Answers
Solution:
Given:
\(h=-16t^2+97t+17\)when the height is 71ft,
h = 71
Hence,
\(\begin{gathered} 71=-16t^2+97t+17 \\ 16t^2-97t+71-17=0 \\ 16t^2-97t+54=0 \end{gathered}\)Using the quadratic formula;
\(\begin{gathered} a=16,b=-97,c=54 \\ t=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ t=\frac{-(-97)\pm\sqrt{(-97)^2-(4\times16\times54)}}{2\times16} \end{gathered}\)Hence,
\(\begin{gathered} t=\frac{97\pm77.156}{32} \\ t_1=\frac{97+77.156}{32}=\frac{174.156}{32}=5.442375=5.44s \\ t_2=\frac{97-77.156}{32}=\frac{19.844}{32}=0.620125=0.62s \end{gathered}\)Therefore, the height will be 71 feet at 5.44 seconds or 0.62 seconds.
The object will reach the ground at;
The object will reach the height of 17ft at;
h = 17
\(\begin{gathered} 17=-16t^2+97t+17 \\ 16t^2-97t=0 \\ t(16t-97)=0 \\ t=0 \\ 16t-97=0 \\ 16t=97 \\ t=\frac{97}{16} \\ t=6.0625s \end{gathered}\)Hence, the time it will take to reach the ground will be the time it takes to go up and return back to the ground;
\(\begin{gathered} t=6.0625\times2 \\ t=12.125s \end{gathered}\)It will take 12.125 seconds for the object to reach the ground.
Related Questions
A drum of water is 3/4 full. When 9 litres are drawn from it, it is half full. How much water does the drum hold what is the capacity of the drum
Answers
Answer:
OK, Here is your answer
Step-by-step explanation:
Let's assume the capacity of the drum be C litres.Since the drum is initially 3/4 full, the amount of water in it is 3/4 × C = (3/4)C liters.When 9 liters of water are drawn from the drum, the remaining amount of water is (3/4)C - 9 liters.Since the drum is now half full, the amount of water remaining in it is (1/2)C liters.Therefore, we can write the equation: (3/4)C - 9 = (1/2)CTo solve for C, let's first get rid of the fractions by multiplying both sides by 4.(3/4)C - 9 = (1/2)C → 3C - 36 = 2C → C = 36Therefore, the capacity of the drum is 36 liters.Hence, the drum holds 3/4 × 36 = 27 liters of water initially and after 9 liters of water are drawn, the remaining amount of water in it is 27 - 9 = 18 liters.
Answer:
18 Lieters.
Step-by-step explanation:
found the answer in his answer. ↑↑↑↑
What is the present value of R13 000 p.a. invested at the beginning of each year for 8years at 10%p.a. compound interest? (NB Use the compound interest tables provided or work to three decimal places only.)
Answers
Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.
To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:
PV = A *\((1 - (1 + r)^(-n)) / r\)
Where:
PV = Present value
A = Annual payment or cash flow
r = Interest rate per period
n = Number of periods
In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).
Using the formula and substituting the given values, we can calculate the present value:
PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)
Calculating this expression:
PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)
= 13000 * (1 - 0.46318) / 0.10
= 13000 * 0.53682 / 0.10
= 6977.66 / 0.10
= 69776.6
Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.
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Find the missing side lengths leave your answer as a racials simplest form
Answers
Answer:
u = 26
v = 13√3
it's 30-60-90 triangle
A bin contains seven red chips, nine green chips, three yellow chips, and six blue chips. Find the probability of drawing a red chip or a blue chip.
Group of answer choices
a.) 13/25
b.) 13/50
c.) 42/625
d.) 1/25
Answers
A triangle has the vertices at A(1,3), B(4,2), and C(3,8). What transformation would produce an image with the vertices A’(3,-1),B’(2,-4), C’(8,-3)?
A) Reflection over the x axis
B) Reflection over the line y=x
C) Rotation 90° CW about the origin
D) Rotation 180° about the origin
Answers
9514 1404 393
Answer:
C) Rotation 90° CW about the origin
Step-by-step explanation:
The transformation for rotation CW 90° is ...
