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3 years ago

A 100-gallon fish tank fills at a rate of x gallons per minute. The tank has already been filling for 5 minutes. The

Mathematics

1 answer:

vagabundo [1.1K]3 years ago

6 0

Answer:

was shifted 5 unit right side then stretched vertically by the factor 100, Shifted 5 unit right side then stretched vertically by the factor 100

Step-by-step explanation:

Here, parent function,

Transformed function,

Since, if a function f(x) gives cf(x), where c is any number,

Then the function was vertically stretched by factor c,

While, the function gives f(x-c),

Then the function was shifted c unit right.

Hence, the graph of was shifted 5 unit right side then stretched vertically by the factor 100 to create the graph of

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Find a ·<br> b. |a| = 80, |b| = 50, the angle between a and b is 3π/4.

mart [117]

Answer:

$a\cdot b=-2000\sqrt{2}$

Step-by-step explanation:

Given information: |a| = 80, |b| = 50, the angle between a and b is 3π/4.

We need to find the dot product a · b.

The formula of dot product is

$a\cdot b=|a||b|\cos \theta$

where, θ is the angle between a and b.

Substitute the given values in the above formula.

$a\cdot b=(80)(50)\cos (\frac{3\pi}{4})$

$a\cdot b=4000\cos (\pi-\frac{\pi}{4})$

$a\cdot b=-4000\cos (\frac{\pi}{4})$ $[\because \cos (\pi-\theta)=-\cos \theta]$

$a\cdot b=-4000\frac{1}{\sqrt{2}}$

$a\cdot b=-\frac{4000}{\sqrt{2}}$

Rationalize the above equation.

$a\cdot b=-\frac{4000}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}$

$a\cdot b=-\frac{4000\sqrt{2}}{2}$

$a\cdot b=-2000\sqrt{2}$

Therefore, the value of a · b is $a\cdot b=-2000\sqrt{2}$ .

7 0

3 years ago

Read 2 more answers

Answer this please. Best answer/correct answer gets Brainliest.

Lynna [10]

Perpendicular lines, C is the answer.

To solve this equation, Simplify the first and then the second.

First will be solved like: -y=3x+3, y=-3x-3. The second will be simplified as: 9y=3x+2, y=1/3x+2/9. Then you divide by 3.t.

3 0

3 years ago

Read 2 more answers

A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The prem

MAVERICK [17]

x = 160 gal

y = 80 gal

160 gallons of water and 80 gallons of premium antifreeze solution must be mixed.

8 0

2 years ago

Calcule o valor numérico da expressão a seguir -2/3+1-3/2.8/9

Zolol [24]

Answer:

The calculated value is "0.214"

Step-by-step explanation:

Given expression :

$\bold {\frac{-2}{3}+ 1 -\frac{3}{\frac{2.8}{9}} }\\$

solution:

$\Rightarrow \frac{-2}{3}+ 1 -\frac{3}{\frac{2.8}{9}}\\\\\Rightarrow \frac{-2}{3}+ 1 -\frac{3}{\frac{2.8}{\frac{9}{1}}}\\\\\Rightarrow \frac{-2}{3}+ 1 -\frac{3}{2.8} \times \frac{1}{9}}}\\\\\Rightarrow \frac{-2}{3}+ 1 -\frac{1}{8.4}\\\\\Rightarrow \frac{-16.8 + 25.2- 3}{25.2}\\\\\Rightarrow \frac{5.4}{25.2}\\\\\Rightarrow 0.214$

8 0

2 years ago

According to the new remuneration scheme, the starting pay of a lecturer a is RM3,087 per month and the annual increment is RM19

vichka [17]

Step-by-step explanation:

arithmetic sequence : every new item of the sequence is created by adding a constant term to the previous item - in this case 195.

a1 = 3087 (that's our starting value)

a2 = a1 + 195

a3 = a2 + 195 = a1 + 2×195

an = a1 + (n-1)×195

when he is 45 years old, that is 20 years (and 20 annual increments) plus to our starting value.

so, n = 1+20 = 21

a21 = a1 + 20×195 = 3087 + 20×195 = 6987

so, when he is 45 years old, his monthly salary will be RM6,987

how many years (= how big is n) until he gets 8937 ?

8937 = a1 + (n-1)×195 = 3087 + (n-1)×195 =

= 3087 + n×195 - 195 = 2892 + n×195

6045 = n×195

n = 6045/195 = 31

so, a31 = 8937

and that means, he has to work 30 additional years (31 minus the starting level 1) to earn monthly RM8,937.

that means he will be 25+30 = 55 years old.

7 0

3 years ago