IR 1 sn Jason launched a rocket for a physics experiment. This equation can be used to find the height (h), in feet, of the rocket after t seconds. h = -16t2 + 288t + 8 How many seconds will it take for the rocket to reach the max height?
Answers
The given equation is,
\(h=-16t^2+288t+8\)For maximum height,
\(\begin{gathered} h^{\prime}(t)=0 \\ -32t+288=0 \\ t=9\text{ sec.} \\ h^{\doubleprime}(t)=-32<0 \end{gathered}\)Thus, t=9 second is the required time to reach maximum height.
Related Questions
Write the decimal expansion of 3/5
Answers
Answer:0.6
Step-by-step explanation:
To convert any fraction to decimal form, we just need to divide its numerator by denominator. Here, the fraction is 3/5 which means we need to perform 3 ÷ 5. This gives the answer as 0.6. So, 3/5 as a decimal is 0.6.
Solve the logarithmic equation. Show steps
Answers
\(\begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \underset{\stackrel{\uparrow }{\textit{let's use this one}}}{a^{log_a x}=x} \end{array} \\\\[-0.35em] ~\dotfill\)
\(\log_4(x+10)-\log_4(x-2)=\log_4(x)\implies \log_4\left( \cfrac{x+10}{x-2} \right)=\log_4(x) \\\\\\ \stackrel{\textit{exponentializing both sides}}{4^{\log_4\left( \frac{x+10}{x-2} \right)}=4^{\log_4(x)}}\implies \cfrac{x+10}{x-2}=x\implies x+10=x^2-2x \\\\\\ 10=x^2-3x\implies 0=x^2-3x-10 \\\\\\ 0=(x-5)(x+2)\implies x= \begin{cases} 5~~\checkmark\\ -2 \end{cases}\)
notice, -2 is a valid value for the quadratic, however, the argument value for a logarithm can never 0 or less, it has to be always greater than 0, so for the logarithmic expression with (x-2), using x = -2 will give us a negative value, so -2 is no dice.
NEED HELP FAST ON THESE 2 questions
Answers
Answer:
hope it helped u a lot
Step-by-step explanation:
plss give me braniest
what is y=80.9x-1011.86 in standard form?
Answers
Answer:
50593
Step-by-step explanation:
the daily totals of enrollments at sunny side daycare last monday through saturday were 17, 19, 23, 14, 25, and 28
Answers
The average number of enrollments per day at the Sunnyside Daycare is 21.
What is an average?An average is a result obtained by summing some numerical values and then dividing the total by the number of values or variables.
An average is the mean, which is one of the central tendency values.
Data and Calculations:Day Number of Enrollments
Monday 17
Tuesday 19
Wednesday 23
Thursday 14
Friday 25
Saturday 28
Total = 126
Average enrollments = 21 (126/6)
Thus, the average number of enrollments per day at the Sunnyside Daycare is 21.
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Question Completion:What was the average number of enrollments per day?
I dont get this question equation
y=0.5 (6) - 4
I know that 0.5 is equivalent to 1/2 but I just don’t get this question
Answers
To solve the equation, you first need to simplify 0.5(6) to get 3, since 0.5 is equivalent to 1/2 and multiplying 6 by 1/2 gives you 3. So the equation becomes:
y = 3 - 4
Next, you need to subtract 4 from 3 to get -1. So the solution to the equation is:
y = -1
Therefore, when the value of the independent variable is 6, the value of the dependent variable is -1.
Answer
\(\pink\sf{y=-1}\)
Step-by-step explanation
I'm assuming that this exercise is asking us to simplify the equation \(\sf{y=0.5(6)-4}\).
