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2 years ago

Trigonometry, IF answer is delivered on time WILL give BRANLIEST

Mathematics

1 answer:

Lunna [17]2 years ago

8 0

Answer:

x=37°

y=6

Step-by-step explanation:

(ASSUMING BD is a perpendicular bisector of AC, otherwise answers maybe be wrong)

Consider the triangle ABC:

AB is the same length as BC (marked), meaning ABC is an isosceles triangle.

Since ABC is isosceles, ∠BAC=∠BCA=53

All angles in a triangle add up to 180:

180=∠ABC + ∠BAC + ∠BCA

180= ∠ABC + 53 +53

∠ABC = 180 - 106

∠ABC = 74

Assuming BD bisects ∠ABC perfectly, x is half of ∠ABC.

x=74/2=37

If BD bisects AC perfectly, AD=DC=y=6

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Solve for x. 2x+5+6x-1=120

svetlana [45]

Answer:

x=14.5

Step-by-step explanation:

2x+5+6x-1=120

Combine like terms (combine all of the variables and then combine all of the constants)

8x+4=120

subtract 4 on both sides

8x=116

Divide 8

x=14.5

Hope this helps!

8 0

2 years ago

The radius of a cone is increasing at a constant rate of 7 meters per minute, and the volume is decreasing at a rate of 236 cubi

storchak [24]

Answer:

The rate of change of the height is 0.021 meters per minute

Step-by-step explanation:

From the formula

$V = \frac{1}{3}\pi r^{2}h$

Differentiate the equation with respect to time t, such that

$\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)$

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)$

To differentiate the product,

Let r² = u, so that

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)$

Then, using product rule

$\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}]$

Since $u = r^{2}$

Then, $\frac{du}{dr} = 2r$

Using the Chain's rule

$\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}$

∴ $\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})]$

Then,

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

Now,

From the question

$\frac{dr}{dt} = 7 m/min$

$\frac{dV}{dt} = 236 m^{3}/min$

At the instant when $r = 99 m$

and $V = 180 m^{3}$

We will determine the value of h, using

$V = \frac{1}{3}\pi r^{2}h$

$180 = \frac{1}{3}\pi (99)^{2}h$

$180 \times 3 = 9801\pi h$

$h =\frac{540}{9801\pi }$

$h =\frac{20}{363\pi }$

Now, Putting the parameters into the equation

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

$236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)]$

$236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386]$

$708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}$

$708 = 30790.75 \frac{dh}{dt} + 76.36$

$708 - 76.36 = 30790.75\frac{dh}{dt}$

$631.64 = 30790.75\frac{dh}{dt}$

$\frac{dh}{dt}= \frac{631.64}{30790.75}$

$\frac{dh}{dt} = 0.021 m/min$

Hence, the rate of change of the height is 0.021 meters per minute.

3 0

2 years ago

The equation of the line through point (-4,0) and parallel to the y-axis is

seraphim [82]

Answer:y=-4

Step-by-step explanation:

3 0

2 years ago

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Helppp!!! i need help

klio [65]

Answer:

rectangle

kite

Step-by-step explanation:

4 0

2 years ago

How would I turn 0.46 into a fraction

Pepsi [2]

Step 1: 0.46 = 46⁄100
Step 2: Simplify 46⁄100 = 23⁄50 hope this helped u

6 0

2 years ago

Read 2 more answers