Answer: the rate of change of the distance between the car and the person at that instant is 4 meters per second
Step-by-step explanation:
According to the Pythagorean theorem, we have:
d^2 = (12^2 + 9^2)
Differentiating both sides with respect to time:
2d * (dd/dt) = 0 + 2(9) * (9''), Simplifying the equation, we get:
2d * (dd/dt) = 2(9) * (9'')
Substituting the given values:
2d * (dd/dt) = 2(9) * (4) [the car is moving at a constant velocity of 4 m/s]
Simplifying further:
2d * (dd/dt) = 72
we divide both sides by 2d:
dd/dt = 72 / (2d)
substitute this value into the equation to find the rate of change of the distance:
dd/dt = 72 / (2 * 9) = 4 m/s
The rate of change of the distance between the car and the person at that instant is -12/5 meters per second.
Given information:
The person is standing 12 meters east of the intersection.
The car is driving away from the intersection to the north at a constant speed of 4 meters per second.
At a certain instant, the car is 9 meters from the intersection.
Using the Pythagorean theorem, determine D(t) in terms of the car's distance from the intersection, which we'll call x(t).
Since the person is 12 meters east of the intersection, the distance D(t) can be expressed as:
[tex]D(t) = \sqrt{(x(t)^2 + 12^2)[/tex]
Differentiating both sides of the equation with respect to time, we get:
[tex]dD/dt = (1/2) * (x(t)^2 + 12^2)^{(-1/2)} * 2x(t) * dx(t)/dt[/tex]
So, dx(t)/dt = -4
Substituting this value into the equation for dD/dt, we have:
[tex]dD/dt = (1/2) * (x(t)^2 + 12^2)^{(-1/2)} * 2x(t) * (-4)[/tex]
[tex]dD/dt = -4x(t) / \sqrt{(x(t)^2 + 144)[/tex]
At the instant when the car is 9 meters from the intersection, substitute x(t) = 9 into the equation:
[tex]dD/dt = -4(9) / \sqrt{(9^2 + 144)[/tex]
= -36 / √(81 + 144)
= -36 / √225
= -36 / 15
= -12/5
Therefore, the rate of change is -12/5 meters per second.
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What value, written as a decimal, should Lena use as the common ratio?
Answer:
an=1*2.5^(n-1)
=2.5^(n-1)
Step-by-step explanation:
Complete question below:
What value, written as a decimal, should Lena use as the common ratio? Lena is asked to write an explicit formula for the graphed geometric sequence. On a coordinate plane, 3 points are plotted. The points are (1, 1), (2, 2.5), (3, 6.25).
Solution
Point (1, 1), (2, 2.5), (3, 6.25).
a=1
ar=2.5
ar^2=6.25
From ar and ar^2
r=6.25/2.5
=2.5
r=2.5
an=ar^(n-1)
Therefore, the explicit formula is
an=1*2.5^(n-1)
=2.5^(n-1)
your asked to add 15mEq of pittassium choride to 1,000mL of NaCI. potassium chloride is avalable as 20mEq/10 mL. whats the coreect dosage?
Answer:
7.5ml
Step-by-step explanation:
20/10=15/x
20x=10(15)
20x=150
x=150/20
x=7.5
So you’d add 7.5ml of NaCl to the 1,000ml IV.
D
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box, Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan Click the trashcan to clear all your answers.
Solve by factoring
x2 + 6.9. Hint. This is a double root.
3
9
12131415161718
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Answer:
–3 and –3
Step-by-step explanation:
x² + 6x = – 9
Rearrange
x² + 6x + 9 = 0
Multiply the first term i.e x² and last term i.e 9 together. The result is 9x².
Next, we shall find two factors of 9x² such that when we add them together, the result will be the same as the 2nd term i.e 6x in the expression above.
The factors are 3x and 3x.
Next, we shall replace 6x with 3x and 3x in the equation above as shown below:
x² + 6x + 9 = 0
x² + 3x + 3x + 9 =0
Factorise
x(x + 3) + 3(x + 3) = 0
(x + 3)(x +3) = 0
x + 3 = 0 or x + 3 =
x = – 3 or x = – 3
Therefore, the solutions are –3 and –3
Hillary has to drive 225 miles in four and a half hours. What should her average speed be in order to arrive on time? 56 mph 45 mph 50 mph 48 mph
Answer:
50 mph
Step-by-step explanation:
225 in 4.5 Hours
1 Hour - 50 miles
(225 ÷ 4.5 = 50)
Hope this helps.
Answer:
50mph
Step-by-step explanation:
To figure this out you would just have to divide the number of miles which is 255 by the number of hours which is 4.5 and you would get 50mph.
Below are the distances that each of Davi the Dragon Keeper's four dragons can blow fire (in meters). 0.9, 0.5, 0.3, 1.1. Find the mean absolute deviation (MAD) of the data set.
