Answer:x-2+10=12
We move all terms to the left:
x-2+10-(12)=0
We add all the numbers together, and all the variables
x-4=0
We move all terms containing x to the left, all other terms to the right
x=4
Step-by-step explanation:
Find the circumference of the circle. Round to the nearest tenth.
Formula for the circumference of a circle: C = pi x diameter
We are given the radius here, but we need the diameter. The diameter of a circle is equal to two times the radius.
diameter = 40 x 2 = 80 in
C = pi x 80
C = 80pi = 251.3 in
Hope this helps!! :)
Answer:
251.3 in
Step-by-step explanation:
The formula for circumference is π·d
Double 40 to get your radius, 80
Then, multiply π·80
The circumference is about 251.3 in
What is the value of 5(y +3)–3x² when x=4 and y=2?
OA) -23
OB) –10
OC) 10
OD) 23
Answer:
-23
Step-by-step explanation:
Plug in the x and the y into the equation:
5((2)+3)-3(4)^2
On the left side of the equation distribute the 5 to the 2 and the three to get:
(10+15)-3(4)^2
which would give us
(25)-3(4)^2
lets solve the other side now
4^2 is 16 and multiply that by 3 to get 48
so it should look like this:
25-48
=-23
Answer: The answer is -23
5(2+3)-3(4)^2 = -23
Step-by-step explanation:
:)
What is the value of p?
(Geometry Question)
Answer:
p = 92
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angle
p+45 = (p-47)+p
Combine like terms
p+45 = 2p-47
Subtract p from each side
p-p+45 = 2p-p-47
45 = p-47
Add 47 to each side
45+47 = p-47+47
92 = p
A 15-minute TV program consists of one commercial of 1
1
4
minutes long, and two equal‐length entertainment segments. How long is each entertainment segment? Enter your answer as a mixed fraction.
Answer:
6 7/8 minutes
Step-by-step explanation:
Say the entertainment segments are each x minutes long. Then, we have the equation:
x + x + 1 1/4 = 15
2x + 1 1/4 = 15
2x = 15 - 1 1/4
We need a common denominator. 1 1/4 = 5/4 and 15 = 60/4, so we now have:
60/4 - 5/4 = 55/4. Then: 2x = 55/4
Divide by 2 from both sides:
(55/4) / 2 = 55/8 = 6 7/8
Thus, each entertainment segment is 6 7/8 minutes long.
Hope this helps!
Answer:
6⅞ minutes
Step-by-step explanation:
15 - 1¼
60/4 - 5/4
55/4
Each segment:
55/4 ÷ 2
55/8
(48 + 7)/8
6 ⅞
A civil engineer is making a scale model of a highway on ramp. The length is 4 inches. The actual length on the ramp is 500ft. Ik scale model is 1/125 but how many times as long as the actual on ramp is the model?
Answer:
1500 Time the multiple of model scale is the actual length of the ramp.
Step-by-step explanation:
Given:
Actual length of ramp is 500ft
Modelling scale is 1/125.
To Find:
how many times as long as the actual on ramp is the model.
Solution:
Actual length is 500 ft
When Civil engineer is modelling the ramp on model then it is about 1/125 of the actual length present at that site.
So
=500*1/125
=4 inches
So on model scale engineer took inches as a unit for scale.
Actual length is 500 ft and model length is 4 inches
So 1 ft corresponds to 12 inches hence 500*12=6000 inches
6000 inches corresponds to 4 inches on model scale
i.e it is about 1500 time multiple of the model scale.
To find out how many times longer the actual on-ramp is than the model, we can use the following steps:
1. **Convert the model length to the same unit as the actual on-ramp:** Since the model's length is given in inches and the actual length is given in feet, we need to convert one of the measurements to the other unit so that they are comparable. Here, we will convert the model's length into feet. There are 12 inches in 1 foot, so to convert inches to feet, we divide by 12.
Model length in feet = Model length in inches / 12
Model length in feet = 4 inches / 12 inches per foot
Model length in feet = 1/3 foot
2. **Compare the actual length to the model length:** Once both lengths are in the same unit, we divide the actual on-ramp length by the model length to find out how many times longer the actual on-ramp is.
Times longer = Actual length / Model length
Times longer = 500 feet / (1/3 foot)
3. **Solve the division:** Now we solve the division by multiplying the actual length by the reciprocal of the model length.
Times longer = 500 feet * (3/1)
Times longer = 1500
So, the actual on-ramp is 1500 times longer than the model.