(x, y) ⇒ (y, -x)
This is apparently the transformation that gets ...
A(1, 3) ⇒ A'(3, -1)
__
Additional comment
Attached is a list of the commonly used transformations for your reference.
Answer:
C
Step-by-step explanation:
Whats the answer please help its worth 10 points!
Answers
This is the correct answer. Hope it helps :)
A line is drawn parallel to y = x. It has the same slope, so it’s equation has the form y = x + b. The new line passed through the point (2, 5). What is its y- intercept (b)?
Answers
Answer:
b = 3
Step-by-step explanation:
(2,5) is information! x = 2 and y = 5.
Use these values in the equation:
y = x + b
5 = 2 + b
Subtract 2.
3 = b
The equation of the line is y = x + 3.
Question 1 of 10
Which expressions are equivalent to the one below? Check all that apply.
log 2-log 4
A. log(¹)
B. log 1
C. log(2) + log(¹)
D. log 2
Answers
"The correct option is C." The only expression that is equivalent to log 2 - log 4 is option C: log(2) + log(¹).
The expression "log 2 - log 4" can be simplified using logarithmic properties. Specifically, the property states that "log(a) - log(b) = log(a/b)." Applying this property to the given expression, we have "log 2 - log 4 = log(2/4) = log(1/2) = -log(2)."
The expression log 2 - log 4 can be simplified using logarithmic properties. Let's analyze each option:
A. log(¹): This expression is not equivalent to log 2 - log 4. The logarithm of 1 is 0, but it does not cancel out the terms log 2 and log 4.
B. log 1: This expression is equivalent to 0, but it does not cancel out the terms log 2 and log 4.
C. log(2) + log(¹): This expression is equivalent to log 2 + 0, which simplifies to just log 2. It is not equivalent to log 2 - log 4.
D. log 2: This expression is not equivalent to log 2 - log 4. It represents the logarithm of 2, but it does not account for the subtraction of log 4.
Option C, "log(2) + log(¹)," again uses an exponentiation notation without an exponent and is not a valid mathematical expression.
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tìm một đoạn nghiệm của phương trình
3/x+1 +4/(x+1)^2+5/(x+1)^3+6/(x+1)^4=10
Answers
Answer:
btfrt34598fc
Step-by-step explanation:
I NEED HELP ASAP Fanks luv
Answers
Answer:
P = 9; A = 3
Step-by-step explanation:
a)
1. ATC is similar to GDO
2. 12 / 3 = 4
3. Triangle A has to be divided by 4 to figure out what Triangle B is
4. GD = 3, GO = 4, DO = 2
5. P = 3 + 4 + 2 + 9
b)
1. B = 2, H = 3
2. Plug into given equation (A = 1/2bh)
3. A = 1/2*2*3
4. 1/2 * 6
5. A = 3
find by a digit to make the number divisible by 3 1234?
Answers
A digit to make the number divisible by 3 is by adding the digit 2 to the number 1234.
To make the number 1234 divisible by 3, we can find the sum of its digits and determine if it is divisible by 3. If the sum of the digits is divisible by 3, then the original number is also divisible by 3.
Let's calculate the sum of the digits in 1234:
1 + 2 + 3 + 4 = 10
The sum of the digits is 10. Since 10 is not divisible by 3, we need to add or subtract a digit to make the sum divisible by 3.
To find the digit we need to add or subtract, we can use the fact that the difference between the original sum and the next multiple of 3 is the required digit.
The next multiple of 3 greater than 10 is 12 (12 - 10 = 2). Therefore, we need to add 2 to the number 1234 to make it divisible by 3.
1234 + 2 = 1236
we obtain the number 1236, which is divisible by 3.
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Which of the following would be considered a ‘large’ effect size according to Cohen?
Answers
According to Cohen's guidelines, a "large" effect size is generally considered to be Cohen's d of 0.8 or higher. However, it is important to consider the specific field and context of the research when interpreting effect sizes.