Answer:
Step-by-step explanation:
MAD is simply the average distance that all of the numbers in your data set are from the mean. Your first step is to put your data in order, then determine the mean. Let’s look at this data set:0.3, 0.5, 0.9, 1.1
The mean of this data set is 0.7Starting with the lower extreme, and checking every number in your data set, determine how far each number is from the mean. First, put the numbers in numerical order, from least to greatest. Determine the distance each number is from 0.7. 0.3=0.40.5=0.20.9=0.21.1=0.4Add up all of the distances. Total distance from the mean (12) ÷ 4 numbers in our data set = a mean absolute deviation of 3.I added a PowerPoint that I made so that if you didn't understand it you could read off of it.
Answer:
[tex]0.3[/tex] - written in [tex]2/14/2021[/tex]
Step-by-step explanation:
The answer is [tex]0.3[/tex] because, [tex]\frac{0.9+0.5+0.3+1.1}{4} =\frac{2.8}{4} =0.7[/tex], so [tex]0.7[/tex] is the mean. After having found the mean, we have to subtract [tex]0.7[/tex] from the numbers, or the numbers from [tex]0.7[/tex]:
Data Point | Distance from the mean
[tex]0.9[/tex] | [tex]0.9-0.7=0.2[/tex]
[tex]0.5[/tex] | [tex]0.7-0.5=0.2[/tex]
[tex]0.3[/tex] | [tex]0.7-0.3=0.4[/tex]
[tex]1.1[/tex] | [tex]1.1-0.7=0.4[/tex]
After finding out the Distance from the mean we'll use their sums and add them all up: [tex]0.2+0.2+0.4+0.4[/tex], then divide them by [tex]4[/tex] because there are [tex]4[/tex] numbers combined together: [tex]\frac{0.2+0.2+0.4+0.4}{4}=\frac{1.2}{4}=0.3[/tex].
So that's why the answer is [tex]0.3[/tex] (Happy Valentines Day!)
Compare 6 ⋅ 108 to 3 ⋅ 106. 6 ⋅ 108 is 2,000 times larger than 3 ⋅ 106. 6 ⋅ 108 is 200 times larger than 3 ⋅ 106. 6 ⋅ 108 is 20 times larger than 3 ⋅ 106. 6 ⋅ 108 is 2 times larger than 3 ⋅ 106.
Answer:
[tex]\boxed{Option \ 2}[/tex]
Step-by-step explanation:
[tex]6*10^8\\=> 600000000[/tex]
[tex]3*10^6\\=> 3000000[/tex]
Dividing both
=> 600000000 ÷ 3000000
=> 200
So,
[tex]6*10^8[/tex] is 200 times larger than [tex]3* 10^6[/tex]
Answer:
[tex]\boxed{\mathrm{Option \: 2}}[/tex]
Step-by-step explanation:
[tex]6 \times 10^8 = 600000000[/tex]
[tex]3 \times 10^6 =3000000[/tex]
[tex]\frac{600000000}{3000000} =200[/tex]
6 × 10⁸ is 200 times larger than 3 × 10⁶.
A prism has a volume of 238 cubic millimeters. Which is the correct substitution for finding the length of the prism?
Answer:
D. V = l w h. 238 = l times 8 and one-half times 3 and one-half
Step-by-step explanation:
A prism has a volume of 238 cubic millimeters.
A prism has a length of l millimeters, height of 3 and one-half millimeters, and width of 8 and one-half millimeters.
Which is the correct substitution for finding the length of the prism?
A. V = l w h. 238 = l + 8 and one-half + 3 and one-half
B. V = l w h. V = 238 times 8 and one-half times 3 and one-half
C. V = l w h. l times 8 and one-half times 3 and one-half
D. V = l w h. 238 = l times 8 and one-half times 3 and one-half
From the question
V=lwh
Volume of a prism=length)(width)(height)
Volume=238
l= l mm
w= 8 1/2
h= 3 1/2
Substituting all the values
V=lwh
238= l * 8 1/2 * 3 1/2
D. V = l w h. 238 = l times 8 and one-half times 3 and one-half
Answer:
D
Step-by-step explanation:
got it right on edge 2020
Solve both of the fields. First correct answer gets brainliest and 5 stars with 1 thanks
Answer:
Step-by-step explanation:
f(1)=45*4/5
=9*4
=36
BEST ANSWER GETS BRAINLIEST, PLZ ANSWER!!!!
Answer:
they both = 100
Step-by-step explanation:
One number is 5 more than 4 times another their sum is 20
Answer:
3, 17
Step-by-step explanation:
1st number = x
2nd number = 4x+5
x+4x+5=20
5x=15
x=3
1st number = 3
2nd number = 4(3)+5=12+5=17
In how many different ways can 5 people be seated at a round table?