As for the mention of a scale of 1/125, this doesn't come into play in this specific comparison, as we are only comparing lengths. However, if we want to double-check the work, we can ensure that the scale is consistent with our findings.
Given a scale of 1/125, it means that 1 unit on the model represents 125 units in reality. If our model is 4 inches, that would mean:
Actual length at this scale = Model length * Scale factor
Actual length at this scale = 4 inches * 125
Actual length at this scale = 500 inches
Now, to convert this into feet:
Actual length at this scale in feet = 500 inches / 12 inches per foot
Actual length at this scale in feet = 41.6667 feet (approximately)
Now, this is not the actual length we've been given for the on-ramp (which is 500 feet), so it seems there might be some confusion with the scale provided. The scale factor is not needed when directly comparing the model's length to the actual on-ramp's length, as long as we convert into the same units for a fair comparison.
please, i need help :(
Answer:
First of all, find x from the Pythagorean theorem [tex]a^2+b^2=c^2[/tex], which c is the hypotenuse.
[tex]7^2+24^2=c^2[/tex]
[tex]49+576=c^2[/tex]
[tex]c^2=625[/tex]
c=25 or x=25
Next, we have to figure out the value of y and z. So, you need to use inverse trigonometric functions.
arctan[tex](\frac{7}{24})=y=16.3[/tex] degrees. arctan[tex](\frac{24}{7})=z=73.7[/tex] degrees.
All in all, the values are
x=25
y=16.3
z=73.7
Hope this helps and have a nice day!
Write an equation that represents “The sum of a number and two, divided by 5 is equal to the number plus four.”
Answer:
[tex]\frac{x+2}{5} = x+4[/tex]
Step-by-step explanation:
"sum of a number and two" => addition of x and 2
"divided by 5" => division by 5
"equal" => "="
"plus four" => add 4
The value of the number such that the given phrase satisfy will be -4.5 and the equation will be (x + 2)/5 = x + 4.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
Suppose that number is x.
The Sum of x and 2 will be x + 2.
It is divided by 5 thus, (x + 2)/5
It is equal to x + 4.
(x + 2)/5 = x + 4
(x + 2) = 5(x + 4)
x + 2 = 5x + 20
5x - x = 2 - 20
4x = -18
x = -4.5
Hence "The value of the number such that the given phrase satisfy will be -4.5 and the equation will be (x + 2)/5 = x + 4".
For more about the equation,
https://brainly.com/question/10413253
#SPJ2
You park you car in a pay lot. Because you have a coupon, you get the first 4 hr and 45 min free. You pay for an extra 1 1/2hr. How long did you park?
Answer:
6 hours and 15 minutes
Step-by-step explanation:
4 hours + 45 minutes + 1 hour + 30 minutes = 5 hours + 75 minutes = 6 hours + 15 minutes
Answer:
The answer is 6 hours and 15 minutes.
Step-by-step explanation:
You just need to add the 4 hours and 45 minutes to the extra 1 hour 30 minutes you had to pay for. So 4 hours and 45 minutes plus 1 hour 30 minutes gives you 6 hours 15 minutes.
Circle C has intersecting chords AB and DE as shown.
A) type the equation needed to solve for X?
B) what is the value of X in the diagram?
Please help!
Answer:
x = 30
Step-by-step explanation:
The measure of the chord- chord angle is one half the the sum of the arcs intercepted by the angle and its vertical angle, that is
A
[tex]\frac{1}{2}[/tex] (2x + 10 + x + 20) = 60
B
Multiply both sides by 2 to clear the fraction
2x + 10 + x + 20 = 120, that is
3x + 30 = 120 ( subtract 30 from both sides )
3x = 90 ( divide both sides by 3 )
x = 30
Use the graph.
a. Which plant was the tallest at the beginning?
b. Which plant had the greatest rate of change over the 6 weeks?
1.) plant 3; plant 1
2.) plant 2; plant 2
3.) plant 3; plant 3
4.) plant 1; plant 3
Answer:
3) plant 3; plant 3
Step-by-step explanation:
it was 3 inches at the beginning and grew up to 7 by the end, while the others were shorter and grew less over the time period.
