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3 years ago

11

The smaller triangle was dilated to form the larger triangle. What is the value of x? A smaller triangle has side lengths of 3 a

nd 5. A larger triangle has side lengths of 9 and x + 1. 10 11 14 15

2 answers:

Shkiper50 [21]3 years ago

8 0

Answer: 14

Step-by-step explanation:

just olya [345]3 years ago

4 0

Answer:

14 is the answer

Step-by-step explanation:

I hope I helped

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Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

Leni [432]

Answer: $\dfrac{2x^2-1}{x(x^2-1)}$

Step-by-step explanation:

The given function : $y=\ln(x(x^2 - 1)^{\frac{1}{2}})$

$\Rightarrow\ y=\ln x+\ln (x^2-1)^{\frac{1}{2}}$ [ $\because \ln(ab)=\ln a +\ln b$ ]

$\Rightarrow y=\ln x+\dfrac{1}{2}\ln (x^2-1)}$ [ $\because \ln(a)^n=n\ln a$ ]

Now , Differentiate both sides with respect to x , we will get

$\dfrac{dy}{dx}=\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})\dfrac{d}{dx}(x^2-1)$ (By Chain rule)

[Note : $\dfrac{d}{dx}(\ln x)=\dfrac{1}{x}$ ]

$\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})(2x-0)$

[ $\because \dfrac{d}{dx}(x^n)=nx^{n-1}$ ]

$=\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})(2x) = \dfrac{1}{x}+\dfrac{x}{x^2-1}\\\\\\=\dfrac{(x^2-1)+(x^2)}{x(x^2-1)}\\\\\\=\dfrac{2x^2-1}{x(x^2-1)}$

Hence, the derivative of the given function is $\dfrac{2x^2-1}{x(x^2-1)}$ .

8 0

3 years ago

Sorry last question :(

elena55 [62]

Area of rectangle=30•12=360 square meters
Area of semicircle=3.14•15•15=353.25 square meters
360+353.25=713.25 square meters

6 0

3 years ago

What is the first proportion? Someone please help, I have no idea what this means.

Olenka [21]

Answer:1 is called the first term of the proportion, 2 is the second term, 5 is the third, and 10, the fourth. We say that 5 corresponds to 1, and 10 corresponds to 2.

Step-by-step explanation:

1 is called the first term of the proportion, 2 is the second term, 5 is the third, and 10, the fourth. We say that 5 corresponds to 1, and 10 corresponds to 2.

7 0

3 years ago

Determine the slope of the line that contains the points A(0, 2) and B(7,3). *

IgorC [24]

<h3><u>Given</u><u> </u><u>points</u><u>:</u><u>-</u></h3>

A (0,2)
B (7,3)

We know that

${\boxed{\sf Slope_{(m)}=\dfrac {y_2-y_1}{x_2-x_1}}}$

Substitute the values

$\qquad\quad {:}\longrightarrow\tt m=\dfrac {3-2}{7-0}$

$\qquad\quad {:}\longrightarrow\tt m=\dfrac {1}{7}$

$\therefore \sf Slope\:of\:the\:line\:is\:\dfrac {1}{7}$

5 0

3 years ago

A person is walking at a rate of 9 feet every 4 seconds.(b) Given the rate in (a), how far would this

Crank

Answer:

2.25 feet

31.5 feet

Step-by-step explanation:

Given that the person travels 9 feet every 4 seconds, it means that in one second, the distance walked

= 9/4

= 2.25 feet

If the person walks 2.25 feet in a second then in 14 seconds, the distance walked

= 2.25*14/1

= 31.5 feet

8 0

3 years ago