Answer 120
Step-by-step explanation:
this is the question pls help me 4 friends evenly divided up an n-slice pizza. One of the friends, Harris, ate 1 fewer slice than he received. How many slices of pizza did Harris eat? Write your answer as an expression.
Answer:
[tex]\frac{n}{4}-1[/tex]
Step-by-step explanation:
If we have a pizza that has [tex]n[/tex] slices and we want to split it between 4 friends, then each friend will get [tex]\frac{n}{4}[/tex] slices.
Now, Harris is one of those friends so he receives [tex]\frac{n}{4}[/tex] slices, but he eats one less than he receives. Therefore, we subtract one from this expression to get our final answer of [tex]\frac{n}{4}-1[/tex].
Hope this helped!
Answer:
(n/4 - 1) slices
Step-by-step explanation:
The pizza would be divided into n slices, which in turn would be split among 4 people:
n slices
----------------- = (n/4) slices per person
4 people
Harris must have eaten (n/4 - 1) slices.
how would you verify the trigonometric identity 2x = 2sinx cosx
Step-by-step explanation:
Hi, there!!
I hope you mean sin2x=2sinx . cosx
so, let's begin in a simple way; by adding, alright:
sin2x= sin(x+x) (as 2x=x+x).
now, let's use compound formula for sin,
so, we get:
sin (x+x)= sinx.cosx + cosx. sinx (as sin(A+B)=sin A. cosB + cosA . sinB)
or, sin (x+x)=2sinx.cosx (adding both).
Therefore, sin 2x = 2sinx. cosx.
Hope it helps..
Answer:
Step-by-step explanation:
2x = 2sinx cosx is not an identity. An identity is "always true," whereas a conditional equation is true only for specific value(s) of the unknown. Double check to ensure that you have copied down this problem correctly.
i need help i need help
Answer:
H1 H2 H3 H4 H5 H6
T1 T2 T3 T4 T5 T6
Step-by-step explanation:
When we roll a die we get 1,2,3,4,5,6
When get flip a coin get get H or T for heads or tails
The top right lists the possible outcomes, one for the heads or tails and one of the die outcomes
H1 H2 H3 H4 H5 H6
T1 T2 T3 T4 T5 T6
Answer:
H1 H2 H3 H4 H5 H6
T1 T2 T3 T4 T5 T6
Step-by-step explanation:
what is the smallest number by which 2408 should be multiplied to get a perfect cube
Answer:
90601
Step-by-step explanation:
we have to find smallest number by which 2408 should be multiplied to get a perfect cube.
First lets find prime factor of 2408 and power these prime factors have
2408 = 2*1204 = 2*2*602 = 2*2*2*301= 2*2*2*7*43
thus,
2408 = 2^3*7*31
we know that a cube is a number raised to the power three
in 2408
2 has a power of three
but 7 and 31 and there is power of one,
thus we need to make
power of 7 and 31 three by multiplying
7 with 7*7
and 31 with 31*31
thus,
2^3*7*31*7*7*31*31 is the minimum cube value for this number
2^3*7*31*7*7*31*31 = 2^3*7^3*31^3 = 2408 * 7^2*31^2 = 2408*90601
Thus, smallest number which should be multiplied with 2408 to make it a perfect cube is 90601
Given the equation of the circle below, find the center coordinate of the circle,
and the radius of the circle.
x² + y2 + 4y = 32
Center : (0, 2)
Center : (0, 2)
Center : (0, -2)
Center : (0, -2)
R = 26
R = 6
R = 36
R = 6
Answer:
Center : (0,-2), R=6
Step-by-step explanation:
x² + y² + 4 y = 32
x² + y² +4 y+4=36
x² + (y+2)²=36
Center : (0,-2), R=6
Diego cut 7 smaller boards of equal length from a board that is 9 and one-third feet long. How long is each of the 7 smaller boards? Four-thirds StartFraction 7 over 9 EndFraction StartFraction 9 over 7 EndFraction Three-fourths
Answer:
9 over 7 end fraction three-fourths
Step-by-step explanation:
The length of the 7 smaller boards will be ''Four-thirds'' (4/3 feet).
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Diego cut 7 smaller boards of equal length from a board that is 9 1/3 feet long.
Now,
Since, Diego cut 7 smaller boards of equal length from a board that is 9 and one-third feet long.
So, The length of the 7 smaller boards = 9 1/3 ÷ 7
= 28/3 ÷ 7
= 28/3 × 1/7
= 4/3 feet
Thus, The length of the 7 smaller boards will be ''Four-thirds'' (4/3 feet).
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In the school election, votes were cast for Sam, Mary, and Bill in the ratio 4:3:2. If a total of 2178 votes were cast, how many votes did Mary receive?
