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3 years ago

Find the derivative of g(t)=t2+5t at t=7 algebraically.

Mathematics

1 answer:

Elanso [62]3 years ago

3 0

The power rule applies to each term.

... (d/dt)(t^n) = n·t^(n-1)

... g'(t) = 2t +5

... g'(7) = 2·7 +5 = 19

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Peter leaves Mitchell's house traveling 30 mph. Mitchell leaves 15 min later, trying to catch up to peter, going 40 mph. if they

UkoKoshka [18]

Answer:

45 minutes

Step-by-step explanation:

At 30 mph for 1/4 hour, Peter has a 7.5 mile head start. After he leaves, Mitchell closes that gap at the rate of 40-30 = 10 miles per hour. It will take him ...

t = d/s

t = (7.5 mi)/(10 mi/h) = 0.75 h

to catch Peter.

Mitchell will catch Peter in 45 minutes.

<em>Alternate Solution</em>

Another way to look at it is that Mitchell's 10 mph advantage is 1/3 of Peter's speed, so it will take 1/(1/3) = 3 times the period of Peter's head start:

3 × 15 minutes = 45 minutes . . . for Mitchell to catch Peter

_____

You can write equations involving time and distance and see where the distances traveled become the same. You need to be careful choosing the time reference, since you're concerned with Mitchell's travel time. I personally prefer to work "head start" problems by considering the differences in time and speed, as above. This is where you end up using the equations approach, anyway.

4 0

2 years ago

Algebraic expression and identity 1)simplify the following (3a+b)3 +(3a-b)3

mylen [45]

Answer:

$(3a+b)^3+(3a-b)^3=54a^3+18ab^2$

Step-by-step explanation:

Given: $(3a+b)^3+(3a-b)^3$

Formula: $x^3+y^3=(x+y)(x^2-xy+y^2)$

$(x+y)^2=x^2+2xy+y^2$

$(x-y)^2=x^2-2xy+y^2$

$x\rightarrow 3a+b$

$y\rightarrow 3a-b$

$\Rightarrow (3a+b+3a-b)((3a+b)^2-(3a+b)(3a-b)+(3a-b)^2)$

$\Rightarrow (6a)(9a^2+b^2+6ab-9a^2+b^2+9a^2+b^2-6ab)$

$\Rightarrow (6a)(9a^2+3b^2)$

$\Rightarrow 54a^3+18ab^2$

5 0

3 years ago

Please help with this question

natita [175]

Answer:

$12\sin{(2\theta)}\cos{(\theta)}$

Step-by-step explanation:

The appropriate trig identity is ...

$\sin{a}+\sin{b}=2\sin{\left(\dfrac{a+b}{2}\right)}\cos{\left(\dfrac{a-b}{2}\right)}$

Here, you have a scale factor of 6 and a=3θ, b=θ. Filling in these values gives ...

$6\sin{3\theta}+6\sin{\theta}=12\sin{\left(\dfrac{3\theta+\theta}{2}\right)}\cos{\left(\dfrac{3\theta-\theta}{2}\right)}\\\\=12\sin{(2\theta)}\cos{(\theta)}$

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2 years ago

you deposit $2,000 in an account that earns simple interest. after 6 months the account earns $210 in interest. what is the annu

Luden [163]

Answer:

21%

Step-by-step explanation:

210 is 10.5% of the amount that is for 6 months doubling it will make it 420 that is 21% of the total amount of 2000.

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2 years ago

Match with correct description

fgiga [73]

First one: If the leading coeff. is negative, the graph begins in Quadrant III and ends in Quadrant IV. It's an even function. The fourth graph represents it.

If the leading coeff. is positive, but everything else remains the same, the graph opens upward, beginning in Q II and ending in Q I.

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3 years ago