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2 years ago

The monthly interest rate payable on Jessica’s credit card is 1.15%. What is the APR

Mathematics

1 answer:

irina1246 [14]2 years ago

8 0

Jjnbbvv
Mañana
Man. A
Nana Anna
Nannabanbaba

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What is 1-2sin^2x=sinx <br> Please show steps and find all solutions in interval [0,2pi)

Svetlanka [38]

Answer:

$\large\boxed{x=\dfrac{3\pi}{2}\ \vee\ x=\dfrac{\pi}{6}\ \vee\ x=\dfrac{5\pi}{6}}$

Step-by-step explanation:

$1-2\sin^2x=\sin x\\\\\text{substitute}\ t=\sin x,\ t\in[-1,\ 1]\\\\1-2t^2=t\qquad\text{subtract t from both sides}\\\\-2t^2-t+1=0\qquad\text{change the signs}\\\\2t^2+t-1=0\\\\2t^2+2t-t-1=0\\\\2t(t+1)-1(t+1)=0\\\\(t+1)(2t-1)=0\iff t+1=0\ \vee\ 2t-1=0\\\\t+1=0\qquad\text{subtract 1 from both sides}\\\boxed{t=-1}\\\\2t-1=0\qquad\text{add 1 to both sides}\\2t=1\qquad\text{divide both sides by 2}\\\boxed{t=\dfrac{1}{2}}$

$\sin x=-1\to x=-\dfrac{\pi}{2}+2k\pi,\ k\in\mathbb{Z}\\\\\sin x=\dfrac{1}{2}\to x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi,\ k\in\mathbb{Z}\\\\x\in[0,\ 2\pi)$

$x=-\dfrac{\pi}{2}\notin[0,\ 2\pi)\\\\x=-\dfrac{\pi}{2}+2\pi=\dfrac{3\pi}{2}\in[0,\ 2\pi)\\\\x=-\dfrac{\pi}{2}+4\pi=\dfrac{7\pi}{2}\notin[0,\ 2\pi)\\\\x=\dfrac{\pi}{6}\in[0,\ 2\pi)\\\\x=\dfrac{\pi}{6}+2\pi=\dfrac{13\pi}{6}\notin[0,\ 2\pi)\\\\x=\dfrac{5\pi}{6}\in[0,\ 2\pi)\\\\x=\dfrac{5\pi}{6}+2\pi=\dfrac{17\pi}{6}\notin[0,\ 2\pi)$

4 0

4 years ago

Andrew jogs for 3 miles each day on the weekdays and for 6.5 miles each day over the weekend. What is the average distance that

kirill [66]

Set up the data:
3,3,3,3,3,6.5,6.5
15+13=28
28/7=4

He runs an average of 4 miles a day

7 0

3 years ago

Read 2 more answers

The sum of 5 consecutive integers is 265. What is the fifth number in this sequence ?

Yanka [14]

Hello,
Let's assume n,n+1,n+2,n+3,n+4 the 5 numbers

n+(n+1)+...+(n+4)=5n+10=265
5n=265-10
5n=255
n=51
The 5th number is 51+4=55

6 0

3 years ago

Math sequences number patterns

grandymaker [24]

Answer:

see explanation

Step-by-step explanation:

(a)

Note the squared value in column 3 which is the square of 1 more than the row number, that is

row 2 → (2 + 1)² →3²

row 3 → (3 + 1)² → 4²

Find the square root of 676 = 26 → (25 + 1)² = 26²

Hence the row number is 25

(b)

The pattern in column 1 is [ row number × (row number + 2 ) + 1 ]

row number is n then n(n + 2) + 1 = n² + 2n + 1

4 0

3 years ago

Please help i've been stuck on these for a bit now!

lisov135 [29]

Answer:

Q6. D

Q8. A

Step-by-step explanation:

Q6. In 40 trials, he flipped '2 heads and 1 tail' 16 times.

For 2 heads, probability= 16/40= 4/10

For 120 trials, number of times= 4/10 × 120= 48

Q8.

$125x + 200 \geqslant 1200 \\ 125x \geqslant 1200 - 200 \\ 125x \geqslant 1000 \\ x \geqslant 1000 \div 125 \\ x \geqslant 8$

Answer is A because the inequality shows that x is equal or greater than 8 so the dot at 8 has to be coloured.

Note that we do not change the inequality sign unless we are dividing the whole thing by -1.

5 0

3 years ago