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kramer
3 years ago
13

Pls help it’s solve the expression it’s in the attatchmenr

Mathematics
1 answer:
kondor19780726 [428]3 years ago
3 0

Answer:

-16+\sqrt{31}

Step-by-step explanation:

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1)cot a/2 -tan a/2 = 2 cot a<br>2) cot b/2 + tan b/2= 2 cosec b<br> prove​
VladimirAG [237]
1)

LHS = cot(a/2) - tan(a/2)

= (1 - tan^2(a/2))/tan(a/2)

= (2-sec^2(a/2))/tan(a/2)

= 2cot(a/2) - cosec(a/2)sec(a/2)

= 2(1+cos(a))/sin(a) - 1/(cos(a/2)sin(a/2))

= 2 (1+cos(a))/sin(a) - 2/sin(a)) (product to sums)

= 2[(1+cos(a) -1)/sin(a)]

=2cot a

= RHS

2.

LHS = cot(b/2) + tan(b/2)

= [1 + tan^2(b/2)]/tan(b/2)

= sec^2(b/2)/tan(b/2)

= 1/sin(b/2)cos(b/2)

using product to sums

= 2/sin(b)

= 2cosec(b)

= RHS
8 0
2 years ago
Amelia worked for 5 hours and 30 minutes. how should she write that on her time card?
trapecia [35]
5 hours and 30 minutes or 5.5 hours
6 0
3 years ago
Need help pls<br>thank you in advance ​
ira [324]

Answer:

<h3><u>Mean</u></h3>

<u />

\textsf{Mean}\:\overline{X}=\sf \dfrac{\textsf{sum of all the data values}}{\textsf{total number of data values}}

\implies \sf Mean\:(Nilo)=\dfrac{5+6+14+15}{4}=\dfrac{40}{4}=10

\implies \sf Mean\:(Lisa)=\dfrac{8+9+11+12}{4}=\dfrac{40}{4}=10

<h3><u>Standard Deviation</u></h3>

\displaystyle \textsf{Standard Deviation }s=\sqrt{\dfrac{\sum X^2-\dfrac{(\sum X)^2}{n}}{n-1}}

\begin{aligned}\displaystyle \textsf{Standard Deviation (Nilo)} & =\sqrt{\dfrac{(5^2+6^2+14^2+15^2)-\dfrac{(5+6+14+15)^2}{4}}{4-1}}\\\\& = \sqrt{\dfrac{482-\dfrac{40^2}{4}}{3}}\\\\& = \sqrt{\dfrac{82}{3}}\\\\& = 5.23\end{aligned}

\begin{aligned}\displaystyle \textsf{Standard Deviation (Lisa)} & =\sqrt{\dfrac{(8^2+9^2+11^2+12^2)-\dfrac{(8+9+11+12)^2}{4}}{4-1}}\\\\& = \sqrt{\dfrac{410-\dfrac{40^2}{4}}{3}}\\\\& = \sqrt{\dfrac{10}{3}}\\\\& = 1.83\end{aligned}

<h3><u>Summary</u></h3>

Nilo has a mean score of 10 and a standard deviation of 5.23.

Lisa has a mean score of 10 and a standard deviation of 1.83.

The <u>mean</u> scores are the <u>same</u>.

Nilo's standard deviation is higher than Lisa's.  Therefore, Nilo's test scores are more <u>spread out</u> that Lisa's, which means Lisa's test scores are more <u>consistent</u>.

5 0
1 year ago
What is the slope of the graph?
VMariaS [17]

<u>Given</u>:

Given that an aquarium is being filled with water.

The given graph shows the height of the water over time as the aquarium is being filled.

We need to determine the slope of the graph.

<u>Slope</u>:

The slope of the given graph can be determined using the formula,

m=\frac{y_2-y_1}{x_2-x_1}

Since, the slope is same for all the points on the straight line, then let us consider the points (2,5) and (4,10)

Substituting these points in the above formula, we get;

m=\frac{10-5}{4-2}

Simplifying, we get;

m=\frac{5}{2}

m=2.5

Thus, the slope of the given graph is 2.5

8 0
3 years ago
a 5 digit number had the digits 0,5,7,9, and 0. to the nearest thousand, it rounds to 80000 what is the number? explain.
Murljashka [212]
The Number is 79500, since the nearest thousand for 79500 is 80000
7 0
2 years ago
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