We know that 0.5 (6) means 0.5 multiplied by 6. That is the same as 6 divided by 2, which is 3:
\(\sf{y=3-4}\)
And now we just simplify the last part:
\(\sf{y=-1}\)
∴ answer: y = -1
\( \rm \lim_{ n \to \infty } \frac{ \sqrt[ {n}^{2} ]{1! \times 2! \times 3! \times 4! \times \dots \times n!} }{ \sqrt{n} } \\ \)
Answers
Trying this again. Take a logarithm and expand it:
\(\ln\left(\dfrac{\sqrt[n^2]{1! \times 2! \times \cdots \times n!}}{\sqrt n}\right) = \dfrac{\ln(1!\times2!\times\cdots\times n!)}{n^2} - \dfrac{\ln(n)}2\)
\(=\dfrac{\ln(1) + (\ln(1)+\ln(2)) + \cdots + (\ln(1)+\ln(2)+\cdots+\ln(n))}{n^2} - \dfrac{\ln(n)}2\)
\(=\displaystyle \sum_{k=1}^n \frac{(n-k+1) \ln(k)}{n^2} - \frac{\ln(n)}2\)
\(=\displaystyle \frac1n \sum_{k=1}^n \left(1 - \frac{k-1}n\right) \ln(k) - \frac{\ln(n)}2\)
With some rewriting, this is equivalent to
\(=\displaystyle \frac1n \sum_{k=1}^n \left(1 - \frac{k-1}n\right) (\ln(k) - \ln(n) + \ln(n)) - \frac{\ln(n)}2\)
\(=\displaystyle \frac1n \sum_{k=1}^n \left(1 - \frac{k-1}n\right) \ln\left(\dfrac kn\right) + \frac{\ln(n)}n \sum_{k=1}^n \left(1 - \frac{k-1}n\right) - \frac{\ln(n)}2\)
As n → ∞, the first sum converges to a definite integral,
\(\displaystyle \lim_{n\to\infty} \frac1n \sum_{k=1}^n \left(1 - \frac{k-1}n\right) \ln\left(\dfrac kn\right) = \int_0^1 (1-x) \ln(x) \, dx = -\frac34\)
while the second sum is
\(\displaystyle \sum_{k=1}^n \left(1 - \frac{k-1}n\right) = n - \dfrac1n\times\dfrac{n(n+1)}2 - \dfrac nn = \dfrac{n+1}2\)
so that the other two terms converge to zero,
\(\displaystyle \lim_{n\to\infty} \left(\frac{\ln(n)}n \sum_{k=1}^n \left(1 - \frac{k-1}n\right) - \frac{\ln(n)}2\right) = \lim_{n\to\infty} \left(\dfrac{(n+1)\ln(n)}{2n} - \frac{\ln(n)}2\right) = 0\)
Therefore
\(\displaystyle \lim_{n\to\infty} \frac{\sqrt[n^2]{1!\times2!\times\cdots\times n!}}{\sqrt n} = \boxed{e^{-3/4}}\)
Determine whether 548 is greater than or less than 373. Then write the expression showing this using < or >.
Answers
Answer:
548 > 373
Step-by-step explanation:
548 is greater than 373 because when we compare the digits from left to right, we find that the first digit of 548 (5) is greater than the first digit of 373 (3). Therefore, we can conclude that 548 is greater than 373.
The ">" symbol is used to represent "greater than" in mathematical comparisons.
Hope this helps!
The joint density function of X and Y is f(x,y) = {210 (2x +y), 2
0, otherwise Find
E(X),
E(Y),
E(XY),
E(X2),
E(Y2),
Var(X),
Var(Y),
Cov(X,Y),
i.p
Answers
Answer:
e(x)
Step-by-step explanation:
i think this is the answer
need some help asap, giving brainliest
Answers
Answer:
16.19
Step-by-step explanation:
Use the cosine rule:
\(\sqrt{a^{2} +b^{2} -2abcosy} \\\\\sqrt{16^{2} +20^{2} -(2)(16)(20)cos(52)} \\\\\\= 16.19cm\)
The ages of job applicants for a security guard position are uniformly distributed between 25 and 65. Could a 25-year-old job applicant be two standard deviations below the mean (or more than two standard deviations)?
Answers
Answer:
No, a 25-year-old job applicant cannot be two standard deviations below the mean
Step-by-step explanation:
There are two frequencies 25 and 65
Mean of the two frequencies = 25+65/2 = 45
Standard deviation =
\(\frac{65-25}{\sqrt{12} } \\= 11.55\)
Mean - 2 x standard deviation \(= 45 - 2 * 11.55 = 21.9\)
\(21.9 < 25\)
Thus, a 25-year-old job applicant cannot be two standard deviations below the mean
What is the equation of a line, in slope-intercept form, that connects the following two data points? (5.0, 1200) (6.0, -850) Enter your answer by filling in the following blanks. Enter each of your answers as whole numbers without any rounding. y=____x + ____ (find m & b)
Answers
The slope intercept form equation of the line passing through the two points is y = -2050x+11450
The line is passing through the points (5.0, 1200) (6.0, -850).
The equation of the line will be given as,
(y-(-850))/(x-6) = (1200-(-850))/(5-6)
The right hand side of the equation is the slope m of the line. This equation mentioned above can be deduced as the slope intercept form of the line at the end of the answer.
So, solving further,
y+850/x-6 = 2050/-1
y+850 = -2050x + 12300
y = -2050+11450
The term 11450 is the intercept b and -2050 is the slope of the line, so, the slope intercept form of the equation of the line is y = -2050+11450.
