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3 years ago

A perpendicular bisector must be the same length as the segment it bisects True or false

1 answer:

6 0

False

A perpendicular bisector does not have to be the same length as the segment it bisects, it only needs to bisect the segment through its center.

Hope this helps!

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Write logarithmic expression as a single logarithm.<br><br> (1/3) log 8 + log 6 - log 4

marusya05 [52]

Answer:

log3

Step-by-step explanation:

$\frac{1}{3} log8 + log6 - log4 \\ = log {8}^{ \frac{1}{3} } + log( \frac{6}{4} ) \\ = log2 + log( \frac{3}{2} ) \\ = log(2 \times \frac{3}{2} ) \\ = log3$

7 0

3 years ago

I need help with part "C" and "D"

dmitriy555 [2]

3x²cos( x³ ) and 3sin²( x ) cos( x ) are the derivatives of the composite functions f(x) = sin(x³) and f(x) = sin³(x) respectively.

<h3>What are the derivative of f(x) = sin(x³) and f(x) = sin³(x)?</h3>

Chain rule simply shows how to find the derivative of a composite function. It states that;

d/dx[f(g(x))] = f'(g(x))g'(x)

Given the data in the question;

f(x) = sin(x³) = ?

f(x) = sin³(x) = ?

First, we find the derivate of the composite function f(x) = sin(x³) using chain rule.

d/dx[f(g(x))] = f'(g(x))g'(x)

f(x) = sin(x)

g(x) = x³

Apply chain rule, set u as x³

d/du[ sin( u )] d/dx[ x³ ]

cos( u ) d/dx[ x³ ]

cos( x³ ) d/dx[ x³ ]

Now, differentiate using power rule.

d/dx[ xⁿ ] is nxⁿ⁻¹

cos( x³ ) d/dx[ x³ ]

In our case, n = 3

cos( x³ ) ( 3x² )

Reorder the factors

3x²cos( x³ )

Next, we find the derivative of f(x) = sin³(x)

d/dx[f(g(x))] = f'(g(x))g'(x)

f( x ) = x³

g( x ) = sin( x )

Apply chain rule, set u as sin( x )

d/du[ u³ ] d/dx[ sin( x )]

Now, differentiate using power rule.

d/dx[ xⁿ ] is nxⁿ⁻¹

d/du[ u³ ] d/dx[ sin( x )]

3u² d/dx[ sin( x )]

Replace the u with sin( x )

3sin²(x) d/dx[ sin( x )]
Derivative of sin x with respect to x is cos (x)

3sin²( x ) cos( x )

Therefore, the derivatives of the functions are 3x²cos( x³ ) and 3sin²( x ) cos( x ).

Learn more about chain rule here: brainly.com/question/2285262

#SPJ1

4 0

1 year ago

You are planning to take to a trip to Montreal, Canada during the month of April and you want to bring clothing that is appropri

EastWind [94]

Answer:

1. E(Y) = 50.54°F

2. SD(Y) = 11.34°F

Step-by-step explanation:

We are given that The daily high temperature X in degrees Celsius in Montreal during April has expected value E(X) = 10.3°C with a standard deviation SD(X) = 3.5°C.

The conversion of X into degrees Fahrenheit Y is Y = (9/5)X + 32.

(1) Y = (9/5)X + 32

E(Y) = E((9/5)X + 32) = E((9/5)X) + E(32)

= (9/5) * E(X) + 32 { $\because$ expectation of constant is constant}