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2 years ago

What are 2 ways to solve the problem 9×1×5 = ?

Mathematics

1 answer:

aliina [53]2 years ago

6 0

2ways you can solve that is by multiplying 9 by 1 then by 5 or 9by 5 then by 1

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(1/1+sintheta)=sec^2theta-secthetatantheta pls help me verify this

Xelga [282]

Answer:

See Below.

Step-by-step explanation:

We want to verify the equation:

$\displaystyle \frac{1}{1+\sin\theta} = \sec^2\theta - \sec\theta \tan\theta$

To start, we can multiply the fraction by (1 - sin(θ)). This yields:

$\displaystyle \frac{1}{1+\sin\theta}\left(\frac{1-\sin\theta}{1-\sin\theta}\right) = \sec^2\theta - \sec\theta \tan\theta$

Simplify. The denominator uses the difference of two squares pattern:

$\displaystyle \frac{1-\sin\theta}{\underbrace{1-\sin^2\theta}_{(a+b)(a-b)=a^2-b^2}} = \sec^2\theta - \sec\theta \tan\theta$

Recall that sin²(θ) + cos²(θ) = 1. Hence, cos²(θ) = 1 - sin²(θ). Substitute:

$\displaystyle \displaystyle \frac{1-\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta \tan\theta$

Split into two separate fractions:

$\displaystyle \frac{1}{\cos^2\theta} -\frac{\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta\tan\theta$

Rewrite the two fractions:

$\displaystyle \left(\frac{1}{\cos\theta}\right)^2-\frac{\sin\theta}{\cos\theta}\cdot \frac{1}{\cos\theta}=\sec^2\theta - \sec\theta \tan\theta$

By definition, 1 / cos(θ) = sec(θ) and sin(θ)/cos(θ) = tan(θ). Hence:

$\displaystyle \sec^2\theta - \sec\theta\tan\theta \stackrel{\checkmark}{=} \sec^2\theta - \sec\theta\tan\theta$

Hence verified.

8 0

2 years ago

William invested $800 in an account that paid 5% simple interest per year.

Blababa [14]

A) Interest = principal * rate * time

I = (800)(0.05)(3) = $120

b) $800 + $120 = $920 after the three years. $920 * (1 - 0.02) = $901.60.

3 0

2 years ago

If 6 less than one third of Christine age is no more than 18 , how old is she . And how did u get the answer

SCORPION-xisa [38]

Answer: >72

Step-by-step explanation:

x*1/3-6=<18

1/3*x=<24

x=<72

Christine is more than 72 years old

5 0

2 years ago

How do you know weather the quotient of two integers will be a positive number

jeka57 [31]

If the two integers are both the same sign (both positive or both negative), then the quotient will be positive.

5 0

2 years ago

What is the value of the remaining variable? P=2L+2W; L=68, W=71

pantera1 [17]

$P=2L+2W$

We know that L = 68 and W = 71. Plug these into our equation above.

$P=2(68)+2(71)$

According to the order of operations, we must multiply first.
2×68 = 136, 2×71 = 142

$P=136+142$

$\boxed{P=278}$

7 0

3 years ago