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2 years ago

What is the are of a triangle (picture provided)

Mathematics

1 answer:

77julia77 [94]2 years ago

3 0

Answer:

Area Δ = 102.3 units² ⇒ The answer is (d)

Step-by-step explanation:

* Use the formula of the area:

∵ Area of the triangle = 1/2 (a)(b) sin(C)

∵ We have the length of the 3 sides

∴ Use cos Rule to find the angle C

∵ cos(C) = (a² + b² - c²)/2ab

∵ a = 25 , b = 13 , c = 17

∴ cos(C) = (25² + 13² - 17²)/2(25)(13) = 625 + 169 - 289/650 = 505/650

∴ m∠C = 39°

∴ Area Δ = (1/2)(25)(13)sin(39) = 102.3 units²

∴ The answer is (d)

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At what points on the given curve x = 4t3, y = 3 + 40t − 2t2 does the tangent line have slope 1?

dexar [7]

ANSWER

The points are:

(32,-85)

and

$( \frac{500}{27} , \frac{577}{9} )$

EXPLANATION

The given parametric equation that defines the curve is:

$x = 4 {t}^{3}$

$y = 3 + 40t - 2 {t}^{2}$

We differentiate to get,

$\frac{dx}{dt} = 12 {t}^{2}$

$\frac{dy}{dt} = 40 - 4t$

The slope of the tangent is given by;

$\frac{dy}{dx} = \frac{ \frac{dy}{dt} }{ \frac{dx}{dt} }$

$\frac{dy}{dx} = \frac{12 {t}^{2} }{40 - 4t}$

For the slope to be 1, then we must solve the following equation for t.

$\frac{12 {t}^{2} }{40 - 4t} = 1$

$12 {t}^{2} = 40 - 4t$

$12 {t}^{2} + 4t - 4 0 = 0$

$3{t}^{2} + t - 10 = 0$

$(t + 2)(3t - 5) = 0$

$t = - 2 \: \: or \: \: t = \frac{5}{3}$

When t=-2, we put -2 into the expression for x and y to get

x=4(-2)³ and y=3+40(-2)-2(-2)²

This implies that,

x=32, y=-85

Hence one point is (32,-85)

Similarly, when

$t = \frac{5}{3}$

$x = \frac{500}{27} ,y = \frac{577}{9}$

Another point is

$( \frac{500}{27} , \frac{577}{9} )$

7 0

2 years ago

The angles of a triangle are in the ratio 11 : 5 : 2. The side opposite the largest angle is 5.5 centimeters. The length of the

beks73 [17]

The side opposite the lasrgest angle will also be the largest side in the triangle

Here it s 5.5 cms.

so using the given ratios we have

2/11 = x /5.5 where x is the smallest side (opposite the smallest angle)

x = (2*5.5) / 11 = 1 cm.

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2 years ago

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Harrizon [31]

8 = 8v - 4 (v + 8)

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combine like terms

8 = 4v - 32

add 32 to both sides

8 + 32 = 4v -32 + 32

combine like terms

40 = 4v

divide each side by 4

40/10 = v

4 = v

v= 4

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2 years ago

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Bingel [31]

Solution:

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Therefore, multiplying and dividing by 5 + √2, we have

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