To solve this problem, we must assume that the man undergoes constant acceleration as he goes down the river (therefore no other forces must act on him except gravity). Therefore we can use the formula below to calculate for the duration of his fall:
y = y0 + v0 t + 0.5 a t^2
where y is the distance and y0 = 0 since we set the reference point at the bridge, v0 is the initial velocity and is also equal to v0 = 0 since the man started from rest, therefore the equation becomes:
y = 0 + 0 t + 0.5 a t^2
y = 0.5 a t^2
Rewriting in terms of t:
t^2 = 2 y / a
t = sqrt (2y / a)
a is acceleration due to gravity = 9.8 m/s^2
t = sqrt [2 * 23 / 9.8]
t = 2.17 s
Therefore the jump last only about 2.17 seconds.
Carol spends 17 hours in a 2-week period practicing her culinary skills. How many hours does she practice in 5 weeks?
Final answer:
Carol practices for 8.5 hours per week, so in a 5-week period, she would practice for a total of 42.5 hours.
Explanation:
The student asked how many hours Carol practices her culinary skills in a 5-week period, if she practices for 17 hours in a 2-week period. To find the answer, we calculate how many hours Carol practices per week by dividing the total hours she practices in two weeks by two. Then we multiply the weekly hours by the number of weeks in question, which is five.
The calculation is as follows: Carol practices for 17 hours / 2 weeks = 8.5 hours per week. Then, 8.5 hours/week x 5 weeks = 42.5 hours in total for a 5-week period.
2x-5y=-6; 2x-7y=-14
A blimp is 1100 meters high in the air and measures the angles of depression to two stadiums to the west of the blimp. If those measurements are 75.2° and 17.9°, how far apart are the two stadiums?
The angle of depression represents the angle from a horizontal layout to a lower surface. The distance between the two stadiums is 3115.1 meters
The given parameters have been illustrated using the attached image of triangles.
The stadiums are represented with A and B.
First, calculate distance BO using:
[tex]\tan T =\frac{BO}{TO}[/tex]
Where:
[tex]\angle T = 90 -75.2 = 14.8[/tex]
[tex]TO = 1100[/tex]
So, we have:
[tex]\tan(14.8^o) = \frac{BO}{1100}[/tex]
Make BO the subject
[tex]BO = 1100 * \tan(14.8^o)[/tex]
[tex]BO = 1100 * 0.2642[/tex]
[tex]BO = 290.62[/tex]
Next, calculate distance AO using:
[tex]\tan T =\frac{AO}{TO}[/tex]
But in this case:
[tex]\angle T = 90 -17.9 = 72.1[/tex]
[tex]TO = 1100[/tex]
So, we have:
[tex]\tan(72.1^o) = \frac{AO}{1100}[/tex]
Make AO the subject
[tex]AO = 1100 * \tan(72.1^o)[/tex]
[tex]AO = 1100 * 3.0961[/tex]
[tex]AO = 3405.71[/tex]
The distance AB between the 2 stadiums is:
[tex]AB = AO - BO[/tex]
[tex]AB = 3405.71-290.61[/tex]
[tex]AB = 3115.1[/tex]
Hence, the distance between the 2 stadiums is 3115.1 meters.
Read more about angles of depression at:
https://brainly.com/question/13697260
Find the equation for the tangent line of f(x)=−3x2−7x+3 at x=3.
I SERIOUSLY NEED HELP HERE!!!!!
PLEASE SOMEONE HELP ME ON THIS!!!!!
NEED MAJOR HELP HERE CALCULATOR QUIT ON ME!!!!!!!
scientific calculator of a TI83 or TI84 ( does that help?)
Use the data below to find the correlation coefficient. (Remember to choose DiagnosticOn on your calculator.)
x y
270 70
230 75
250 68
310 82
285 80
275 76
281 73
267 81
252 72
246 79
The correlation coefficient is _____. Round to the nearest thousandth.
THESE ARE MY OPTIONS:
a. 0.438
b. 0.192
c. 0.5
d. 0.720
A rectangle has a length of the cube root of 81 inches and a width of 3 to the 2 over 3 power inches. Find the area of the rectangle.
3 to the 2 over 3 power inches squared
3 to the 8 over 3 power inches squared
9 inches squared
9 to the 2 over 3 power inches squared
Answer:
9 square inches.
