I need help plz aijahsg

A 4-foot tall child walks directly away from a 12-foot tall lamppost at 2 mph. How quickly is the length of her shadow increasin

xz_007 [3.2K]

Answer:

The length of the shadow is increasing with the rate of 1.5 feet per sec

Step-by-step explanation:

Let AB and CD represents the height of the lamppost and child respectively ( shown below )

Also, let E be a point represents the position of child.

In triangles ABE and CDE,

$\angle ABE\cong \angle CDE$ ( right angles )

$\angle AEB\cong \angle CED$ ( common angles )

By AA similarity postulate,

$\triangle ABE\sim \triangle CDE$

∵ Corresponding sides of similar triangles are in same proportion,

$\implies \frac{AB}{CD}=\frac{BE}{DE}$

We have, AB = 12 ft, CD = 4 ft, BE = BD + DE = 6 + DE,

$\implies \frac{12}{4}=\frac{6+DE}{DE}$

$12DE = 24 + 4DE$

$8DE = 24$

$DE=3$

Now, the speed of walking = 2 mph = $\frac{2\times 5280}{3600}\approx 2.933\text{ ft per sec}$

Note: 1 mile = 5280 ft, 1 hour = 3600 sec

Thus, the time taken by child to reach at E

$= \frac{\text{Walked distance}}{\text{Walking speed}}$

$=\frac{6}{2.933}$

= 2.045 hours

Hence, the change rate in the length of shadow

$= \frac{\text{Length of shadow}}{\text{Time taken}}$

$=\frac{3}{2.045}$

= 1.5 ft per sec.

3 0

3 years ago

0.6x + 3 = 0.1x - 7 what value of x makes the question true

svetlana [45]

Answer:x=-20

Step-by-step explanation:

7 0

4 years ago

What are the steps to solve this inequality?

Alex787 [66]

-9.5 + 6x > 42.1

> is the greater than symbol. So it has to be greater than 42.1

x = 8.6 (at least)

8 0

4 years ago

Which decimal number has the smallest value: 6.2; 0.62; 62.0; or 6.002?

eimsori [14]

Answer:

0.62

Step-by-step explanation:

Think of the answer like it's money. If I have 0.62 cents and everyone else has a total of 6 dollars, I would have the smallest amount of money.

Hope this helps :D

7 0

3 years ago

Read 2 more answers

Need some help with number word problems, tysm if you do :)

lord [1]

Answer:

Read below

Step-by-step explanation:

x is always the smaller number

y is always the larger number

underlined means it's the question

bolded means it's the answer

1.

One number is 6 times as large as another. Their sum is 42. Find the numbers.

The numbers need to fit the criteria:

6x=y
x+y=42

A. 6+36=42 (correct)

B. 7+42=49 (incorrect)

C. 7+35=42 (incorrect because it doesn't follow the 1st rule)

D. 6+42=48 (incorrect)

Only A. 6, 36 fits the criteria.

2.

One number is 3 less than another. Four times the smaller is 4 more than 3 times the larger. Find the numbers.

The numbers need to fit the criteria:

x+3=y
4x-4=3y

A.

4+3=7

12-6≠21 (incorrect)

B.

7+3=10

28-3≠30 (incorrect)

C.

13+3=16

52-4=48 (correct)

D.

9+3≠13 (incorrect)

Only C. 13, 16 fits the criteria.

3.

One number is 4 less than another. Five times the smaller is 3 less than 4 times the larger. Find the numbers.

The numbers need to fit the criteria:

x+4=y
5x+3=4y

A.

13+4=17

65+3=68 (correct)

B.

-23+4= -19

-115+3≠ -76 (incorrect)

C.

17+4=21

85+3≠84 (incorrect)

D.

-11+4+ -7

-35+3≠ -33 (incorrect)

Only A. 13, 17 fits the criteria.

4.

The sum of two numbers is 23. When three times the smaller is subtracted from the larger, the result is 3. Find the numbers.

The numbers need to fit the criteria:

x+y=23
y-3x=3

A.

5+18=23

18-15=3 (correct)

B.

8+15=23

15-24≠3 (incorrect)

C.

-13+36=23

36+39≠3 (incorrect)

D.

-5+28=23

28+15≠3 (incorrect)

Only A. 5, 18 fits the criteria.

5.

The sum of two numbers is 26. When twice the smaller is subtracted from the larger, the result is 2. Find the numbers.

The numbers need to fit the criteria:

x+y=26
y-2x=2

A.

8+18=26

18-16=2 (correct)

B.

9+17=26

17-18≠2 (incorrect)

C.

7+19=26

19-14≠2 (incorrect)

D.

6+20=26

20-12≠2 (incorrect)

Only A. 8, 18 fits the criteria.

4 0

4 years ago

I need help plz aijahsg​

I need help plz aijahsg