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4 years ago

Solving for t in this equation

Mathematics

1 answer:

liberstina [14]4 years ago

6 0

Answer:

The answer is

Step-by-step explanation:

$\frac{56}{63} = \frac{t}{9} \\$

First of all reduce the fraction on the left with 7

We have

$\frac{7}{9} = \frac{t}{9} \\$

Since the denominators are the same we can compare the numerators

We have the final answer as

Hope this helps you

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A cylindrical tank with radius 3 m is being filled with water at a rate of 4 m3/min. How fast is the height of the water increas

Fittoniya [83]

Height of the water increasing is at rate of $#(dh)/(dt)=3/(25 pi)m/(min)#$

<h3>How to solve?</h3>

With related rates, we need a function to relate the 2 variables, in this case it is clearly volume and height. The formula is:

$#V=pi r^2 h#$

There is radius in the formula, but in this problem, radius is constant so it is not a variable. We can substitute the value in:

$#V=pi (5m)^2 h#$

Since the rate in this problem is time related, we need to implicitly differentiate wrt (with respect to) time:

$#(dV)/(dt)=(25 m^2) pi (dh)/(dt)#$

In the problem, we are given $#3(m^3)/min# which is #(dV)/(dt)#.$

So we need to substitute this in:

$#(dh)/(dt)=(3m^3)/(min (25m^2) pi)=3/(25 pi)m/(min)#$

Hence, Height of the water increasing is at rate of $#(dh)/(dt)=3/(25 pi)m/(min)#$

<h3>Formula used: </h3>

$#V=pi r^2 h#$

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4 0

2 years ago

Read 2 more answers

If tan0=-3/4 and 0 is in quadrant IV, cos20= (33/25, -17/25, 32/25, 7/25, 24/25?) and tan20= (24/7, -24/7, 7/25, -7/25, 13/7, -1

Oksana_A [137]

Answer:

cos(2θ) = 7/25
tan(2θ) = -24/7

Step-by-step explanation:

Sometimes, it is easiest to let a calculator do the work. (See below)

The magnitude of the tangent is less than 1, so the reference angle will be less than 45°. Then double the angle will be less than 90°, so will remain in the 4th quadrant, where the cosine is positive and the tangent is negative.

You can also use the identities ...

cos(2θ) = (1 -tan(θ)²)/(1 +tan(θ)²)

cos(2θ) = (1 -(-3/4)²)/(1 +(-3/4)²) = ((16-9)/16)/((16+9)/16)

cos(2θ) = 7/25

tan(2θ) = 2tan(θ)/(1 -tan(θ)²) = 2(-3/4)/((16-9/16) = (-6/4)(16/7)

tan(2θ) = -24/7

3 0

3 years ago

Please help with this

omeli [17]

Answer:

$y = \frac{1}{8} x - 3$

Step-by-step explanation:

Formula for straight lines:

$y = mx + b$

where m = slope, b = constant

Given:

y-intercept = -3 (0, -3)

m = ⅛

Substitute into formula to find b.

$- 3 = \frac{1}{8} (0) + b \\ - 3 = 0 + b \\ b = - 3$

Substitute b into original formula

$y = mx + b \\ y = \frac{1}{8} x + ( - 3) \\ y = \frac{1}{8} x - 3$

4 0

3 years ago

Graph the line that represents this equation:<br> y = -5.1 +2

Mrac [35]

That's for the equation I got from the picture

4 0

3 years ago

2 questions here:

solmaris [256]

<span>1. Make y the subject
a) 4y=12x+18
y = 3x + 4.5

b) 2x=7-3y
3y = -2x + 7
y = -2/3x + 7/3

2.
a) what is the equation of the line which passes through both (-2,-4) and (6,16)

slope = (16 + 4)/(6 +2) = 20/8 = 2.5
y = mx + b
-4 =2.5(-2) +b
-4 = -5 +b
b = 1

equation
y = 2.5x + 1

b) what is the equation of the line perpendicular to y= 1/2X + 7 passing through point (3,9)

</span>y= 1/2X + 7
slope = 1/2

slope of line perpendicular = -2

passing through point (3,9)

y = mx + b
9 = -2 (3) + b
b = 15

equation

y = -2x + 15

6 0

3 years ago

Read 2 more answers