt{\dfrac{x-4}{x}}\right)}[/tex]
A 5-inch candle burns down in 4 hours. How far has it burned after 7 1/2 hours?
Answer:
9 3/8 inches
Step-by-step explanation:
Inches of candle : hours it burned
= 5 inches : 4 hours
How far has it burned after 7 1/2 hours?
Let
x = how far it has burned (inches)
Inches of candle : hours it burned = x inches : 7 1/2 hours
Equate both ratios
5 inches : 4 hours = x inches : 7 1/2 hours
5/4 = x ÷ 7 1/2
5/4 = x ÷ 15/2
5/4 = x * 2/15
5/4 = 2x/15
Cross product
5 * 15 = 4 * 2x
75 = 8x
x = 75/8
x = 9 3/8 inches
x = how far it has burned (inches) = 9 3/8 inches
In this diagram, radius AD = 5 mm, radius BD = 12 mm and chord
CD = 8 mm. Find the exact length of AB, in surd form.
Answer:
The exact length of AB is [tex]3 + 4\sqrt{10}[/tex] milimeters.
Step-by-step explanation:
Both triangles ACD and BCD are isosceles and triangles AEC, ADE, BDE and BCE are right-angled, where E is the point where line segments AB and CD meet each other. We can determine the exact length of AB by means of two horizontal right triangles (i.e. AEC, BCE) and the Pythagorean Theorem:
[tex]AB = \sqrt{AC^{2}-CE^{2}}+\sqrt{CB^{2}-CE^{2}}[/tex]
If we know that [tex]AD = AC[/tex], [tex]BC = BD[/tex], [tex]AC = 5\,mm[/tex], [tex]BC = 12\,mm[/tex] and [tex]CE = 4\,mm[/tex], then the exact length of AB is:
[tex]AB = \sqrt{(5\,mm)^{2}-(4\,mm)^{2}}+\sqrt{(12\,mm)^{2}-(4\,mm)^{2}}[/tex]
[tex]AB = 3 + 4\sqrt{10}\,[mm][/tex]
Which of the following shows the coordinates of Q(3,-5) after a translation of
3 units right?
Q'(0,-5)
Q'(6,-5)
Q'(6,-2)
Q'(3,-2)
Answer:
(0,-5)
Step-by-step explanation:
move the x point to the right three times im pretty sure
PLZ HELP PLZ PLZ ILL MARK AS BRAINLIESTT!!
In the month of September, a bird population increased by a factor of 1.25 every day for those 30 days. The function below shows the number of birds, f(x), after x days:
Answer:
0 ≤ x ≤ 30
Step-by-step explanation:
In the month of September, a bird population increased by a factor of 1.25 every day for those 30 days. The function below shows the number of birds, f(x), after x days:
f(x) = 250(1.25)ˣ
Which of the following is a reasonable domain for the function?
0 ≤ x ≤ 250
0 ≤ x ≤ 30
All positive integers greater than 100
All real numbers
Solution:
Given that f(x) = 250(1.25)ˣ, where x is the number of days and f(x) is the population of the birds after x days. This means that at the beginning of the month of September (i.e. at x = 0), the population of the birds was 250. And as each day goes by, the population of the bird increases by a factor of 1.25.
The domain of a function is the set of all possible independent variables. In this case the number of days (x) is the independent variable. Since in the month of September there are 30 days, therefore the domain is:
0 ≤ x ≤ 30
Can Some one help fast easy question
Answer: x = 2
Step-by-step explanation:
4x + 4 = 2x + 8
2x = 4
x = 2
Answer: x = 2.
Step-by-step explanation: 4x+4=2x+8 subtract 4 from both sides.
4x = 2x+4 subtract 2x on both sides
2x = 4 divide both sides by two
x = 2
I hope this helps, have a nice day.
which type of parent function is f(x) = 3^x?
Answer:
c
Step-by-step explanation:
because there is a 3 in front of the root it is a cubed root since
2= square- the two is invisible but its there
3= cubed
Question 8 (1 point)
At your high school, you are trying to determine the probability that a student takes
Spanish given that the student is taking Marketing. Which of the following
statements explains how to BEST gather the data to determine this probability?
