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3 years ago

Verify the identity algebraically: Csc(-x)tanx =-secx

Mathematics

1 answer:

weqwewe [10]3 years ago

5 0

Step-by-step explanation:

Recall that

$\sin(-x) = -\sin x$

Therefore,

$\csc(-x) = \dfrac{1}{\sin(-x)} = -\dfrac{1}{\sin x}$

$\csc(-x)\tan x = \left(-\dfrac{1}{\sin x}\right)\left(\dfrac{\sin x}{\cos x}\right)$

$\:\:\:\:\:\:\:\:\:= -\dfrac{1}{\cos x} = -\sec x$

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The cost for an order of 100 kilograms of steel bars is $230. The cost for an order of 150 kilograms of steel bars is $320. Writ

luda_lava [24]

Answer:

y = 9x/5 + 50

Step-by-step explanation:

We are represent the information as coordinate (x,y)

If the cost for an order of 100 kilograms of steel bars is $230, this is expressed as (100, 230)

Also if the cost for an order of 150 kilograms of steel bars is $320, this is expressed as;

(150, 320)

Find the equation of a line passing through the points. The standard form of the equation is expressed as y = mx+c

m is the slope

c is the intercept

Get the slope;

m = y2-y1/x2-x1

m = 320-230/150-100

m = 90/50

m = 9/5

Get the y-intercept by substituting m = 9/5 and any point say (100, 230) into the expression y = mx+c

230 = 9/5(100)+c

230 = 9(20)+c

230 = 180 + c

c = 230-180

c = 50

Get the required equation

y = mx+c

y = 9/5 x + 50

Hence an equation for the cost of an order of steel bars (y) in terms of the weight of steel bars ordered (x) is y = 9x/5 + 50

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3 years ago

An engineer would like to design a parking garage in the most cost-effective manner. He reads that the average height of pickup

aleksley [76]

The answer is: Yes, all conditions for inference are met.

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2 years ago

You deposit $400 each month into an account earning 8% interest compounded monthly. Round to the nearest cent as needed. a) How

Debora [2.8K]

If I deposit $400 each month into an account earning 8% interest compounded monthly, I will have $6,517 in my account in 35 years. The total money that I will put into the account is $168,000. I will earn a total compound interest of $6,117.

Calculating the Sum of Money in 35 years

Given information is as follows,

Principal, P = $400

Rate = 8%

Time, T = 35 years

n = 12 (Compounded monthly)

The amount for compound interest is given as,

A = $P\frac{(1+\frac{R}{n} )^{nT} -1}{R/n}$

A = $400\frac{(1+\frac{0.08}{12} )^{12.35} -1}{0.08/12}$

A = 6,517.02

A = $6,517 (to the nearest cents)

Calculating the Amount Put in Account

Since, $400 is deposited every month for 35 years,

Amount Put in 35 years for this compound interest =$400 × 12 × 35

= $168,000

Calculating the Compound Interest

A = P + CI

Thus, the compound interest is given by,

CI = A - P

CI = 6517 - 400

CI = $6,117

I will earn a total interest of $6,117

Learn more about compound interest here:

brainly.com/question/14295570

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2 years ago

On a test Matilda answer 12 are the first 15 problems correctly at this rate continues how many of the next 25 problems while sh

Feliz [49]

12/15=x/25
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3 years ago

Seriously, I don't like when they put "Not enough information". I feel like there is something missing.

Marizza181 [45]

Hey there Gary!

If Angle DBC is 73, you do subtract it from 180 to get ABD.

180 - 73 = 107

Angle ABD = 107
Angle DBC = 73

Angle ABD > DBC
or
Angle DBC < ABD

The line BD/DB is the same length in both angles, proving line AD is greater than CD. This is also justified by the fact that lines AB and CB are congruent.

I hope this helps, let me know if there's something wrong about my answer.

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3 years ago

Read 2 more answers