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3 years ago

A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal?

Mathematics

2 answers:

Natali [406]3 years ago

5 0

Answer:

Length of a diagonal = 41 units

Step-by-step explanation:

Given : A rectangle has a width of 9 units and a length of 40 units.

To Find : the length of a diagonal

Solution :

Since all angles of rectangle measures 90°.

So, to find length of diagonal use Pythagoras theorem i.e.

$(Hypotenuse)^{2}=(Perpendicular )^{2} + (Base)^{2}$

Refer attached figure

Since ΔADC is right angled triangle

So, $(AC)^{2}=(AD )^{2} + (DC)^{2}$

Where AC is the diagonal

AD = Length = 40 units

DC= Width = 9 units

Thus, $(AC)^{2}=(40 )^{2} + (9)^{2}$

$(AC)^{2}=1681$

$AC=\sqrt{1681}$

$AC=41$

Hence, Length of a diagonal = 41 units

DedPeter [7]3 years ago

3 0

Pythagoras tells us that the diagonal is √(9²+40²) = 41.
Answer C.

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$\begin{cases} x(t) = 2(1-t) + 5t = 3t - 2 \\ y(t) = 0(1-t) + 4t = 4t \end{cases} \implies \begin{cases} x'(t) = 3 \\ y'(t) = 4 \end{cases}$

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$\displaystyle \int u\,dv = uv - \int v\,du$

$\implies \displaystyle 5 \int_0^1 (3t-2) e^{4t} \,dt = \frac54 (3t-2) e^{4t} \bigg|_{t=0}^{t=1} - \frac{15}4 \int_0^1 e^{4t} \,dt \\\\ ~~~~~~~~ = \frac54 (e^4 + 2) - \frac{15}{16} e^{4t} \bigg|_{t=0}^{t=1} \\\\ ~~~~~~~~ = \frac54 (e^4 + 2) - \frac{15}{16} (e^4 - 1) = \boxed{\frac{5e^4 + 55}{16}}$

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1 year ago

the rectangular metallic block is 30cm long ,25cm broad and8cm high.how many pieces of rectangular slices each of 5mm thick can

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2 years ago

find the smallest number of terms of the AP "-54,-52.5,-51,-49.5" ....that must be taken for the sum of the terms to be positive

wel

The smallest number of terms of the AP that will make the sum of terms positive is 73.

Since we need to know the number for the sum of terms, we find the sum of terms of the AP

<h3>Sum of terms of an AP</h3>

The sum of terms of an AP is given by S = n/2[2a + (n - 1)d] where

n = number of terms,
a = first term and
d = common difference

Since we have the AP "-54,-52.5,-51,-49.5" ....", the first term, a = -54 and the second term, a₂ = -52.5.

The common difference, d = a₂ - a

= -52.5 - (-54)

= -52.5 + 54

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<h3>Number of terms for the Sum of terms to be positive</h3>

Since we require the sum of terms , S to be positive for a given number of terms, n.

So, S ≥ 0

n/2[2a + (n - 1)d] ≥ 0

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n[1.5n - 109.5] ≥ 0

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n ≥ 0 or 1.5n ≥ 109.5

n ≥ 0 or n ≥ 109.5/1.5

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Since n > 0, the minimum value of n is 73.

So, the smallest number of terms of the AP that will make the sum of terms positive is 73.

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