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3 years ago

The ratio of length to width on a rectangle is

Mathematics

1 answer:

kvasek [131]3 years ago

5 0

Answer:

$Let~the~length~of~rectangle~be~'l'~and~its~width~be~'b'.\\According ~to ~question,\\l:b=11:3\\or, \frac{l}{b} =\frac{11}{3} \\or, l = \frac{11b}{3}\\Also,\\Perimeter~of~the~rectangle=308\\or, 2(l+b)=308\\or, l+b=154\\or, \frac{11 b}{3}+b =154 \\or, \frac{11b+3b}{3} =154\\or, 14b = 154(3)\\or, b=33 units\\So, ~the~width~of~rectangle~is~33units.$

Alternative method:

$Let~the~length~and~width~of~the~rectangle~be~11x~and~3x.\\Given,\\Perimeter~of~the~rectangle = 308\\or, 2(11x+3x)=308\\or, 14x = 154\\or, x = 11\\Now,\\Width~of~the~rectangle,3x = 3(11)=33 units\\So,~the~width~of~the~rectangle~is~33units.$

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nasty-shy [4]

The answer is B. 35, because if the exterior angle is 95 degrees, this makes the angle on the inside 85, so that they both add up to 180 degrees. All the angle measure of a triangle add up to 180, so 60+85= 145. 180-145= 35 degrees. Hope this helped.

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4 years ago

Find an explicit solution of the given initial-value problem.dy/dx = ye^x^2, y(3) = 1.

tamaranim1 [39]

Answer:

$y=exp(\int\limits^x_4 {e^{-t^{2} } } \, dt)$

Step-by-step explanation:

This is a separable equation with an initial value i.e. y(3)=1.

Take y from right hand side and divide to left hand side ;Take dx from left hand side and multiply to right hand side:

$\frac{dy}{y} =e^{-x^{2} }dx$

Take t as a dummy variable, integrate both sides with respect to "t" and substituting x=t (e.g. dx=dt):

$\int\limits^x_3 {\frac{1}{y} } \, \frac{dy}{dt} dt=\int\limits^x_3 {e^{-t^{2} } } dt$

Integrate on both sides:

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Use initial condition i.e. y(3) = 1:

$ln(y(x))-(ln1)=\int\limits^x_3 {e^{-t^{2} } } \, dt\\ln(y(x))=\int\limits^x_3 {e^{-t^{2} } } \, dt\\$

Taking exponents on both sides to remove "ln":

$y=exp (\int\limits^x_3 {e^{-t^{2} } } \, dt)$

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3 years ago

A brace for a shelf has the shape of a right triangle. Its hypotense is 16 incges long and the two legs are equal in length. How

Len [333]

We use trigonometry because we know an angle and a side length.

We are looking for one of the sides that isn't the hypotenuse:
As illustrated by the picture I made below:

We know both unknown angles will be 45 degrees, as there are 180 degrees in a triangle, we know the triangle is a right angle triangle (has 90 degrees) so, (180-90)/2 = 45

Using SOH CAH TOA, short for : SIN- OH COS- AH TAN- OA

We are looking for the one with H, as we know what H is.
I am picking "SIN- OH", but we could use "COS- AH"

The formula for this is: Sin(angle) = O/H
<u /><u>We substitute the angle (45) and the length for H (16)
</u>
Sin(45)= O/16 <- rearrange it
Sin(45)*16= O <- Solve in the calculator
13.6145 (4 DP)= O
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The legs have a length of "13.6145 (4 DP)" each

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wolverine [178]

g(x):

flip f(x) over x-axist and next translate 2 units down.

Look at the picture.

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Translations

y = f (x) + m up m units

y = f (x) - m down m units

y = f (x + m) left m units

y = f (x - m) right m units

Stretches/Shrinks

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y = f (1/n x) stretch horizonally by a factor of n

y = f (nx) shrink horizontally by a factor of n (stretch by 1/n)

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