Answer:
hmmmmm
Step-by-step explanation:
1. The range between the highest and lowest temperatures recorded in
Houston is 78 °F. If the record high is 100 °F, what is the record low
temperature? *
Answer:
58 °F
have a wonderful day you are amazing :)
Answer:
22 degrees
Step-by-step explanation:
100-78=22
Salim had a flock of 300 chickens 15%
Answer:
what is the question
Step-by-step explanation:
Salim has a flock of 300 chickens, and 15% of them are infected with a virus. He plans to take a Simple Random Sample (SRS) of 7 chickens to test for the virus.
Salim has a flock of 300 chickens, and 15% of them are infected with a virus. This means there are 45 infected chickens in the flock. To test for the virus, Salim plans to take a Simple Random Sample (SRS) of 7 chickens from the entire flock.
A Simple Random Sample involves selecting a subset of individuals from a larger population in such a way that each individual has an equal chance of being selected. This ensures that the sample is representative of the entire population.
Salim's decision to take a sample of 7 chickens is based on the practical constraints of time, resources, and cost. Testing all 300 chickens would be time-consuming and expensive. By taking a smaller sample, Salim can still obtain valuable information about the prevalence of the virus in his flock while minimizing costs and resources.
However, it's important to note that the accuracy of the sample depends on how well it represents the entire population. To ensure the sample is truly random and representative, Salim should use a random selection method, such as drawing names from a hat or using a random number generator.
Once Salim selects his sample, he can conduct tests to determine the presence of the virus in these chickens. The results of these tests will provide valuable insights into the overall prevalence of the virus in his flock, helping him make informed decisions about disease management and control.
The complete question is:
Salim had a flock of 300 chickens 15% of which are infected with a virus he plans on taking a SRS of 7 chickens to test for the virus.
Miguel wrote the predicted and residual values for a data set using the line of best fit y = 1.82x – 4.3. He left out two of the values. A 4-column table with 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled given with entries negative 2.3, negative 0.9, 1.1, 3.1. The third column is labeled predicted value with entries negative 2.48, negative 0.66, a, 2.98. The fourth column is labeled residual value with entries 0.18, negative 0.24, negative 0.06, b. Which represents the missing values of a and b?
a = 1.16 and b = 0.12
a = 1.16 and b = –0.12
a = 0.5 and b = 6.08
a = 0.5 and b = –6.08
Answer:
actually the answer is A
Step-by-step explanation:
a = 1.16 and b = 0.12
brainliest????
Which of these could be the dimensions of a unit cube? Select all that apply.
1ſt by 1 it by 1 ft.
1 in by 2 in by 1 in.
1 it by 1 in by 1 cm
1 mm by 1 mm by 1 mm
1 m by 1 m by 2 m
Answer:
Answer:jhmghmnb
bnm nbb
Step-by-step explanation:nbm nmnm bbbbbbbbbbbbbbbbbbbbbbbbbbbbb
The dimensions that could be the dimensions of a unit cube are:
A. 1 ft by 1 ft by 1 ftD. 1 mm by 1 mm by 1 mmA unit cube is a cube with side lengths of 1 unit, where the unit can be any length (such as inches, feet, centimeters, etc.). Therefore, to be the dimensions of a unit cube, all three side lengths must be equal to 1 unit.
Let's go through the options:
A. 1 ft by 1 ft by 1 ft: This represents a cube where all sides are 1 foot long. Since each side is 1 unit, this is a unit cube. (Correct)
B. 1 in by 2 in by 1 in: One of the side lengths is not 1 unit. Therefore, this cannot be the dimensions of a unit cube. (Incorrect)
C. 1 ft by 1 in by 1 cm: All sides are of one unit, but not of the same unit (feet, inch and centimeter given). Therefore, this cannot be the dimensions of a unit cube. (Incorrect)
D. 1 mm by 1 mm by 1 mm: Each side is 1 millimeter long, which is a unit of length. Therefore, this represents a unit cube. (Correct)
E. 1 m by 1 m by 2 m: One of the side lengths is not 1 unit. Therefore, this cannot be the dimensions of a unit cube. (Incorrect)
The question is:
Which of these could be the dimensions of a unit cube? Select all that apply.
A. 1 ft by 1 ft by 1 ft.
B. 1 in by 2 in by 1 in.
C. 1 ft by 1 in by 1 cm
D. 1 mm by 1 mm by 1 mm
E. 1 m by 1 m by 2 m
Find the area of the blue sectors formed by angle DFE. Round answer to
the nearest tenth.
