Estimate the area of the irregular shape. Explain your method and show your work

The ratio of green apples to red apples at a grocery store is 2 to 3. There are 78 red apples at the grocery store. What is the

Talja [164]

Answer:

52

Step-by-step explanation:

78 divided by 3 is 26

26 times 2 is 52

3 0

3 years ago

A taxi cab charges $0.55 per mile in addition to a $1.75 flat rate fee. Susie has $10 to spend on a taxi cab ride. The taxi driv

Olenka [21]

The taxi driver doesn't give anyone a ride unless it's 2 miles away, as such you need to add at least $0.55x2 in addition to the $1.75 at the start
1.75+(0.55x2)=2.85
As Susie only has 10 dollars to spend, she can't exceed that. So Susie must spend more than $2.85(minimum from the taxi) and less than $10(her money)
so,
$2.85<Susie<$10

6 0

3 years ago

Let g be the function given by g(x) = the integral from 0 to x sin(t^2) for -1 < or equal to x < or equal to 3. Find the i

grin007 [14]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2841990

_______________

• According to what is given,

$\mathsf{g(x)=\displaystyle\int_0^x sin(t^2)\,dt\qquad\qquad(-1\le x\le 3)}$

• Now, differentiate g by using the Fundamental Theorem of Calculus:

$\mathsf{\displaystyle g'(x)=\frac{d}{dx}\int_0^x sin(t^2)\,dt}\\\\\\
\mathsf{\displaystyle g'(x)=sin(x^2)}$

• g is increasing in the interval where g'(x) is positive. So now, just solve this inequality:

$\mathsf{g'(x)\ \textgreater \ 0}\\\\
\mathsf{sin(x^2)\ \textgreater \ 0}$

• The sine function is positive for angles that lie either in the first or the second quadrant. So,

$\mathsf{0\ \textless \ x^2\ \textless \ \pi}$

• The inequality above involves only non-negative terms. So, the sign of the inequality keeps the same for the square root of those terms:

$\mathsf{0\ \textless \ x\ \textless \ \sqrt{\pi}\qquad\quad(i)}$

• Checking the intersection between the interval we just found above and the domain of g:

Notice that

$-1\le 0\ \textless \ x\ \textless \ \sqrt{\pi}\le 3$

which implies that

$\mathsf{\left]0,\,\sqrt{\pi}\right[\subset [1,\,3]}\\\\
\mathsf{\left]0,\,\sqrt{\pi}\right[\subset Dom(g)}.$

Therefore,

g is increasing on the interval $\mathsf{\left]0,\,\sqrt{\pi}\right[.}$

I hope this helps. =)

Tags: derivative fundamental theorem of calculus increasing interval differential integral calculus

8 0

3 years ago

What is the height of the tree to the nearest tenth of a foot?

Ugo [173]

Answer:

The height of the tree is approximately 21.4 feet

Step-by-step explanation:

We list out the question parameters first as follows;

The distance from the base of the tree where the angle of elevation is measured, d = 10 feet

The angle of elevation to the top of the tree from 10 feet from the base, θ = 65°

Let 'h' represent the height of the tree, then we have;

The line formed by the angle 65° angle, the height of the tree, 'h', and the distance 'd', form a right triangle with 'h' being the opposite leg to the given reference angle, 65°, and 'd' being the adjacent leg

By trigonometric ratio, we have;

$tan(\theta) = \dfrac{Opposite \ leg \ length}{Adjacent\ leg \ length} = \dfrac{h}{d}$