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msanger7587
26.10.2020 •
Mathematics
In an isosceles triangle the length of the legs is 8 cm and the angle between them is 150°. Find the altitude to the legs and the area of the triangle. Find AH and Aᴬᴮᶜ
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Ответ:
AH = 4 units
Area of ΔABC = 16 square units
Step-by-step explanation:
Since ΔABC is an isosceles triangle,
AC = BC
∠CAB ≅ ∠ABC [Opposite angles of the equal sides in a triangle are equal]
In ΔABC,
m∠CAB + m∠ABC + m∠ACB = 180°
m∠ABC + m∠ABC + 150° = 180°
2m∠ABC = 30°
m∠ABC = 15°
Now we apply cosine rule in ΔABC,
AB² = AC² + BC² - 2(AB)(BC)cos(m∠ACB)
AB² = 8² + 8² - 2(8)(8)cos(150°)
AB² = 128 + 110.85
AB =![\sqrt{238.85}](/tpl/images/0839/3224/32fce.png)
AB = 15.45
In ΔABH,
sin(m∠ABH) =![\frac{AH}{AB}](/tpl/images/0839/3224/0cdec.png)
sin(15°) =![\frac{AH}{15.45}](/tpl/images/0839/3224/d5c55.png)
AH = 15.45sin(15°)
AH = 3.998
AH ≈ 4.0 units
HC =![\sqrt{8^{2}-4^2}](/tpl/images/0839/3224/8354a.png)
=![\sqrt{48}](/tpl/images/0839/3224/9e5fe.png)
= 6.93
Area of the triangle ABC =![\frac{1}{2}(BC)(AH)](/tpl/images/0839/3224/0f376.png)
=![\frac{1}{2}(8)(4)](/tpl/images/0839/3224/5776b.png)
= 16 square units
Ответ:
k = 1
P(t) = (t + 20)²
Step-by-step explanation:
P' = k√P = k P⁰•⁵
To solve for k,
P' = 10 rabbits/month
P = 100 rabbits
10 = k √100
10 = 10k
k = 1
To solve for P(t)
P' = dP/dt
(dP/dt) = kP⁰•⁵
dP/P⁰•⁵ = k dt
P⁻⁰•⁵ dP = k dt
∫ P⁻⁰•⁵ dP = ∫ k dt
2P⁰•⁵ = kt + c
At t = 0, P = 100
2(100)⁰•⁵ = 0 + c
2 × 10 = c
c = 20
2P⁰•⁵ = kt + c
2P⁰•⁵ = kt + 20
Recall, k = 1
2P⁰•⁵ = t + 20
P⁰•⁵ = (t + 20)
P(t) = (t + 20)²