137°E
F28 m
Answer choices
1552.7
1525.7
1255.7
1555.7
Answer:
1525.7 square meters, approximately.Step-by-step explanation:
Notice that the radius is 28 meters, and the angle of the orange sector is 137°. However, the angle of the blue sector is:
360° - 137° = 223°
The area of a circular sector is
[tex]A=\frac{\pi r^{2} \alpha}{360\°}[/tex]
Replacing given values, we have
[tex]A=\frac{(3.14)(28)^{2} (223\°)}{360\° }=\frac{548972.48}{360} \approx 1525[/tex]
Therefore, the right answer is the second choice.
Answer:
B. 1,525.7 square meters
Correct graph:
The correct graph is attached below.
Source:
Previous question that can be found at chegg
Step-by-step explanation:
Let's recall that the formula of the area of a sector of a circle is:
Area = π * r² * (C/360 ), where:
r is the radius of the circle of which the sector is part
C is the central angle in degrees
Replacing with the values provided, we have:
r = 28 meters
C = 360 - 137 = 223 (We're being asked about the blue sector area not the orange sector area)
Area = π * 28² * (223/360 )
Area = 3.1416 * 784 * 0.6194
Area = 1,525.7 m²
The correct answer is B. 1,525.7 m²
Solve 2(3∕4z + 2) = 2(1∕8z – 1∕2) for z.
Question 1 options:
A)
z = –4
B)
z = –3
C)
z = 5
D)
z = 2
Answer:
A) z= -4
Step-by-step explanation:
Answer:
z= -4
Step-by-step explanation:
Lindsay needs to purchase a car. The car she is planning on purchasing costs $8000 and she has $2000
If g(x) is the graph of f(x) shifted up 5 units and right 1 units, write formula for g(x)
Answer:
( x+1, y+5 )
Step-by-step explanation:
x+1 because adding 1 to the x coordinate would shift it over 1
y+5 because adding 5 to the y coordinate would shift it up 5
Formula for g(x) is g(f(x)) = ( x+1, y+5 )
What is graph?
A graph can be defined as a pictorial representation or a diagram that represents data or values.
Vertical shifting of a graph is done by adding any arbitrary constant to the function in shifting.
For example, If shift up by 1 unit, add 1 to function
If shift down by 4 units, subtract 4 from function
x+1 because adding 1 to the x coordinate would shift it over 1
y+5 because adding 5 to the y coordinate would shift it up 5
g(f(x)) = ( x+1, y+5 )
Hence, formula for g(x) is g(f(x)) = ( x+1, y+5 )
Learn more about graph
https://brainly.com/question/16608196
#SPJ2
If a 4x 16 rectangle has the same area as a square, what is the length of a side of the square?
Ο Α. 10
Ο B. 12
Ο C. 6
Ο D. 8
Answer:
D
Step-by-step explanation:
4*16=64
8*8=64
Answer:
D. 8
Step-by-step explanation:
8*8= 64 =4*16
i need help i cant get this right :(
Complete the sentence:
If Angle J X M has a value of 57 degrees, then Angle N X P has a value of
Answer:
33 is the correct answer.
Step-by-step explanation:
Answer:
33
Step-by-step explanation:
please give brainliest
solve for x: 4x^2-6x+2=0
Answer:X=1 or 0.5
Step-by-step explanation:
Use general quadratic equation
That is
X=(-b+or√(b²-4ac))/2a
Where
a=4
b=-6
c=2
Answer:
Step-by-step explanation:
hello :
4x²-6x+2=0
2(2x²-3x+1)=0 means : 2x²-3x+1 = 0
(x-1)(2x-1)=0
x-1=0 or 2x-1=0
x=1 or x= 1/2
In this problem, you're multiplying 7 by 10. What is 10 called in this math problem?
Answer:
the first digit like 10 x 7
Step-by-step explanation:
ur multiplying it byyyyyy 10
Answer:
multiplier
Step-by-step explanation:
7 is what's multiplying
10 is called the multiplier
PLS ANSWER FAST!!!!Which sentences contain phrases that are hyphenated correctly? Select 3 options
Answer:
The middle three sentences are hyphenated correctly.
Step-by-step explanation:
How do you get the answer
Answer:
(x + 2)(x - 4)
Step-by-step explanation:
Given the zeros of a function, say x = a and x = b, then
the factors are (x - a) and (x - b)
From the graph
The zeros are x = - 2 and x = 4, thus the factors are
(x - (- 2)) and (x - 4), that is (x + 2) and (x - 4)
The expression 10,600(1.0385)x represents the amount of money in an investment account with interest that compounds annually for x years. Interpret the meaning of the expression.