According to Cohen's guidelines, an effect size can be classified as small, medium, or large. Cohen's d is a commonly used effect size measure, which is calculated by taking the difference between the means of two groups and dividing it by the pooled standard deviation.
The interpretation of what constitutes a "large" effect size can vary across different fields of study. However, Cohen proposed general guidelines for interpreting effect sizes:
Small Effect Size: Cohen's d around 0.2
A small effect size suggests that there is a noticeable, but not substantial, difference between the groups or conditions being compared. It is typically considered a modest effect.
Medium Effect Size: Cohen's d around 0.5
A medium effect size indicates a moderate difference between the groups or conditions. It is generally considered a meaningful effect that is noticeable and important.
Large Effect Size: Cohen's d around 0.8 or higher
A large effect size represents a substantial and substantial difference between the groups or conditions being compared. It is considered a strong and robust effect that is often considered highly significant.
It is important to note that these guidelines are not set in stone and can vary depending on the field of study, the specific research question, and the context of the research. Additionally, effect sizes can also be influenced by factors such as the measurement scale used, the specific statistical analysis, and the sample size.
In summary, according to Cohen's guidelines, a "large" effect size is generally considered to be Cohen's d of 0.8 or higher. However, it is important to consider the specific field and context of the research when interpreting effect sizes.
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write an equation in point-slope form for the line through the given point with the given slope
(10,-9)m is -2
Answers
Answer:
Step-by-step explanation:
Point: 10,-9
k=-2
y=-2x+b
So: 9, -7
8,-5
7,-3
6,-1
5,1
4,3
3,5
2,7
1,9
0,11
y=-2x+11
Answer:
y + 9 = - 2(x - 10)
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = - 2 and (a, b ) = (10, - 9 ) , then
y - (- 9) = - 2(x - 10) , that is
y + 9 = - 2(x - 10)
I need help with this
Answers
Answer:
90 degrees
Step-by-step explanation:
Hope thishelps. :) :D
If there are 21 students in class today, how much would it
cost for the class and your teacher to ride the Sandia
Aerial Tram? Show your work.
a.
Create an equation to represent the cost the class
and your teacher taking a ride on the Sandia Aerial
Tram. Let f(x) be the total cost.
b.
Does the above scenario represent a function,
explain your reasoning.
Rates: $25 Adults, $20 Seniors 62+ & Teens 13-20 yrs,
$15 Youth 5-12 yrs.
Students, write your response
Answers
Answer:
a. f(x) = 21 (20) +1 (25) = 445
b. The scenario is a function because each student just have to pay once.
Can you please help with this question?
Answers
The flower arrangements with $200 has lower unit price than the flower arrangements with $70 unit price.
What is meant by unit price?The average price of a product is calculated by dividing the total sales income by the total number of units sold. When a same product is supplied in variants, such as bottle sizes, managers must define "similar" units. Average prices can be estimated by dividing distinct unit selling prices by the percentage of unit sales (mix) for each product variant. When we utilize a standard rather than an actual mix of sizes and product variations, the result is price per statistical unit. Statistical units are sometimes known as analogous units.
Unit price for 15 flower arrangements for $200 is,
200/15=13.33
Unit price for 5 flower arrangements for $70 is,
70/5=14
Therefore, 14>13.33
So, the flower arrangements with $200 has lower unit price than the flower arrangements with $70 unit price.
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plsssssssssss just helppppp
Answers
Answer:
46
Step-by-step explanation:
The missing length is 10-4 = 6
Therefore perimeter = 5 + 6 + 8+ 4+13 +10
=46
Points F (0,0), G (9,0) and H (9,12) of vertical triangle
What is the distance between f to h
Answers
Answer:
15 is the distance
Step-by-step explanation:
fast answer for this plz I need all correct answers if anyome know properly
Answers
Answer:
1) c
2) c
3) c
4) c
Step-by-step explanation:
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
\(BC=5.1\)
\(B=23^{\circ}\)
\(C=116^{\circ}\)
Step-by-step explanation:
The diagram shows triangle ABC, with two side measures and the included angle.
To find the measure of the third side, we can use the Law of Cosines.