Step-by-step explanation:
We have been given that a rectangle has a length of the [tex]\sqrt[3]{81}[/tex] inches and a width of [tex]3^{\frac{2}{3}}[/tex] power inches. We are asked to find the area of given rectangle.
We know that area of rectangle in length times width of rectangle.
[tex]\text{Area of rectangle}=\sqrt[3]{81}\times 3^{\frac{2}{3}}[/tex]
We can write 81 as [tex]3^4[/tex] as:
[tex]\text{Area of rectangle}=\sqrt[3]{3^4}\times 3^{\frac{2}{3}}[/tex]
Using exponent rule [tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex], we can write [tex]\sqrt[3]{3^4}=3^{\frac{4}{3}}[/tex].
[tex]\text{Area of rectangle}=3^{\frac{4}{3}}\times 3^{\frac{2}{3}}[/tex]
Using exponent rule [tex]a^b\cdot a^c=a^{b+c}[/tex], we will get:
[tex]\text{Area of rectangle}=3^{\frac{4}{3}+\frac{2}{3}}[/tex]
[tex]\text{Area of rectangle}=3^{\frac{4+2}{3}}[/tex]
[tex]\text{Area of rectangle}=3^{\frac{6}{3}}[/tex]
[tex]\text{Area of rectangle}=3^{2}[/tex]
[tex]\text{Area of rectangle}=9[/tex]
Therefore, the area of given rectangle is 9 square inches.
What number must be added to the expression below to complete the square?
x^2+3x
A. 9
B. 9/4
C. 3/2
D. 3
I think it is c or D but it should be C
hope that help
[I don't think it did lol ]
BMK
Assume a plane is flying directly north at 200 mph, but there is a wind blowing west at 23 mph. Part I: Express both the velocity of the plane and the velocity of the wind as vectors, using proper notation to represent each direction of motion. Part II: What is the velocity vector of the plane? Part III: What is the ground speed of the plane?
The velocity of the plane is 200 mph due north and the velocity of the wind is 23 mph due west. The velocity vector of the plane is 200 mph due north minus 23 mph due west. The ground speed of the plane can be found using the Pythagorean theorem.
Explanation:Part I: The velocity of the plane can be represented as 200 mph due north, and the velocity of the wind can be represented as 23 mph due west.
Part II: To find the velocity vector of the plane, we subtract the velocity of the wind from the velocity of the plane. The resultant velocity vector of the plane is 200 mph due north minus 23 mph due west.
Part III: The ground speed of the plane is the magnitude of the resultant velocity vector of the plane. We can calculate it using the Pythagorean theorem: ground speed = square root of (200^2 + 23^2).
which other angle must also measure 130°
opposite angles are identical so if angle 1 = 130
than angle 3 is also 130 degrees
Answer:
Angle 3
Step-by-step explanation:
we know that
[tex]m<1=m<3[/tex] -----> by vertical angles
we have
[tex]m<1=130\°[/tex]
therefore
[tex]m<3=130\°[/tex]
What is the arc length of a circle that has a 6-inch radius and a central angle that is 65 degrees? Use 3. 14 for pi and round your answer to the nearest hundredth
place a square on a coordinate graph and label each vertex with variables. prove that the diagonals of a square are congruent and perpendicular to each other.
Final answer:
To prove that the diagonals of a square are congruent and perpendicular, label the vertices of a square on a coordinate grid and calculate the slopes and lengths using the slope formula and distance formula respectively. The diagonals have slopes of +1 and -1, proving they are perpendicular, and they have equal lengths, proving they are congruent.
Explanation:
To prove that the diagonals of a square are congruent and perpendicular, we place a square with its vertices on a coordinate grid and label each vertex with variables.
Let's consider a unit square where c = 1 for simplicity, which means the length of each side is 1 unit. Place the square so that one vertex is at the origin (0,0), and label the vertices A(0,0), B(1,0), C(1,1), and D(0,1).
The diagonal AC will have endpoints at A(0,0) and C(1,1), and diagonal BD will have endpoints at B(1,0) and D(0,1). The slope of diagonal AC is (1 - 0)/(1 - 0) = 1, and the slope of diagonal BD is (1 - 0)/(0 - 1) = -1. Since the product of their slopes is -1 (1 * -1 = -1), this proves that they are perpendicular to each other.
