A building is 1450ft tall. How many meters tall is the building ? Use the fact that 1m = 3.28ft

In the figure above, sin 52=17/c. Based on the figure, which of the following equations is also true

hram777 [196]

Answer:

c. Cos 52 = 17/c

Step-by-step explanation:

sin(x) = cos(90-x)

3 0

3 years ago

Use the substitution of x=e^{t} to transform the given Cauchy-Euler differential equation to a differential equation with consta

kherson [118]

By the chain rule,

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}\implies\dfrac{\mathrm dy}{\mathrm dt}=x\dfrac{\mathrm dy}{\mathrm dx}$

which follows from $x=e^t\implies t=\ln x\implies\dfrac{\mathrm dt}{\mathrm dx}=\dfrac1x$ .

$\dfrac{\mathrm dy}{\mathrm dt}$ is then a function of $x$ ; denote this function by $f(x)$ . Then by the product rule,

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1x\dfrac{\mathrm dy}{\mathrm dt}\right]=-\dfrac1{x^2}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac1x\dfrac{\mathrm df}{\mathrm dx}$

and by the chain rule,

$\dfrac{\mathrm df}{\mathrm dx}=\dfrac{\mathrm df}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}=\dfrac1x\dfrac{\mathrm d^2y}{\mathrm dt^2}$

so that

$\dfrac{\mathrm d^2y}{\mathrm dt^2}-\dfrac{\mathrm dy}{\mathrm dt}=x^2\dfrac{\mathrm d^2y}{\mathrm dx^2}$

Then the ODE in terms of $t$ is

$\dfrac{\mathrm d^2y}{\mathrm dt^2}+8\dfrac{\mathrm dy}{\mathrm dt}-20y=0$

The characteristic equation

$r^2+8r-20=(r+10)(r-2)=0$

has two roots at $r=-10$ and $r=2$ , so the characteristic solution is

$y_c(t)=C_1e^{-10t}+C_2e^{2t}$

Solving in terms of $x$ gives

$y_c(x)=C_1e^{-10\ln x}+C_2e^{2\ln x}\implies\boxed{y_c(x)=C_1x^{-10}+C_2x^2}$

4 0

3 years ago

Find an expression which represents the sum of (6x + 1) and (-8x – 2) in simplest terms.

bearhunter [10]

Answer:

-(2x+1) ,6x-8x=-2x,+1-2=1

7 0

3 years ago

Pls help me with this question

Paraphin [41]

Answer:

x = 70 degrees, y = 35 degrees.

Step-by-step explanation:

The angle marked x is a central angle, so its measure is the same as the measure of the intercepted arc.

The angle marked y is an inscribed angle, so its measure is half the measure of the intercepted arc.

7 0

2 years ago

two different subtraction problems that use only odd numbers for numerators and each have different of 3/4.

Irina18 [472]

Answer:

3/2 - 3/4
5/3 - 11/12
5/4 - 1/2
7/5 - 13/20
5/6 - 1/2
9/7 - 15/28
9/8 - 3/8
9/10 - 3/20
9/11 - 3/44

Step-by-step explanation:

We did a systematic search for subtraction problems of this type, eliminating ones that are too trivial, such as 1/1 - 1/4 and equivalents of those with integers added, such as 3/1 - 9/4. Even so, there are an infinite number of possibilities. some of the ones involving larger numbers in the range we looked at include ...

41/45 - 29/180
41/49 - 17/196
41/53 - 5/212

___

A reasonable approach to doing this by hand seems to be to choose a denominator for the minuend, then a denominator 4 times that value for the subtrahend. Express 3/4 using the latter denominator, and find two numbers that differ by that numerator, one of which is divisible by 4, but not by 8.

Example: Choose 13 as the minuend denominator. Then 52 is the subtrahend denominator, and the difference you need to create is 39/52. The smallest odd number we can add to 39 to make it divisible by 4 but not 8 is 5. So, we can use (39+5)/52 and 5/52 as our numbers that differ by 3/4. In reduced form, that subtraction is ...

11/13 - 5/52

Note that if you choose an even denominator, then the exact procedure will vary depending on what power of 2 is a factor of the denominator.

8 0

3 years ago