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If x^6=60 and w^10=20, what is x^12×w^-10? A. 36, B. 60, C. 180 or D. 360
Answers
Answer:
\( x^{12} w^{-10}\)
And we can find this rewriting the expression in terms of the info given and we got:
\(x^{12} w^{-10} = (x^6)^2 (w^{10})^{-1}\)
And replacing we got:
\(x^{12} w^{-10} = (60)^2 (20)^{-1}= \frac{60^2}{20}= 180\)
And the best option would be:
C. 180
Step-by-step explanation:
For this case we know that:
\( x^6, w^{10} = 20\)
And we want to find the value for:
\( x^{12} w^{-10}\)
And we can find this rewriting the expression in terms of the info given and we got:
\(x^{12} w^{-10} = (x^6)^2 (w^{10})^{-1}\)
And replacing we got:
\(x^{12} w^{-10} = (60)^2 (20)^{-1}= \frac{60^2}{20}= 180\)
And the best option would be:
C. 180
Pls help!!! Will name Brainliest
Solve for x:
Answers
Answer:
I think it’s 10
Find the Value of X.
Answers
The measure of the unknown sides is equivalent to 12.6
Circle geometry problemThe given figure is a circle geometry with the perpendicular lines intersecting both segments of the circle.
We need to determine the measure of x. Since the measure of the perpendicular lines are equal, hence the measure of the line of the segments will also be equal.
Hence:
x = 6.3 + 6.3
x = 12.6
Therefore the measure of x from the given diagram is equivalent to 12.6
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A boy spends one sixth of his pocket money on ice cream, two sevenths on chocolates and five twelfths on football stickers. What fraction of his pocket money is left?
Give your answer in its simplest form.
Answers
Answer:
11/84 was the amount he was left with
at needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle of elevation of the tree from one position on a flat path from the tree is Upper H equals 60 degrees commaH=60°, and from a second position Upper L equals 20 feetL=20 feet farther along this path it is Upper B equals 40 degrees .B=40°. What is the height of the tree?
Answers
Answer:
32.6 feet
Step-by-step explanation:
The computation of the height of the tree is shown below:
Data provided in the question
One position H = 60 degree
Second position L = 20
B = 40 degree
Based on the above information, the calculations are as follows
In triangle ZWX,
\(\frac{h}{x}=tan(60^{\circ}) => x=\frac{h}{tan(60^{\circ})}\)
In triangle ZWY
\(\frac{h}{x+L}=tan(40^{\circ}) => h=tan(40^{\circ})(x+20) => x=\frac{h}{tan(40^{\circ})}-20\)
Now from equation 1 and equation 2
\(x=\frac{h}{tan(60^{\circ})}=\frac{h}{tan(40^{\circ})}-20\)
i.e
\(20=\frac{h}{tan(40^{\circ})}-\frac{h}{tan(60^{\circ})} => h[1.1917535926-0.57735026919]=20\)
Hence,
\(h=\frac{20}{[1.1917535926-0.57735026919]}\)
= 32.55190728
= 32.6 feet
Hence, the height of the tree is 32.6 feet
1. A local pizzeria sold 70 pizzas yesterday.
(a) The owner offers the employees a bonus if the number of pizzas sold increases by 30% today. How many pizzas must the pizzeria sell for employees to receive the bonus?
2. A certain TV can be purchased from the manufacturer for $150. A certain online retailer has a standard markup of 30%, and a certain superstore has a standard markup of 40%.
(a) What is the price of the TV when purchased online?
(b) What is the price of the TV when purchased at the superstore?
3. You have saved $140 for a new pair of skis. They have a regular price of $189. They have been reduced by 30%. There is a 13% tax as well.
a. What is the discount?
b. What is the new price?
c. What is the tax?
d. What was the total price of the shoes, after the discount and tax?
e. Do you have enough money? Please explain in a complete sentence
Answers
Answer:
1. 91 = 70*1.30
2a. 195= 150*1.30
2b. 210 = 150*1.40
3a. 56.70 = 156* .30
3b. 132.30 = 156-56.70
3c. 17.20 = 132.30 *0.13
3d. 149.50 = 132.30+17.20
3e. You do not have enough money, because you need $9.50 more.