\(\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}\)
In this case, A is the angle, and BC is the side opposite angle A, so:
\(BC^2=AB^2+AC^2-2(AB)(AC) \cos A\)
Substitute the given side lengths and angle in the formula, and solve for BC:
\(BC^2=7^2+3^2-2(7)(3) \cos 41^{\circ}\)
\(BC^2=49+9-2(7)(3) \cos 41^{\circ}\)
\(BC^2=49+9-42\cos 41^{\circ}\)
\(BC^2=58-42\cos 41^{\circ}\)
\(BC=\sqrt{58-42\cos 41^{\circ}}\)
\(BC=5.12856682...\)
\(BC=5.1\; \sf (nearest\;tenth)\)
Now we have the length of all three sides of the triangle and one of the interior angles, we can use the Law of Sines to find the measures of angles B and C.
\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)
In this case, side BC is opposite angle A, side AC is opposite angle B, and side AB is opposite angle C. Therefore:
\(\dfrac{\sin A}{BC}=\dfrac{\sin B}{AC}=\dfrac{\sin C}{AB}\)
Substitute the values of the sides and angle A into the formula and solve for the remaining angles.
\(\dfrac{\sin 41^{\circ}}{5.12856682...}=\dfrac{\sin B}{3}=\dfrac{\sin C}{7}\)
Therefore:
\(\dfrac{\sin B}{3}=\dfrac{\sin 41^{\circ}}{5.12856682...}\)
\(\sin B=\dfrac{3\sin 41^{\circ}}{5.12856682...}\)
\(B=\sin^{-1}\left(\dfrac{3\sin 41^{\circ}}{5.12856682...}\right)\)
\(B=22.5672442...^{\circ}\)
\(B=23^{\circ}\)
From the diagram, we can see that angle C is obtuse (it measures more than 90° but less than 180°). Therefore, we need to use sin(180° - C):
\(\dfrac{\sin (180^{\circ}-C)}{7}=\dfrac{\sin 41^{\circ}}{5.12856682...}\)
\(\sin (180^{\circ}-C)=\dfrac{7\sin 41^{\circ}}{5.12856682...}\)
\(180^{\circ}-C=\sin^{-1}\left(\dfrac{7\sin 41^{\circ}}{5.12856682...}\right)\)
\(180^{\circ}-C=63.5672442...^{\circ}\)
\(C=180^{\circ}-63.5672442...^{\circ}\)
\(C=116.432755...^{\circ}\)
\(C=116^{\circ}\)
\(\hrulefill\)
Additional notes:
I have used the exact measure of side BC in my calculations for angles B and C. However, the results will be the same (when rounded to the nearest degree), if you use the rounded measure of BC in your angle calculations.
What Is the correct answer?
Answers
The correct answer is x/ 7 = 9. Option D
What are algebraic expressions?Algebraic expressions are simply defined as expressions comprising of terms, variables, coefficients, constants and factors.
They are also made up of mathematical operations such as addition, subtraction, multiplication, division, bracket, etc.
It is important to note that quotient represents division.
Example;
The quotient of 1 and 2 is 1/ 2
The quotient of 3 and 4 is 3/ 4
From the information given, we have that;
The quotient of a number and 7 is 9
Let the number be x
We have;
x/ 7 = 9
Thus, the correct answer is x/ 7 = 9. Option D
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PLEASE HELP!! 30 POINTS!!!!
People were asked to choose one of four activities they would prefer to do in hot weather. The table shows data about the responses. Which activity was chosen by most adults over 18 years old?
A
sports
B
movies
C
reading
D
walking
Answers
Answer:
It's D
Step-by-step explanation:
When you add the 19-50 and over 50 then you get the highest answer
x minus 4 = 2 a. –6 c. 7 b. 6 d. –2
Answers
Answer:
6
Step-by-step explanation:
x-4=2
+4 +4
x=6
Hope this helps!
URGENT Please help!!!!!!
Divide 6.1 x 1020 by 3.2 x 105. Express your answer in scientific notation.
Answers
The value of the division of the expression will be; 19.52 x 10^{25}.
