3. A person standing 3 feet away from the base of a lamp post casts a shadow 4 feet long. If the person is 6 feet tall and walks away from the lamp post at a speed of 400 feet per minute, at what rate will his shadow lengthen
Answers
Answer:
533.33 ft/min
Step-by-step explanation:
We are given that
x=3 feet
y=4 feet
Height of person,h=6 feet
[tex]\frac{dx}{dt}=400 ft/min[/tex]
Triangle ABC and A'B'C are similar because all right triangles are similar
By using similarity property
[tex]\frac{h'}{6}=\frac{7}{4}[/tex]
[tex]h'=10.5 feet[/tex]
[tex]x+y=3+4=7 feet[/tex]
[tex]\frac{h'}{6}=\frac{x+y}{y}[/tex]
[tex]\frac{10.5}{6}=\frac{x+y}{y}[/tex]
[tex]10.5y=6x+6y[/tex]
[tex]10.5y-6y=6x[/tex]
[tex]4.5y=6x[/tex]
Differentiate w.r.t t
[tex]4.5\frac{dy}{dt}=6\frac{dx}{dt}[/tex]
[tex]\frac{dy}{dt}=\frac{6\times 400}{4.5}ft/min[/tex]
[tex]\frac{dy}{dt}=533.33ft/min[/tex]
Hence, If the person is 6 feet tall and walks away from the lamp post at a speed of 400 feet per minute then his shadow moving at the rate 533.33 ft/min
Related Questions
Which expression is equivalent to 1 x +3 - 3x + (-2)?
Answers
Answer:
1 - 2x
Step-by-step explanation:
Simplify the expression.
1x + 3 - 3x + (-2)
Bring all the like terms together.
= 1x - 3x + 3 - 2
Simplify again.
= 1 - 2x
Combine like terms 0.5(x⁴-3)+12
Answers
i think you're wanting this simplified; 0.5x^4 + 10.5
Answer: 0.5x^4+10.5
Step-by-step explanation: hope this helps!
Fill in the blank.
There are 178 stuffed toys in a toy shop.
There are 227 fewer stuffed toys than puzzles in the toy shop.
How many puzzles are in the toy shop?
Answers
Answer:49
Step-by-step explanation:
please help and can someone explain what a integer is
Answers
w = -18
x = -10
y = -2
z = 10
x and z are opposite, x= -10, where as z = 10, Hence x times (-1) equals z.
An integer is a non-fractional number real number. It can be either negative or positive, it simply cannot be a fraction.
"w", "x", and "y" are negative, and hence less than zero.
Which number is greatest? 89.91, 81.900, 81.90, or 81.9?
Answers
Answer:
the first option (89.91) is the greatest
A baker sold 20 cakes. He sold 3/5 of them before noon. How many cakes did he sell that morning?
Answers
Answer:
He sold 12 cakes
Step-by-step explanation:
1/5 of 20 is 4 so 3 X 4= 12 so 12 cakes
Algebra basics Graphing lines and slope
Question: Detereme the intercepts of the line
y - intercept ( , ) ( , )
x - intercept ( , ) ( , )
Answers
Answer:
y= (-40,-1) x=(-10-17)
Step-by-step explanation:
Find the percent change from the first value to the second.
60; 90
Answers
Answer:
Step-by-step explanation:
90 is half again as much as 60: 60 + (1/2)(60) = 90
This is a 150% increase.
Evaluate f(x+3) when f(x)=-x^2-2x+2
Answers
Answer:
f(x + 3) = -x² - 8x - 13
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationExpandingTerms/Coefficients/DegreesStep-by-step explanation:
Step 1: Define
f(x) = -x² - 2x + 2
f(x + 3) is x = x + 3
Step 2: Find
Substitute in x: f(x + 3) = -(x + 3)² - 2(x + 3) + 2Expand: f(x + 3) = -(x² + 6x + 9) - 2x - 6 + 2Distribute -1: f(x + 3) = -x² - 6x - 9 - 2x - 6 + 2Combine like terms: f(x + 3) = -x² - 8x - 13Pls help I’m so confused
Answers
Step-by-step explanation:
1560 sq yards
for Sure I have done this question before
and have just soved it
You can say thanks in comment
I need help bc i dont understand so plz help due tomorrow
Answers
Answer:
c = 3 is the only thing i can think of lmk if im wrong..
