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2 years ago

Find the measures of the exterior angle using the degrees of 75 and 50

Mathematics

1 answer:

ivann1987 [24]2 years ago

8 0

Answer:

measure of exterior angle is 125°

Step-by-step explanation:

measure of exterior angle is equal to sum of measures of opposite interior angles,

so,

exterior angle ( e ) = 75° + 50°

=》e = 125°

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Determine the values of the constants b and c so that the function given below is differentiable. f(x)={2xbx2+cxx≤1x>1

Lera25 [3.4K]

Assuming the function is

$f(x)=\begin{cases}2x&\text{for }x\le1\\bx^2+cx&\text{for }x>1\end{cases}$

For $f(x)$ to be differentiable, it necessarily has to be continuous. For this condition to be met, we need

$\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1^+}f(x)=f(1)$
$\iff\displaystyle\lim_{x\to1}2x=\lim_{x\to1}(bx^2+cx)$
$\iff2=b+c$

For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have

$f'(x)=\begin{cases}2&\text{for }x1\end{cases}$

$\displaystyle\lim_{x\to1^-}2=\lim_{x\to1^+}(2bx+c)$
$\iff2=2b+c$

Now we solve for $b$ and $c$ :

$\begin{cases}b+c=2\\2b+c=2\end{cases}\implies b=0,c=2$

5 0

2 years ago

5n+5=45 what does n =

joja [24]

5n+5=45
Subtract 5 from both sides
5n=40
Divide both sides by 5
n=8

I hope this helps

4 0

2 years ago

Which function is represented by the graph below?

Ymorist [56]

Answer:

$f(x)=2^x$

Step-by-step explanation:

Exponential function:

$f(x)=a(b^x)+c$

Step 1. Find a, y-intercept

Step 2. Find b, slope

Step 3. Find c, horizontal asymptote

a = 1

m = (y₂ - y₁)/(x₂ - x₁)

m = (3 - 1)/(1 - 0) = 2/1

b = 2

c = 0

$f(x)=1(2^x)+0\\f(x)=2^x$

5 0

1 year ago

A new savings account is opened with $800 and gains 4.5% annual interest continuously. How much is in the account after 3 years

alexira [117]

A=800×e^(0.045×3)
A=915.63

7 0

2 years ago

Read 2 more answers

a man covers a distance of 15kn, in 3 hours partly by walking and partly by running. if he walks at 3km/h and runs at 9km/h, fin

irinina [24]

Speed = distance/time
distance = speed * time

let x = time covered by running
15 = run distance + walk distance
15 = 9(x) + 3(3-x)
15 = 9x + 9 - 3x
15 - 9 = 6x
6 = 6x
x = 1 hour

Therefore:
Running distance = speed * time
RD = 9km/hr * 1 hr
RD = 9km

5 0

2 years ago