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Umnica [9.8K]
3 years ago
13

A six-meter-long ladder is leaned against a building. If the ladder makes

Mathematics
2 answers:
Dima020 [189]3 years ago
8 0
The base of the ladder would be 3 meters away from the wall
e-lub [12.9K]3 years ago
4 0

Answer:

Step-by-step explanation:

Answer and Explanation: The length of the ladder = 6 m . The angle made by the ladder with the ground = 60o . Let us assume that the distance of the ladder from the wall = x meters. Here, x is the adjacent side to the angle 60o and 6 is the hypotenuse.

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Identify the expression with nonnegative limit values. More info on the pic. PLEASE HELP.
marshall27 [118]

Answer:

\lim _{x\to 2}\:\frac{x-2}{x^2-2}\\\\  \lim _{x\to 11}\:\frac{x^2+6x-187}{x^2+3x-154}\\\\ \lim _{x\to \frac{5}{2}}\left\frac{2x^2+x-15}{2x-5}\right

Step-by-step explanation:

a) \lim _{x\to 3}\:\frac{x^2-10x+21}{x^2+4x-21}=\lim \:_{x\to \:3}\:\frac{\left(x-7\right)\left(x-3\right)}{\left(x+7\right)\left(x-3\right)}=\lim \:_{x\to \:3}\:\frac{x-7}{x+7}=\frac{3-7}{3+7}=-\frac{4}{10}=-\frac{2}{5}

b) \lim _{x\to -\frac{3}{2}}\left(\frac{2x^2-5x-12}{2x+3}\right)=\lim \:_{x\to -\frac{3}{2}}\:\frac{\left(2x+3\right)\left(x-4\right)}{\left(2x+3\right)}=\lim \:\:_{x\to \:-\frac{3}{2}}\:\left(x-4\right)=-\frac{3}{2}-4\\ \\ \lim _{x\to -\frac{3}{2}}\left(\frac{2x^2-5x-12}{2x+3}\right)=-\frac{11}{2}

c) \lim _{x\to 2}\:\frac{x-2}{x^2-2}=\frac{2-2}{\left(2\right)^2-2}=\frac{0}{4-2}=0

d) \lim _{x\to 11}\:\frac{x^2+6x-187}{x^2+3x-154}=\lim _{x\to 11}\:\frac{\left(x-11\right)\left(x+17\right)}{\left(x-11\right)\left(x+14\right)}=\lim _{x\to 11}\:\frac{\left(x+17\right)}{\left(x+14\right)}=\frac{11+17}{11+14}=\frac{28}{25}

e) \lim _{x\to 3}\:\frac{x^2-8x+15}{x-3}=\lim \:_{x\to \:3}\:\frac{\left(x-3\right)\left(x-5\right)}{x-3}=\lim _{x\to 3}\left(x-5\right)=3-5=-2

f) \lim _{x\to \frac{5}{2}}\left(\frac{2x^2+x-15}{2x-5}\right)=\lim \:_{x\to \:\frac{5}{2}}\frac{\left(2x-5\right)\left(x+3\right)}{2x-5}=\lim \:\:_{x\to \:\:\frac{5}{2}}\left(x+3\right)=\frac{5}{2}+3=\frac{11}{2}

4 0
3 years ago
In a small town, electricity prices have been rising 2% each year since 2008. Which
mihalych1998 [28]
<h3>Answer: p = 0.12*(1.02)^t</h3>

Explanation:

The general exponential growth equation is

p = A*B^t

where t is the number of years that have gone by after 2008, A is the starting amount, B is the growth multiplier, and p is the price t years after 2008

We know that A = 0.12 is the starting price

The value of B is B = 1.02 which is in the form 1+r since 1.02 = 1 + 0.02 = 1+r

The r value is r = 0.02 and it is positive to represent growth. Keep in mind that 2% = 2/100 = 0.02

So we go from

p = A*B^t

to

p = 0.12*(1.02)^t

4 0
3 years ago
If g (x) = 2x + 2, find g (a + h) - g <br> a. .<br> a. 2h<br> b. 2h + 4<br> c. h + 2
katrin [286]
G(x) = 2x + 2

g(a + h) - g(a) = 2(a+h) + 2 - (2(a) + 2)

g(a + h) - g(a) = 2a + 2h + 2 - 2a - 2

g(a + h) - g(a) = 2h + 2 - 2

g(a + h) - g(a) = 2h


Your final answer is a. 2h.
6 0
3 years ago
Read 2 more answers
Name the formula:<br> y = a(1 + r)t
givi [52]

Answer:

The exponential growth formula.

5 0
3 years ago
TRUE OR FALSE? The equation of a line with slope m = -3 and including point (5, 5) is y = -3x + 20.
kodGreya [7K]

Answer:

True.

Step-by-step explanation:

y = -3x + 20

Put x as 5, then y output should be 5.

y = -3(5) + 20

y = -15 + 20

y = 5

True, the line with slope -3 passes through points (5, 5).

8 0
3 years ago
Read 2 more answers
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