Answer:
Step-by-step explanation:
Mary received 726 votes.
How many gallons each of 15% alcohol and 5% alcohol should be mixed to obtain 10 gal of 14% alcohol?
How many gallons of 15% alcohol should be in the mixture? ____ gal
Answer:
Step-by-step explanation:
Refer https://brainly.com/question/17122506
solve for linear equations y=--2x+18 4y-x+9=0
Answer:
I hope it will help uh......
Carlos creates a basic budget using the equation Money Left Over = a - b - C, where
Income = a, Needs b, and Wants = c. His monthly income is $3210, his mortgage
payment is $1350, and he spends an additional $950 each month on groceries, utilities, and
insurance. Finally, he buys four concert tickets for $300.
Which amount represents his needs?
Answer:
$2300
Step-by-step explanation:
Carlos's needs will include ...
mortgage: $1350groceries, utilities, insurance: $950These total $2300.
Carlos's needs amount to $2300 per month.
Answer:
$950
This is because he needs groceries, utilities, and insurance.
Which of the following best describes the expression 5(x + 2)? pls help me :,D
Answer:
5 is a constant. (it has no variables)
x + 2 is not a constant. It does, however, have two terms, x and 2.
(terms are seperated by addition/subtraction)
This rules out a and b.
As for c... 5(x+2) implies multiplication, which would be a product, not a sum.
The product of a constant factor 5 and a 2-term factor x+2
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
5(x + 2)
The constant factor is 5. x + 2 is not constant.
The brackets represent multiplication.
Can someone help me ?
Answer:
>
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Step-by-step explanation:
Currently stuck on this problem, Please help me out
Answer:
4.24 blocks
hope this helps :)
The correct answer should theoretically be 4.24
Because the triangle has a vertical reflection across the center (AD)
What is the value of the expression
Answer:
6
Step-by-step explanation:
2(7)-(-4)/3
(14+4)/3
18/3
=6
If it's right can i get brainliest.
Answer:
D) 6
Step-by-step explanation:
Plug in the values of a & b
[tex]\frac{/2a/-b}{3}= \frac{/2*7/-[-4]}{3}\\\\=\frac{/14/ + 4}{3}\\\\=\frac{14+4}[3}\\\\=\frac{18}{3}\\\\=6[/tex]
hi can you please help me and explain step by step if possible thank you
Answer: see image
Step-by-step explanation:
Count how many spaces the vertex is away from the line x = -1. Then place that vertex the same distance on the other side of the line x = -1.
The triangles in the figure are similar: ΔABC ∼ ΔDEF. Which of the following statements must be true? options: A) AB/DE=BC/EF=CA/FD B) None of these statements are true. C) AB=BC D) AB/DE=2
Answer:
Answer A
Step-by-step explanation:
We see that ABC is similar to DEF. Pay attention to the order of these letters. The order that they read (left-to-right) is the order that they are similar. For example, AB is similar to DE. Despite being different triangles, they are both the first two letters in the triangle. So, knowing this, we can conclude that answer choice A is correct.
Answer:
The answer is A
Step-by-step explanation:
Find 4 1/5 · 7 2/3 . a. 32 1/5 b. 32 3/5 c. 28 2/15 d. 28 3/10
Answer:
Hey there!
4 1/5 · 7 2/3= 32 1/5
Hope this helps :)
Answer:
32 1/5
Step-by-step explanation:
4 1/5 * 7 2/3
Change to improper fractions
( 5*4+1)/5 * ( 3*7+2)/3
21/5 * 23/3
Rewriting
21/3 * 23/5
7 * 23/5
161/5
Change back to a mixed number
5 goes into 161 32 times with 1 left over
32 1/5
Simplify to create an equivalent expression. \qquad{-4(z+3)-4(5-4z)}−4(z+3)−4(5−4z)minus, 4, left parenthesis, z, plus, 3, right parenthesis, minus, 4, left parenthesis, 5, minus, 4, z, right parenthesis Choose 1 answer: Choose 1 answer: (Choice A) A -24z-32−24z−32minus, 24, z, minus, 32 (Choice B) B 12z+812z+812, z, plus, 8 (Choice C) C 12z-3212z−3212, z, minus, 32 (Choice D) D 12z+3212z+32
Answer:
D) 12z -32
Step-by-step explanation:
Simplify to create an equivalent expression.
-4(z+3)-4(5-4z)}−4(z+3)−4(5−4z)
Choose 1 answer:
A) A -24z-32
B) B 12z+8
C) C 12z-32
D) D 12z+32
-4(z+3)-4(5-4z)
= -4z -12 -20 + 16z
= 12z -32 (D)
37.4
Solve for x and y.
A. x = 26.4 y = 20.4
B. x = 26.4, y = 17
C. x = 18.3. y = 20.4
D.
x = 18.3. y= 17