Step-by-step explanation:
good luck
Question 1:
70 x 1.30 is 91 - 70 is equal to 21 pizzas, they would have to sell 91 total pizzas, which is 21 more than what was sold the previous day
Question 2:
Both parts are solved below:
Step-by-step explanation:
Given:
Purchase price = 150
Part A
As the online trailer marks up 30% so the price would be:
= 150 + 30% of 150
=150 + 0.3(150)
= 150 + 45
Price online= $195
° ♡ ₒ ♡ °
Part B
As the superstore marks up the price by 40% so the price would be:
= 150 + 40% of 150
=150 + 0.4(150)
= 150 + 60
Price at superstore = $210
° ♡ ₒ ♡ °
Difference
Difference = price at superstore - price online
Difference = 210 - 195
Difference = $15
Difference in markup = 40% - 30% = 10%
So a 10% difference leads to the difference of $15 in price.
7.
(02.01 MC)
Six-year-old students at an elementary school were given a 20-yard head start in a race. The graph shows how far the average student ran in 30 seconds.
A line graph with Distance, in yards, on the x axis and Age of Runner on the y axis. The x axis has a scale from 0 to 80 in increments of 10. The y axis has a scale of 0 to 8 in increments of 2. A straight line connecting 20, 6 and 60, 6 is drawn.
Which statement best describes the domain of the function represented in the graph? (1 point)
6 ≤ x ≤ 60, or x is from 6 to 60
6 ≤ x ≤ 20, or x is from 6 to 20
0 ≤ x ≤ 20, or x is from 0 to 20
20 ≤ x ≤ 60, or x is from 20 to 60
HELP
Answers
The domain of the function represented in the graph will be 20 ≤ x ≤ 60, or x is from 20 to 60. Then the correct option is D.
What is a line segment?A line segment in mathematics has two different points on it that define its boundaries.
A line segment is sometimes referred to as a section of a path that joins two places.
Six-year-old students at an elementary school were given a 20-yard head start in a race. The graph shows how far the average student ran in 30 seconds.
A line graph with Distance, in yards, on the x-axis and Age of the Runner on the y-axis. The x-axis has a scale from 0 to 80 in increments of 10. The y-axis has a scale of 0 to 8 in increments of 2. A straight line connecting 20, 6, and 60, 6 is drawn.
The domain of the function represented in the graph will be 20 ≤ x ≤ 60, or x is from 20 to 60. Then the correct option is D.
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Answer:
the correct option is D
Step-by-step explanation:
Neal invested $120,000 in stocks and bonds. He earned 18% on his stock investments and 12% on his bond investments. If Neal's combined profits on both types of investments were $17,400, how much did he invest in stocks?
Answers
Answer:
$50,000
Step-by-step explanation:
The given relations can be used to write and solve an equation for the amount invested in stocks.
SetupLet s represent the amount invested in stocks. Then (120,000-s) is the amount invested in bonds. The total earnings by the two investments were ...
0.18s +0.12(120,000 -s) = 17,400
SolutionSimplifying the equation, we have ...
0.06s +14,400 = 17,400
0.06s = 3000 . . . . . . . . . . subtract 14,400
s = 50,000 . . . . . . . . . . . . divide by 0.06
Neal invested $50,000 in stocks.
__
Additional comment
The amount invested in bonds was 70,000. The profit earned was ...
0.18(50,000) +0.12(70,000) = 9,000 +8,400 = 17,400
i need help on 8-9 plss :))
Answers
Answer:
8. SU = 24
9. TU = 16√3
Step-by-step explanation:
Recall: SOH CAH TOA
8. Reference angle (θ) = 30°
Opposite = 8√3
Adjacent = SU
Apply TOA,
Tan θ = Opp/Adj
Substitute
Tan 30° = 8√3/SU
Tan 30° × SU = 8√3
SU = 8√3/Tan 30°
SU = 8√3/(1/√3) (tan 30° = 1/√3)
SU = 8√3*√3/1
SU = 8*3
SU = 24
9. Reference angle (θ) = 30°
Opposite = 8√3
Hypotenuse = TU
Apply SOH,
Sin θ = Opp/Hyp
Substitute
Sin 30° = 8√3/TU
Sin 30° × TU = 8√3
TU = 8√3/sin 30°
TU = 8√3/(½) (sin 30° = ½)
TU = 8√3 × 2/1
TU = 16√3
Which has a greater effect on the volume-changing the radius by a given amount or changing the height by the same amount? Why?