To show they are congruent, we calculate their lengths using the distance formula: the distance between two points (x1,y1) and (x2,y2) is √[(x2 - x1)² + (y2 - y1)²]. Applying this to AC and BD reveals both lengths to be √[(1-0)² + (1-0)²] = √[1 + 1] = √2, proving the diagonals are congruent.
Expand (2x-3y)^4 using Pascal's Triangle. Show work
Answer:
16x^4 - 96x^3y + 216x^2y^2 - 216xy^3 + 81y^4
Step-by-step explanation:
(2x - 3y)^4
Fifth line on a Pascal Triangle
1, 4, 6 4, 1
(1) 2x^4
2^4 = 16
2x^4 = 16x^4
16x^4
(4) 2x^3 (-3y)^1
2^3 = 8
-3^1 = -3
8 times -3 times 4 = -96
-96x^3y
(6) 2x^2 (-3y)^2
2^2 = 4
-3^2 = 9
4 times 9 times 6 = 216
216x^2y^2
(4) 2x^1 (-3y)^3
2^1 = 2
-3^3 = -27
2 times - 27 times 4 = -216
-216xy^3
(1) (-3y)^4
-3^4 = 81
81y^4
16x^4 - 96x^3y + 216x^2y^2 - 216xy^3 + 81y^4
The length and width of a rectangle are 4.9^9 cm and 5.3^3 cm, respectively. What is the approximate area of the rectangle, using only positive exponents?
A) 5^6cm^2
B) 4^6cm^2
C) 5^12cm^2
D) 4^12cm^2
Find the equation of the quadratic function with zeros 10 and 14 and vertex at (12, -8).
Law of sines:
Triangle ABC has measures a = 2, b = 2, and m∠A = 30°. What is the measure of angle B?
15°
30°
45°
60°
Answer: Second option is correct.
Step-by-step explanation:
Since we have given that
ΔABC has measures a=2, b=2, m∠A=30⁰
As we know the "Law of sines " i.e.
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}\\[/tex]
so, we put the given values in above formula:
[tex]\frac{2}{\sin 30\textdegree}=\frac{2}{\sin B}\\\\\implies \sin 30\textdegree=\sin B\\\\\implies B=30\textdegreee[/tex]
Hence, Second option is correct.
What is the area of the composite figure?
(6π + 4) cm2
(6π + 16) cm2
(12π + 4) cm2
(12π + 16) cm2
The area of the composite figure is 6π + 16 cm²
Composite Figure:Composite figures are composed of different dimensional figures. The area of a composite figure is the sum of the whole 2 dimensional figures that forms the composite figure.
Therefore, the figure above has 3 semi circle and 1 square.
Therefore, the area can be calculated as follows;
area = sum of the area of the 3 semi circle + area of the squarearea = 1 / 2 πr² + 1 / 2 πr² + 1 / 2 πr² + L²
area = 3 / 2 (πr²) + L²
where
r = 2 cm
L = 4 cm
Therefore,
area of the composite figure = 3 / 2(π × 4) + 4²
area of the composite figure = 3 / 2(4π) + 16
area of the composite figure = 6π + 16 cm²
learn more on composite figures here: https://brainly.com/question/1639299
Daria applied a transformation to triangle ABC to obtain triangle A′B′C′. The two triangles are not congruent. Which of the following could be the transformation Daria applied?
What is the quotient (3x3 + 10x2 + 10x + 4) ÷ (x + 2)?
a. 3x2 + 16x + 42
b. 3x2 + 4x + 2
c. 3x2 − 16x + 42
d. 3x2 − 4x + 2
Answer:
Option B is correct.
[tex]3x^2+4x+2[/tex].
Step-by-step explanation:
We are asked to find the quotient obtained by dividing the expression [tex](3x^3+10x^2+10x+4)[/tex] by the expression [tex](x+2)[/tex]
We can also write this expression as i.e. we are asked to find the value of the expression:
[tex]\dfrac{3x^3+10x^2+10x+4}{x+2}[/tex]
We can write the expression on the numerator as:
[tex]3x^3+10x^2+10x+4=(3x^2+4x+2)(x+2)[/tex]
Hence,
[tex]\dfrac{3x^3+10x^2+10x+4}{x+2}=\dfrac{(3x^2+4x+2)(x+2)}{x+2}[/tex].
Hence,
[tex]\dfrac{3x^3+10x^2+10x+4}{x+2}=3x^2+4x+2[/tex].
Hence, option B is correct.
