All categories

3 years ago

Which expression will give the closest approximation to the square root of 156.

Mathematics

1 answer:

topjm [15]3 years ago

3 0

Answer:

Step-by-step explanation:

the Sq root for 156 HAS to be a # between 12 and 13.

12+ (13-12)/2

12+ 1/2

12.5

You might be interested in

Show that √(1-cos A/1+cos A) =cosec A - cot A

Gennadij [26K]

Hi there!

$\sqrt{\frac{1-cosA}{1+cosA}} =$

We can begin by multiplying by its conjugate:

$\sqrt{\frac{1-cosA}{1+cosA}} * \sqrt{\frac{1+cosA}{1+cosA}} = \\\\\sqrt{\frac{(1-cosA)(1 + cosA)}{(1+cosA)(1 + cosA)}} =$

Simplify using the identity:

$1 - cos^2A = sin^2A$

$\sqrt{\frac{(1-cos^2A)}{(1+cosA)^2}} =\\\\\sqrt{\frac{(sin^2A)}{(1+cosA)^2}} =$

Take the square root of the expression:

${\frac{sinA}{1+cosA} =$

Multiply again by the conjugate to get a SINGLE term in the denominator:

${\frac{sinA}{1+cosA} * {\frac{1-cosA}{1-cosA} =\\$

Simplify:

${\frac{sinA(1-cosA)}{1-cos^2A} =$

Use the above trig identity one more:

${\frac{sinA(1-cosA)}{sin^2A} =$

Cancel out sinA:

${\frac{(1-cosA)}{sinA} =$

Split the fraction into two:

${\frac{1}{sinA} - \frac{cosA}{sinA} =$

Recall:

$1/sinA = cscA\\\\cosA/sinA = cotA$

Simplify:

$\frac{1}{sinA} + \frac{cosA}{sinA} = \boxed{cscA - cotA}$

5 0

2 years ago

Beatrice charges $10/h and gets a $5 automatic tip. Beatrice needs $100 to buy a present for her mother. She wants to find out t

Evgesh-ka [11]

10+5=15 so $100/15= 6.67hrs. She could work about 7hrs.
she could work 7 hrs if rounded to nearest tenth

8 0

3 years ago

Here is a right angled triangle work out the value of x using trigonometry

Zolol [24]

$~~~~~\sin 30^{\circ} = \dfrac{\text{Perpendicular}}{\text{Hypotenuse} }\\\\\\\implies \dfrac 12 = \dfrac{8}x\\\\\\\implies x = 8\cdot2\\\\\\\implies x = 16 ~ \text{cm.}$

8 0

2 years ago

(3x+2)^4 <br> Can someone help me with this answer !

andriy [413]

Answer:

9x^2+24x+16

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

kandy is financing a $335,000 mortgage for 30 years at a fixed rate of 7.5% what is the total cost of the principal and interest

-BARSIC- [3]

Given:
<span>F= $335,000
n = 30 years at a fixed rate of i = 7.5%

Required:
the total cost of the principal

Solution:
F = P(1+i)^n
P = F/(1+i)^n
P = 335,000 / (1.0.075)^30
P = 38,264.05</span>

8 0

3 years ago