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3 years ago

Question

Mathematics

1 answer:

NeTakaya3 years ago

3 0

9514 1404 393

Answer:

80 minutes
34.4 km

Step-by-step explanation:

Use the second equation to substitute for d in the first equation.

0.43t = 0.33t +8

Subtract 0.33t from both sides

0.10t = 8

Multiply by 10

t = 80 . . . . . . Michelle will catch Jen in 80 minutes

The distance traveled will be ...

d = 0.43t = 0.43×80 = 34.4 . . . . km

The girls will have traveled 34.4 km when they meet.

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10) The line FG is a diameter of the circle with centre C (6, 1). Given F is (2.-3), find the coordinates of G.

Maurinko [17]

Answer:

Coordinates of the endpoint g is (10,5)

Step-by-step explanation:

The coordinates of a midpoint can be found using the formula;

(x,y) = (x1 + x2)/2 , (y1 + y2)/2

In this case, we have the mid point but we want to get the end point

Thus;

(6,1) = (x1 + 2)/2 , (y1-3)/2

x1 + 2 = 2(6)

x1 + 2 = 12

x1 = 12-2

x1 = 10

y1 - 3 = 2(1)

y1 -3 = 2

y1 = 2 + 3

y1 = 5

The coordinates of G are (10,5)

6 0

3 years ago

1( below is the pre image dilate by a factor of 2

bonufazy [111]

Before:It's too short. Write at least 20 characters to explain it well.

After:It's too short. Write at least 20 characters to explain it well.

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cint%20t%5E2%2B1%20%5C%20dt" id="TexFormula1" title="\frac{d}{dx} \

Kisachek [45]

Answer:

$\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2} t^2+1 \ \text{dt} \ = \ 2x^5-8x^2+2x-2$

Step-by-step explanation:

$\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2} t^2+1 \ \text{dt} = \ ?$

We can use Part I of the Fundamental Theorem of Calculus:

$\displaystyle\frac{d}{dx} \int\limits^x_a \text{f(t) dt = f(x)}$

Since we have two functions as the limits of integration, we can use one of the properties of integrals; the additivity rule.

The Additivity Rule for Integrals states that:

$\displaystyle\int\limits^b_a \text{f(t) dt} + \int\limits^c_b \text{f(t) dt} = \int\limits^c_a \text{f(t) dt}$

We can use this backward and break the integral into two parts. We can use any number for "b", but I will use 0 since it tends to make calculations simpler.

$\displaystyle \frac{d}{dx} \int\limits^0_{2x} t^2+1 \text{ dt} \ + \ \frac{d}{dx} \int\limits^{x^2}_0 t^2+1 \text{ dt}$

We want the variable to be the top limit of integration, so we can use the Order of Integration Rule to rewrite this.

The Order of Integration Rule states that:

$\displaystyle\int\limits^b_a \text{f(t) dt}\ = -\int\limits^a_b \text{f(t) dt}$

We can use this rule to our advantage by flipping the limits of integration on the first integral and adding a negative sign.

$\displaystyle \frac{d}{dx} -\int\limits^{2x}_{0} t^2+1 \text{ dt} \ + \ \frac{d}{dx} \int\limits^{x^2}_0 t^2+1 \text{ dt}$

Now we can take the derivative of the integrals by using the Fundamental Theorem of Calculus.

When taking the derivative of an integral, we can follow this notation:

$\displaystyle \frac{d}{dx} \int\limits^u_a \text{f(t) dt} = \text{f(u)} \cdot \frac{d}{dx} [u]$
where u represents any function other than a variable

For the first term, replace $\text{t}$ with $2x$ , and apply the chain rule to the function. Do the same for the second term; replace

$\displaystyle-[(2x)^2+1] \cdot (2) \ + \ [(x^2)^2 + 1] \cdot (2x)$

Simplify the expression by distributing $2$ and $2x$ inside their respective parentheses.

$[-(8x^2 +2)] + (2x^5 + 2x)$
$-8x^2 -2 + 2x^5 + 2x$

Rearrange the terms to be in order from the highest degree to the lowest degree.

$\displaystyle2x^5-8x^2+2x-2$

This is the derivative of the given integral, and thus the solution to the problem.

6 0

3 years ago

Can anyone help fast please???

Rina8888 [55]

The inverse will be 2x+3/4 or D in your picture

6 0

4 years ago

The graph shows the relationship between the height of a tree and its age in years. What is the unit rate of growth for the tree

xxMikexx [17]

Answer:

The unit rate is 2 feet per year

Step-by-step explanation:

The graph is missing (See attachment)

To determine the unit growth;

First, we have to pick any two corresponding on the x and y axis

When x = 5; y = 10

When x = 1; y = 2

These can be represented as;

$(x_1,y_1) = (5,10)$

$(x_2,y_2) = (1,2)$

Next, is to determine the slope using;

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute values for x and y

$m = \frac{2 - 10}{1 - 5}$

$m = \frac{-8}{-4}$

$m = 2$

<em>Hence, the unit rate is 2 feet per year</em>

3 0

4 years ago