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3 years ago

Triangle ABC is isosceles where AC = CB. AC = 6a - 8 and CB = 4a - 2. Find AC.

Mathematics

1 answer:

anastassius [24]3 years ago

3 0

Answer:

Step-by-step explanation:

AC = CB

6a - 8 = 4a - 2

a = 3

6(3) - 8 = 10

AC = 10

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What is 3/4 divided by 3 1 /4

OleMash [197]

Answer:

30/31

Step-by-step explanation:

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2 years ago

Read 2 more answers

the radius of a sheridan balloon is increasing at a rate of 3 centimeters per minute. how fast is the volume changing when the r

san4es73 [151]

The volume of the balloon is $2352\pi cc/min$

Explanation:

The radius of the balloon is increasing at a rate of 3 cm/min.

To determine the volume of the balloon when the radius is 14 cm, we shall use the formula $V=\frac{4}{3} \pi r^3$

The rate of change of r with respect to time t is given by,

$\frac{d}{d t}(r)=3 \mathrm{cm} / \mathrm{minute}$

Now, we shall determine the $\frac{d}{d t}(V)$

$\begin{aligned}\frac{d}{d t}(V) &=\frac{d}{d t}\left(\frac{4}{3} \pi r^{3}\right) \\&=\frac{4}{3} \pi\left(3 r^{2}\right)\frac{d}{d t}(r) \\&=4 \pi r^{2}\frac{d}{d t}(r)\end{aligned}$

Now, we shall determine the $\frac{d}{d t}(V)$ at $r=14 \mathrm{cm}$ and substituting $\frac{d}{d t}(r)=3 \mathrm{cm} / \mathrm{minute}$ , we get,

$\begin{aligned}\left(\frac{d V}{d t}\right)_{r=14} &=4 \pi r^{2} \frac{d}{d t}(r)\\&=4 \pi(14)^{2} (3)\\&=4 \pi 196 (3)\\&=2352\end{aligned}$

Thus, The volume of the balloon is $2352\pi cc/min$

7 0

2 years ago

Cube root <img src="https://tex.z-dn.net/?f=%20-%204%20%5Csqrt%5B3x%5D%7Bx%20%2B%2025%20%3D%2035%7D%20" id="TexFormula1" titl

Taya2010 [7]

Answer:

$\large\boxed{x=-\dfrac{44,475}{64}}$

Step-by-step explanation:

$-4\sqrt[3]{x+25}=35\\\\\left(-4\sqrt[3]{x+25}\right)^3=35^3\\\\-4^3(x+25)=42,875\\\\-64(x+25)=42,875\qquad\text{use distributive property}\\\\-64x-1,600=42,875\qquad\text{add 1,600 to both sides}\\\\-64x=44,475\qquad\text{divide both sides by (-64)}\\\\x=-\dfrac{44,475}{64}$

8 0

2 years ago

Question 2 Evaluate the expression 2(x - 3) + 3y when x = 5 and y = 3. Mark the correct answer.

8_murik_8 [283]

Answer:

A. 13

Step-by-step explanation:

2(x - 3) + 3y

2(5 - 3) + 3×3

2× 2 + 3×3

4 + 9

7 0

2 years ago

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A tree 12m high is broken by the wind in such a way that its top touches the ground and makes an angle 60° with the ground. at w

Katena32 [7]

The height of broken part of tree from ground is 5.569m.

Justification:

Let BD is a tree of height 12 m.

Suppose it got bent at a point C and let the part CD take the position CA, meeting the ground at A.

i.e., CD = AC = h m

Broken part makes 60° angle from ground

So, ∠BAC = 60°

Now, height of remaining part of tree = (12 – h)m.

In right angled ∆ABC,

sin 60° = BC/AC

⇒ √3/2 = (12 - h)/h

⇒ √3h = 2(12 – h)

⇒ √3h = 24 – 2h

⇒ √3h + 2h = 24

⇒ h(√3 + 2) = 24

⇒ h(1.732 + 2) = 24

⇒ h(3.732) = 24

⇒ h = 24/3.732 = 6.4308 m

Hence, height of broken tree from ground

⇒ BC = 12 – h

⇒ 12 – 6.4308 = 5.569m

Hence, tree is broken 5.569 m from ground.

Note: See attached picture.

4 0

2 years ago

Triangle ABC is isosceles where AC = CB. AC = 6a - 8 and CB = 4a - 2. Find AC.​

Triangle ABC is isosceles where AC = CB. AC = 6a - 8 and CB = 4a - 2. Find AC.