Step-by-step explanation: Imagine you have 1 cookie, and a friend gives you 1 more, that means your total amount of cookies is 2. So that proves that 1+1=2!

8 0

2 years ago

Help math question derivative!

atroni [7]

Let $f(x)=\sec^{-1}x$ . Then $\sec f(x)=x$ , and differentiating both sides with respect to $x$ gives

$(\sec f(x))'=\sec f(x)\tan f(x)\,f'(x)=1$
$f'(x)=\dfrac1{\sec f(x)\tan f(x)}$

Now, when $x=\sqrt2$ , you get

$(\sec^{-1})'(\sqrt2)=f'(\sqrt2)=\dfrac1{\sec\left(\sec^{-1}\sqrt2\right)\tan\left(\sec^{-1}\sqrt2\right)}$

You have $\sec^{-1}\sqrt2=\dfrac\pi4$ , so $\sec\left(\sec^{-1}\sqrt2\right)=\sqrt2$ and $\tan\left(\sec^{-1}\sqrt2\right)=1$ . So $(\sec^{-1})'(\sqrt2)=\dfrac1{\sqrt2\times1}=\dfrac1{\sqrt2}$

5 0

3 years ago

Pete borrowed $400 for 1 year. He paid back a total of $440. What was the interest rate per year?

OleMash [197]

I=PRT/100

1. Make R (rate) subject

R/100= I/PT

2. Substitute and calculate

r/100= i/pt

r/100= 40/400 × 1

(40 is from 440-400.The interest)

r/100= 0.1

r/100×100= 0.1×100

r=10% (interest rate per year)

To confirm

I=PRT

I= 400×10/100×1

I= $40 (Interest)

5 0

3 years ago

Read 2 more answers

Tiana's math test score are 85 and 91 . She has one more test left. In order to earn and A, her average test score must be at le

Zanzabum

85 + 91 + x ÷3 ≥94

You didn't give any choices but this represents the problem.

3 0

3 years ago

4. Use SUBSTITUTION to solve the system. x= y + 5 2y + x = -4​

4. Use SUBSTITUTION to solve the system. x= y + 5 2y + x = -4