How does scientific notations work?The number is written in the form \(a \times 10^b\) where we have \(1 \leq a < 10\)
The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10.
Scientific notations have some of the profits; Better readability due to compact representation that value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.
Given the expression as 6.1 x \(10^{20}\) by 3.2 x 10⁵
We have to divide the expression
( 6.1 x \(10^{20}\) ) / (3.2 x 10⁵)
= 19.52 x \(10^{20 + 5}\)
= 19.52 x \(10^{25}\)
Therefore, the value of the division of the expression will be; 19.52 x \(10^{25}\).
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write the equation that is the translation of y= |x| left 9 units and up 11 units.A) Y=|X+9|+11B) Y=|X-9| +11C) Y=|X-11|-9D) Y=|X+11|-9
Answers
We start with the function y=|x|.
If we translate the function 9 units to the left (negative side of the x-axis).
This means that the values of y that were for x, will happen for x+9, as we moved to axis to the right (or the function to the left).
We can test this with the value of y(0)=0. With the translated function, we have to have y=0 when x=-9, so f(-9)=|-9+9|=|0|=0.
Then,
\(y=|x+9|\)Now, we translate the function 11 units up.
Then the value of the function is always 11 units up for every value of x. It can be done by adding a constant of value 11.
The function becomes:
\(y=|x+9|+11\)Answer:
A) Y=|X+9|+11
GIVING 15 POINTS PLS FAST
Drag the tiles to the boxes to form correct pairs.
Match each addition operation to the correct sum.
-24 8 + 30
131.87
28.98+(-52.22)
65
45%+39
-23.24
56.75 +75.12
Reset
Next
Next
Answers
Answer:
Hope this helps! All you needed to do was add and subtract. Go through the slides, I added the step by step explanation, as well as the final table which contains the answers.
The value of the expressions are:
24(5/9) +30(7/9) = 6(2/9)
45(2/9) +39(3/9) = 84(5/9)
28.98 + (-52.22) =-23.24
56.75 + 75.12 = 131.87
We have,
Expressions:
-24(5/9) +30(7/9)
Simplifying the fractions.
This can be written as,
= (-24 + 30) +(-5/9 + 7/9)
= 6 + 2/9
= 6(2/9)
45(2/9) +39(3/9)
= (45 + 39) + (2/9 + 3/9)
= 84 + 5/9
= 84(5/9)
28.98 + (-52.22)
= 28.98 - 52.22
= -23.24
56.75 + 75.12
= 131.87
Thus,
The value of the expressions are:
24(5/9) +30(7/9) = 6(2/9)
45(2/9) +39(3/9) = 84(5/9)
28.98 + (-52.22) =-23.24
56.75 + 75.12 = 131.87
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What is the solution to
-3x÷4<3
Answers
Answer:
x>-1/4
Step-by-step explanation:
-3x/4<3
x/4>-1
x>-1/4
Answer:
x∠-4
Step-by-step explanation:
Like and give 5 star rating
What is the value of the expression (2)⁶
HELP!!
Answers
Answer:
64
Step-by-step explanation:
you would multiply 2x2 then 2x4 then 2x8 then 2x16 then 2x32 and youget 64
(the first one just makes 2)
Answer:
Its 2 to the sixth power so 64
What is the probability that the second sock is black?
Please help ASAP!!! Brainliest if correct!!! Thank you !
A- 5/7
B- 3/7
C- 5/8
D- 3/8
Answers
Answer:
WEGGWEGEWGEWGGEWGWE
Step-by-step explanation:
EWGWEGWEW
Suppose z varies inversely with t and that z = 10 when t = 12. What is the value of z when t = 5?
Answers
\(\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill\)
\(\stackrel{\textit{"z" varies inversely with "t"}}{z = \cfrac{k}{t}}\hspace{5em}\textit{we also know that} \begin{cases} z=10\\ t=12 \end{cases} \\\\\\ 10=\cfrac{k}{12}\implies 120 = k\hspace{9em}\boxed{z=\cfrac{120}{t}} \\\\\\ \textit{when t = 5, what's "z"?}\qquad z=\cfrac{120}{5}\implies z=24\)