Answers
Answer: Changing the radius of an object by a given amount has a greater effect on the volume than changing the height by the same amount. The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. If we change the radius by a given amount, say x, the new radius would be r+x. Hence, the new volume would be V' = π(r+x)²h = π(r²+2rx+x²)h = V + 2πrxh + πx²h. We can see that the volume change equals 2πrxh + πx²h. The first term is proportional to both the radius and the height, whereas the second term is proportional to the square of the radius and the height. Assuming that the height change is also x, the new volume would be V'' = πr²(h+x) = V + πr²x. We can see that the volume change is proportional to the radius squared and the change in height. Therefore, changing the radius by a given amount has a greater effect on the volume than changing the height by the same amount.
calculate the Area of parallelogram GDEF if the base is 5m and the altitude is 3,2m
Answers
Step-by-step explanation:
the area of a parallelogram is
baseline × height = 5 × 3.2 = 16 m²
What is 1 whole and 5/8 as a decimal
Answers
Answer:
1 whole and 5/8 as a decimal is 1.625
Steps: Convert 1 5/8 to a improper fraction-> 13/5 and dived the numerator by the denominator. 13/5= 1.265
Please help!!!!
\((\pi \sqrt 81 \frac{\sqrt[3]{8}}{2} ) / 3\pi = ???\)
Answers
Step-by-step explanation:
\((9\pi \frac{2}{2} )\div 3\pi \\ \)
\( \frac{9\pi}{3\pi} \\ \)
\(3\pi\)
3π is the answer
Solve for x: 3 (square root2-2x)+1=13
Answers
Answer:
x=7
Step-by-step explanation:
3√(2-2x) + 1 = 13
subtract 1 from both sides
3√(2-2x) = 12
Divide 3 from both sides
√2-2x= 4
square both sides
2-2x = 16
subtract 2 from both sides
2x= 14
x=7
HELP ME!!!!
ZEARN!!!!!!!!!
Answers
A common denominator is a shared multiple of the denominators of the fractions involved when adding or subtracting fractions. It enables fraction comparison and addition/subtraction.
Simplification is the process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. This is done to represent fractions in the simplest terms viable.
Conversion: The process of transferring a fraction from one form to another while retaining its equal value is known as conversion. Finding a common denominator or expressing a fraction in terms of a specified unit or fraction may be required.
Fraction Addition/Subtraction: When adding or subtracting fractions, a common denominator is required. This entails determining a common multiple of
To rewrite the expression 3 + 1/5 + 2/3 using fifteenths as the common denominator, we need to find a common denominator for 5 and 3, which is 15 (since 5 and 3 are both factors of 15).
First, let's convert the fractions 1/5 and 2/3 to fifteenths:
\((\frac{1}{5})(\frac{3}{3}) = \frac{3}{15}\)
\((\frac{2}{3})(\frac{5}{5}) = \frac{10}{15}\)
Now we can rewrite the expression using the common denominator:
\(3 + \frac{3}{15}+\frac{10}{15}\)
Need help asapppppppppdhhdhdhdhdhdhdhdhdhdhdhdhfh
Answers
Answer:
-11 to the power of 3
Step-by-step explanation:
MNO and MPO are isosceles triangles. Find angle t
Answers
Answer:
t = 20°
Step-by-step explanation:
Recall that the base angles of an isosceles ∆ are equal to each other.
This means that:
<NMO and <NOM of ∆MNO are congruent to each other.
Thus,
m<NMO = ½(180 - m<N) = ½(180 - 70)
m<NMO = ½(110)
m<NMO = 55°
Also, <PMO and <POM are congruent to each other. Thus:
m<PMO = ½(180 - m<P) = ½(180 - 110)
m<PMO = ½(70)
m<PMO = 35°
Therefore,
m<NMO = t + m<PMO (angle addition postulate)
55° = t + 35° (substitution)
Subtract 35 from each side
55° - 35° = t
20° = t
t = 20°
What is the equation of the line that is parallel to the line defined by the equation y = 3x−7 and goes through the point (4, 2)?
Answers
Answer:
\(y-2=3(x-4)\)
Step-by-step explanation:
Pre-SolvingWe are given a line contains the point (4, 2).
We also know that the line is parallel to y= 3x - 7.
We want to write the equation of this line.
Parallel lines have the same slopes.
First, let's find the slope of y = 3x - 7.
3 is in the place of where m (the slope) is, so that means it is the slope of that line.
It is also the slope of the line whose equation we want to write.
The equation of the line can be written in three ways:
Slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept. Standard form, which is ax+by=c, where a, b, and c are free integer coefficients. a and b cannot be 0, and a is usually non-negative as well. Point-slope form, which is \(y-y_1=m(x-x_1)\), where m is the slope and \((x_1, y_1)\) is a point.All of these ways are valid, but for this problem, let's write the equation in point-slope form, as it is the easiest.
SolvingSubstitute 3 as m in \(y-y_1=m(x-x_1)\).
\(y-y_1=3(x-x_1)\)
Now, substitute 4 as \(x_1\) and 2 as \(y_1\).
\(y-2=3(x-4)\)
Topic: parallel and perpendicular lines
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