A
The initial investment is $10,385, and the growth rate of the investment is 1.06%.
B
The initial investment is $10,385, and the growth rate of the investment is 6%.
C
The initial investment is $10,600, and the growth rate of the investment is 1.0385%.
D
The initial investment is $10,600, and the growth rate of the investment is 3.85%.
Answer:
The correct option is option (D)
The initial investment is $10,600 and the growth rate of the investment is 3.85%.
Step-by-step explanation:
The formula of compound interest:
[tex]A=P(1+r)^n[/tex]
A= Total amount after n years
P= Initial value of deposit
r= rate of interest compound annually
n= time is in year
Given expression is
[tex]A=10,600(1.0385)^x[/tex]
[tex]A=10,600(1+0.0385)^x[/tex]
Now we compare the given expression with the compound interest formula
So,
P= 10,600
r=0.0385 =3.85%
So, the initial investment is $10,600 and the growth rate of the investment is 3.85%.
PLEASE HELP ME!!! 30 POINTS
Select the statement that correctly completes the sentence. When using more than one adjective, ________.
A. an order only needs to be followed sometimes
B. there is an order, but it should never be followed
C. there is an order that should be followed
D. there is not an order that should be followed
Final answer:
When using multiple adjectives, there is a specific order that should be followed to make sentences sound natural and to convey descriptions clearly. Therefore, the correct answer is option D
Explanation:
When using more than one adjective, there is an order that should be followed (option D). In English grammar, adjectives are typically arranged in a specific order when they are used together before a noun. The general sequence is opinion, size, age, shape, color, origin, material, and purpose. Following this adjective order helps sentences sound natural to native speakers and makes the description clearer and easier to understand. For example, you might describe a sweater as a 'beautiful, small, old, red woolen sweater' to adhere to the standard adjective order.
The price of a gallon of milk at a particular convenience store has been recorded over the course of 10 weeks. At the end of the third week, the price $3.38 and at the end of the eighth week the price is $3.55. The price has been observed to increase exponentially.
Given:
The price of milk at the end of the third week = $3.38.
The price of milk at the end of the eighth week = $3.55.
To find:
The approximate increase in price of milk per week and the cost of milk at the end of the tenth week.
Solution:
To determine the increase in the price per week, we divide the difference in price over n number of weeks by n.
Here we know the prices of milk at the end of the third and the eighth week. There are 5 weeks between these two.
The approximate increase in the price of milk [tex]= \frac{3.55-3.38}{5} = \frac{0.17}{5} = 0.034.[/tex]
So there is an increase of $0.034 per week.
To determine the price at the end of the tenth week, we add the increase in price over two weeks to the price at the end of the eighth week.
The price of milk at the end of the eighth week = $3.55.
The increase in price over two weeks [tex]=2(0.034) = 0.068.[/tex]
The price of the milk at the end of the tenth week [tex]= 3.55+0.068=3.618.[/tex]
Rounding this off to the nearest cent, we get the price of milk at the end of the tenth week is $3.62.
2. Jessica is a waitress. Her customer’s bills totaled $300. She earned $45 in tips. What percent did her customers tip her? ___
Answer:
15%
Step-by-step explanation:
$45/$300 = 0.15 = 15%
Candice is an interior designer, and she is currently trying to change the look of a room. Candice found that the area of a room could be given by the expression 3x2 + 2x. The aread of the rug she wants to spread on the floor is given by the expression x2 + 24x - 144. What expression represents the area of the room not covered by the rug?
Answer:
[tex]A(x) = 2x^2-22x+144[/tex]
Step-by-step explanation:
We are given the following in the question:
Area of room =
[tex]3x^2 + 2x[/tex]
Area of rug =
[tex]x^2 + 24x - 144[/tex]
We have to find the area of of the room not covered by the rug.
Area of of the room not covered by the rug =
Area of room - Area of rug
[tex]A(x)=(3x^2 + 2x) - ( x^2 + 24x - 144)\\A(x)=3x^2 + 2x-x^2 -24x + 144\\A(x)=(3x^2-x^2)+(2x -24x) + 144\\A(x)=2x^2-22x+144[/tex]
is the required expression for the area of floor not covered by the rug.
