All categories

2 years ago

What is the largest flag jake can draw

Mathematics

1 answer:

alexgriva [62]2 years ago

5 0

The ratio of length to width is 3/2. Let's set up equations of ratios using first the 25 cm length of the paper and then the 20 cm width:

3 25 cm
--- = ----------
2 x

Solving for x, 3x = 50 cm, and x =16 2/3 cm. This is possible, since 16 2/3 is less than the paper width 20 cm.

3 20 cm
--- = -----------
2 x

Solving for x: 3x = 40 cm; x = 40/3 cm, or x= 13 1/3 cm. This is possible, but does not make maximum use of the 20 by 30 cm paper.

Answer: the largest flag Jake can draw on the paper given is 20 cm (length) by 16 2/3 cm.

You might be interested in

I need this done asap will give brainliest

lapo4ka [179]

2,4 and I am not too sure but I think -4

3 0

2 years ago

If a(x) = 3x + 1 and b(x)= √x-4 , what is the domain of (b*a)(x)

kondor19780726 [428]

A(x) = 3x + 1
b(x) = √(x-4)

Therefore
$(b \circ a) (x) = \sqrt{3x+1-4} =\sqrt{3x-3}$
This composition of functions is only defined as a real number when x≥0.
Therefore its domain is x = [1,∞]

Answer: [1,∞]

5 0

3 years ago

Read 2 more answers

An aquarium owns 8 identical tanks. All together, the tanks can hold 90.2 gallons of water. How much water can each tank hold?

kobusy [5.1K]

11.275 gallons in each tank.

7 0

3 years ago

Read 2 more answers

Which of these numbers is irrational?

Sidana [21]

Which of these numbers is irrational?
a. square root of 3
b. 0.25
c. 1/5
d. square root of 9

answer
a. square root of 3
--------------------------------
What is (-7)^5 in expanded form?
a. -7 • -7 • -7 • -7 • -7
b. -7 • 5
c. (-7) • 7 • (-7) • 7 • (-7) • -7
d. 5 • 5 • 5 • 5 • 5 • 5 • 5

answer

a. -7 • -7 • -7 • -7 • -7

6 0

2 years ago

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!

8 0

3 years ago

Read 2 more answers