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3 years ago

6

5. For the equation: x = sin

ex-formula"> + 3 and y = cos $t$ , find $\frac{dy}{dx}$ .

1 answer:

Rufina [12.5K]3 years ago

5 0

<h2><u>Answer:</u></h2><h2> $\boxed{cos(y)=-sin(y),sin(x)=cos(x)}$ </h2><h2 /><h2><u>Solution Steps:</u></h2>

______________________________

<h3>(Below)</h3>

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A circle's radius that has an initial radius of 0 cm is increasing at a constant rate of 5 cm per second.

djyliett [7]

Answer:

a) $r(t)=5t$

b) $A=\pi\cdot r^2$

c) $A=\pi\cdot (5t)^2$

d) $A=25\pi t^2$

Step-by-step explanation:

We know that the circle is increasing its radio from an initial state of r=0 cm, at a rate of 5 cm/s.

This can be expressed as:

$r(0)=0\\\\dr/dt=5\\\\r(t)=r(0)+dr/dt\cdot t=0+5t\\\\r(t)=5t$

a) Radius of the circle, r (in cm), in terms of the number of seconds, t since the circle started growing:

$r(t)=5t$

b) Area of the circle, A (in square cm), in terms of the circle's radius, r (in cm):

$A=\pi\cdot r^2$

c) Circle's area, A (in square cm), in terms of the number of seconds, t, since the circle started growing:

$A=\pi\cdot r^2\\\\A=\pi\cdot (5t)^2$

d) Expanded form for the area A:

$A=\pi\cdot (5t)^2=25\pi\cdot t^2$

3 0

3 years ago

What is the inequality -3x + 1 < 7 look like on a number line.

grandymaker [24]

Step-by-step explanation:

First you must simplify the equation:

$-3x+1$

subtract 1 from both sides:

$-3x$

than divide both sides by -3, which switches the inequality sign:

$x>-2$

This inequality means that all values of x greater than -2 work for the equation. because it is not $\geq$ , -2 is not included, so there will be a hollow circle there. than the inequality will have a line from that dot to the right so that all values of x that work for the inequality are on that line.

8 0

3 years ago

A tank was 1/3 full of water. After 2950 ml of water were added, the tank was 3/4 full. Find the capacity of the tank in litres?

Ganezh [65]

C- capacity
c/3+2950=3c/4 the common denominator is 12.
4c+2950*12=3c*3
4c+35400=9c
35400=9c-4c
35400=5c
c=7080 ml =7.08l

4 0

3 years ago

Point P(-5, 2) is translated using the rule (x+3, y-1). What is the x-coordinate of P' ?

ss7ja [257]

Translate, in math, is just a fancy word for "change" or "move". We're changing (-5, 2) using x + 3 and y - 1. If the x value is -5, what is x + 3?

(-5) + 3 = -2

And for the y - 1?

(2) - 1 = 1.

Your answer is P'(-2, 1)
<em /><em>
</em><em>Don't forget to rate this answer the Brainliest!</em>

4 0

3 years ago

Determine if the sequence is arithmetic or geometric, and find the common difference or ratio.

melamori03 [73]

Answer:

The sequence is arithmetic with a common difference of -10

Step-by-step explanation:

From the question, we want to determine if the sequence is arithmetic or geometric

From the question

f(1) = 5

f(2) = -5

f(3) = -15

Mathematically for the common difference;

f(3) - f(2) = f(2) - f(1)

Since;

-15-(-5) = -5-5

-10 = -10

Since the common difference here is same , then the sequence is arithmetic with a common difference of -10

8 0

3 years ago