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Svetlanka [38]
3 years ago
15

The height of a triangle is twice the length of its base. The

Mathematics
1 answer:
lions [1.4K]3 years ago
6 0

Answer:

height = 14.2 m , base = 7.1 m

Step-by-step explanation:

let the base be b then height h = 2b

The area (A) of a triangle is calculated as

A = \frac{1}{2} bh

Here A = 50 , then

\frac{1}{2} × b × 2b = 50

b² = 50 ( take square root of both sides )

b = \sqrt{50} ≈ 7.1 ( to the nearest tenth )

Then base = 7.1 m and height = 2 × 7.1 = 14.2 m

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Verify the identity:<br> tan(x+pi/2)=-cotx<br><br> please!!
olya-2409 [2.1K]
First we use sin(a+b)= sinacosb+sinbcosa
and cos(a+b)=cosa cosb -sinasinb

tan(x+pi/2)= sin(x+pi/2) / cos(x+pi/2)
and sin(x+pi/2) = sinxcospi/2 + sinpi/2cosx =cosx, 
<span>cos(x+pi/2) = cosxcospi/2- sinxsinpi/2= - sinx, 
</span> because <span>cospi/2 =0,  </span>and <span>sinpi/2=1

</span><span>=tan(x+pi/2)= sin(x+pi/2) / cos(x+pi/2)= cosx / -sinx = -1/tanx = -cotx
</span>from where <span>tan(x+pi/2)=-cotx</span> 
5 0
3 years ago
Use Newton’s Method to find the solution to x^3+1=2x+3 use x_1=2 and find x_4 accurate to six decimal places. Hint use x^3-2x-2=
luda_lava [24]

Let f(x) = x^3 - 2x - 2. Then differentiating, we get

f'(x) = 3x^2 - 2

We approximate f(x) at x_1=2 with the tangent line,

f(x) \approx f(x_1) + f'(x_1) (x - x_1) = 10x - 18

The x-intercept for this approximation will be our next approximation for the root,

10x - 18 = 0 \implies x_2 = \dfrac95

Repeat this process. Approximate f(x) at x_2 = \frac95.

f(x) \approx f(x_2) + f'(x_2) (x-x_2) = \dfrac{193}{25}x - \dfrac{1708}{125}

Then

\dfrac{193}{25}x - \dfrac{1708}{125} = 0 \implies x_3 = \dfrac{1708}{965}

Once more. Approximate f(x) at x_3.

f(x) \approx f(x_3) + f'(x_3) (x - x_3) = \dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125}

Then

\dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125} = 0 \\\\ \implies x_4 = \dfrac{5,881,319,037}{3,324,107,515} \approx 1.769292663 \approx \boxed{1.769293}

Compare this to the actual root of f(x), which is approximately <u>1.76929</u>2354, matching up to the first 5 digits after the decimal place.

4 0
2 years ago
A gym employee is paid monthly. After working for three months, he had earned $4,500. To
Leto [7]

Answer:

$9000

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After six months he will earn = 6 × his monthly salary

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5 0
3 years ago
90°<br> 46°<br> Find the unknown. angle measure<br> please help :)
Ganezh [65]

Answer:

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Step-by-step explanation:

180-90-46

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44

5 0
2 years ago
Read 2 more answers
What is the difference?
strojnjashka [21]

Answer:

1.8940279x10^9+27

Step-by-step explanation:

5.972(10^{24} )-1.9(10^{27})\\5.972(1e+24) -1.9(1e+27)\\

6 0
3 years ago
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