Determine the number of students taking Marketing, the number of students
taking Spanish, the total number of students, and the distribution of students.
Survey students taking Marketing to determine how many also take Spanish.
Survey students taking Spanish to determine how many also take Marketing.
Determine the number of students taking Marketing, the number of students
taking Spanish, and the total number of students.
Juan tiene que salir de su casa a estrenar futbol 20 minutos antes de las 4 PM. Escribe 4 formas diferentes de decir esa hora
Respuesta:
03:40 pm;
15: 40;
20 minutos antes de las 4 pm;
40 minutos después de las 3 pm
Explicación paso a paso:
20 minutos antes de las 4 de la tarde se pueden expresar de las siguientes formas:
Basado en un tiempo de 12 horas, podría escribirse tiene: 3: 40 pm
Usando el formato de reloj de 24 horas; donde 3 pm es equivalente a 15; por lo tanto, podría escribirse como: 15:40
Además, el tiempo se puede informar en palabras de la siguiente manera:
20 minutos antes de las 4 pm
También ;
40 minutos después de las 3 pm
Largest 3 digit number which is divisible by 6
Answer:
996
Step-by-step explanation:
largest 3 digit number is 999
then just reduce slowly to find ans
Answer:
The largest 3-digit number divisible by 6 is 996.
4x-6=30
i need help really bad !!!
Answer:
4x-6=30
4x=36
x=9
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
x = 9
Explanation:
Move all terms that do not contain x to the right side and solve.
ITEMS
The calculator shown costs $160.00 after a discount of $40.00 was given
Calculate the cost of the calculator before the discount
Answer:
mp=160
dis=40
now,
sp=mp-dis
=Rs. 160-Rs.40
=Rs. 120
Please help me solve this math it’s due in 1 hour
Determine if each equation will have 0, 1, or 2 solutions. Equation A: x(x−3)=0 This equation has ____ solutions because... Equation B: x2=−81 This equation has ____ solutions because... Equation C: (x−1)(x−1)=0 This equation has ____ solutions because...
Answer:
See below
Step-by-step explanation:
Given the expression
x(x-3) = 0
This can be written as x = 0 and x - 3 = 0
x = 0 and x = 0+3
x = 0 and x = 3
Hence the equation has 2 solutions since it is a quadratic equation
B) Given x^2 = -81
Take the square root of both sides
√x² = ±√-81
x =±√-81
Note that √-1 = i
x = ±9i
x = 9i and -9i
Hence this equation has 2 solutions because of its quadratic nature
C) (x−1)(x−1)=0
x - 1 = 0 and x = 1 = 0
x = 1 twice
Hence this equation has 1 solution because of its repitition of root
please help! 20 points. if you guess or just comment to take points i will make sure ur account gets banned, thanks! i want a simple explanation pls
Answer: x=15
Step-by-step explanation: Since 3x+5 is equal to 50, you can write 3x+5=50, and 3x=45, x=15.
is "6x – (3x + 8) = 16x" a no solution
Answer:
no x = -8/13
Step-by-step explanation:
6x – (3x + 8) = 16x
Combine like terms
6x -3x -8 = 16
3x-8 = 16
Subtract 3x from each side
3x-8-3x = 16-3x
-8 = 13x
Divide by 13
-8/13 = 13x/13
-8/13 =x
Answer:
No, the answer would be -8/13
Step-by-step explanation:
6x-(3x+8)=16x
6x-3x-8=16x
3x-16x=8
-13x=8
x=-8/13
A woman weighs herself. Her mass is 43.4 kg and she is trying to increase .She successfully increases her mass by 8%. a) Work out the increase in her mass. b) Work out her new mass.
Answer:
Increase in her mass = 3.472 kg
Her new mass = 46.872 kg
Step-by-step explanation:
Her original mass = 43.4 kg
Percentage increase in her mass = 8%
Increase in her mass = 8% of 43.4 kg
= 8/100 * 43.4 kg
= 0.08 * 43.4 kg
= 3.472 kg
Increase in her mass = 3.472 kg
b) Work out her new mass
Her new mass = Her original mass + Increase in her mass
= 43.4 kg + 3.472 kg
= 46.872 kg
Her new mass = 46.872 kg