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3 years ago

When Ben does his math homework, he finishes 10 problems every 7 minutes. At this rate, how long will

Mathematics

1 answer:

Agata [3.3K]3 years ago

8 0

Answer:

in 7 minutes he solve 10 problems

he solve one problem in = 7/10= 0.7 minute

he solve 35 problem in = 0.7x35= 24.5 minute

Step-by-step explanation:

hope it helps ❤️

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If f(x)=3x^2+2×=1 find f(x+2)

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Answer:

f(x+2) = 3(x+2)^2 + 2(x+2 + 1

Step-by-step explanation:

you need to replace the x with x+2

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3 years ago

What is the largest prime factor of 38

miskamm [114]

Answer:

The greatest prime factor of 38 is 19

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3 years ago

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Find all possible values of α+

const2013 [10]

Answer:

$\rm\displaystyle 0,\pm\pi$

Step-by-step explanation:

please note that to find but α+β+γ in other words the sum of α,β and γ not α,β and γ individually so it's not an equation

===========================

we want to find all possible values of α+β+γ when tanα+tanβ+tanγ = tanαtanβtanγ to do so we can use algebra and trigonometric skills first

cancel tanγ from both sides which yields:

$\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \alpha ) \tan( \beta ) \tan( \gamma ) - \tan( \gamma )$

factor out tanγ:

$\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \gamma ) (\tan( \alpha ) \tan( \beta ) - 1)$

divide both sides by tanαtanβ-1 and that yields:

$\rm\displaystyle \tan( \gamma ) = \frac{ \tan( \alpha ) + \tan( \beta ) }{ \tan( \alpha ) \tan( \beta ) - 1}$

multiply both numerator and denominator by-1 which yields:

$\rm\displaystyle \tan( \gamma ) = - \bigg(\frac{ \tan( \alpha ) + \tan( \beta ) }{ 1 - \tan( \alpha ) \tan( \beta ) } \bigg)$

recall angle sum indentity of tan:

$\rm\displaystyle \tan( \gamma ) = - \tan( \alpha + \beta )$

let α+β be t and transform:

$\rm\displaystyle \tan( \gamma ) = - \tan( t)$

remember that tan(t)=tan(t±kπ) so

$\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm k\pi )$

therefore when k is 1 we obtain:

$\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm \pi )$

remember Opposite Angle identity of tan function i.e -tan(x)=tan(-x) thus

$\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm \pi )$

recall that if we have common trigonometric function in both sides then the angle must equal which yields:

$\rm\displaystyle \gamma = - \alpha - \beta \pm \pi$

isolate -α-β to left hand side and change its sign:

$\rm\displaystyle \alpha + \beta + \gamma = \boxed{ \pm \pi }$

when is 0:

$\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta \pm 0 )$

likewise by Opposite Angle Identity we obtain:

$\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm 0 )$

recall that if we have common trigonometric function in both sides then the angle must equal therefore:

$\rm\displaystyle \gamma = - \alpha - \beta \pm 0$

isolate -α-β to left hand side and change its sign:

$\rm\displaystyle \alpha + \beta + \gamma = \boxed{ 0 }$

and we're done!

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3 years ago

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Fill in the missing reason for the last step.

jek_recluse [69]

Answer:

Division

Step-by-step explanation:

You divided both sides of the inequality by -3. Multiplying/dividing by negative numbers change the sign of the inequality, so you have ">" turned into "<".

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3 years ago

If f and t are both even functions, is the product ft even? If f and t are both odd functions, is ft odd? What if f is even and

Natali5045456 [20]

Answer:

(a) If f and t are both even functions, product ft is even.

(b) If f and t are both odd functions, product ft is even.

Step-by-step explanation:

Even function: A function g(x) is called an even function if

$g(-x)=g(x)$

Odd function: A function g(x) is called an odd function if

$g(-x)=-g(x)$

(a)

Let f and t are both even functions, then

$f(-x)=f(x)$

$t(-x)=t(x)$

The product of both functions is

$ft(x)=f(x)t(x)$

$ft(-x)=f(-x)t(-x)$

$ft(-x)=f(x)t(x)$

$ft(-x)=ft(x)$

The function ft is even function.

(b)

Let f and t are both odd functions, then

$f(-x)=-f(x)$

$t(-x)=-t(x)$

The product of both functions is

$ft(x)=f(x)t(x)$

$ft(-x)=f(-x)t(-x)$

$ft(-x)=[-f(x)][-t(x)]$

$ft(-x)=ft(x)$

The function ft is even function.

(c)

Let f is even and t odd function, then

$f(-x)=f(x)$

$t(-x)=-t(x)$

The product of both functions is

$ft(x)=f(x)t(x)$

$ft(-x)=f(-x)t(-x)$

$ft(-x)=[f(x)][-t(x)]$

$ft(-x)=-ft(x)$

The function ft is odd function.

7 0

2 years ago