Step-by-step explanation:
c =3 because 12÷4 (pentagons)= 3
What is the measure of P?
Answers
Answer:
111?
Step-by-step explanation: Did u even try...
Prove that the triangle with vertices A(0,1), B(3,3), and C(3,-1) is an isosceles triangle. Select the two sides that are congruent.
Answers
Answer:
AB and AC are congruent
Step-by-step explanation:
To show that the triangle is isosceles, we need to show that two of the sides of the triangle are equal.
Get AB
Using the formula for calculating the distance between two points
AB = √(x2-x1)²+(y2-y1)²
A(0,1), B(3,3)
AB = √(3-0)²+(3-1)²
AB = √3²+2²
AB = √9+4
AB = √13
Get BC
B(3,3), and C(3,-1)
BC = √(3-3)²+(-1-3)²
BC = √0²+-4²
BC= √0+16
BC = √16
BC = 4
Get AC
A(0,1), and C(3,-1)
AC = √(3-0)²+(-1-1)²
AC = √3²+(-2)²
AC = √9+4
AC= √13
Since AB = AC, this shows that the triangle ABC is an isosceles triangle.
The two sides that are congruent are AB and AC
PLEASE ANSWER ASAP!!!!!!!!!!!!!
Is 1 + 4(3x - 10) - 12x equivalent to -9? EXPLAIN and show your work.
Answers
Answer:
Since you have to distribute the 4 to both terms in parentheses, the equation is simplified like this:
1 + 12x - 40 -12x
= 1 - 40
= -39
Step-by-step explanation:
Answer: No
Step-by-step explanation:
1 + 4(3x - 10) - 12x = 9
simplifies to
1+12x - 40 -12x =9
combine like terms to get
-39 = 9
This is not possible so the answer is no.
how many interior angles of a triangle can be equal to 85°
Answers
the insructions for a model car show a scale of 1 inch to 48 inches. How long is the actual car if the drawing is 4 inches
Answers
Answer:
192
Step-by-step explanation:
Answer:
192
Step-by-step explanation:
The ratio of inches to inches is 1:48
To get 4:x
You have to multiply, 4/1 = 4, 4 by 48.
4*1 = 4
4*48 = 192
4:192 = 1:48 * 4
!!!!!!!!PLEASE HELP!!!!
Answers
Answer:
The answer is C
Step-by-step explanation:
Are the triangles congruent? Why or why not?
Yes, AngleA ≅ AngleD and AB ≅ DE.
Yes, they are congruent by either AAS or ASA.
No, AngleC is not congruent to any angle in TriangleDEF.
No, the congruent sides do not correspond.
Answers
Answer:b
Step-by-step explanation:
Ed
Answer:b
Step-by-step explanation: edge said ti was right
A rock climber ascends 18 feet to the top of a rock ledge. The climber
descends 8 feet and takes a break on a rock outcrop. Write and evaluate
an addition expression to show how much farther the rock climber must
descend to reach the original level.
Answers
Answer:
10 feet
Step-by-step explanation:
18-8=10 so the remaining 10 feet is what he needs to descend.
Which problem situation can be represented by the equation below?
150 – 3x = 60
Answer choices : A .Mrs. Santos spent a total of $150 on clothing. She bought 3 shirts for $10 each and 6 sweaters that cost the same amount each. What is x, the cost of each sweater?
B Two numbers have a difference of 60. The larger number is 150. What is the smaller number, x?
C Karen had a gift card for $150. She bought 3 gifts for her sisters. The gifts cost the same amount, x. After paying for the gifts, her gift card had a balance of $60. How much did each gift cost?
D Leanne still had 150 pages of her book to read. She read 60 pages in 3 hours. What is x, the number of pages she read each hour?
