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2 years ago

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Mathematics

2 answers:

Alexxx [7]2 years ago

3 0

Answer:

2034.72

Step-by-step explanation:

i took the k-12 quiz and got the answer-

Nadya [2.5K]2 years ago

3 0

Answer:

2034.72

Step-by-step explanation:

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A lamp post with a height of 12 ft casts a shadow of 6 ft. A fire hydrant near it casts a shadow that is 1.5 ft long. How tall i

alex41 [277]

Answer:

3ft

Step-by-step explanation:

We are given that

Height of lamp, h=12ft

Height of shadow, l=6ft

Height of shadow of hydrant, l'=1.5ft

Let height of hydrant=h'

We have to find the height of fire hydrant.

All right triangles are similar

When two triangles are similar then, the ratio of their corresponding sides are equal.

Using the property

$\frac{h}{h'}=\frac{l}{l'}$

$\frac{12}{h'}=\frac{6}{1.5}$

$h'=\frac{12\times 1.5}{6}$

$h'=3$ ft

Hence, the height of fire hydrant=3 ft

3 0

2 years ago

Find the 2th term of the expansion of (a-b)^4.

vladimir1956 [14]

The second term of the expansion is $-4a^3b$ .

Solution:

Given expression:

$(a-b)^4$

To find the second term of the expansion.

$(a-b)^4$

Using Binomial theorem,

$(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}$

Here, a = a and b = –b

$$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}$

Substitute i = 0, we get

$$\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}=1 \cdot \frac{4 !}{0 !(4-0) !} a^{4}=a^4$

Substitute i = 1, we get

$$\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}=\frac{4 !}{3!} a^{3}(-b)=-4 a^{3} b$

Substitute i = 2, we get

$$\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}=\frac{12}{2 !} a^{2}(-b)^{2}=6 a^{2} b^{2}$

Substitute i = 3, we get

$$\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}=\frac{4}{1 !} a(-b)^{3}=-4 a b^{3}$

Substitute i = 4, we get

$$\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}=1 \cdot \frac{(-b)^{4}}{(4-4) !}=b^{4}$

Therefore,

$$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}$

$=\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}+\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}+\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}+\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}+\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}$ $=a^{4}-4 a^{3} b+6 a^{2} b^{2}-4 a b^{3}+b^{4}$

Hence the second term of the expansion is $-4a^3b$ .

3 0

2 years ago

**WILL GIVE 100 POINTS AND BRAINLIEST**

aleksklad [387]

Answer:

below:

Step-by-step explanation:

came along this question a week ago site in picture has a step by step explanation that's verified. ctrl c and ctrl v it into your search engine

5 0

1 year ago

Mily recycled 66 cans in February, 94 cans in March, 122 cans in April, and 150 cans in May. If this pattern went from January t

Mice21 [21]

Answer:

38 cans

Step-by-step explanation:

while looking at the numbers given I noticed that the number of cans recycled went up by 28 cans, so I took February's number, 66, and subtracted 28 to get 38

6 0

2 years ago

For 98 points:I just need this

svp [43]

Answer:

1. You can tell because every y value divided by its corresponding 3 value is 1/3, except 0 because 0 divided by 0 is 0.

2. Samuel is incorrect because when his sister's age is divided by his age, it differs every year.

(Example: 5/10 ≠ 10/15)

7 0

2 years ago