Hence, the quotient is:
[tex]3x^2+4x+2[/tex].
Temperature dropped from 11 below zero to 4 below zero how much did the temperature drop
Multiply 3 [ 1 5 -5 6 0 0 ]
Simply multiply the number outside the brackets with each one inside it..
3 [ 1 5 -5 6 0 0 ]
3 x 1 = 3
3 x 5 = 15
3 x -5 = -15
3 x 6 = 18
3 x 0 = 0
3 x 0 = 0
[ 3 15 -15 18 0 0 ]
[ 3 15 ]
[ -15 18 ]
[ 0 0]
The answer is B and I hope I explained this well for you.
Alex has been serving 2/3 cup of lemonade to each student. If he has 1 1/3 cups of lemonade left, how many students can still get lemonade?
Question 2 options:
1
2
3
0
Is it possible for a line segment to have more than one bisector?
Yes, it is possible to have more than one bisector in a line segment.
Bisector is a line that divides a line or an angle in to two equivalent parts. There are two types of Bisectors based on what geometrical shape it bisects.
Bisector of a Line Angle BisectorIn general 'to bisect' something means to cut it into two equal parts. The bisector is the one that doing the cutting process.
With a line bisector, we cut a line segment into two equal parts with another line - the bisector. Just imagine the line PQ is being cut into two equal lengths (PF and FQ) by the bisector line AB.
Whenever AB intersects at a right angle, it is called the "perpendicular bisector" of PQ. If it crosses at any other angle it is simply called a bisector. Drag the points A or B and see both types.
For obvious reasons, the point F is called the midpoint of the line PQ,
evaluate 2^-3
No, there are no answer choices, but it has to be in fraction form.
Help? @texaschic101
Parabola and its vertex
If f(x) is an odd function, which statement about the graph of f(x) must be true?
It has rotational symmetry about the origin.
It has line symmetry about the line y = –x.
It has line symmetry about the y-axis.
It has line symmetry about the x-axis.
An odd function, by definition, is a function that is symmetric about the origin.
An even function, by definition, is a function that is symmetric with respect to the y-axis.
Since the question says that f(x) is an odd function, it has rotational symmetry about the origin. First option is correct.
ANSWER: symmetric about the origin.
Answer:It has rotational symmetry about the origin.
Step-by-step explanation:
An odd function : is a function that is symmetric about the origin.
An even function : is a function that is symmetric with respect to the y-axis.
Since , f(x) is an odd function, it has rotational symmetry about the origin.
its meaning that its graph remains unchanged after rotation of 180 degrees about the origin.
Therefore, It has rotational symmetry about the origin.
3 -1 ___ 1/4 which one is the correct answer.
=
<
>
3-1 = 2
2 is greater than 1/4
so > is the answer
What is the sum of the first five terms of a geometric series with a1 = 10 and r = 1/5?
Answer: 12.496
Step-by-step explanation:
The formula to find the sum of geometric progression is given by :-
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
Given : The first term : [tex]a_1=10[/tex]
Common ratio = [tex]r=\dfrac{1}{5}=0.2[/tex]
Then , the sum of first five terms of a geometric series is given by :-
[tex]S_5=\dfrac{10(1-(0.2)^5)}{1-0.2}=12.496[/tex]
Hence, the sum of the first five terms of given geometric series =12.496
I'm not sure what this is exactly?
Linda is putting money into a savings account. She starts with $450 in the savings account, and each week she adds $70 .
Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Linda has been adding money. Write an equation relating S to W . Then use this equation to find the total amount of money in the savings account after 19 weeks.
The equation of a line is 2(y+1)=10x+3
The y-intercept of the line is ___, and the slope of the line is ___.
Answer: The answer is 0.5 and 5.
Step-by-step explanation: The given equation of the line is
[tex]2(y+1)=10x+3.[/tex]
We are to find the y-intercept and the slope of the given line.
We know that the slope-intercept form of a line is given by
y = mx + c, where, 'm' is the slope and 'c' is the y-intercept of the line.
We have
[tex]2(y+1)=10x+3\\\\\Rightarrow 2y+2=10x+3\\\\\Rightarrow 2y=10x+3-2\\\\\Rightarrow 2y=10x+1\\\\\Rightarrow y=5x+0.5.[/tex]
Therefore, c = 0.5 and m = 5.
Thus, the y-intercept of the line is 0.5 and the slope is 5.