Answers
Answer:
C, and x=30
Step-by-step explanation:
Equations for each problem:
A) 150 =3(10)+6x
120=6x
x=20
B)150-x=60
x=90
C) 150 -3x =60
3x=90
x=30
D)x=60/3
x=20
Answer:
C, and x=30
Step-by-step explanation:
Equations for each problem:
A) 150 =3(10)+6x
120=6x
x=20
Write an equation of the line in slope-intercept form. (3, 3)
(0, 2)
Answers
Answer:
Step-by-step explanation:
3-2 change in y = 1
3-0 change in x= 3
y=1/3x+ c
Find the circumference 7.44ft
Answers
triangle KLM ~ triangle KCD are similar. Solve for x.
Answers
Answer:
x=14
Step-by-step explanation:
28/16 = 1.75
1.75 is the constant of proportionality
63/1.75 = 36
therefore, 2x+8 should be equal to 36
2x+8 = 36 >> subtract 8 from both sides
2x = 28 >> divide both side by 2 to get x alone
x = 14
Hi, Can you help me out pls? A rental company charges $15 plus $4 per hour to rent a bicycle. If Marley does not want to spend more than $27 for her rental, WRITE and SOLVE an inequality (in the space below) to find how many hours she can rent the bicycle and not spend more than $27. Please show your work
Answers
15 • y + 4 is less than or equal to 27
subtract the 4
15 • y is less than or equal to 23
divide the 15
y is less than or equal to 23/15
she can rent her bike for 1 hour
Analysis of variance is used to ______. A. simultaneously compare several population means B. compute a t test C. compare nominal data D. compare population proportions
Answers
Answer:
"Option A" is the right alternative.
Step-by-step explanation:
ANOVA could also be utilized to predict the dependent variable of even more with around 2 categories and seems to be compared to the general population extra influential throughout this circumstance. Throughout addition, ANOVA variants typically include covariates that encourage somebody to manipulate numerically for confounding factors as well as to recognize interactions wherein the factor progressives the implications of some other factor.Other provided preferences weren’t comparable to the same circumstances in question.
If P=(-3,4), find: Rx-axis (P)
Answers
Answer:
(-3,-4)
If it was on the y-axis it would be (3,4)
Step-by-step explanation:
Rx-axis (P) = (-3, -4)
What is reflection about x-axis?"When we reflect a point about x-axis then the x-coordinate remains the same, but the y-coordinate changes its symbol."
For given example,
we have been given a point P = (-3, 4)
We need to find Rx-axis (P)
That is we need to reflect given point about x-axis.
We know, when we reflect a point about x-axis then the x-coordinate remains the same, but the y-coordinate changes its symbol.
So, the reflected point would be (-3, -4)
Therefore, Rx-axis (P) = (-3, -4)
Learn more about reflection about x-axis here:
https://brainly.com/question/12155993
#SPJ2
Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.
r= 3 inches, s = 15 inches
Answers
Answer:
45 inches
Step-by-step explanation:
Answer:
ok
Step-by-step explanation:
The length of a rectangle is 3 less than twice the width. If the
perimeter is 72 cm, what is the length of the rectangle?
Answers
Answer:
Ihave made it in above pic
1st figure is wrong 2nd is correct
Answer:
length = 23
breadth = 13
x = 13 , okay
Step-by-step explanation:
see the explanation in attachment.
PLEASE HELP IM GIVING OUT BRAINLIEST (30 POINTS)
Answers
Answer:
1.) ax2+Bx+c
2.) parabola
3.) I don't know
4.) I don't know
5.) maximum
6.) minimum
7/8) The solutions of a quadratic equation are also called roots, zeroes, and x -intercepts.
I hope this kinda helped.
Answer:
1.) ax2+Bx+c
2.) parabola
3.) I don't know
4.) I don't know
5.) maximum
6.) minimum
7/8) The solutions of a quadratic equation are also called roots, zeroes, and x -intercepts.
I hope this kinda helped.
Landon has 3 black shirts, 2 white shirts, and 2 blue shirts. He also has 2 pairs of black shorts and 2 pairs of khaki shorts. Landon randomly chooses one shirt and one pair of shorts. What is the probability Landon will choose a blue shirt and a black pair of shorts?
Answers
Answer:
Step-by-step explanation:
123Step-by-step explanation: