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2 years ago

Solve a triangle when A=40 B = 50 , and C=14.

Mathematics

1 answer:

tekilochka [14]2 years ago

6 0

Answer:

(c)=81°, a=9.1, b=12.

Step-by-step explanation:

m<A=40°, m<B=59

m<C=180-(40+59)=81

c=14

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If QP=25, MN=35, and SR=13, calculate the area of LMN.

Olenka [21]

The two triangles are similar. When two figures are similar, the ratios of the lengths of their corresponding sides are equal. We use this fact in order to calculate the height of the bigger triangle. We do as follows:

QP / SL = MN / SL+SR
25 / SL = 35 / SL + 13
SL = 32.5

Area = height x base / 2
Area = SL x MN / 2
Area = 32.5 x 35 / 2 = 568.75

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3 years ago

Finding Derivatives Implicity In Exercise,Find dy/dx implicity. xey - 10x + 3y = 0

uranmaximum [27]

Answer:

$\dfrac{dy}{dx}=\dfrac{10-e^y}{(xe^y+3)}$

Step-by-step explanation:

Given:

The implicit equation is given as:

$xe^y-10x+3y=0$

In implicit differentiation, we treat 'y' as a function of 'x' and differentiate both sides of the equation with respect to 'x' and then collect all the $\frac{dy}{dx}$ together and finally solve for $\frac{dy}{dx}$ .

So, differentiating both sides of the above equation with respect to 'x'. This gives,

$\frac{d}{dx}(xe^y-10x+3y)=\frac{d}{dx}(0)\\\\\frac{d}{dx}(xe^y)+\frac{d}{dx}(-10x)+\frac{d}{dx}(3y)=0\\\\\textrm{Using product rule, (uv)' = uv' + vu'}\\\\(x\cdot e^y\cdot \frac{dy}{dx}+e^y\cdot 1)-10\cdot1+3\frac{dy}{dx}=0\\\\\frac{dy}{dx}(xe^y)+e^y-10+\frac{dy}{dx}(3)=0\\\\\textrm{Grouping}\ \frac{dy}{dx}\textrm{ terms together}\\\\\frac{dy}{dx}(xe^y+3)+e^y-10=0\\\\\frac{dy}{dx}(xe^y+3)=10-e^y\\\\\dfrac{dy}{dx}=\dfrac{10-e^y}{(xe^y+3)}$

Therefore, the derivative $\frac{dy}{dx}$ implicitly is:

$\dfrac{dy}{dx}=\dfrac{10-e^y}{(xe^y+3)}$

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2 years ago

A textbook costs $65.49 before tax. The tax on the textbook is 6.5%. What is the total cost of the textbook? Round your answer t

Ghella [55]

Answer: $69.75.

Step-by-step explanation:

Given: Cost of textbook before tax=$65.49

The tax on the textbook = 6.5%

∴ The tax amount = 6.5% of $65.49

$=\frac{65}{1000}\times65.49=4.25685\approx4.26$

⇒The tax amount = $4.26

The total cost of the textbook=Cost of textbook before tax+tax amount

=$65.49+$4.26

=$69.75

∴ The total cost of the textbook is $69.75.

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Sergio [31]

Answer:

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Step-by-step explanation:

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Thepotemich [5.8K]

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