A long jumper leaves the ground at an angle of
22
°
above the horizontal, at a speed of
9
/
m
s
. The height of the jumper can be modeled by
=
h
x
+
−
0.046
x
2
0.362
x
, where
h
is the jumper's height in meters and
x
is the horizontal distance from the point of launch.
Answer:
a) = 3.96
b) = 0.72
c) = 7.94
Step-by-step explanation:
Complete question.
(A long jumper leaves the ground at an angle of 20° above the horizontal, at a speed of 11 m/sec. The height of the jumper can be modeled by h(x) = -0.046x2+ 0.364x, where h is the jumper's height in meters and x is the horizontal distance from the point of launch. a. At what horizontal distance from the point of launch does the maximum height occur? Round to 2 decimal places. b. What is the maximum height of the long jumper? Round to 2 decimal places. c.What is the length of the jump? Round to 1 decimal place.)
Solution.
Data
Θ = 20
v = 11m/s
h(x) = -0.046x² + 0.364x
x = horizontal distance
h = height
a.
h(x) = -0.046x² + 0.364x
at maximum height,
d / dx (h) = 2(-0.46x) + 0.364
d / dx (h) = -0.092x + 0.364
at maximum height d / dx (h) = 0
0 = -0.092x + 0.364
0.092x = 0.364
x = 3.96.
b).
Hmax = -0.046x² + 0.364x
Hmax = -0.046(3.96) + 0.364(3.96)
Hmax = -0.72 + 1.44
Hmax = 0.72
c) the length of the jump can be calculated using the formula for range of a projectile
R = v² sin2Θ / g
g = 9.8m/s²
R = 11² * sin 2(20) / 9.8
R = 121 * sin40 / 9.8
R = 77.777 / 9.8
R = 7.936 = 7.94
a. The maximum height occurs at a horizontal distance of 3.96 meters.
b. The maximum height of the long jumper is 0.72 meters.
c. The length of the long jumper's jump is approximately 7.94 meters.
a. The maximum height occurs when the derivative of the height function with respect to horizontal distance is equal to zero.
Given h(x) = -0.046x² + 0.364x
Taking the derivative of h(x) with respect to x:
dh/dx = -0.092x + 0.364
Setting dh/dx to zero and solving for x:
0 = -0.092x + 0.364
0.092x = 0.364
x = 3.96
Therefore, the maximum height occurs at a horizontal distance of 3.96 meters.
b. To find the maximum height, substitute x = 3.96 into the height function h(x):
h(3.96) = -0.046(3.96)² + 0.364(3.96)
h(3.96) = -0.72 + 1.44
h(3.96) = 0.72
The maximum height of the long jumper is 0.72 meters.
c. The length of the jump, also known as the range, can be calculated using the formula for the range of a projectile:
R = v^2 * sin(2θ) / g
Given:
v = 11 m/s
θ = 20°
g = 9.8 m/s²
Substitute these values into the formula:
R = 11^2 * sin(40°) / 9.8
R = 121 * sin(40°) / 9.8
R = 121 * 0.6428 / 9.8
R = 77.777 / 9.8
R ≈ 7.94
Therefore, the length of the long jumper's jump is approximately 7.94 meters.
Complete question :
(A long jumper leaves the ground at an angle of 20° above the horizontal, at a speed of 11 m/sec. The height of the jumper can be modeled by h(x) = -0.046x2+ 0.364x, where h is the jumper's height in meters and x is the horizontal distance from the point of launch. a. At what horizontal distance from the point of launch does the maximum height occur? Round to 2 decimal places. b. What is the maximum height of the long jumper? Round to 2 decimal places. c.What is the length of the jump? Round to 1 decimal place.)
Solution.
Data
Θ = 20
v = 11m/s
h(x) = -0.046x² + 0.364x
x = horizontal distance
h = height
a.
h(x) = -0.046x² + 0.364x
at maximum height,
d / dx (h) = 2(-0.46x) + 0.364
d / dx (h) = -0.092x + 0.364
at maximum height d / dx (h) = 0
0 = -0.092x + 0.364
0.092x = 0.364
x = 3.96.
b).
Hmax = -0.046x² + 0.364x
Hmax = -0.046(3.96) + 0.364(3.96)
Hmax = -0.72 + 1.44
Hmax = 0.72
c) the length of the jump can be calculated using the formula for range of a projectile
R = v² sin2Θ / g
g = 9.8m/s²
R = 11² * sin 2(20) / 9.8
R = 121 * sin40 / 9.8
R = 77.777 / 9.8
R = 7.936 = 7.94.